TSTP Solution File: PUZ078+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ078+1 : TPTP v8.1.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 : Sun Sep 18 14:11:23 EDT 2022
% Result : Theorem 0.23s 0.47s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : PUZ078+1 : TPTP v8.1.0. Released v3.5.0.
% 0.08/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.16/0.36 % Computer : n013.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri Sep 2 18:47:47 EDT 2022
% 0.16/0.37 % CPUTime :
% 0.16/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.37 Usage: tptp [options] [-file:]file
% 0.16/0.37 -h, -? prints this message.
% 0.16/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.37 -m, -model generate model.
% 0.16/0.37 -p, -proof generate proof.
% 0.16/0.37 -c, -core generate unsat core of named formulas.
% 0.16/0.37 -st, -statistics display statistics.
% 0.16/0.37 -t:timeout set timeout (in second).
% 0.16/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.37 -<param>:<value> configuration parameter and value.
% 0.16/0.37 -o:<output-file> file to place output in.
% 0.23/0.47 % SZS status Theorem
% 0.23/0.47 % SZS output start Proof
% 0.23/0.47 tff(truthday_type, type, (
% 0.23/0.47 truthday: $i > $o)).
% 0.23/0.47 tff(monday_type, type, (
% 0.23/0.47 monday: $i)).
% 0.23/0.47 tff(tptp_fun_X_3_type, type, (
% 0.23/0.47 tptp_fun_X_3: $i)).
% 0.23/0.47 tff(consecutive_type, type, (
% 0.23/0.47 consecutive: $i > $i)).
% 0.23/0.47 tff(tptp_fun_X_2_type, type, (
% 0.23/0.47 tptp_fun_X_2: $i)).
% 0.23/0.47 tff(day3_type, type, (
% 0.23/0.47 day3: $i > $o)).
% 0.23/0.47 tff(day2_type, type, (
% 0.23/0.47 day2: $i > $o)).
% 0.23/0.47 tff(tptp_fun_X_1_type, type, (
% 0.23/0.47 tptp_fun_X_1: $i)).
% 0.23/0.47 tff(day1_type, type, (
% 0.23/0.47 day1: $i > $o)).
% 0.23/0.47 tff(tuesday_type, type, (
% 0.23/0.47 tuesday: $i)).
% 0.23/0.47 tff(tptp_fun_X_0_type, type, (
% 0.23/0.47 tptp_fun_X_0: $i)).
% 0.23/0.47 tff(sunday_type, type, (
% 0.23/0.47 sunday: $i)).
% 0.23/0.47 tff(saturday_type, type, (
% 0.23/0.47 saturday: $i)).
% 0.23/0.47 tff(thursday_type, type, (
% 0.23/0.47 thursday: $i)).
% 0.23/0.47 tff(wednesday_type, type, (
% 0.23/0.47 wednesday: $i)).
% 0.23/0.47 tff(friday_type, type, (
% 0.23/0.47 friday: $i)).
% 0.23/0.47 tff(1,plain,
% 0.23/0.47 (^[X: $i] : refl((day2(X) <=> day3(consecutive(X))) <=> (day2(X) <=> day3(consecutive(X))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(2,plain,
% 0.23/0.47 (![X: $i] : (day2(X) <=> day3(consecutive(X))) <=> ![X: $i] : (day2(X) <=> day3(consecutive(X)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.47 tff(3,plain,
% 0.23/0.47 (![X: $i] : (day2(X) <=> day3(consecutive(X))) <=> ![X: $i] : (day2(X) <=> day3(consecutive(X)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(4,axiom,(![X: $i] : (day2(X) <=> day3(consecutive(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day3_follows_day2')).
% 0.23/0.47 tff(5,plain,
% 0.23/0.47 (![X: $i] : (day2(X) <=> day3(consecutive(X)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.23/0.47 tff(6,plain,(
% 0.23/0.47 ![X: $i] : (day2(X) <=> day3(consecutive(X)))),
% 0.23/0.47 inference(skolemize,[status(sab)],[5])).
% 0.23/0.47 tff(7,plain,
% 0.23/0.47 (![X: $i] : (day2(X) <=> day3(consecutive(X)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.23/0.47 tff(8,plain,
% 0.23/0.47 ((~![X: $i] : (day2(X) <=> day3(consecutive(X)))) | (day2(X!2) <=> day3(consecutive(X!2)))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(9,plain,
% 0.23/0.47 (day2(X!2) <=> day3(consecutive(X!2))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.23/0.47 tff(10,plain,
% 0.23/0.47 (?[X: $i] : day2(X) <=> ?[X: $i] : day2(X)),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(11,axiom,(?[X: $i] : day2(X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day2_once')).
% 0.23/0.47 tff(12,plain,
% 0.23/0.47 (?[X: $i] : day2(X)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.23/0.47 tff(13,plain,(
% 0.23/0.47 day2(X!2)),
% 0.23/0.47 inference(skolemize,[status(sab)],[12])).
% 0.23/0.47 tff(14,plain,
% 0.23/0.47 ((~(day2(X!2) <=> day3(consecutive(X!2)))) | (~day2(X!2)) | day3(consecutive(X!2))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(15,plain,
% 0.23/0.47 ((~(day2(X!2) <=> day3(consecutive(X!2)))) | day3(consecutive(X!2))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.23/0.47 tff(16,plain,
% 0.23/0.47 (day3(consecutive(X!2))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[15, 9])).
% 0.23/0.47 tff(17,plain,
% 0.23/0.47 (?[X: $i] : day3(X) <=> ?[X: $i] : day3(X)),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(18,axiom,(?[X: $i] : day3(X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day3_once')).
% 0.23/0.47 tff(19,plain,
% 0.23/0.47 (?[X: $i] : day3(X)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.23/0.47 tff(20,plain,(
% 0.23/0.47 day3(X!3)),
% 0.23/0.47 inference(skolemize,[status(sab)],[19])).
% 0.23/0.47 tff(21,plain,
% 0.23/0.47 (^[X: $i, Y: $i] : refl(((X = Y) | (~day3(Y)) | (~day3(X))) <=> ((X = Y) | (~day3(Y)) | (~day3(X))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(22,plain,
% 0.23/0.47 (![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X))) <=> ![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[21])).
% 0.23/0.47 tff(23,plain,
% 0.23/0.47 (^[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)))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(24,plain,
% 0.23/0.47 (![X: $i, Y: $i] : ((~(day3(X) & day3(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[23])).
% 0.23/0.47 tff(25,plain,
% 0.23/0.47 (![X: $i, Y: $i] : ((~(day3(X) & day3(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(day3(X) & day3(Y))) | (X = Y))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(26,plain,
% 0.23/0.47 (^[X: $i, Y: $i] : rewrite(((day3(X) & day3(Y)) => (X = Y)) <=> ((~(day3(X) & day3(Y))) | (X = Y)))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(27,plain,
% 0.23/0.47 (![X: $i, Y: $i] : ((day3(X) & day3(Y)) => (X = Y)) <=> ![X: $i, Y: $i] : ((~(day3(X) & day3(Y))) | (X = Y))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[26])).
% 0.23/0.47 tff(28,axiom,(![X: $i, Y: $i] : ((day3(X) & day3(Y)) => (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day3_unique')).
% 0.23/0.47 tff(29,plain,
% 0.23/0.47 (![X: $i, Y: $i] : ((~(day3(X) & day3(Y))) | (X = Y))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.23/0.47 tff(30,plain,
% 0.23/0.47 (![X: $i, Y: $i] : ((~(day3(X) & day3(Y))) | (X = Y))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.23/0.47 tff(31,plain,(
% 0.23/0.47 ![X: $i, Y: $i] : ((~(day3(X) & day3(Y))) | (X = Y))),
% 0.23/0.47 inference(skolemize,[status(sab)],[30])).
% 0.23/0.47 tff(32,plain,
% 0.23/0.47 (![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.23/0.47 tff(33,plain,
% 0.23/0.47 (![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.23/0.47 tff(34,plain,
% 0.23/0.47 (((~![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)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(35,plain,
% 0.23/0.47 (((X!3 = consecutive(X!2)) | (~day3(consecutive(X!2))) | (~day3(X!3))) <=> ((~day3(X!3)) | (~day3(consecutive(X!2))) | (X!3 = consecutive(X!2)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(36,plain,
% 0.23/0.47 (((~![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))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[35])).
% 0.23/0.47 tff(37,plain,
% 0.23/0.47 (((~![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)))),
% 0.23/0.47 inference(transitivity,[status(thm)],[36, 34])).
% 0.23/0.47 tff(38,plain,
% 0.23/0.47 ((~![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))) | ((X!3 = consecutive(X!2)) | (~day3(consecutive(X!2))) | (~day3(X!3)))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(39,plain,
% 0.23/0.47 ((~![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))) | (~day3(X!3)) | (~day3(consecutive(X!2))) | (X!3 = consecutive(X!2))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.23/0.47 tff(40,plain,
% 0.23/0.47 (X!3 = consecutive(X!2)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[39, 33, 20, 16])).
% 0.23/0.47 tff(41,assumption,(~truthday(monday)), introduced(assumption)).
% 0.23/0.47 tff(42,plain,
% 0.23/0.47 (^[X: $i] : refl(((~day1(X)) | (truthday(X) <=> (~truthday(monday)))) <=> ((~day1(X)) | (truthday(X) <=> (~truthday(monday)))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(43,plain,
% 0.23/0.47 (![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday)))) <=> ![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[42])).
