%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ018_1 : TPTP v9.0.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:23:10 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : PUZ018_1 : TPTP v9.0.0. Bugfixed v5.0.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 02:41:56 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(on_type, type, (
% 0.12/0.36 on: ( person * day ) > $o)).
% 0.12/0.36 tff(tuesday_type, type, (
% 0.12/0.36 tuesday: day)).
% 0.12/0.36 tff(b_type, type, (
% 0.12/0.36 b: person)).
% 0.12/0.36 tff(thursday_type, type, (
% 0.12/0.36 thursday: day)).
% 0.12/0.36 tff(a_type, type, (
% 0.12/0.36 a: person)).
% 0.12/0.36 tff(same_person_type, type, (
% 0.12/0.36 same_person: ( person * person ) > $o)).
% 0.12/0.36 tff(same_day_type, type, (
% 0.12/0.36 same_day: ( day * day ) > $o)).
% 0.12/0.36 tff(sunday_type, type, (
% 0.12/0.36 sunday: day)).
% 0.12/0.36 tff(wednesday_type, type, (
% 0.12/0.36 wednesday: day)).
% 0.12/0.36 tff(monday_type, type, (
% 0.12/0.36 monday: day)).
% 0.12/0.36 tff(all_on_type, type, (
% 0.12/0.36 all_on: day > $o)).
% 0.12/0.36 tff(saturday_type, type, (
% 0.12/0.36 saturday: day)).
% 0.12/0.36 tff(friday_type, type, (
% 0.12/0.36 friday: day)).
% 0.12/0.36 tff(c_type, type, (
% 0.12/0.36 c: person)).
% 0.12/0.36 tff(consecutive_type, type, (
% 0.12/0.36 consecutive: ( day * day ) > $o)).
% 0.12/0.36 tff(1,assumption,(~on(b, tuesday)), introduced(assumption)).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 ((~on(b, thursday)) <=> (~on(b, thursday))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(3,axiom,(~on(b, thursday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b_off_thursday')).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (~on(b, thursday)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 ((~on(a, thursday)) <=> (~on(a, thursday))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(6,axiom,(~on(a, thursday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_off_thursday')).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 (~on(a, thursday)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 ((~on(a, tuesday)) <=> (~on(a, tuesday))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(9,axiom,(~on(a, tuesday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_off_tuesday')).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (~on(a, tuesday)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 (^[X: person, Y: day, Z: day, W: person] : refl((same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y)) <=> (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y)))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 (![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y)) <=> ![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 (![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y)) <=> ![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 (^[X: person, Y: day, Z: day, W: person] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((on(X, Y) | on(X, Z)) <=> (on(X, Z) | on(X, Y))), (((on(X, Y) | on(X, Z)) | on(W, Y)) <=> ((on(X, Z) | on(X, Y)) | on(W, Y)))), rewrite(((on(X, Z) | on(X, Y)) | on(W, Y)) <=> (on(W, Y) | on(X, Z) | on(X, Y))), (((on(X, Y) | on(X, Z)) | on(W, Y)) <=> (on(W, Y) | on(X, Z) | on(X, Y)))), ((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) <=> ((on(W, Y) | on(X, Z) | on(X, Y)) | on(W, Z)))), rewrite(((on(W, Y) | on(X, Z) | on(X, Y)) | on(W, Z)) <=> (on(W, Y) | on(W, Z) | on(X, Z) | on(X, Y))), ((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) <=> (on(W, Y) | on(W, Z) | on(X, Z) | on(X, Y)))), (((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) | same_person(X, W)) <=> ((on(W, Y) | on(W, Z) | on(X, Z) | on(X, Y)) | same_person(X, W)))), rewrite(((on(W, Y) | on(W, Z) | on(X, Z) | on(X, Y)) | same_person(X, W)) <=> (on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))), (((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) | same_person(X, W)) <=> (on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y)))), ((((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) | same_person(X, W)) | same_day(Y, Z)) <=> ((on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y)) | same_day(Y, Z)))), rewrite(((on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y)) | same_day(Y, Z)) <=> (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))), ((((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) | same_person(X, W)) | same_day(Y, Z)) <=> (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(15,plain,
% 0.12/0.36 (![X: person, Y: day, Z: day, W: person] : (((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) | same_person(X, W)) | same_day(Y, Z)) <=> ![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.36 tff(16,axiom,(![X: person, Y: day, Z: day, W: person] : (((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) | same_person(X, W)) | same_day(Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','no_two_off_twice_together')).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 (![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 (![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.12/0.36 tff(19,plain,(
% 0.12/0.36 ![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))),
% 0.12/0.36 inference(skolemize,[status(sab)],[18])).
% 0.12/0.36 tff(20,plain,
% 0.12/0.36 (![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 ((~same_day(tuesday, thursday)) <=> (~same_day(tuesday, thursday))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(22,axiom,(~same_day(tuesday, thursday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','tuesday_not_thursday')).
% 0.12/0.36 tff(23,plain,
% 0.12/0.36 (~same_day(tuesday, thursday)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.36 tff(24,plain,
% 0.12/0.36 ((~same_person(a, b)) <=> (~same_person(a, b))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(25,axiom,(~same_person(a, b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_not_b')).
