%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ018-1 : TPTP v9.0.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ018-1 : TPTP v9.0.0. Bugfixed v1.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 02:41:16 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(on_type, type, (
% 0.19/0.41 on: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tuesday_type, type, (
% 0.19/0.41 tuesday: $i)).
% 0.19/0.41 tff(c_type, type, (
% 0.19/0.41 c: $i)).
% 0.19/0.41 tff(thursday_type, type, (
% 0.19/0.41 thursday: $i)).
% 0.19/0.41 tff(sunday_type, type, (
% 0.19/0.41 sunday: $i)).
% 0.19/0.41 tff(a_type, type, (
% 0.19/0.41 a: $i)).
% 0.19/0.41 tff(same_day_type, type, (
% 0.19/0.41 same_day: ( $i * $i ) > $o)).
% 0.19/0.41 tff(same_person_type, type, (
% 0.19/0.41 same_person: ( $i * $i ) > $o)).
% 0.19/0.41 tff(wednesday_type, type, (
% 0.19/0.41 wednesday: $i)).
% 0.19/0.41 tff(all_on_type, type, (
% 0.19/0.41 all_on: $i > $o)).
% 0.19/0.41 tff(monday_type, type, (
% 0.19/0.41 monday: $i)).
% 0.19/0.41 tff(b_type, type, (
% 0.19/0.41 b: $i)).
% 0.19/0.41 tff(consecutive_type, type, (
% 0.19/0.41 consecutive: ( $i * $i ) > $o)).
% 0.19/0.41 tff(saturday_type, type, (
% 0.19/0.41 saturday: $i)).
% 0.19/0.41 tff(friday_type, type, (
% 0.19/0.41 friday: $i)).
% 0.19/0.41 tff(1,assumption,(~on(c, thursday)), introduced(assumption)).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 ((~on(c, sunday)) <=> (~on(c, sunday))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(3,axiom,(~on(c, sunday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_off_sunday')).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (~on(c, sunday)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 ((~on(a, thursday)) <=> (~on(a, thursday))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(6,axiom,(~on(a, thursday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_off_thursday')).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (~on(a, thursday)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 ((~on(a, sunday)) <=> (~on(a, sunday))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(9,axiom,(~on(a, sunday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_off_sunday')).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (~on(a, sunday)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((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) | same_day(Y, Z) | on(W, Y)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((on(X, Y) | on(X, Z)) | on(W, Y)) <=> (on(X, Z) | on(X, Y) | on(W, Y))), ((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) <=> ((on(X, Z) | on(X, Y) | on(W, Y)) | on(W, Z)))), rewrite(((on(X, Z) | on(X, Y) | on(W, Y)) | on(W, Z)) <=> (on(W, Z) | on(X, Z) | on(X, Y) | on(W, Y))), ((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) <=> (on(W, Z) | on(X, Z) | on(X, Y) | on(W, Y)))), (((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) | same_person(X, W)) <=> ((on(W, Z) | on(X, Z) | on(X, Y) | on(W, Y)) | same_person(X, W)))), rewrite(((on(W, Z) | on(X, Z) | on(X, Y) | on(W, Y)) | same_person(X, W)) <=> (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | on(W, Y))), (((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) | same_person(X, W)) <=> (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | on(W, Y)))), ((((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) | same_person(X, W)) | same_day(Y, Z)) <=> ((same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | on(W, Y)) | same_day(Y, Z)))), rewrite(((same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | on(W, Y)) | same_day(Y, Z)) <=> (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))), ((((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) | same_person(X, W)) | same_day(Y, Z)) <=> (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) | same_person(X, W)) | same_day(Y, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.41 tff(16,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((((on(X, Y) | on(X, Z)) | on(W, Y)) | on(W, Z)) | same_person(X, W)) | same_day(Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_two_off_twice_together')).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.41 tff(19,plain,(
% 0.19/0.41 ![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))),
% 0.19/0.41 inference(skolemize,[status(sab)],[18])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 ((~same_day(sunday, thursday)) <=> (~same_day(sunday, thursday))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(22,axiom,(~same_day(sunday, thursday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sunday_not_thursday')).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (~same_day(sunday, thursday)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 ((~same_person(a, c)) <=> (~same_person(a, c))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(25,axiom,(~same_person(a, c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_not_c')).