% 0.23/0.47 tff(44,plain,
% 0.23/0.47 (![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday)))) <=> ![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(45,plain,
% 0.23/0.47 (^[X: $i] : rewrite(((~day1(X)) | (truthday(X) <=> ((~truthday(monday)) & (~truthday(tuesday))))) <=> ((~day1(X)) | (truthday(X) <=> (~truthday(monday)))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(46,plain,
% 0.23/0.47 (![X: $i] : ((~day1(X)) | (truthday(X) <=> ((~truthday(monday)) & (~truthday(tuesday))))) <=> ![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[45])).
% 0.23/0.47 tff(47,plain,
% 0.23/0.47 (^[X: $i] : rewrite((day1(X) => (truthday(X) <=> ((~truthday(monday)) & (~truthday(tuesday))))) <=> ((~day1(X)) | (truthday(X) <=> ((~truthday(monday)) & (~truthday(tuesday))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(48,plain,
% 0.23/0.47 (![X: $i] : (day1(X) => (truthday(X) <=> ((~truthday(monday)) & (~truthday(tuesday))))) <=> ![X: $i] : ((~day1(X)) | (truthday(X) <=> ((~truthday(monday)) & (~truthday(tuesday)))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[47])).
% 0.23/0.47 tff(49,axiom,(![X: $i] : (day1(X) => (truthday(X) <=> ((~truthday(monday)) & (~truthday(tuesday)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','statement1')).
% 0.23/0.47 tff(50,plain,
% 0.23/0.47 (![X: $i] : ((~day1(X)) | (truthday(X) <=> ((~truthday(monday)) & (~truthday(tuesday)))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.23/0.47 tff(51,plain,
% 0.23/0.47 (![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.23/0.47 tff(52,plain,
% 0.23/0.47 (![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.23/0.47 tff(53,plain,(
% 0.23/0.47 ![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))),
% 0.23/0.47 inference(skolemize,[status(sab)],[52])).
% 0.23/0.47 tff(54,plain,
% 0.23/0.47 (![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.23/0.47 tff(55,plain,
% 0.23/0.47 (?[X: $i] : day1(X) <=> ?[X: $i] : day1(X)),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(56,axiom,(?[X: $i] : day1(X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day1_once')).
% 0.23/0.47 tff(57,plain,
% 0.23/0.47 (?[X: $i] : day1(X)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.23/0.47 tff(58,plain,(
% 0.23/0.47 day1(X!1)),
% 0.23/0.47 inference(skolemize,[status(sab)],[57])).
% 0.23/0.47 tff(59,plain,
% 0.23/0.47 (((~![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))) | ((~day1(X!1)) | (truthday(X!1) <=> (~truthday(monday))))) <=> ((~![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))) | (~day1(X!1)) | (truthday(X!1) <=> (~truthday(monday))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(60,plain,
% 0.23/0.47 ((~![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))) | ((~day1(X!1)) | (truthday(X!1) <=> (~truthday(monday))))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(61,plain,
% 0.23/0.47 ((~![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))) | (~day1(X!1)) | (truthday(X!1) <=> (~truthday(monday)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.23/0.47 tff(62,plain,
% 0.23/0.47 (truthday(X!1) <=> (~truthday(monday))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[61, 58, 54])).
% 0.23/0.47 tff(63,plain,
% 0.23/0.47 ((~(truthday(X!1) <=> (~truthday(monday)))) | truthday(X!1) | truthday(monday)),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(64,plain,
% 0.23/0.47 (truthday(X!1) | truthday(monday)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.23/0.47 tff(65,plain,
% 0.23/0.47 (truthday(X!1)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[64, 41])).
% 0.23/0.47 tff(66,plain,
% 0.23/0.47 (?[X: $i] : truthday(X) <=> ?[X: $i] : truthday(X)),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(67,axiom,(?[X: $i] : truthday(X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','truth_once')).
% 0.23/0.47 tff(68,plain,
% 0.23/0.47 (?[X: $i] : truthday(X)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.23/0.47 tff(69,plain,(
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% 0.23/0.47 inference(skolemize,[status(sab)],[68])).
% 0.23/0.47 tff(70,plain,
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% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(71,plain,
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% 0.23/0.47 inference(quant_intro,[status(thm)],[70])).
% 0.23/0.47 tff(72,plain,
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% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(73,plain,
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% 0.23/0.47 inference(quant_intro,[status(thm)],[72])).
% 0.23/0.47 tff(74,plain,
% 0.23/0.47 (![X: $i, Y: $i] : ((~(truthday(X) & truthday(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(truthday(X) & truthday(Y))) | (X = Y))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(75,plain,
% 0.23/0.47 (^[X: $i, Y: $i] : rewrite(((truthday(X) & truthday(Y)) => (X = Y)) <=> ((~(truthday(X) & truthday(Y))) | (X = Y)))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(76,plain,
% 0.23/0.47 (![X: $i, Y: $i] : ((truthday(X) & truthday(Y)) => (X = Y)) <=> ![X: $i, Y: $i] : ((~(truthday(X) & truthday(Y))) | (X = Y))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[75])).
% 0.23/0.47 tff(77,axiom,(![X: $i, Y: $i] : ((truthday(X) & truthday(Y)) => (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','truth_unique')).
% 0.23/0.47 tff(78,plain,
% 0.23/0.47 (![X: $i, Y: $i] : ((~(truthday(X) & truthday(Y))) | (X = Y))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.23/0.47 tff(79,plain,
% 0.23/0.47 (![X: $i, Y: $i] : ((~(truthday(X) & truthday(Y))) | (X = Y))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.23/0.47 tff(80,plain,(
% 0.23/0.47 ![X: $i, Y: $i] : ((~(truthday(X) & truthday(Y))) | (X = Y))),
% 0.23/0.47 inference(skolemize,[status(sab)],[79])).
% 0.23/0.47 tff(81,plain,
% 0.23/0.47 (![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.23/0.47 tff(82,plain,
% 0.23/0.47 (![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.23/0.47 tff(83,plain,
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% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(84,plain,
% 0.23/0.47 (((X!1 = X!0) | (~truthday(X!1)) | (~truthday(X!0))) <=> ((~truthday(X!0)) | (~truthday(X!1)) | (X!1 = X!0))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(85,plain,
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% 0.23/0.47 inference(monotonicity,[status(thm)],[84])).
% 0.23/0.47 tff(86,plain,
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% 0.23/0.47 inference(transitivity,[status(thm)],[85, 83])).
% 0.23/0.47 tff(87,plain,
% 0.23/0.47 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((X!1 = X!0) | (~truthday(X!1)) | (~truthday(X!0)))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(88,plain,
% 0.23/0.47 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(X!0)) | (~truthday(X!1)) | (X!1 = X!0)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.23/0.47 tff(89,plain,
% 0.23/0.47 ((~truthday(X!1)) | (X!1 = X!0)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[88, 82, 69])).
% 0.23/0.47 tff(90,plain,
% 0.23/0.47 (X!1 = X!0),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[89, 65])).
% 0.23/0.47 tff(91,plain,
% 0.23/0.47 ((X!0 = X!2) <=> (X!2 = X!0)),
% 0.23/0.47 inference(commutativity,[status(thm)],[])).
% 0.23/0.47 tff(92,plain,
% 0.23/0.47 (^[X: $i] : refl((day1(X) <=> day2(consecutive(X))) <=> (day1(X) <=> day2(consecutive(X))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(93,plain,
% 0.23/0.47 (![X: $i] : (day1(X) <=> day2(consecutive(X))) <=> ![X: $i] : (day1(X) <=> day2(consecutive(X)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[92])).
% 0.23/0.48 tff(94,plain,
% 0.23/0.48 (![X: $i] : (day1(X) <=> day2(consecutive(X))) <=> ![X: $i] : (day1(X) <=> day2(consecutive(X)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(95,axiom,(![X: $i] : (day1(X) <=> day2(consecutive(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day2_follows_day1')).
% 0.23/0.48 tff(96,plain,
% 0.23/0.48 (![X: $i] : (day1(X) <=> day2(consecutive(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.23/0.48 tff(97,plain,(
% 0.23/0.48 ![X: $i] : (day1(X) <=> day2(consecutive(X)))),
% 0.23/0.48 inference(skolemize,[status(sab)],[96])).
% 0.23/0.48 tff(98,plain,
% 0.23/0.48 (![X: $i] : (day1(X) <=> day2(consecutive(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.23/0.48 tff(99,plain,
% 0.23/0.48 ((~![X: $i] : (day1(X) <=> day2(consecutive(X)))) | (day1(X!1) <=> day2(consecutive(X!1)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(100,plain,
% 0.23/0.48 (day1(X!1) <=> day2(consecutive(X!1))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.23/0.48 tff(101,plain,
% 0.23/0.48 ((~(day1(X!1) <=> day2(consecutive(X!1)))) | (~day1(X!1)) | day2(consecutive(X!1))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(102,plain,
% 0.23/0.48 ((~(day1(X!1) <=> day2(consecutive(X!1)))) | day2(consecutive(X!1))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[101, 58])).
% 0.23/0.48 tff(103,plain,
% 0.23/0.48 (day2(consecutive(X!1))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[102, 100])).