% 0.12/0.36 tff(26,plain,
% 0.12/0.36 (~same_person(a, b)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.36 tff(27,plain,
% 0.12/0.36 (((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_person(a, b) | same_day(tuesday, thursday) | on(b, thursday) | on(a, tuesday) | on(a, thursday) | on(b, tuesday))) <=> ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | same_person(a, b) | same_day(tuesday, thursday) | on(b, thursday) | on(a, tuesday) | on(a, thursday) | on(b, tuesday))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(28,plain,
% 0.12/0.36 ((same_day(tuesday, thursday) | on(b, tuesday) | same_person(a, b) | on(b, thursday) | on(a, thursday) | on(a, tuesday)) <=> (same_person(a, b) | same_day(tuesday, thursday) | on(b, thursday) | on(a, tuesday) | on(a, thursday) | on(b, tuesday))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(29,plain,
% 0.12/0.36 (((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_day(tuesday, thursday) | on(b, tuesday) | same_person(a, b) | on(b, thursday) | on(a, thursday) | on(a, tuesday))) <=> ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_person(a, b) | same_day(tuesday, thursday) | on(b, thursday) | on(a, tuesday) | on(a, thursday) | on(b, tuesday)))),
% 0.12/0.36 inference(monotonicity,[status(thm)],[28])).
% 0.12/0.36 tff(30,plain,
% 0.12/0.36 (((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_day(tuesday, thursday) | on(b, tuesday) | same_person(a, b) | on(b, thursday) | on(a, thursday) | on(a, tuesday))) <=> ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | same_person(a, b) | same_day(tuesday, thursday) | on(b, thursday) | on(a, tuesday) | on(a, thursday) | on(b, tuesday))),
% 0.12/0.37 inference(transitivity,[status(thm)],[29, 27])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_day(tuesday, thursday) | on(b, tuesday) | same_person(a, b) | on(b, thursday) | on(a, thursday) | on(a, tuesday))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | same_person(a, b) | same_day(tuesday, thursday) | on(b, thursday) | on(a, tuesday) | on(a, thursday) | on(b, tuesday)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[32, 26, 23, 20, 10, 7, 4, 1])).
% 0.12/0.37 tff(34,plain,(on(b, tuesday)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 ((~on(b, saturday)) <=> (~on(b, saturday))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(36,axiom,(~on(b, saturday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b_off_saturday')).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (~on(b, saturday)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (^[X: day] : refl(((~all_on(X)) | on(b, X)) <=> ((~all_on(X)) | on(b, X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (![X: day] : ((~all_on(X)) | on(b, X)) <=> ![X: day] : ((~all_on(X)) | on(b, X))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 (![X: day] : ((~all_on(X)) | on(b, X)) <=> ![X: day] : ((~all_on(X)) | on(b, X))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 (^[X: day] : rewrite((all_on(X) => on(b, X)) <=> ((~all_on(X)) | on(b, X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (![X: day] : (all_on(X) => on(b, X)) <=> ![X: day] : ((~all_on(X)) | on(b, X))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[41])).
% 0.12/0.37 tff(43,axiom,(![X: day] : (all_on(X) => on(b, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','all_on_b_on')).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (![X: day] : ((~all_on(X)) | on(b, X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 (![X: day] : ((~all_on(X)) | on(b, X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.12/0.37 tff(46,plain,(
% 0.12/0.37 ![X: day] : ((~all_on(X)) | on(b, X))),
% 0.12/0.37 inference(skolemize,[status(sab)],[45])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 (![X: day] : ((~all_on(X)) | on(b, X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 (((~![X: day] : ((~all_on(X)) | on(b, X))) | ((~all_on(saturday)) | on(b, saturday))) <=> ((~![X: day] : ((~all_on(X)) | on(b, X))) | (~all_on(saturday)) | on(b, saturday))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(49,plain,
% 0.12/0.37 ((~![X: day] : ((~all_on(X)) | on(b, X))) | ((~all_on(saturday)) | on(b, saturday))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(50,plain,
% 0.12/0.37 ((~![X: day] : ((~all_on(X)) | on(b, X))) | (~all_on(saturday)) | on(b, saturday)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 (~all_on(saturday)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[50, 47, 37])).
% 0.12/0.37 tff(52,plain,
% 0.12/0.37 ((~all_on(friday)) <=> (~all_on(friday))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(53,axiom,(~all_on(friday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_all_on_friday')).
% 0.12/0.37 tff(54,plain,
% 0.12/0.37 (~all_on(friday)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.12/0.37 tff(55,plain,
% 0.12/0.37 (^[X: day] : refl(((~all_on(X)) | on(a, X)) <=> ((~all_on(X)) | on(a, X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(56,plain,
% 0.12/0.37 (![X: day] : ((~all_on(X)) | on(a, X)) <=> ![X: day] : ((~all_on(X)) | on(a, X))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[55])).