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (~same_person(a, c)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, c) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(c, sunday) | on(c, thursday))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | same_person(a, c) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(c, sunday) | on(c, thursday))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 ((same_person(a, c) | on(c, thursday) | on(a, thursday) | on(a, sunday) | same_day(sunday, thursday) | on(c, sunday)) <=> (same_person(a, c) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(c, sunday) | on(c, thursday))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, c) | on(c, thursday) | on(a, thursday) | on(a, sunday) | same_day(sunday, thursday) | on(c, sunday))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, c) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(c, sunday) | on(c, thursday)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, c) | on(c, thursday) | on(a, thursday) | on(a, sunday) | same_day(sunday, thursday) | on(c, sunday))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | same_person(a, c) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(c, sunday) | on(c, thursday))),
% 0.19/0.41 inference(transitivity,[status(thm)],[29, 27])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, c) | on(c, thursday) | on(a, thursday) | on(a, sunday) | same_day(sunday, thursday) | on(c, sunday))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | same_person(a, c) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(c, sunday) | on(c, thursday)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[32, 26, 23, 20, 10, 7, 4, 1])).
% 0.19/0.42 tff(34,plain,(on(c, thursday)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(35,assumption,(on(b, monday)), introduced(assumption)).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 ((~on(b, thursday)) <=> (~on(b, thursday))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(37,axiom,(~on(b, thursday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_off_thursday')).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (~on(b, thursday)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 ((~on(a, tuesday)) <=> (~on(a, tuesday))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(40,axiom,(~on(a, tuesday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_off_tuesday')).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (~on(a, tuesday)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 ((~same_day(tuesday, thursday)) <=> (~same_day(tuesday, thursday))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(43,axiom,(~same_day(tuesday, thursday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','tuesday_not_thursday')).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (~same_day(tuesday, thursday)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 ((~same_person(a, b)) <=> (~same_person(a, b))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(46,axiom,(~same_person(a, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_not_b')).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (~same_person(a, b)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, b) | same_day(tuesday, thursday) | on(a, thursday) | on(a, tuesday) | on(b, thursday) | on(b, tuesday))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | same_person(a, b) | same_day(tuesday, thursday) | on(a, thursday) | on(a, tuesday) | on(b, thursday) | on(b, tuesday))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 ((same_person(a, b) | on(b, thursday) | on(a, thursday) | on(a, tuesday) | same_day(tuesday, thursday) | on(b, tuesday)) <=> (same_person(a, b) | same_day(tuesday, thursday) | on(a, thursday) | on(a, tuesday) | on(b, thursday) | on(b, tuesday))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, b) | on(b, thursday) | on(a, thursday) | on(a, tuesday) | same_day(tuesday, thursday) | on(b, tuesday))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, b) | same_day(tuesday, thursday) | on(a, thursday) | on(a, tuesday) | on(b, thursday) | on(b, tuesday)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, b) | on(b, thursday) | on(a, thursday) | on(a, tuesday) | same_day(tuesday, thursday) | on(b, tuesday))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | same_person(a, b) | same_day(tuesday, thursday) | on(a, thursday) | on(a, tuesday) | on(b, thursday) | on(b, tuesday))),
% 0.19/0.42 inference(transitivity,[status(thm)],[50, 48])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, b) | on(b, thursday) | on(a, thursday) | on(a, tuesday) | same_day(tuesday, thursday) | on(b, tuesday))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | same_person(a, b) | same_day(tuesday, thursday) | on(a, thursday) | on(a, tuesday) | on(b, thursday) | on(b, tuesday)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (on(b, tuesday)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[53, 47, 44, 20, 41, 7, 38])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, b) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(b, thursday) | on(b, sunday))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | same_person(a, b) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(b, thursday) | on(b, sunday))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 ((same_person(a, b) | on(b, thursday) | on(a, thursday) | on(a, sunday) | same_day(sunday, thursday) | on(b, sunday)) <=> (same_person(a, b) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(b, thursday) | on(b, sunday))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, b) | on(b, thursday) | on(a, thursday) | on(a, sunday) | same_day(sunday, thursday) | on(b, sunday))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, b) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(b, thursday) | on(b, sunday)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[56])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, b) | on(b, thursday) | on(a, thursday) | on(a, sunday) | same_day(sunday, thursday) | on(b, sunday))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | same_person(a, b) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(b, thursday) | on(b, sunday))),