% 0.23/0.48 tff(104,plain,
% 0.23/0.48 (^[X: $i, Y: $i] : refl(((X = Y) | (~day2(Y)) | (~day2(X))) <=> ((X = Y) | (~day2(Y)) | (~day2(X))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(105,plain,
% 0.23/0.48 (![X: $i, Y: $i] : ((X = Y) | (~day2(Y)) | (~day2(X))) <=> ![X: $i, Y: $i] : ((X = Y) | (~day2(Y)) | (~day2(X)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[104])).
% 0.23/0.48 tff(106,plain,
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% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(107,plain,
% 0.23/0.48 (![X: $i, Y: $i] : ((~(day2(X) & day2(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | (~day2(Y)) | (~day2(X)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[106])).
% 0.23/0.48 tff(108,plain,
% 0.23/0.48 (![X: $i, Y: $i] : ((~(day2(X) & day2(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(day2(X) & day2(Y))) | (X = Y))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(109,plain,
% 0.23/0.48 (^[X: $i, Y: $i] : rewrite(((day2(X) & day2(Y)) => (X = Y)) <=> ((~(day2(X) & day2(Y))) | (X = Y)))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(110,plain,
% 0.23/0.48 (![X: $i, Y: $i] : ((day2(X) & day2(Y)) => (X = Y)) <=> ![X: $i, Y: $i] : ((~(day2(X) & day2(Y))) | (X = Y))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[109])).
% 0.23/0.48 tff(111,axiom,(![X: $i, Y: $i] : ((day2(X) & day2(Y)) => (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day2_unique')).
% 0.23/0.48 tff(112,plain,
% 0.23/0.48 (![X: $i, Y: $i] : ((~(day2(X) & day2(Y))) | (X = Y))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.23/0.48 tff(113,plain,
% 0.23/0.48 (![X: $i, Y: $i] : ((~(day2(X) & day2(Y))) | (X = Y))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.23/0.48 tff(114,plain,(
% 0.23/0.48 ![X: $i, Y: $i] : ((~(day2(X) & day2(Y))) | (X = Y))),
% 0.23/0.48 inference(skolemize,[status(sab)],[113])).
% 0.23/0.48 tff(115,plain,
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% 0.23/0.48 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.23/0.48 tff(116,plain,
% 0.23/0.48 (![X: $i, Y: $i] : ((X = Y) | (~day2(Y)) | (~day2(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[115, 105])).
% 0.23/0.48 tff(117,plain,
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% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(118,plain,
% 0.23/0.48 (((X!2 = consecutive(X!1)) | (~day2(consecutive(X!1))) | (~day2(X!2))) <=> ((~day2(X!2)) | (~day2(consecutive(X!1))) | (X!2 = consecutive(X!1)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(119,plain,
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% 0.23/0.48 inference(monotonicity,[status(thm)],[118])).
% 0.23/0.48 tff(120,plain,
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% 0.23/0.48 inference(transitivity,[status(thm)],[119, 117])).
% 0.23/0.48 tff(121,plain,
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% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(122,plain,
% 0.23/0.48 ((~![X: $i, Y: $i] : ((X = Y) | (~day2(Y)) | (~day2(X)))) | (~day2(X!2)) | (~day2(consecutive(X!1))) | (X!2 = consecutive(X!1))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.23/0.48 tff(123,plain,
% 0.23/0.48 (X!2 = consecutive(X!1)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[122, 116, 13, 103])).
% 0.23/0.48 tff(124,plain,
% 0.23/0.48 (consecutive(X!1) = X!2),
% 0.23/0.48 inference(symmetry,[status(thm)],[123])).
% 0.23/0.48 tff(125,assumption,(X!1 = X!0), introduced(assumption)).
% 0.23/0.48 tff(126,assumption,(day2(consecutive(consecutive(consecutive(monday))))), introduced(assumption)).
% 0.23/0.48 tff(127,plain,
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% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(128,plain,
% 0.23/0.48 (day1(consecutive(consecutive(monday))) <=> day2(consecutive(consecutive(consecutive(monday))))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[127, 98])).
% 0.23/0.48 tff(129,plain,
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% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(130,plain,
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% 0.23/0.48 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.23/0.48 tff(131,plain,
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% 0.23/0.48 inference(unit_resolution,[status(thm)],[130, 126])).
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% 0.23/0.48 tff(133,plain,
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% 0.23/0.48 inference(quant_intro,[status(thm)],[132])).
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% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(135,plain,
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% 0.23/0.48 inference(quant_intro,[status(thm)],[134])).
% 0.23/0.48 tff(136,plain,
% 0.23/0.48 (![X: $i, Y: $i] : ((~(day1(X) & day1(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(day1(X) & day1(Y))) | (X = Y))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(137,plain,
% 0.23/0.48 (^[X: $i, Y: $i] : rewrite(((day1(X) & day1(Y)) => (X = Y)) <=> ((~(day1(X) & day1(Y))) | (X = Y)))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(138,plain,
% 0.23/0.48 (![X: $i, Y: $i] : ((day1(X) & day1(Y)) => (X = Y)) <=> ![X: $i, Y: $i] : ((~(day1(X) & day1(Y))) | (X = Y))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[137])).
% 0.23/0.48 tff(139,axiom,(![X: $i, Y: $i] : ((day1(X) & day1(Y)) => (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day1_unique')).
% 0.23/0.48 tff(140,plain,
% 0.23/0.48 (![X: $i, Y: $i] : ((~(day1(X) & day1(Y))) | (X = Y))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.23/0.48 tff(141,plain,
% 0.23/0.48 (![X: $i, Y: $i] : ((~(day1(X) & day1(Y))) | (X = Y))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.23/0.48 tff(142,plain,(
% 0.23/0.48 ![X: $i, Y: $i] : ((~(day1(X) & day1(Y))) | (X = Y))),
% 0.23/0.48 inference(skolemize,[status(sab)],[141])).
% 0.23/0.48 tff(143,plain,
% 0.23/0.48 (![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.23/0.48 tff(144,plain,
% 0.23/0.48 (![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[143, 133])).
% 0.23/0.48 tff(145,plain,
% 0.23/0.48 (((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((~day1(X!1)) | (~day1(consecutive(consecutive(monday)))) | (X!1 = consecutive(consecutive(monday))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | (~day1(X!1)) | (~day1(consecutive(consecutive(monday)))) | (X!1 = consecutive(consecutive(monday))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(146,plain,
% 0.23/0.48 (((X!1 = consecutive(consecutive(monday))) | (~day1(consecutive(consecutive(monday)))) | (~day1(X!1))) <=> ((~day1(X!1)) | (~day1(consecutive(consecutive(monday)))) | (X!1 = consecutive(consecutive(monday))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(147,plain,
% 0.23/0.48 (((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((X!1 = consecutive(consecutive(monday))) | (~day1(consecutive(consecutive(monday)))) | (~day1(X!1)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((~day1(X!1)) | (~day1(consecutive(consecutive(monday)))) | (X!1 = consecutive(consecutive(monday)))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[146])).
% 0.23/0.48 tff(148,plain,
% 0.23/0.48 (((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((X!1 = consecutive(consecutive(monday))) | (~day1(consecutive(consecutive(monday)))) | (~day1(X!1)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | (~day1(X!1)) | (~day1(consecutive(consecutive(monday)))) | (X!1 = consecutive(consecutive(monday))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[147, 145])).
% 0.23/0.48 tff(149,plain,
% 0.23/0.48 ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((X!1 = consecutive(consecutive(monday))) | (~day1(consecutive(consecutive(monday)))) | (~day1(X!1)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(150,plain,
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% 0.23/0.48 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.23/0.48 tff(151,plain,
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% 0.23/0.48 inference(unit_resolution,[status(thm)],[150, 144, 58])).
% 0.23/0.48 tff(152,plain,
% 0.23/0.48 (X!1 = consecutive(consecutive(monday))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[151, 131])).
% 0.23/0.48 tff(153,plain,
% 0.23/0.48 (consecutive(consecutive(monday)) = X!1),
% 0.23/0.48 inference(symmetry,[status(thm)],[152])).
% 0.23/0.48 tff(154,plain,
% 0.23/0.48 (consecutive(consecutive(monday)) = X!0),
% 0.23/0.48 inference(transitivity,[status(thm)],[153, 125])).
% 0.23/0.48 tff(155,plain,
% 0.23/0.48 ((consecutive(consecutive(monday)) = consecutive(X!1)) <=> (X!0 = X!2)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[154, 124])).
% 0.23/0.48 tff(156,plain,
% 0.23/0.48 ((consecutive(consecutive(monday)) = consecutive(X!1)) <=> (X!2 = X!0)),
% 0.23/0.48 inference(transitivity,[status(thm)],[155, 91])).
% 0.23/0.48 tff(157,plain,
% 0.23/0.48 ((X!2 = X!0) <=> (consecutive(consecutive(monday)) = consecutive(X!1))),
% 0.23/0.48 inference(symmetry,[status(thm)],[156])).
% 0.23/0.48 tff(158,plain,
% 0.23/0.48 ((day2(consecutive(consecutive(consecutive(monday)))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))) | (~day2(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(159,plain,
% 0.23/0.48 (day2(consecutive(consecutive(consecutive(monday)))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[158, 126])).
% 0.23/0.48 tff(160,plain,
% 0.23/0.48 (^[X: $i] : refl(((~day2(X)) | (truthday(X) <=> (day2(consecutive(consecutive(consecutive(monday)))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))))) <=> ((~day2(X)) | (truthday(X) <=> (day2(consecutive(consecutive(consecutive(monday)))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
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% 0.23/0.48 inference(quant_intro,[status(thm)],[160])).