% 0.12/0.37 tff(57,plain,
% 0.12/0.37 (![X: day] : ((~all_on(X)) | on(a, X)) <=> ![X: day] : ((~all_on(X)) | on(a, X))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(58,plain,
% 0.12/0.37 (^[X: day] : rewrite((all_on(X) => on(a, X)) <=> ((~all_on(X)) | on(a, X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(59,plain,
% 0.12/0.37 (![X: day] : (all_on(X) => on(a, X)) <=> ![X: day] : ((~all_on(X)) | on(a, X))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[58])).
% 0.12/0.37 tff(60,axiom,(![X: day] : (all_on(X) => on(a, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','all_on_a_on')).
% 0.12/0.37 tff(61,plain,
% 0.12/0.37 (![X: day] : ((~all_on(X)) | on(a, X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.37 tff(62,plain,
% 0.12/0.37 (![X: day] : ((~all_on(X)) | on(a, X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.12/0.37 tff(63,plain,(
% 0.12/0.37 ![X: day] : ((~all_on(X)) | on(a, X))),
% 0.12/0.37 inference(skolemize,[status(sab)],[62])).
% 0.12/0.37 tff(64,plain,
% 0.12/0.37 (![X: day] : ((~all_on(X)) | on(a, X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.12/0.37 tff(65,plain,
% 0.12/0.37 (((~![X: day] : ((~all_on(X)) | on(a, X))) | ((~all_on(thursday)) | on(a, thursday))) <=> ((~![X: day] : ((~all_on(X)) | on(a, X))) | (~all_on(thursday)) | on(a, thursday))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(66,plain,
% 0.12/0.37 ((~![X: day] : ((~all_on(X)) | on(a, X))) | ((~all_on(thursday)) | on(a, thursday))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(67,plain,
% 0.12/0.37 ((~![X: day] : ((~all_on(X)) | on(a, X))) | (~all_on(thursday)) | on(a, thursday)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.12/0.37 tff(68,plain,
% 0.12/0.37 (~all_on(thursday)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[67, 64, 7])).
% 0.12/0.37 tff(69,plain,
% 0.12/0.37 ((~on(a, sunday)) <=> (~on(a, sunday))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(70,axiom,(~on(a, sunday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_off_sunday')).
% 0.12/0.37 tff(71,plain,
% 0.12/0.37 (~on(a, sunday)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.12/0.37 tff(72,plain,
% 0.12/0.37 (((~![X: day] : ((~all_on(X)) | on(a, X))) | ((~all_on(sunday)) | on(a, sunday))) <=> ((~![X: day] : ((~all_on(X)) | on(a, X))) | (~all_on(sunday)) | on(a, sunday))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(73,plain,
% 0.12/0.37 ((~![X: day] : ((~all_on(X)) | on(a, X))) | ((~all_on(sunday)) | on(a, sunday))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(74,plain,
% 0.12/0.37 ((~![X: day] : ((~all_on(X)) | on(a, X))) | (~all_on(sunday)) | on(a, sunday)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.12/0.37 tff(75,plain,
% 0.12/0.37 (~all_on(sunday)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[74, 64, 71])).
% 0.12/0.37 tff(76,plain,
% 0.12/0.37 (((~![X: day] : ((~all_on(X)) | on(a, X))) | ((~all_on(tuesday)) | on(a, tuesday))) <=> ((~![X: day] : ((~all_on(X)) | on(a, X))) | (~all_on(tuesday)) | on(a, tuesday))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(77,plain,
% 0.12/0.37 ((~![X: day] : ((~all_on(X)) | on(a, X))) | ((~all_on(tuesday)) | on(a, tuesday))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(78,plain,
% 0.12/0.37 ((~![X: day] : ((~all_on(X)) | on(a, X))) | (~all_on(tuesday)) | on(a, tuesday)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.12/0.37 tff(79,plain,
% 0.12/0.37 (~all_on(tuesday)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[78, 64, 10])).
% 0.12/0.37 tff(80,plain,
% 0.12/0.37 ((~on(c, sunday)) <=> (~on(c, sunday))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(81,axiom,(~on(c, sunday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_off_sunday')).
% 0.12/0.37 tff(82,plain,
% 0.12/0.37 (~on(c, sunday)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.12/0.37 tff(83,plain,
% 0.12/0.37 ((~same_day(sunday, thursday)) <=> (~same_day(sunday, thursday))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(84,axiom,(~same_day(sunday, thursday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sunday_not_thursday')).
% 0.12/0.37 tff(85,plain,
% 0.12/0.37 (~same_day(sunday, thursday)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.12/0.37 tff(86,plain,
% 0.12/0.37 ((~same_person(a, c)) <=> (~same_person(a, c))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(87,axiom,(~same_person(a, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_not_c')).
% 0.12/0.37 tff(88,plain,
% 0.12/0.37 (~same_person(a, c)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.12/0.37 tff(89,plain,
% 0.12/0.37 (((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_person(a, c) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(c, sunday) | on(c, thursday))) <=> ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | same_person(a, c) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(c, sunday) | on(c, thursday))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(90,plain,
% 0.12/0.37 ((same_day(sunday, thursday) | on(c, sunday) | same_person(a, c) | on(c, thursday) | on(a, thursday) | on(a, sunday)) <=> (same_person(a, c) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(c, sunday) | on(c, thursday))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(91,plain,
% 0.12/0.37 (((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_day(sunday, thursday) | on(c, sunday) | same_person(a, c) | on(c, thursday) | on(a, thursday) | on(a, sunday))) <=> ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_person(a, c) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(c, sunday) | on(c, thursday)))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[90])).