% 0.19/0.42 inference(transitivity,[status(thm)],[57, 55])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, b) | on(b, thursday) | on(a, thursday) | on(a, sunday) | same_day(sunday, thursday) | on(b, sunday))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | same_person(a, b) | same_day(sunday, thursday) | on(a, thursday) | on(a, sunday) | on(b, thursday) | on(b, sunday)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (on(b, sunday)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[60, 47, 23, 20, 10, 7, 38])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (^[W: $i, Z: $i, Y: $i, U: $i, X: $i] : refl(((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y))) <=> ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y))) <=> ![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y))) <=> ![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (^[W: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~consecutive(X, Y)) | (~consecutive(Y, Z))) | (~consecutive(Z, W))) <=> ((~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))), (((((~consecutive(X, Y)) | (~consecutive(Y, Z))) | (~consecutive(Z, W))) | (~on(U, X))) <=> (((~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y))) | (~on(U, X))))), rewrite((((~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y))) | (~on(U, X))) <=> ((~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))), (((((~consecutive(X, Y)) | (~consecutive(Y, Z))) | (~consecutive(Z, W))) | (~on(U, X))) <=> ((~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y))))), ((((((~consecutive(X, Y)) | (~consecutive(Y, Z))) | (~consecutive(Z, W))) | (~on(U, X))) | (~on(U, Y))) <=> (((~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y))) | (~on(U, Y))))), rewrite((((~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y))) | (~on(U, Y))) <=> ((~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))), ((((((~consecutive(X, Y)) | (~consecutive(Y, Z))) | (~consecutive(Z, W))) | (~on(U, X))) | (~on(U, Y))) <=> ((~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y))))), (((((((~consecutive(X, Y)) | (~consecutive(Y, Z))) | (~consecutive(Z, W))) | (~on(U, X))) | (~on(U, Y))) | (~on(U, Z))) <=> (((~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y))) | (~on(U, Z))))), rewrite((((~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y))) | (~on(U, Z))) <=> ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))), (((((((~consecutive(X, Y)) | (~consecutive(Y, Z))) | (~consecutive(Z, W))) | (~on(U, X))) | (~on(U, Y))) | (~on(U, Z))) <=> ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((((~consecutive(X, Y)) | (~consecutive(Y, Z))) | (~consecutive(Z, W))) | (~on(U, X))) | (~on(U, Y))) | (~on(U, Z))) <=> ![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.42 tff(67,axiom,(![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((((~consecutive(X, Y)) | (~consecutive(Y, Z))) | (~consecutive(Z, W))) | (~on(U, X))) | (~on(U, Y))) | (~on(U, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_on_for_3_days')).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.42 tff(70,plain,(
% 0.19/0.42 ![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[69])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (consecutive(tuesday, wednesday) <=> consecutive(tuesday, wednesday)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(73,axiom,(consecutive(tuesday, wednesday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wednesday_follows_tuesday')).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (consecutive(tuesday, wednesday)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (consecutive(monday, tuesday) <=> consecutive(monday, tuesday)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(76,axiom,(consecutive(monday, tuesday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','tuesday_follows_monday')).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (consecutive(monday, tuesday)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (consecutive(sunday, monday) <=> consecutive(sunday, monday)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(79,axiom,(consecutive(sunday, monday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','monday_follows_sunday')).