% 0.23/0.48 tff(162,plain,
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% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(163,plain,
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% 0.23/0.48 inference(quant_intro,[status(thm)],[162])).
% 0.23/0.48 tff(164,plain,
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% 0.23/0.48 tff(165,plain,
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% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(166,plain,
% 0.23/0.48 (![X: $i] : (day2(X) => (truthday(X) <=> ((day2(thursday) | day2(saturday)) | day2(sunday)))) <=> ![X: $i] : ((~day2(X)) | (truthday(X) <=> (day2(thursday) | day2(saturday) | day2(sunday))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[165])).
% 0.23/0.48 tff(167,axiom,(![X: $i] : (day2(X) => (truthday(X) <=> ((day2(thursday) | day2(saturday)) | day2(sunday))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','statement2')).
% 0.23/0.48 tff(168,plain,
% 0.23/0.48 (![X: $i] : ((~day2(X)) | (truthday(X) <=> (day2(thursday) | day2(saturday) | day2(sunday))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.23/0.48 tff(169,plain,
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% 0.23/0.48 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.23/0.48 tff(170,plain,
% 0.23/0.48 (![X: $i] : ((~day2(X)) | (truthday(X) <=> (day2(consecutive(consecutive(consecutive(monday)))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[169, 163])).
% 0.23/0.48 tff(171,plain,(
% 0.23/0.48 ![X: $i] : ((~day2(X)) | (truthday(X) <=> (day2(consecutive(consecutive(consecutive(monday)))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))))))),
% 0.23/0.48 inference(skolemize,[status(sab)],[170])).
% 0.23/0.48 tff(172,plain,
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% 0.23/0.48 inference(modus_ponens,[status(thm)],[171, 161])).
% 0.23/0.48 tff(173,plain,
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% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(174,plain,
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% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(175,plain,
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% 0.23/0.48 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.23/0.48 tff(176,plain,
% 0.23/0.48 (truthday(X!2) <=> (day2(consecutive(consecutive(consecutive(monday)))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[175, 13, 172])).
% 0.23/0.48 tff(177,plain,
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% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(178,plain,
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% 0.23/0.48 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.23/0.48 tff(179,plain,
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% 0.23/0.48 inference(unit_resolution,[status(thm)],[178, 159])).
% 0.23/0.48 tff(180,plain,
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% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(181,plain,
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% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(182,plain,
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% 0.23/0.48 inference(monotonicity,[status(thm)],[181])).
% 0.23/0.48 tff(183,plain,
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% 0.23/0.48 inference(transitivity,[status(thm)],[182, 180])).
% 0.23/0.48 tff(184,plain,
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% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(185,plain,
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% 0.23/0.48 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.23/0.48 tff(186,plain,
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% 0.23/0.48 inference(unit_resolution,[status(thm)],[185, 82, 69])).
% 0.23/0.48 tff(187,plain,
% 0.23/0.48 (X!2 = X!0),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[186, 179])).
% 0.23/0.48 tff(188,plain,
% 0.23/0.48 (consecutive(consecutive(monday)) = consecutive(X!1)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[187, 157])).
% 0.23/0.48 tff(189,plain,
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% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(190,plain,
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% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(191,plain,
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% 0.23/0.49 tff(251,plain,
% 0.23/0.49 (![X: $i] : ((~day3(X)) | (truthday(X) <=> ((~truthday(wednesday)) & (~truthday(friday)))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[250, 246])).
% 0.23/0.49 tff(252,plain,
% 0.23/0.49 (![X: $i] : ((~day3(X)) | (truthday(X) <=> ((~truthday(consecutive(consecutive(monday)))) & (~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[251, 245])).
% 0.23/0.49 tff(253,plain,(
% 0.23/0.49 ![X: $i] : ((~day3(X)) | (truthday(X) <=> ((~truthday(consecutive(consecutive(monday)))) & (~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))),
% 0.23/0.49 inference(skolemize,[status(sab)],[252])).
% 0.23/0.49 tff(254,plain,
% 0.23/0.49 (![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[253, 243])).
% 0.23/0.49 tff(255,plain,
% 0.23/0.49 (![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[254, 241])).
% 0.23/0.49 tff(256,plain,
% 0.23/0.49 (((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | ((~day3(X!3)) | (truthday(X!3) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) <=> ((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | (~day3(X!3)) | (truthday(X!3) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(257,plain,
% 0.23/0.49 ((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | ((~day3(X!3)) | (truthday(X!3) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(258,plain,
% 0.23/0.49 ((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | (~day3(X!3)) | (truthday(X!3) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.23/0.49 tff(259,plain,
% 0.23/0.49 (truthday(X!3) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[258, 20, 255])).
% 0.23/0.49 tff(260,plain,
% 0.23/0.49 ((~(truthday(X!3) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))))) | truthday(X!3) | (truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(261,plain,
% 0.23/0.49 (truthday(X!3) | (truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.23/0.49 tff(262,plain,
% 0.23/0.49 (truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[261, 239])).
% 0.23/0.49 tff(263,assumption,(~day1(consecutive(consecutive(monday)))), introduced(assumption)).
% 0.23/0.49 tff(264,plain,
% 0.23/0.49 (day1(X!1) <=> day1(X!0)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[90])).
% 0.23/0.49 tff(265,plain,
% 0.23/0.49 (day1(X!0)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[58, 264])).
% 0.23/0.49 tff(266,assumption,(consecutive(consecutive(monday)) = X!0), introduced(assumption)).
% 0.23/0.49 tff(267,plain,
% 0.23/0.49 (day1(consecutive(consecutive(monday))) <=> day1(X!0)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[266])).
% 0.23/0.49 tff(268,plain,
% 0.23/0.49 (day1(X!0) <=> day1(consecutive(consecutive(monday)))),
% 0.23/0.49 inference(symmetry,[status(thm)],[267])).
% 0.23/0.49 tff(269,assumption,(day1(X!0)), introduced(assumption)).
% 0.23/0.49 tff(270,plain,
% 0.23/0.49 (day1(consecutive(consecutive(monday)))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.23/0.49 tff(271,plain,
% 0.23/0.49 ($false),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[263, 270])).
% 0.23/0.49 tff(272,plain,((~(consecutive(consecutive(monday)) = X!0)) | day1(consecutive(consecutive(monday))) | (~day1(X!0))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.49 tff(273,plain,
% 0.23/0.49 (~(consecutive(consecutive(monday)) = X!0)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[272, 265, 263])).
% 0.23/0.49 tff(274,assumption,(~(consecutive(consecutive(monday)) = X!0)), introduced(assumption)).
% 0.23/0.49 tff(275,assumption,(truthday(consecutive(consecutive(monday)))), introduced(assumption)).
% 0.23/0.49 tff(276,plain,
% 0.23/0.49 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(consecutive(consecutive(monday)))) | (~truthday(X!0)) | (consecutive(consecutive(monday)) = X!0))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(consecutive(consecutive(monday)))) | (~truthday(X!0)) | (consecutive(consecutive(monday)) = X!0))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(277,plain,
% 0.23/0.49 (((consecutive(consecutive(monday)) = X!0) | (~truthday(consecutive(consecutive(monday)))) | (~truthday(X!0))) <=> ((~truthday(consecutive(consecutive(monday)))) | (~truthday(X!0)) | (consecutive(consecutive(monday)) = X!0))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(278,plain,
% 0.23/0.49 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((consecutive(consecutive(monday)) = X!0) | (~truthday(consecutive(consecutive(monday)))) | (~truthday(X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(consecutive(consecutive(monday)))) | (~truthday(X!0)) | (consecutive(consecutive(monday)) = X!0)))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[277])).
% 0.23/0.49 tff(279,plain,
% 0.23/0.49 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((consecutive(consecutive(monday)) = X!0) | (~truthday(consecutive(consecutive(monday)))) | (~truthday(X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(consecutive(consecutive(monday)))) | (~truthday(X!0)) | (consecutive(consecutive(monday)) = X!0))),
% 0.23/0.49 inference(transitivity,[status(thm)],[278, 276])).
% 0.23/0.49 tff(280,plain,
% 0.23/0.49 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((consecutive(consecutive(monday)) = X!0) | (~truthday(consecutive(consecutive(monday)))) | (~truthday(X!0)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(281,plain,
% 0.23/0.49 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(consecutive(consecutive(monday)))) | (~truthday(X!0)) | (consecutive(consecutive(monday)) = X!0)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.23/0.49 tff(282,plain,
% 0.23/0.49 ($false),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[281, 82, 69, 275, 274])).
% 0.23/0.49 tff(283,plain,((~truthday(consecutive(consecutive(monday)))) | (consecutive(consecutive(monday)) = X!0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.49 tff(284,plain,
% 0.23/0.49 (~truthday(consecutive(consecutive(monday)))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[283, 273])).
% 0.23/0.49 tff(285,plain,
% 0.23/0.49 ((~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))) | truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(286,plain,
% 0.23/0.49 (truthday(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[285, 284, 262])).
% 0.23/0.49 tff(287,assumption,(~(consecutive(consecutive(consecutive(consecutive(monday)))) = X!0)), introduced(assumption)).
% 0.23/0.49 tff(288,assumption,(truthday(consecutive(consecutive(consecutive(consecutive(monday)))))), introduced(assumption)).