% 0.12/0.37 tff(92,plain,
% 0.12/0.37 (((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_day(sunday, thursday) | on(c, sunday) | same_person(a, c) | on(c, thursday) | on(a, thursday) | on(a, sunday))) <=> ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | same_person(a, c) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(c, sunday) | on(c, thursday))),
% 0.12/0.37 inference(transitivity,[status(thm)],[91, 89])).
% 0.12/0.37 tff(93,plain,
% 0.12/0.37 ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_day(sunday, thursday) | on(c, sunday) | same_person(a, c) | on(c, thursday) | on(a, thursday) | on(a, sunday))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(94,plain,
% 0.12/0.37 ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | same_person(a, c) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(c, sunday) | on(c, thursday)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.12/0.37 tff(95,plain,
% 0.12/0.37 (on(c, thursday)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[94, 88, 85, 20, 71, 7, 82])).
% 0.12/0.37 tff(96,plain,
% 0.12/0.37 ((~same_day(sunday, tuesday)) <=> (~same_day(sunday, tuesday))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(97,axiom,(~same_day(sunday, tuesday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sunday_not_tuesday')).
% 0.12/0.37 tff(98,plain,
% 0.12/0.37 (~same_day(sunday, tuesday)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.12/0.37 tff(99,plain,
% 0.12/0.37 (((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_person(a, c) | same_day(sunday, tuesday) | on(a, tuesday) | on(a, sunday) | on(c, sunday) | on(c, tuesday))) <=> ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | same_person(a, c) | same_day(sunday, tuesday) | on(a, tuesday) | on(a, sunday) | on(c, sunday) | on(c, tuesday))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(100,plain,
% 0.12/0.37 ((same_day(sunday, tuesday) | on(c, sunday) | same_person(a, c) | on(c, tuesday) | on(a, tuesday) | on(a, sunday)) <=> (same_person(a, c) | same_day(sunday, tuesday) | on(a, tuesday) | on(a, sunday) | on(c, sunday) | on(c, tuesday))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(101,plain,
% 0.12/0.37 (((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_day(sunday, tuesday) | on(c, sunday) | same_person(a, c) | on(c, tuesday) | on(a, tuesday) | on(a, sunday))) <=> ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_person(a, c) | same_day(sunday, tuesday) | on(a, tuesday) | on(a, sunday) | on(c, sunday) | on(c, tuesday)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[100])).
% 0.12/0.38 tff(102,plain,
% 0.12/0.38 (((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_day(sunday, tuesday) | on(c, sunday) | same_person(a, c) | on(c, tuesday) | on(a, tuesday) | on(a, sunday))) <=> ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | same_person(a, c) | same_day(sunday, tuesday) | on(a, tuesday) | on(a, sunday) | on(c, sunday) | on(c, tuesday))),
% 0.12/0.38 inference(transitivity,[status(thm)],[101, 99])).
% 0.12/0.38 tff(103,plain,
% 0.12/0.38 ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_day(sunday, tuesday) | on(c, sunday) | same_person(a, c) | on(c, tuesday) | on(a, tuesday) | on(a, sunday))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(104,plain,
% 0.12/0.38 ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | same_person(a, c) | same_day(sunday, tuesday) | on(a, tuesday) | on(a, sunday) | on(c, sunday) | on(c, tuesday)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.12/0.38 tff(105,plain,
% 0.12/0.38 (on(c, tuesday)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[104, 88, 98, 20, 71, 10, 82])).
% 0.12/0.38 tff(106,plain,
% 0.12/0.38 (^[X: day, Y: day, Z: day, W: day, U: person] : refl(((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z))) <=> ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(107,plain,
% 0.12/0.38 (![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z))) <=> ![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[106])).
% 0.12/0.38 tff(108,plain,
% 0.12/0.38 (^[X: day, Y: day, Z: day, W: day, U: person] : trans(monotonicity(rewrite((consecutive(X, Y) & consecutive(Y, Z) & consecutive(Z, W) & on(U, X) & on(U, Y) & on(U, Z)) <=> (~((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z))))), ((~(consecutive(X, Y) & consecutive(Y, Z) & consecutive(Z, W) & on(U, X) & on(U, Y) & on(U, Z))) <=> (~(~((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z))))))), rewrite((~(~((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z))))) <=> ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))), ((~(consecutive(X, Y) & consecutive(Y, Z) & consecutive(Z, W) & on(U, X) & on(U, Y) & on(U, Z))) <=> ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(109,plain,
% 0.12/0.38 (![X: day, Y: day, Z: day, W: day, U: person] : (~(consecutive(X, Y) & consecutive(Y, Z) & consecutive(Z, W) & on(U, X) & on(U, Y) & on(U, Z))) <=> ![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[108])).