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (consecutive(sunday, monday)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | ((~on(b, sunday)) | (~consecutive(sunday, monday)) | (~on(b, tuesday)) | (~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~on(b, monday)))) <=> ((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | (~on(b, sunday)) | (~consecutive(sunday, monday)) | (~on(b, tuesday)) | (~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~on(b, monday)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (((~on(b, tuesday)) | (~on(b, monday)) | (~on(b, sunday)) | (~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~consecutive(sunday, monday))) <=> ((~on(b, sunday)) | (~consecutive(sunday, monday)) | (~on(b, tuesday)) | (~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~on(b, monday)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | ((~on(b, tuesday)) | (~on(b, monday)) | (~on(b, sunday)) | (~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~consecutive(sunday, monday)))) <=> ((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | ((~on(b, sunday)) | (~consecutive(sunday, monday)) | (~on(b, tuesday)) | (~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~on(b, monday))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[82])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | ((~on(b, tuesday)) | (~on(b, monday)) | (~on(b, sunday)) | (~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~consecutive(sunday, monday)))) <=> ((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | (~on(b, sunday)) | (~consecutive(sunday, monday)) | (~on(b, tuesday)) | (~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~on(b, monday)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[83, 81])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | ((~on(b, tuesday)) | (~on(b, monday)) | (~on(b, sunday)) | (~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~consecutive(sunday, monday)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | (~on(b, sunday)) | (~consecutive(sunday, monday)) | (~on(b, tuesday)) | (~consecutive(tuesday, wednesday)) | (~consecutive(monday, tuesday)) | (~on(b, monday))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[86, 80, 77, 74, 71, 61, 54, 35])).
% 0.20/0.43 tff(88,plain,(~on(b, monday)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (^[X: $i] : refl(((~all_on(X)) | on(b, X)) <=> ((~all_on(X)) | on(b, X)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (![X: $i] : ((~all_on(X)) | on(b, X)) <=> ![X: $i] : ((~all_on(X)) | on(b, X))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (![X: $i] : ((~all_on(X)) | on(b, X)) <=> ![X: $i] : ((~all_on(X)) | on(b, X))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(92,axiom,(![X: $i] : ((~all_on(X)) | on(b, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','all_on_b_on')).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (![X: $i] : ((~all_on(X)) | on(b, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.43 tff(94,plain,(
% 0.20/0.43 ![X: $i] : ((~all_on(X)) | on(b, X))),
% 0.20/0.43 inference(skolemize,[status(sab)],[93])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (![X: $i] : ((~all_on(X)) | on(b, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (((~![X: $i] : ((~all_on(X)) | on(b, X))) | ((~all_on(monday)) | on(b, monday))) <=> ((~![X: $i] : ((~all_on(X)) | on(b, X))) | (~all_on(monday)) | on(b, monday))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 ((~![X: $i] : ((~all_on(X)) | on(b, X))) | ((~all_on(monday)) | on(b, monday))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 ((~![X: $i] : ((~all_on(X)) | on(b, X))) | (~all_on(monday)) | on(b, monday)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (~all_on(monday)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[98, 95, 88])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 ((~on(b, saturday)) <=> (~on(b, saturday))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(101,axiom,(~on(b, saturday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_off_saturday')).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (~on(b, saturday)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (((~![X: $i] : ((~all_on(X)) | on(b, X))) | ((~all_on(saturday)) | on(b, saturday))) <=> ((~![X: $i] : ((~all_on(X)) | on(b, X))) | (~all_on(saturday)) | on(b, saturday))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 ((~![X: $i] : ((~all_on(X)) | on(b, X))) | ((~all_on(saturday)) | on(b, saturday))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 ((~![X: $i] : ((~all_on(X)) | on(b, X))) | (~all_on(saturday)) | on(b, saturday)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (~all_on(saturday)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[105, 95, 102])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 ((~all_on(friday)) <=> (~all_on(friday))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(108,axiom,(~all_on(friday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_all_on_friday')).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (~all_on(friday)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 (^[X: $i] : refl(((~all_on(X)) | on(a, X)) <=> ((~all_on(X)) | on(a, X)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (![X: $i] : ((~all_on(X)) | on(a, X)) <=> ![X: $i] : ((~all_on(X)) | on(a, X))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (![X: $i] : ((~all_on(X)) | on(a, X)) <=> ![X: $i] : ((~all_on(X)) | on(a, X))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(113,axiom,(![X: $i] : ((~all_on(X)) | on(a, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','all_on_a_on')).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (![X: $i] : ((~all_on(X)) | on(a, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.43 tff(115,plain,(