% 0.23/0.49 tff(289,plain,
% 0.23/0.49 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))) | (~truthday(X!0)) | (consecutive(consecutive(consecutive(consecutive(monday)))) = X!0))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))) | (~truthday(X!0)) | (consecutive(consecutive(consecutive(consecutive(monday)))) = X!0))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(290,plain,
% 0.23/0.49 (((consecutive(consecutive(consecutive(consecutive(monday)))) = X!0) | (~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))) | (~truthday(X!0))) <=> ((~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))) | (~truthday(X!0)) | (consecutive(consecutive(consecutive(consecutive(monday)))) = X!0))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(291,plain,
% 0.23/0.49 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((consecutive(consecutive(consecutive(consecutive(monday)))) = X!0) | (~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))) | (~truthday(X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))) | (~truthday(X!0)) | (consecutive(consecutive(consecutive(consecutive(monday)))) = X!0)))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[290])).
% 0.23/0.49 tff(292,plain,
% 0.23/0.49 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((consecutive(consecutive(consecutive(consecutive(monday)))) = X!0) | (~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))) | (~truthday(X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))) | (~truthday(X!0)) | (consecutive(consecutive(consecutive(consecutive(monday)))) = X!0))),
% 0.23/0.49 inference(transitivity,[status(thm)],[291, 289])).
% 0.23/0.49 tff(293,plain,
% 0.23/0.49 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((consecutive(consecutive(consecutive(consecutive(monday)))) = X!0) | (~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))) | (~truthday(X!0)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(294,plain,
% 0.23/0.49 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))) | (~truthday(X!0)) | (consecutive(consecutive(consecutive(consecutive(monday)))) = X!0)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.23/0.50 tff(295,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[294, 82, 69, 288, 287])).
% 0.23/0.50 tff(296,plain,((~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))) | (consecutive(consecutive(consecutive(consecutive(monday)))) = X!0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.50 tff(297,plain,
% 0.23/0.50 (consecutive(consecutive(consecutive(consecutive(monday)))) = X!0),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[296, 286])).
% 0.23/0.50 tff(298,plain,
% 0.23/0.50 (day1(consecutive(consecutive(consecutive(consecutive(monday))))) <=> day1(X!0)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[297])).
% 0.23/0.50 tff(299,plain,
% 0.23/0.50 (day1(X!0) <=> day1(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.50 inference(symmetry,[status(thm)],[298])).
% 0.23/0.50 tff(300,plain,
% 0.23/0.50 (day1(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[265, 299])).
% 0.23/0.50 tff(301,assumption,(~day1(consecutive(consecutive(consecutive(consecutive(monday)))))), introduced(assumption)).
% 0.23/0.50 tff(302,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[301, 300])).
% 0.23/0.50 tff(303,plain,(truthday(monday) | day1(consecutive(consecutive(consecutive(consecutive(monday))))) | day1(consecutive(consecutive(monday))) | (truthday(X!3) <=> (~truthday(monday)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.50 tff(304,plain,
% 0.23/0.50 (truthday(monday)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[303, 237, 222, 218])).
% 0.23/0.50 tff(305,plain,
% 0.23/0.50 ((truthday(X!3) <=> (~truthday(monday))) | truthday(X!3) | (~truthday(monday))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(306,plain,
% 0.23/0.50 (truthday(X!3)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[305, 304, 218])).
% 0.23/0.50 tff(307,plain,
% 0.23/0.50 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(monday)) | (~truthday(X!3)) | (monday = X!3))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(monday)) | (~truthday(X!3)) | (monday = X!3))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(308,plain,
% 0.23/0.50 (((monday = X!3) | (~truthday(monday)) | (~truthday(X!3))) <=> ((~truthday(monday)) | (~truthday(X!3)) | (monday = X!3))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(309,plain,
% 0.23/0.50 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((monday = X!3) | (~truthday(monday)) | (~truthday(X!3)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(monday)) | (~truthday(X!3)) | (monday = X!3)))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[308])).
% 0.23/0.50 tff(310,plain,
% 0.23/0.50 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((monday = X!3) | (~truthday(monday)) | (~truthday(X!3)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(monday)) | (~truthday(X!3)) | (monday = X!3))),
% 0.23/0.50 inference(transitivity,[status(thm)],[309, 307])).
% 0.23/0.50 tff(311,plain,
% 0.23/0.50 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((monday = X!3) | (~truthday(monday)) | (~truthday(X!3)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(312,plain,
% 0.23/0.50 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(monday)) | (~truthday(X!3)) | (monday = X!3)),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.23/0.50 tff(313,plain,
% 0.23/0.50 ((~truthday(monday)) | (~truthday(X!3)) | (monday = X!3)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[312, 82])).
% 0.23/0.50 tff(314,plain,
% 0.23/0.50 (monday = X!3),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[313, 306, 304])).
% 0.23/0.50 tff(315,plain,
% 0.23/0.50 ((consecutive(sunday) = monday) <=> (consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))) = monday)),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(316,plain,
% 0.23/0.50 ((consecutive(sunday) = monday) <=> (consecutive(sunday) = monday)),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(317,axiom,(consecutive(sunday) = monday), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','monday_follows_sunday')).
% 0.23/0.50 tff(318,plain,
% 0.23/0.50 (consecutive(sunday) = monday),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.23/0.50 tff(319,plain,
% 0.23/0.50 (consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))) = monday),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[318, 315])).
% 0.23/0.50 tff(320,plain,
% 0.23/0.50 (consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))) = consecutive(X!2)),
% 0.23/0.50 inference(transitivity,[status(thm)],[319, 314, 40])).
% 0.23/0.50 tff(321,plain,
% 0.23/0.50 (day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))) <=> day3(consecutive(X!2))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[320])).
% 0.23/0.50 tff(322,plain,
% 0.23/0.50 (day3(consecutive(X!2)) <=> day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.50 inference(symmetry,[status(thm)],[321])).
% 0.23/0.50 tff(323,plain,
% 0.23/0.50 (day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[16, 322])).
% 0.23/0.50 tff(324,assumption,(~truthday(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))), introduced(assumption)).
% 0.23/0.50 tff(325,plain,
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% 0.23/0.51 (~day1(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[236, 456])).
% 0.23/0.51 tff(458,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[303, 457, 428, 222, 218])).
% 0.23/0.51 tff(459,plain,((truthday(X!3) <=> (~truthday(monday))) | day2(consecutive(consecutive(consecutive(monday))))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.51 tff(460,plain,
% 0.23/0.51 (truthday(X!3) <=> (~truthday(monday))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[459, 217])).
% 0.23/0.51 tff(461,plain,
% 0.23/0.51 ((~(truthday(X!3) <=> (~truthday(monday)))) | truthday(X!3) | truthday(monday)),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(462,plain,
% 0.23/0.51 (truthday(X!3)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[461, 460, 41])).
% 0.23/0.51 tff(463,plain,
% 0.23/0.51 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(X!1)) | (~truthday(X!3)) | (X!1 = X!3))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(X!1)) | (~truthday(X!3)) | (X!1 = X!3))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(464,plain,
% 0.23/0.51 (((X!1 = X!3) | (~truthday(X!1)) | (~truthday(X!3))) <=> ((~truthday(X!1)) | (~truthday(X!3)) | (X!1 = X!3))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(465,plain,
% 0.23/0.51 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((X!1 = X!3) | (~truthday(X!1)) | (~truthday(X!3)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(X!1)) | (~truthday(X!3)) | (X!1 = X!3)))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[464])).
% 0.23/0.51 tff(466,plain,
% 0.23/0.51 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((X!1 = X!3) | (~truthday(X!1)) | (~truthday(X!3)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(X!1)) | (~truthday(X!3)) | (X!1 = X!3))),
% 0.23/0.51 inference(transitivity,[status(thm)],[465, 463])).
% 0.23/0.51 tff(467,plain,
% 0.23/0.51 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((X!1 = X!3) | (~truthday(X!1)) | (~truthday(X!3)))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(468,plain,
% 0.23/0.51 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(X!1)) | (~truthday(X!3)) | (X!1 = X!3)),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.23/0.51 tff(469,plain,
% 0.23/0.51 ((~truthday(X!1)) | (~truthday(X!3)) | (X!1 = X!3)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[468, 82])).
% 0.23/0.51 tff(470,plain,
% 0.23/0.51 (X!1 = X!3),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[469, 462, 65])).
% 0.23/0.51 tff(471,plain,
% 0.23/0.51 (X!0 = X!1),
% 0.23/0.51 inference(symmetry,[status(thm)],[90])).
% 0.23/0.51 tff(472,plain,
% 0.23/0.51 ((~(truthday(X!3) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))))) | (~truthday(X!3)) | (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(473,plain,
% 0.23/0.51 ((~truthday(X!3)) | (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[472, 259])).
% 0.23/0.51 tff(474,plain,
% 0.23/0.51 (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[473, 462])).
% 0.23/0.51 tff(475,plain,
% 0.23/0.51 (((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | ((~day3(consecutive(X!2))) | (truthday(consecutive(X!2)) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) <=> ((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | (~day3(consecutive(X!2))) | (truthday(consecutive(X!2)) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(476,plain,
% 0.23/0.51 ((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | ((~day3(consecutive(X!2))) | (truthday(consecutive(X!2)) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(477,plain,
% 0.23/0.51 ((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | (~day3(consecutive(X!2))) | (truthday(consecutive(X!2)) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.23/0.51 tff(478,plain,
% 0.23/0.51 (truthday(consecutive(X!2)) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[477, 255, 16])).