% 0.12/0.38 tff(110,plain,
% 0.12/0.38 (![X: day, Y: day, Z: day, W: day, U: person] : (~(consecutive(X, Y) & consecutive(Y, Z) & consecutive(Z, W) & on(U, X) & on(U, Y) & on(U, Z))) <=> ![X: day, Y: day, Z: day, W: day, U: person] : (~(consecutive(X, Y) & consecutive(Y, Z) & consecutive(Z, W) & on(U, X) & on(U, Y) & on(U, Z)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(111,plain,
% 0.12/0.38 (^[X: day, Y: day, Z: day, W: day, U: person] : rewrite((~(((((consecutive(X, Y) & consecutive(Y, Z)) & consecutive(Z, W)) & on(U, X)) & on(U, Y)) & on(U, Z))) <=> (~(consecutive(X, Y) & consecutive(Y, Z) & consecutive(Z, W) & on(U, X) & on(U, Y) & on(U, Z))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(112,plain,
% 0.19/0.38 (![X: day, Y: day, Z: day, W: day, U: person] : (~(((((consecutive(X, Y) & consecutive(Y, Z)) & consecutive(Z, W)) & on(U, X)) & on(U, Y)) & on(U, Z))) <=> ![X: day, Y: day, Z: day, W: day, U: person] : (~(consecutive(X, Y) & consecutive(Y, Z) & consecutive(Z, W) & on(U, X) & on(U, Y) & on(U, Z)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[111])).
% 0.19/0.38 tff(113,axiom,(![X: day, Y: day, Z: day, W: day, U: person] : (~(((((consecutive(X, Y) & consecutive(Y, Z)) & consecutive(Z, W)) & on(U, X)) & on(U, Y)) & on(U, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_on_for_3_days')).
% 0.19/0.38 tff(114,plain,
% 0.19/0.38 (![X: day, Y: day, Z: day, W: day, U: person] : (~(consecutive(X, Y) & consecutive(Y, Z) & consecutive(Z, W) & on(U, X) & on(U, Y) & on(U, Z)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.38 tff(115,plain,
% 0.19/0.38 (![X: day, Y: day, Z: day, W: day, U: person] : (~(consecutive(X, Y) & consecutive(Y, Z) & consecutive(Z, W) & on(U, X) & on(U, Y) & on(U, Z)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.19/0.38 tff(116,plain,(
% 0.19/0.38 ![X: day, Y: day, Z: day, W: day, U: person] : (~(consecutive(X, Y) & consecutive(Y, Z) & consecutive(Z, W) & on(U, X) & on(U, Y) & on(U, Z)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[115])).
% 0.19/0.38 tff(117,plain,
% 0.19/0.38 (![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.19/0.38 tff(118,plain,
% 0.19/0.38 (![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[117, 107])).
% 0.19/0.38 tff(119,plain,
% 0.19/0.38 (consecutive(thursday, friday) <=> consecutive(thursday, friday)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(120,axiom,(consecutive(thursday, friday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','friday_follows_thursday')).
% 0.19/0.38 tff(121,plain,
% 0.19/0.38 (consecutive(thursday, friday)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.38 tff(122,plain,
% 0.19/0.38 (consecutive(wednesday, thursday) <=> consecutive(wednesday, thursday)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(123,axiom,(consecutive(wednesday, thursday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thursday_follows_wednesday')).
% 0.19/0.38 tff(124,plain,
% 0.19/0.38 (consecutive(wednesday, thursday)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.38 tff(125,plain,
% 0.19/0.38 (consecutive(tuesday, wednesday) <=> consecutive(tuesday, wednesday)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(126,axiom,(consecutive(tuesday, wednesday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wednesday_follows_tuesday')).
% 0.19/0.38 tff(127,plain,
% 0.19/0.38 (consecutive(tuesday, wednesday)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.38 tff(128,plain,
% 0.19/0.38 (((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | ((~consecutive(tuesday, wednesday)) | (~consecutive(wednesday, thursday)) | (~consecutive(thursday, friday)) | (~on(c, tuesday)) | (~on(c, wednesday)) | (~on(c, thursday)))) <=> ((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | (~consecutive(tuesday, wednesday)) | (~consecutive(wednesday, thursday)) | (~consecutive(thursday, friday)) | (~on(c, tuesday)) | (~on(c, wednesday)) | (~on(c, thursday)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(129,plain,
% 0.19/0.38 ((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | ((~consecutive(tuesday, wednesday)) | (~consecutive(wednesday, thursday)) | (~consecutive(thursday, friday)) | (~on(c, tuesday)) | (~on(c, wednesday)) | (~on(c, thursday)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(130,plain,
% 0.19/0.38 ((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | (~consecutive(tuesday, wednesday)) | (~consecutive(wednesday, thursday)) | (~consecutive(thursday, friday)) | (~on(c, tuesday)) | (~on(c, wednesday)) | (~on(c, thursday))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.38 tff(131,plain,
% 0.19/0.38 (~on(c, wednesday)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[130, 127, 124, 121, 118, 105, 95])).
% 0.19/0.38 tff(132,plain,
% 0.19/0.38 (^[X: day] : refl(((~all_on(X)) | on(c, X)) <=> ((~all_on(X)) | on(c, X)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(133,plain,
% 0.19/0.38 (![X: day] : ((~all_on(X)) | on(c, X)) <=> ![X: day] : ((~all_on(X)) | on(c, X))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[132])).