% 0.20/0.43 ![X: $i] : ((~all_on(X)) | on(a, X))),
% 0.20/0.43 inference(skolemize,[status(sab)],[114])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (![X: $i] : ((~all_on(X)) | on(a, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (((~![X: $i] : ((~all_on(X)) | on(a, X))) | ((~all_on(thursday)) | on(a, thursday))) <=> ((~![X: $i] : ((~all_on(X)) | on(a, X))) | (~all_on(thursday)) | on(a, thursday))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 ((~![X: $i] : ((~all_on(X)) | on(a, X))) | ((~all_on(thursday)) | on(a, thursday))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 ((~![X: $i] : ((~all_on(X)) | on(a, X))) | (~all_on(thursday)) | on(a, thursday)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (~all_on(thursday)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[119, 116, 7])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (((~![X: $i] : ((~all_on(X)) | on(a, X))) | ((~all_on(sunday)) | on(a, sunday))) <=> ((~![X: $i] : ((~all_on(X)) | on(a, X))) | (~all_on(sunday)) | on(a, sunday))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 ((~![X: $i] : ((~all_on(X)) | on(a, X))) | ((~all_on(sunday)) | on(a, sunday))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 ((~![X: $i] : ((~all_on(X)) | on(a, X))) | (~all_on(sunday)) | on(a, sunday)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (~all_on(sunday)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[123, 116, 10])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 (((~![X: $i] : ((~all_on(X)) | on(a, X))) | ((~all_on(tuesday)) | on(a, tuesday))) <=> ((~![X: $i] : ((~all_on(X)) | on(a, X))) | (~all_on(tuesday)) | on(a, tuesday))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 ((~![X: $i] : ((~all_on(X)) | on(a, X))) | ((~all_on(tuesday)) | on(a, tuesday))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 ((~![X: $i] : ((~all_on(X)) | on(a, X))) | (~all_on(tuesday)) | on(a, tuesday)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.43 tff(128,plain,
% 0.20/0.43 (~all_on(tuesday)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[127, 116, 41])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 ((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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 (((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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 (((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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (((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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (((all_on(sunday) | all_on(monday) | all_on(tuesday)) | all_on(wednesday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 (((all_on(sunday) | all_on(monday)) | all_on(tuesday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 ((all_on(sunday) | all_on(monday)) <=> (all_on(sunday) | all_on(monday))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (((all_on(sunday) | all_on(monday)) | all_on(tuesday)) <=> ((all_on(sunday) | all_on(monday)) | all_on(tuesday))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[135])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (((all_on(sunday) | all_on(monday)) | all_on(tuesday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday))),
% 0.20/0.43 inference(transitivity,[status(thm)],[136, 134])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 ((((all_on(sunday) | all_on(monday)) | all_on(tuesday)) | all_on(wednesday)) <=> ((all_on(sunday) | all_on(monday) | all_on(tuesday)) | all_on(wednesday))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[137])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 ((((all_on(sunday) | all_on(monday)) | all_on(tuesday)) | all_on(wednesday)) <=> (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday))),
% 0.20/0.43 inference(transitivity,[status(thm)],[138, 133])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 (((((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))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (((((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))),
% 0.20/0.44 inference(transitivity,[status(thm)],[140, 132])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 ((((((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))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[141])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 ((((((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))),
% 0.20/0.44 inference(transitivity,[status(thm)],[142, 131])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 (((((((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))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[143])).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 (((((((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))),
% 0.20/0.44 inference(transitivity,[status(thm)],[144, 130])).