% 0.23/0.51 tff(479,plain,
% 0.23/0.51 ((~(truthday(consecutive(X!2)) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))))) | truthday(consecutive(X!2)) | (truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(480,plain,
% 0.23/0.51 (truthday(consecutive(X!2)) | (truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[479, 478])).
% 0.23/0.51 tff(481,plain,
% 0.23/0.51 (truthday(consecutive(X!2))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[480, 474])).
% 0.23/0.51 tff(482,plain,
% 0.23/0.51 ((truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))) | (~truthday(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(483,plain,
% 0.23/0.51 (~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[482, 474])).
% 0.23/0.51 tff(484,assumption,(X!1 = X!3), introduced(assumption)).
% 0.23/0.51 tff(485,plain,
% 0.23/0.51 (X!0 = X!1),
% 0.23/0.51 inference(symmetry,[status(thm)],[125])).
% 0.23/0.51 tff(486,assumption,(X!0 = consecutive(consecutive(consecutive(consecutive(monday))))), introduced(assumption)).
% 0.23/0.51 tff(487,plain,
% 0.23/0.51 (consecutive(consecutive(consecutive(consecutive(monday)))) = X!0),
% 0.23/0.51 inference(symmetry,[status(thm)],[486])).
% 0.23/0.51 tff(488,plain,
% 0.23/0.51 (consecutive(consecutive(consecutive(consecutive(monday)))) = consecutive(X!2)),
% 0.23/0.51 inference(transitivity,[status(thm)],[487, 485, 484, 40])).
% 0.23/0.51 tff(489,plain,
% 0.23/0.51 (truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> truthday(consecutive(X!2))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[488])).
% 0.23/0.51 tff(490,plain,
% 0.23/0.51 (truthday(consecutive(X!2)) <=> truthday(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.51 inference(symmetry,[status(thm)],[489])).
% 0.23/0.51 tff(491,assumption,(truthday(consecutive(X!2))), introduced(assumption)).
% 0.23/0.51 tff(492,plain,
% 0.23/0.51 (truthday(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[491, 490])).
% 0.23/0.51 tff(493,assumption,(~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))), introduced(assumption)).
% 0.23/0.51 tff(494,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[493, 492])).
% 0.23/0.51 tff(495,plain,((~(X!0 = consecutive(consecutive(consecutive(consecutive(monday)))))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))) | (~truthday(consecutive(X!2))) | (~(X!1 = X!0)) | (~(X!1 = X!3))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.51 tff(496,plain,
% 0.23/0.51 (~(X!0 = consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[495, 483, 481, 90, 470])).
% 0.23/0.51 tff(497,plain,
% 0.23/0.51 ((~(truthday(consecutive(monday)) <=> (~truthday(monday)))) | truthday(consecutive(monday)) | truthday(monday)),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(498,plain,
% 0.23/0.51 ((~(truthday(consecutive(monday)) <=> (~truthday(monday)))) | truthday(monday)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[497, 426])).
% 0.23/0.51 tff(499,plain,
% 0.23/0.51 (~(truthday(consecutive(monday)) <=> (~truthday(monday)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[498, 41])).
% 0.23/0.51 tff(500,plain,
% 0.23/0.51 (((~![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))) | ((~day1(consecutive(monday))) | (truthday(consecutive(monday)) <=> (~truthday(monday))))) <=> ((~![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))) | (~day1(consecutive(monday))) | (truthday(consecutive(monday)) <=> (~truthday(monday))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(501,plain,
% 0.23/0.51 ((~![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))) | ((~day1(consecutive(monday))) | (truthday(consecutive(monday)) <=> (~truthday(monday))))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(502,plain,
% 0.23/0.51 ((~![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))) | (~day1(consecutive(monday))) | (truthday(consecutive(monday)) <=> (~truthday(monday)))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.23/0.51 tff(503,plain,
% 0.23/0.51 ((~day1(consecutive(monday))) | (truthday(consecutive(monday)) <=> (~truthday(monday)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[502, 54])).
% 0.23/0.51 tff(504,plain,
% 0.23/0.51 (~day1(consecutive(monday))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[503, 499])).
% 0.23/0.51 tff(505,plain,
% 0.23/0.51 ((~![X: $i] : (day1(X) <=> day2(consecutive(X)))) | (day1(consecutive(monday)) <=> day2(consecutive(consecutive(monday))))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(506,plain,
% 0.23/0.51 (day1(consecutive(monday)) <=> day2(consecutive(consecutive(monday)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[505, 98])).
% 0.23/0.51 tff(507,plain,
% 0.23/0.51 ((~(day1(consecutive(monday)) <=> day2(consecutive(consecutive(monday))))) | day1(consecutive(monday)) | (~day2(consecutive(consecutive(monday))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(508,plain,
% 0.23/0.51 (day1(consecutive(monday)) | (~day2(consecutive(consecutive(monday))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[507, 506])).
% 0.23/0.51 tff(509,plain,
% 0.23/0.51 (~day2(consecutive(consecutive(monday)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[508, 504])).
% 0.23/0.51 tff(510,plain,
% 0.23/0.51 ((~![X: $i] : (day2(X) <=> day3(consecutive(X)))) | (day2(consecutive(consecutive(monday))) <=> day3(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(511,plain,
% 0.23/0.51 (day2(consecutive(consecutive(monday))) <=> day3(consecutive(consecutive(consecutive(monday))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[510, 7])).
% 0.23/0.51 tff(512,plain,
% 0.23/0.51 ((~(day2(consecutive(consecutive(monday))) <=> day3(consecutive(consecutive(consecutive(monday)))))) | day2(consecutive(consecutive(monday))) | (~day3(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(513,plain,
% 0.23/0.51 (day2(consecutive(consecutive(monday))) | (~day3(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[512, 511])).
% 0.23/0.51 tff(514,plain,
% 0.23/0.51 (~day3(consecutive(consecutive(consecutive(monday))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[513, 509])).
% 0.23/0.51 tff(515,assumption,(X!0 = consecutive(consecutive(consecutive(monday)))), introduced(assumption)).
% 0.23/0.51 tff(516,plain,
% 0.23/0.51 (consecutive(consecutive(consecutive(monday))) = X!0),
% 0.23/0.51 inference(symmetry,[status(thm)],[515])).
% 0.23/0.51 tff(517,plain,
% 0.23/0.51 (consecutive(consecutive(consecutive(monday))) = consecutive(X!2)),
% 0.23/0.51 inference(transitivity,[status(thm)],[516, 485, 484, 40])).
% 0.23/0.51 tff(518,plain,
% 0.23/0.51 (day3(consecutive(consecutive(consecutive(monday)))) <=> day3(consecutive(X!2))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[517])).
% 0.23/0.51 tff(519,plain,
% 0.23/0.51 (day3(consecutive(X!2)) <=> day3(consecutive(consecutive(consecutive(monday))))),
% 0.23/0.51 inference(symmetry,[status(thm)],[518])).
% 0.23/0.51 tff(520,plain,
% 0.23/0.51 (day3(consecutive(consecutive(consecutive(monday))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[16, 519])).
% 0.23/0.51 tff(521,assumption,(~day3(consecutive(consecutive(consecutive(monday))))), introduced(assumption)).
% 0.23/0.51 tff(522,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[521, 520])).
% 0.23/0.51 tff(523,plain,((~(X!0 = consecutive(consecutive(consecutive(monday))))) | day3(consecutive(consecutive(consecutive(monday)))) | (~(X!1 = X!0)) | (~(X!1 = X!3))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.51 tff(524,plain,
% 0.23/0.51 (~(X!0 = consecutive(consecutive(consecutive(monday))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[523, 514, 90, 470])).
% 0.23/0.51 tff(525,plain,
% 0.23/0.51 (X!3 = X!1),
% 0.23/0.51 inference(symmetry,[status(thm)],[470])).
% 0.23/0.51 tff(526,plain,
% 0.23/0.51 (X!3 = X!0),
% 0.23/0.51 inference(transitivity,[status(thm)],[525, 90])).
% 0.23/0.51 tff(527,plain,
% 0.23/0.51 (day1(X!3) <=> day1(X!0)),
% 0.23/0.51 inference(monotonicity,[status(thm)],[526])).
% 0.23/0.51 tff(528,plain,
% 0.23/0.51 (day1(X!0) <=> day1(X!3)),
% 0.23/0.51 inference(symmetry,[status(thm)],[527])).
% 0.23/0.51 tff(529,plain,
% 0.23/0.51 (day1(X!3)),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[265, 528])).
% 0.23/0.51 tff(530,plain,
% 0.23/0.51 (monday = consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.51 inference(symmetry,[status(thm)],[319])).
% 0.23/0.51 tff(531,plain,
% 0.23/0.51 (day3(monday) <=> day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[530])).
% 0.23/0.51 tff(532,plain,
% 0.23/0.51 ((~day3(monday)) <=> (~day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[531])).
% 0.23/0.51 tff(533,plain,
% 0.23/0.51 ((~(truthday(monday) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))))) | truthday(monday) | (truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(534,plain,
% 0.23/0.51 (~(truthday(monday) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[533, 474, 41])).