% 0.19/0.38 tff(134,plain,
% 0.19/0.38 (![X: day] : ((~all_on(X)) | on(c, X)) <=> ![X: day] : ((~all_on(X)) | on(c, X))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(135,plain,
% 0.19/0.38 (^[X: day] : rewrite((all_on(X) => on(c, X)) <=> ((~all_on(X)) | on(c, X)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(136,plain,
% 0.19/0.38 (![X: day] : (all_on(X) => on(c, X)) <=> ![X: day] : ((~all_on(X)) | on(c, X))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[135])).
% 0.19/0.38 tff(137,axiom,(![X: day] : (all_on(X) => on(c, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','all_on_c_on')).
% 0.19/0.38 tff(138,plain,
% 0.19/0.38 (![X: day] : ((~all_on(X)) | on(c, X))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.38 tff(139,plain,
% 0.19/0.38 (![X: day] : ((~all_on(X)) | on(c, X))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.19/0.38 tff(140,plain,(
% 0.19/0.38 ![X: day] : ((~all_on(X)) | on(c, X))),
% 0.19/0.38 inference(skolemize,[status(sab)],[139])).
% 0.19/0.38 tff(141,plain,
% 0.19/0.38 (![X: day] : ((~all_on(X)) | on(c, X))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.19/0.38 tff(142,plain,
% 0.19/0.38 (((~![X: day] : ((~all_on(X)) | on(c, X))) | ((~all_on(wednesday)) | on(c, wednesday))) <=> ((~![X: day] : ((~all_on(X)) | on(c, X))) | (~all_on(wednesday)) | on(c, wednesday))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(143,plain,
% 0.19/0.38 ((~![X: day] : ((~all_on(X)) | on(c, X))) | ((~all_on(wednesday)) | on(c, wednesday))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(144,plain,
% 0.19/0.38 ((~![X: day] : ((~all_on(X)) | on(c, X))) | (~all_on(wednesday)) | on(c, wednesday)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.19/0.38 tff(145,plain,
% 0.19/0.38 (~all_on(wednesday)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[144, 141, 131])).
% 0.19/0.38 tff(146,plain,
% 0.19/0.38 ((all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday) | all_on(saturday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday) | all_on(saturday))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(147,plain,
% 0.19/0.38 (((all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday)) | all_on(saturday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday) | all_on(saturday))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(148,plain,
% 0.19/0.38 (((all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday)) | all_on(friday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(149,plain,
% 0.19/0.38 (((all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday)) | all_on(thursday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(150,plain,
% 0.19/0.38 (((all_on(sunday) | all_on(monday) | all_on(tuesday)) | all_on(wednesday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(151,plain,
% 0.19/0.38 (((all_on(sunday) | all_on(monday)) | all_on(tuesday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(152,plain,
% 0.19/0.38 ((all_on(sunday) | all_on(monday)) <=> (all_on(sunday) | all_on(monday))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(153,plain,
% 0.19/0.38 (((all_on(sunday) | all_on(monday)) | all_on(tuesday)) <=> ((all_on(sunday) | all_on(monday)) | all_on(tuesday))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[152])).
% 0.19/0.38 tff(154,plain,
% 0.19/0.38 (((all_on(sunday) | all_on(monday)) | all_on(tuesday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday))),
% 0.19/0.38 inference(transitivity,[status(thm)],[153, 151])).
% 0.19/0.38 tff(155,plain,
% 0.19/0.38 ((((all_on(sunday) | all_on(monday)) | all_on(tuesday)) | all_on(wednesday)) <=> ((all_on(sunday) | all_on(monday) | all_on(tuesday)) | all_on(wednesday))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[154])).
% 0.19/0.38 tff(156,plain,
% 0.19/0.38 ((((all_on(sunday) | all_on(monday)) | all_on(tuesday)) | all_on(wednesday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday))),
% 0.19/0.38 inference(transitivity,[status(thm)],[155, 150])).
% 0.19/0.38 tff(157,plain,
% 0.19/0.38 (((((all_on(sunday) | all_on(monday)) | all_on(tuesday)) | all_on(wednesday)) | all_on(thursday)) <=> ((all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday)) | all_on(thursday))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[156])).
% 0.19/0.38 tff(158,plain,
% 0.19/0.38 (((((all_on(sunday) | all_on(monday)) | all_on(tuesday)) | all_on(wednesday)) | all_on(thursday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday))),
% 0.19/0.38 inference(transitivity,[status(thm)],[157, 149])).
% 0.19/0.38 tff(159,plain,
% 0.19/0.38 ((((((all_on(sunday) | all_on(monday)) | all_on(tuesday)) | all_on(wednesday)) | all_on(thursday)) | all_on(friday)) <=> ((all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday)) | all_on(friday))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[158])).
% 0.19/0.38 tff(160,plain,
% 0.19/0.38 ((((((all_on(sunday) | all_on(monday)) | all_on(tuesday)) | all_on(wednesday)) | all_on(thursday)) | all_on(friday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday))),
% 0.19/0.38 inference(transitivity,[status(thm)],[159, 148])).