% 0.20/0.44 tff(146,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/sandbox2/benchmark/theBenchmark.p','all_on_one_day')).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday) | all_on(saturday)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday) | all_on(saturday)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[147, 129])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday) | all_on(saturday)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[148, 129])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday) | all_on(saturday)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[149, 129])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (all_on(sunday) | all_on(monday) | all_on(tuesday) | all_on(wednesday) | all_on(thursday) | all_on(friday) | all_on(saturday)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[150, 129])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 (all_on(monday) | all_on(wednesday)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[151, 128, 124, 120, 109, 106])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 (all_on(wednesday)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[152, 99])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 (^[X: $i] : refl(((~all_on(X)) | on(c, X)) <=> ((~all_on(X)) | on(c, X)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 (![X: $i] : ((~all_on(X)) | on(c, X)) <=> ![X: $i] : ((~all_on(X)) | on(c, X))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[154])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 (![X: $i] : ((~all_on(X)) | on(c, X)) <=> ![X: $i] : ((~all_on(X)) | on(c, X))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(157,axiom,(![X: $i] : ((~all_on(X)) | on(c, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','all_on_c_on')).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 (![X: $i] : ((~all_on(X)) | on(c, X))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.44 tff(159,plain,(
% 0.20/0.44 ![X: $i] : ((~all_on(X)) | on(c, X))),
% 0.20/0.44 inference(skolemize,[status(sab)],[158])).
% 0.20/0.44 tff(160,plain,
% 0.20/0.44 (![X: $i] : ((~all_on(X)) | on(c, X))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 (((~![X: $i] : ((~all_on(X)) | on(c, X))) | ((~all_on(wednesday)) | on(c, wednesday))) <=> ((~![X: $i] : ((~all_on(X)) | on(c, X))) | (~all_on(wednesday)) | on(c, wednesday))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 ((~![X: $i] : ((~all_on(X)) | on(c, X))) | ((~all_on(wednesday)) | on(c, wednesday))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 ((~![X: $i] : ((~all_on(X)) | on(c, X))) | (~all_on(wednesday)) | on(c, wednesday)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 (on(c, wednesday)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[163, 160, 153])).
% 0.20/0.44 tff(165,plain,
% 0.20/0.44 (consecutive(thursday, friday) <=> consecutive(thursday, friday)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(166,axiom,(consecutive(thursday, friday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','friday_follows_thursday')).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 (consecutive(thursday, friday)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.44 tff(168,plain,
% 0.20/0.44 (consecutive(wednesday, thursday) <=> consecutive(wednesday, thursday)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(169,axiom,(consecutive(wednesday, thursday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thursday_follows_wednesday')).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 (consecutive(wednesday, thursday)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.44 tff(171,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | ((~consecutive(tuesday, wednesday)) | (~on(c, wednesday)) | (~consecutive(wednesday, thursday)) | (~on(c, thursday)) | (~on(c, tuesday)) | (~consecutive(thursday, friday)))) <=> ((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | (~consecutive(tuesday, wednesday)) | (~on(c, wednesday)) | (~consecutive(wednesday, thursday)) | (~on(c, thursday)) | (~on(c, tuesday)) | (~consecutive(thursday, friday)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(172,plain,
% 0.20/0.44 (((~on(c, thursday)) | (~on(c, wednesday)) | (~on(c, tuesday)) | (~consecutive(thursday, friday)) | (~consecutive(wednesday, thursday)) | (~consecutive(tuesday, wednesday))) <=> ((~consecutive(tuesday, wednesday)) | (~on(c, wednesday)) | (~consecutive(wednesday, thursday)) | (~on(c, thursday)) | (~on(c, tuesday)) | (~consecutive(thursday, friday)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(173,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | ((~on(c, thursday)) | (~on(c, wednesday)) | (~on(c, tuesday)) | (~consecutive(thursday, friday)) | (~consecutive(wednesday, thursday)) | (~consecutive(tuesday, wednesday)))) <=> ((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | ((~consecutive(tuesday, wednesday)) | (~on(c, wednesday)) | (~consecutive(wednesday, thursday)) | (~on(c, thursday)) | (~on(c, tuesday)) | (~consecutive(thursday, friday))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[172])).