% 0.23/0.51 tff(535,plain,
% 0.23/0.51 (((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | ((~day3(monday)) | (truthday(monday) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) <=> ((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | (~day3(monday)) | (truthday(monday) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))),
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% 0.23/0.51 tff(536,plain,
% 0.23/0.51 ((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | ((~day3(monday)) | (truthday(monday) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(537,plain,
% 0.23/0.51 ((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | (~day3(monday)) | (truthday(monday) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.23/0.51 tff(538,plain,
% 0.23/0.51 ((~day3(monday)) | (truthday(monday) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[537, 255])).
% 0.23/0.51 tff(539,plain,
% 0.23/0.51 (~day3(monday)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[538, 534])).
% 0.23/0.51 tff(540,plain,
% 0.23/0.51 (~day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[539, 532])).
% 0.23/0.51 tff(541,plain,
% 0.23/0.51 ((~(day2(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))) <=> day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | (~day2(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))) | day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(542,plain,
% 0.23/0.51 ((~day2(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))) | day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[541, 357])).
% 0.23/0.51 tff(543,plain,
% 0.23/0.51 (~day2(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[542, 540])).
% 0.23/0.51 tff(544,plain,
% 0.23/0.51 ((~(day1(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) <=> day2(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))))) | (~day1(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(545,plain,
% 0.23/0.51 ((~day1(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[544, 330])).
% 0.23/0.51 tff(546,plain,
% 0.23/0.51 (~day1(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[545, 543])).
% 0.23/0.51 tff(547,plain,
% 0.23/0.51 (consecutive(X!2) = X!3),
% 0.23/0.51 inference(symmetry,[status(thm)],[40])).
% 0.23/0.51 tff(548,assumption,(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))) = consecutive(X!2)), introduced(assumption)).
% 0.23/0.51 tff(549,plain,
% 0.23/0.51 (consecutive(consecutive(consecutive(consecutive(consecutive(monday))))) = X!3),
% 0.23/0.51 inference(transitivity,[status(thm)],[548, 547])).
% 0.23/0.51 tff(550,plain,
% 0.23/0.51 (day1(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) <=> day1(X!3)),
% 0.23/0.51 inference(monotonicity,[status(thm)],[549])).
% 0.23/0.51 tff(551,plain,
% 0.23/0.51 (day1(X!3) <=> day1(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.51 inference(symmetry,[status(thm)],[550])).
% 0.23/0.51 tff(552,assumption,(day1(X!3)), introduced(assumption)).
% 0.23/0.51 tff(553,plain,
% 0.23/0.51 (day1(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.23/0.51 tff(554,assumption,(~day1(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))), introduced(assumption)).
% 0.23/0.51 tff(555,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[554, 553])).
% 0.23/0.51 tff(556,plain,((~(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))) = consecutive(X!2))) | day1(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | (~day1(X!3))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.51 tff(557,plain,
% 0.23/0.51 (~(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))) = consecutive(X!2))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[556, 546, 529])).
% 0.23/0.51 tff(558,plain,
% 0.23/0.51 ((consecutive(consecutive(consecutive(consecutive(consecutive(monday))))) = X!0) <=> (X!0 = consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.51 inference(commutativity,[status(thm)],[])).
% 0.23/0.51 tff(559,plain,
% 0.23/0.51 (X!3 = X!1),
% 0.23/0.51 inference(symmetry,[status(thm)],[484])).
% 0.23/0.51 tff(560,plain,
% 0.23/0.51 (consecutive(X!2) = X!0),
% 0.23/0.51 inference(transitivity,[status(thm)],[547, 559, 125])).
% 0.23/0.51 tff(561,plain,
% 0.23/0.51 ((consecutive(consecutive(consecutive(consecutive(consecutive(monday))))) = consecutive(X!2)) <=> (consecutive(consecutive(consecutive(consecutive(consecutive(monday))))) = X!0)),
% 0.23/0.51 inference(monotonicity,[status(thm)],[560])).
% 0.23/0.51 tff(562,plain,
% 0.23/0.51 ((consecutive(consecutive(consecutive(consecutive(consecutive(monday))))) = consecutive(X!2)) <=> (X!0 = consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.51 inference(transitivity,[status(thm)],[561, 558])).
% 0.23/0.51 tff(563,plain,
% 0.23/0.51 ((X!0 = consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) <=> (consecutive(consecutive(consecutive(consecutive(consecutive(monday))))) = consecutive(X!2))),
% 0.23/0.51 inference(symmetry,[status(thm)],[562])).
% 0.23/0.51 tff(564,assumption,(X!0 = consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))), introduced(assumption)).
% 0.23/0.51 tff(565,plain,
% 0.23/0.51 (consecutive(consecutive(consecutive(consecutive(consecutive(monday))))) = consecutive(X!2)),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[564, 563])).
% 0.23/0.51 tff(566,assumption,(~(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))) = consecutive(X!2))), introduced(assumption)).
% 0.23/0.51 tff(567,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[566, 565])).
% 0.23/0.51 tff(568,plain,((~(X!0 = consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))) | (consecutive(consecutive(consecutive(consecutive(consecutive(monday))))) = consecutive(X!2)) | (~(X!1 = X!0)) | (~(X!1 = X!3))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.51 tff(569,plain,
% 0.23/0.51 (~(X!0 = consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[568, 557, 90, 470])).
% 0.23/0.51 tff(570,plain,
% 0.23/0.51 (~day1(consecutive(consecutive(monday)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[221, 217])).
% 0.23/0.51 tff(571,plain,
% 0.23/0.51 (~(consecutive(consecutive(monday)) = X!0)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[272, 570, 265])).
% 0.23/0.51 tff(572,plain,
% 0.23/0.51 ((X!0 = consecutive(consecutive(monday))) <=> (consecutive(consecutive(monday)) = X!0)),
% 0.23/0.51 inference(commutativity,[status(thm)],[])).
% 0.23/0.51 tff(573,assumption,(X!0 = consecutive(consecutive(monday))), introduced(assumption)).
% 0.23/0.51 tff(574,plain,
% 0.23/0.51 (consecutive(consecutive(monday)) = X!0),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.23/0.51 tff(575,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[274, 574])).
% 0.23/0.51 tff(576,plain,((~(X!0 = consecutive(consecutive(monday)))) | (consecutive(consecutive(monday)) = X!0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.51 tff(577,plain,
% 0.23/0.51 (~(X!0 = consecutive(consecutive(monday)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[576, 571])).
% 0.23/0.51 tff(578,plain,
% 0.23/0.51 ((~(truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> (~truthday(monday)))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))) | truthday(monday)),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(579,plain,
% 0.23/0.51 (~(truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> (~truthday(monday)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[578, 483, 41])).
% 0.23/0.51 tff(580,plain,
% 0.23/0.51 (((~![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))) | ((~day1(consecutive(consecutive(consecutive(consecutive(monday)))))) | (truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> (~truthday(monday))))) <=> ((~![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))) | (~day1(consecutive(consecutive(consecutive(consecutive(monday)))))) | (truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> (~truthday(monday))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(581,plain,
% 0.23/0.51 ((~![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))) | ((~day1(consecutive(consecutive(consecutive(consecutive(monday)))))) | (truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> (~truthday(monday))))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(582,plain,
% 0.23/0.51 ((~![X: $i] : ((~day1(X)) | (truthday(X) <=> (~truthday(monday))))) | (~day1(consecutive(consecutive(consecutive(consecutive(monday)))))) | (truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> (~truthday(monday)))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[581, 580])).
% 0.23/0.51 tff(583,plain,
% 0.23/0.51 ((~day1(consecutive(consecutive(consecutive(consecutive(monday)))))) | (truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> (~truthday(monday)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[582, 54])).
% 0.23/0.51 tff(584,plain,
% 0.23/0.51 (~day1(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[583, 579])).
% 0.23/0.51 tff(585,plain,
% 0.23/0.51 ((~(day1(consecutive(consecutive(consecutive(consecutive(monday))))) <=> day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))) | day1(consecutive(consecutive(consecutive(consecutive(monday))))) | (~day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(586,plain,
% 0.23/0.51 (day1(consecutive(consecutive(consecutive(consecutive(monday))))) | (~day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[585, 234])).
% 0.23/0.51 tff(587,plain,
% 0.23/0.51 (~day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[586, 584])).
% 0.23/0.51 tff(588,plain,
% 0.23/0.51 ((~![X: $i] : (day2(X) <=> day3(consecutive(X)))) | (day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) <=> day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(589,plain,
% 0.23/0.51 (day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) <=> day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[588, 7])).
% 0.23/0.51 tff(590,plain,
% 0.23/0.51 ((~(day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) <=> day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))))) | day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | (~day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(591,plain,
% 0.23/0.51 (day2(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | (~day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[590, 589])).
% 0.23/0.51 tff(592,plain,
% 0.23/0.51 (~day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[591, 587])).
% 0.23/0.51 tff(593,assumption,(X!0 = consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))), introduced(assumption)).
% 0.23/0.51 tff(594,plain,
% 0.23/0.51 (consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) = X!0),
% 0.23/0.51 inference(symmetry,[status(thm)],[593])).
% 0.23/0.51 tff(595,plain,
% 0.23/0.51 (consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) = consecutive(X!2)),
% 0.23/0.51 inference(transitivity,[status(thm)],[594, 485, 484, 40])).
% 0.23/0.51 tff(596,plain,
% 0.23/0.51 (day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))) <=> day3(consecutive(X!2))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[595])).