% 0.19/0.38 tff(161,plain,
% 0.19/0.38 (((((((all_on(sunday) | all_on(monday)) | all_on(tuesday)) | all_on(wednesday)) | all_on(thursday)) | all_on(friday)) | all_on(saturday)) <=> ((all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday)) | all_on(saturday))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[160])).
% 0.19/0.38 tff(162,plain,
% 0.19/0.38 (((((((all_on(sunday) | all_on(monday)) | all_on(tuesday)) | all_on(wednesday)) | all_on(thursday)) | all_on(friday)) | all_on(saturday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday) | all_on(saturday))),
% 0.19/0.38 inference(transitivity,[status(thm)],[161, 147])).
% 0.19/0.38 tff(163,axiom,((((((all_on(sunday) | all_on(monday)) | all_on(tuesday)) | all_on(wednesday)) | all_on(thursday)) | all_on(friday)) | all_on(saturday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','all_on_one_day')).
% 0.19/0.38 tff(164,plain,
% 0.19/0.38 (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday) | all_on(saturday)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.38 tff(165,plain,
% 0.19/0.38 (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday) | all_on(saturday)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[164, 146])).
% 0.19/0.38 tff(166,plain,
% 0.19/0.38 (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday) | all_on(saturday)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[165, 146])).
% 0.19/0.38 tff(167,plain,
% 0.19/0.38 (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday) | all_on(saturday)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[166, 146])).
% 0.19/0.38 tff(168,plain,
% 0.19/0.38 (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday) | all_on(saturday)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[167, 146])).
% 0.19/0.39 tff(169,plain,
% 0.19/0.39 (all_on(monday)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[168, 145, 79, 75, 68, 54, 51])).
% 0.19/0.39 tff(170,plain,
% 0.19/0.39 (((~![X: day] : ((~all_on(X)) | on(b, X))) | ((~all_on(monday)) | on(b, monday))) <=> ((~![X: day] : ((~all_on(X)) | on(b, X))) | (~all_on(monday)) | on(b, monday))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(171,plain,
% 0.19/0.39 ((~![X: day] : ((~all_on(X)) | on(b, X))) | ((~all_on(monday)) | on(b, monday))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(172,plain,
% 0.19/0.39 ((~![X: day] : ((~all_on(X)) | on(b, X))) | (~all_on(monday)) | on(b, monday)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.19/0.39 tff(173,plain,
% 0.19/0.39 (on(b, monday)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[172, 47, 169])).
% 0.19/0.39 tff(174,plain,
% 0.19/0.39 (consecutive(monday, tuesday) <=> consecutive(monday, tuesday)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(175,axiom,(consecutive(monday, tuesday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','tuesday_follows_monday')).
% 0.19/0.39 tff(176,plain,
% 0.19/0.39 (consecutive(monday, tuesday)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.19/0.39 tff(177,plain,
% 0.19/0.39 (((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | ((~consecutive(monday, tuesday)) | (~consecutive(tuesday, wednesday)) | (~consecutive(wednesday, thursday)) | (~on(b, monday)) | (~on(b, tuesday)) | (~on(b, wednesday)))) <=> ((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | (~consecutive(monday, tuesday)) | (~consecutive(tuesday, wednesday)) | (~consecutive(wednesday, thursday)) | (~on(b, monday)) | (~on(b, tuesday)) | (~on(b, wednesday)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(178,plain,
% 0.19/0.39 ((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | ((~consecutive(monday, tuesday)) | (~consecutive(tuesday, wednesday)) | (~consecutive(wednesday, thursday)) | (~on(b, monday)) | (~on(b, tuesday)) | (~on(b, wednesday)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(179,plain,
% 0.19/0.39 ((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | (~consecutive(monday, tuesday)) | (~consecutive(tuesday, wednesday)) | (~consecutive(wednesday, thursday)) | (~on(b, monday)) | (~on(b, tuesday)) | (~on(b, wednesday))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.19/0.39 tff(180,plain,
% 0.19/0.39 ((~on(b, tuesday)) | (~on(b, wednesday))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[179, 176, 127, 124, 118, 173])).
% 0.19/0.39 tff(181,plain,
% 0.19/0.39 (~on(b, wednesday)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[180, 34])).
% 0.19/0.39 tff(182,plain,
% 0.19/0.39 ((~same_day(sunday, wednesday)) <=> (~same_day(sunday, wednesday))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(183,axiom,(~same_day(sunday, wednesday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sunday_not_wednesday')).
% 0.19/0.39 tff(184,plain,
% 0.19/0.39 (~same_day(sunday, wednesday)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.19/0.39 tff(185,plain,
% 0.19/0.39 ((~same_person(b, c)) <=> (~same_person(b, c))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(186,axiom,(~same_person(b, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b_not_c')).