% 0.20/0.44 tff(174,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | ((~on(c, thursday)) | (~on(c, wednesday)) | (~on(c, tuesday)) | (~consecutive(thursday, friday)) | (~consecutive(wednesday, thursday)) | (~consecutive(tuesday, wednesday)))) <=> ((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | (~consecutive(tuesday, wednesday)) | (~on(c, wednesday)) | (~consecutive(wednesday, thursday)) | (~on(c, thursday)) | (~on(c, tuesday)) | (~consecutive(thursday, friday)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[173, 171])).
% 0.20/0.44 tff(175,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | ((~on(c, thursday)) | (~on(c, wednesday)) | (~on(c, tuesday)) | (~consecutive(thursday, friday)) | (~consecutive(wednesday, thursday)) | (~consecutive(tuesday, wednesday)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(176,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~on(U, Z)) | (~on(U, Y)) | (~on(U, X)) | (~consecutive(Z, W)) | (~consecutive(Y, Z)) | (~consecutive(X, Y)))) | (~consecutive(tuesday, wednesday)) | (~on(c, wednesday)) | (~consecutive(wednesday, thursday)) | (~on(c, thursday)) | (~on(c, tuesday)) | (~consecutive(thursday, friday))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.44 tff(177,plain,
% 0.20/0.44 ((~on(c, thursday)) | (~on(c, tuesday))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[176, 74, 170, 167, 71, 164])).
% 0.20/0.44 tff(178,plain,
% 0.20/0.44 (~on(c, tuesday)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[177, 34])).
% 0.20/0.44 tff(179,plain,
% 0.20/0.44 ((~same_day(sunday, tuesday)) <=> (~same_day(sunday, tuesday))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(180,axiom,(~same_day(sunday, tuesday)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sunday_not_tuesday')).
% 0.20/0.44 tff(181,plain,
% 0.20/0.44 (~same_day(sunday, tuesday)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.20/0.44 tff(182,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, c) | same_day(sunday, tuesday) | on(a, sunday) | on(a, tuesday) | on(c, sunday) | on(c, tuesday))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | same_person(a, c) | same_day(sunday, tuesday) | on(a, sunday) | on(a, tuesday) | on(c, sunday) | on(c, tuesday))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(183,plain,
% 0.20/0.44 ((same_person(a, c) | on(c, tuesday) | on(a, tuesday) | on(a, sunday) | same_day(sunday, tuesday) | on(c, sunday)) <=> (same_person(a, c) | same_day(sunday, tuesday) | on(a, sunday) | on(a, tuesday) | on(c, sunday) | on(c, tuesday))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(184,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, c) | on(c, tuesday) | on(a, tuesday) | on(a, sunday) | same_day(sunday, tuesday) | on(c, sunday))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, c) | same_day(sunday, tuesday) | on(a, sunday) | on(a, tuesday) | on(c, sunday) | on(c, tuesday)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[183])).
% 0.20/0.44 tff(185,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, c) | on(c, tuesday) | on(a, tuesday) | on(a, sunday) | same_day(sunday, tuesday) | on(c, sunday))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | same_person(a, c) | same_day(sunday, tuesday) | on(a, sunday) | on(a, tuesday) | on(c, sunday) | on(c, tuesday))),
% 0.20/0.44 inference(transitivity,[status(thm)],[184, 182])).
% 0.20/0.44 tff(186,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | (same_person(a, c) | on(c, tuesday) | on(a, tuesday) | on(a, sunday) | same_day(sunday, tuesday) | on(c, sunday))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(187,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (same_person(X, W) | on(W, Z) | on(X, Z) | on(X, Y) | same_day(Y, Z) | on(W, Y))) | same_person(a, c) | same_day(sunday, tuesday) | on(a, sunday) | on(a, tuesday) | on(c, sunday) | on(c, tuesday)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.20/0.44 tff(188,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[187, 26, 181, 20, 10, 41, 4, 178])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------