% 0.23/0.51 tff(597,plain,
% 0.23/0.51 (day3(consecutive(X!2)) <=> day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.51 inference(symmetry,[status(thm)],[596])).
% 0.23/0.51 tff(598,plain,
% 0.23/0.51 (day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[16, 597])).
% 0.23/0.51 tff(599,assumption,(~day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))), introduced(assumption)).
% 0.23/0.51 tff(600,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[599, 598])).
% 0.23/0.51 tff(601,plain,((~(X!0 = consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))) | day3(consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))) | (~(X!1 = X!0)) | (~(X!1 = X!3))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.51 tff(602,plain,
% 0.23/0.51 (~(X!0 = consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[601, 592, 90, 470])).
% 0.23/0.51 tff(603,assumption,(X!0 = consecutive(monday)), introduced(assumption)).
% 0.23/0.51 tff(604,plain,
% 0.23/0.51 (consecutive(monday) = X!0),
% 0.23/0.51 inference(symmetry,[status(thm)],[603])).
% 0.23/0.51 tff(605,plain,
% 0.23/0.51 (consecutive(monday) = consecutive(X!2)),
% 0.23/0.51 inference(transitivity,[status(thm)],[604, 485, 484, 40])).
% 0.23/0.51 tff(606,plain,
% 0.23/0.51 (truthday(consecutive(monday)) <=> truthday(consecutive(X!2))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[605])).
% 0.23/0.51 tff(607,plain,
% 0.23/0.51 (truthday(consecutive(X!2)) <=> truthday(consecutive(monday))),
% 0.23/0.51 inference(symmetry,[status(thm)],[606])).
% 0.23/0.51 tff(608,plain,
% 0.23/0.51 (truthday(consecutive(monday))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[491, 607])).
% 0.23/0.51 tff(609,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[426, 608])).
% 0.23/0.51 tff(610,plain,((~(X!0 = consecutive(monday))) | (~truthday(consecutive(X!2))) | (~(X!1 = X!0)) | (~(X!1 = X!3))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.51 tff(611,plain,
% 0.23/0.51 (~(X!0 = consecutive(monday))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[610, 481, 90, 470])).
% 0.23/0.51 tff(612,plain,
% 0.23/0.51 (^[X: $i] : trans(monotonicity(rewrite((X = sunday) <=> (X = consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))))), rewrite((X = saturday) <=> (X = consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))), rewrite((X = friday) <=> (X = consecutive(consecutive(consecutive(consecutive(monday)))))), rewrite((X = thursday) <=> (X = consecutive(consecutive(consecutive(monday))))), rewrite((X = wednesday) <=> (X = consecutive(consecutive(monday)))), rewrite((X = tuesday) <=> (X = consecutive(monday))), (((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday)) <=> ((X = consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))) | (X = consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | (X = consecutive(consecutive(consecutive(consecutive(monday))))) | (X = consecutive(consecutive(consecutive(monday)))) | (X = consecutive(consecutive(monday))) | (X = consecutive(monday)) | (X = monday)))), rewrite(((X = consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))) | (X = consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | (X = consecutive(consecutive(consecutive(consecutive(monday))))) | (X = consecutive(consecutive(consecutive(monday)))) | (X = consecutive(consecutive(monday))) | (X = consecutive(monday)) | (X = monday)) <=> ((X = monday) | (X = consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))) | (X = consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | (X = consecutive(consecutive(consecutive(consecutive(monday))))) | (X = consecutive(consecutive(consecutive(monday)))) | (X = consecutive(consecutive(monday))) | (X = consecutive(monday)))), (((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday)) <=> ((X = monday) | (X = consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))) | (X = consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | (X = consecutive(consecutive(consecutive(consecutive(monday))))) | (X = consecutive(consecutive(consecutive(monday)))) | (X = consecutive(consecutive(monday))) | (X = consecutive(monday)))))),
% 0.23/0.52 inference(bind,[status(th)],[])).
% 0.23/0.52 tff(613,plain,
% 0.23/0.52 (![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday)) <=> ![X: $i] : ((X = monday) | (X = consecutive(consecutive(consecutive(consecutive(consecutive(consecutive(monday))))))) | (X = consecutive(consecutive(consecutive(consecutive(consecutive(monday)))))) | (X = consecutive(consecutive(consecutive(consecutive(monday))))) | (X = consecutive(consecutive(consecutive(monday)))) | (X = consecutive(consecutive(monday))) | (X = consecutive(monday)))),
% 0.23/0.52 inference(quant_intro,[status(thm)],[612])).
% 0.23/0.52 tff(614,plain,
% 0.23/0.52 (![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))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(615,plain,
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% 0.23/0.52 (![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))),
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% 0.23/0.52 tff(617,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')).
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% 0.23/0.52 tff(619,plain,
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% 0.23/0.52 inference(modus_ponens,[status(thm)],[618, 614])).
% 0.23/0.52 tff(620,plain,
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% 0.23/0.52 tff(621,plain,(
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% 0.23/0.52 tff(622,plain,
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% 0.23/0.52 inference(monotonicity,[status(thm)],[664])).
% 0.23/0.52 tff(666,plain,
% 0.23/0.52 ((~(monday = friday)) <=> (~(monday = consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(667,plain,
% 0.23/0.52 ((~(monday = friday)) <=> (~(monday = friday))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(668,plain,
% 0.23/0.52 (~(monday = friday)),
% 0.23/0.52 inference(and_elim,[status(thm)],[653])).
% 0.23/0.52 tff(669,plain,
% 0.23/0.52 (~(monday = friday)),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[668, 667])).
% 0.23/0.52 tff(670,plain,
% 0.23/0.52 (~(monday = consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[669, 666])).
% 0.23/0.52 tff(671,plain,
% 0.23/0.52 (~(consecutive(consecutive(consecutive(consecutive(monday)))) = X!0)),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[670, 665])).
% 0.23/0.52 tff(672,plain,
% 0.23/0.52 (~truthday(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[296, 671])).
% 0.23/0.52 tff(673,plain,
% 0.23/0.52 (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[285, 672, 660])).
% 0.23/0.52 tff(674,plain,
% 0.23/0.52 (truthday(X!3)),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[261, 673])).
% 0.23/0.52 tff(675,plain,
% 0.23/0.52 ((~(truthday(X!3) <=> (~truthday(monday)))) | (~truthday(X!3)) | (~truthday(monday))),
% 0.23/0.52 inference(tautology,[status(thm)],[])).
% 0.23/0.52 tff(676,plain,
% 0.23/0.52 (~(truthday(X!3) <=> (~truthday(monday)))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[675, 674, 636])).
% 0.23/0.52 tff(677,plain,
% 0.23/0.52 ((~(truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))) | (truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.52 inference(tautology,[status(thm)],[])).
% 0.23/0.52 tff(678,plain,
% 0.23/0.52 (~(truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[677, 672, 673])).
% 0.23/0.52 tff(679,plain,
% 0.23/0.52 (((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | ((~day3(consecutive(consecutive(consecutive(consecutive(monday)))))) | (truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) <=> ((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | (~day3(consecutive(consecutive(consecutive(consecutive(monday)))))) | (truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(680,plain,
% 0.23/0.52 ((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | ((~day3(consecutive(consecutive(consecutive(consecutive(monday)))))) | (truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))),
% 0.23/0.52 inference(quant_inst,[status(thm)],[])).
% 0.23/0.52 tff(681,plain,
% 0.23/0.52 ((~![X: $i] : ((~day3(X)) | (truthday(X) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday)))))))))) | (~day3(consecutive(consecutive(consecutive(consecutive(monday)))))) | (truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.23/0.53 tff(682,plain,
% 0.23/0.53 ((~day3(consecutive(consecutive(consecutive(consecutive(monday)))))) | (truthday(consecutive(consecutive(consecutive(consecutive(monday))))) <=> (~(truthday(consecutive(consecutive(monday))) | truthday(consecutive(consecutive(consecutive(consecutive(monday))))))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[681, 255])).
% 0.23/0.53 tff(683,plain,
% 0.23/0.53 (~day3(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[682, 678])).
% 0.23/0.53 tff(684,plain,
% 0.23/0.53 ((~![X: $i] : (day2(X) <=> day3(consecutive(X)))) | (day2(consecutive(consecutive(consecutive(monday)))) <=> day3(consecutive(consecutive(consecutive(consecutive(monday))))))),
% 0.23/0.53 inference(quant_inst,[status(thm)],[])).
% 0.23/0.53 tff(685,plain,
% 0.23/0.53 (day2(consecutive(consecutive(consecutive(monday)))) <=> day3(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[684, 7])).
% 0.23/0.53 tff(686,plain,
% 0.23/0.53 ((~(day2(consecutive(consecutive(consecutive(monday)))) <=> day3(consecutive(consecutive(consecutive(consecutive(monday))))))) | (~day2(consecutive(consecutive(consecutive(monday))))) | day3(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(687,plain,
% 0.23/0.53 ((~day2(consecutive(consecutive(consecutive(monday))))) | day3(consecutive(consecutive(consecutive(consecutive(monday)))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[686, 685])).
% 0.23/0.53 tff(688,plain,
% 0.23/0.53 (~day2(consecutive(consecutive(consecutive(monday))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[687, 683])).
% 0.23/0.53 tff(689,plain,
% 0.23/0.53 ($false),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[459, 688, 676])).
% 0.23/0.53 % SZS output end Proof
%------------------------------------------------------------------------------