% 0.19/0.39 tff(187,plain,
% 0.19/0.39 (~same_person(b, c)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.39 tff(188,plain,
% 0.19/0.39 (((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_person(b, c) | same_day(sunday, wednesday) | on(c, sunday) | on(b, sunday) | on(c, wednesday) | on(b, wednesday))) <=> ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | same_person(b, c) | same_day(sunday, wednesday) | on(c, sunday) | on(b, sunday) | on(c, wednesday) | on(b, wednesday))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(189,plain,
% 0.19/0.39 ((same_day(sunday, wednesday) | on(c, sunday) | same_person(b, c) | on(c, wednesday) | on(b, wednesday) | on(b, sunday)) <=> (same_person(b, c) | same_day(sunday, wednesday) | on(c, sunday) | on(b, sunday) | on(c, wednesday) | on(b, wednesday))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(190,plain,
% 0.19/0.39 (((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_day(sunday, wednesday) | on(c, sunday) | same_person(b, c) | on(c, wednesday) | on(b, wednesday) | on(b, sunday))) <=> ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_person(b, c) | same_day(sunday, wednesday) | on(c, sunday) | on(b, sunday) | on(c, wednesday) | on(b, wednesday)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[189])).
% 0.19/0.39 tff(191,plain,
% 0.19/0.39 (((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_day(sunday, wednesday) | on(c, sunday) | same_person(b, c) | on(c, wednesday) | on(b, wednesday) | on(b, sunday))) <=> ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | same_person(b, c) | same_day(sunday, wednesday) | on(c, sunday) | on(b, sunday) | on(c, wednesday) | on(b, wednesday))),
% 0.19/0.39 inference(transitivity,[status(thm)],[190, 188])).
% 0.19/0.39 tff(192,plain,
% 0.19/0.39 ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | (same_day(sunday, wednesday) | on(c, sunday) | same_person(b, c) | on(c, wednesday) | on(b, wednesday) | on(b, sunday))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(193,plain,
% 0.19/0.39 ((~![X: person, Y: day, Z: day, W: person] : (same_day(Y, Z) | on(W, Y) | same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y))) | same_person(b, c) | same_day(sunday, wednesday) | on(c, sunday) | on(b, sunday) | on(c, wednesday) | on(b, wednesday)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.19/0.39 tff(194,plain,
% 0.19/0.39 (on(b, sunday) | on(c, wednesday) | on(b, wednesday)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[193, 187, 184, 20, 82])).
% 0.19/0.39 tff(195,plain,
% 0.19/0.39 (on(b, sunday) | on(b, wednesday)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[194, 131])).
% 0.19/0.39 tff(196,plain,
% 0.19/0.39 (on(b, sunday)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[195, 181])).
% 0.19/0.39 tff(197,plain,
% 0.19/0.39 (consecutive(sunday, monday) <=> consecutive(sunday, monday)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(198,axiom,(consecutive(sunday, monday)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','monday_follows_sunday')).
% 0.19/0.39 tff(199,plain,
% 0.19/0.39 (consecutive(sunday, monday)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.19/0.39 tff(200,plain,
% 0.19/0.39 (((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | ((~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~on(b, monday)) | (~on(b, tuesday)) | (~consecutive(sunday, monday)) | (~on(b, sunday)))) <=> ((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | (~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~on(b, monday)) | (~on(b, tuesday)) | (~consecutive(sunday, monday)) | (~on(b, sunday)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(201,plain,
% 0.19/0.39 (((~consecutive(sunday, monday)) | (~consecutive(monday, tuesday)) | (~consecutive(tuesday, wednesday)) | (~on(b, sunday)) | (~on(b, monday)) | (~on(b, tuesday))) <=> ((~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~on(b, monday)) | (~on(b, tuesday)) | (~consecutive(sunday, monday)) | (~on(b, sunday)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(202,plain,
% 0.19/0.39 (((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | ((~consecutive(sunday, monday)) | (~consecutive(monday, tuesday)) | (~consecutive(tuesday, wednesday)) | (~on(b, sunday)) | (~on(b, monday)) | (~on(b, tuesday)))) <=> ((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | ((~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~on(b, monday)) | (~on(b, tuesday)) | (~consecutive(sunday, monday)) | (~on(b, sunday))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[201])).
% 0.19/0.40 tff(203,plain,
% 0.19/0.40 (((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | ((~consecutive(sunday, monday)) | (~consecutive(monday, tuesday)) | (~consecutive(tuesday, wednesday)) | (~on(b, sunday)) | (~on(b, monday)) | (~on(b, tuesday)))) <=> ((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | (~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~on(b, monday)) | (~on(b, tuesday)) | (~consecutive(sunday, monday)) | (~on(b, sunday)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[202, 200])).
% 0.19/0.40 tff(204,plain,
% 0.19/0.40 ((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | ((~consecutive(sunday, monday)) | (~consecutive(monday, tuesday)) | (~consecutive(tuesday, wednesday)) | (~on(b, sunday)) | (~on(b, monday)) | (~on(b, tuesday)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(205,plain,
% 0.19/0.40 ((~![X: day, Y: day, Z: day, W: day, U: person] : ((~consecutive(X, Y)) | (~consecutive(Y, Z)) | (~consecutive(Z, W)) | (~on(U, X)) | (~on(U, Y)) | (~on(U, Z)))) | (~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~on(b, monday)) | (~on(b, tuesday)) | (~consecutive(sunday, monday)) | (~on(b, sunday))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.19/0.40 tff(206,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[205, 199, 176, 127, 118, 173, 196, 34])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------