%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ035-2 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:23:14 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : PUZ035-2 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 02:41:17 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(isa_type, type, (
% 0.13/0.39 isa: ( $i * $i ) > $o)).
% 0.13/0.39 tff(knave_type, type, (
% 0.13/0.39 knave: $i)).
% 0.13/0.39 tff(asked_type, type, (
% 0.13/0.39 asked: $i)).
% 0.13/0.39 tff(knight_type, type, (
% 0.13/0.39 knight: $i)).
% 0.13/0.39 tff(tell_the_truth_type, type, (
% 0.13/0.39 tell_the_truth: $i > $o)).
% 0.13/0.39 tff(lies_type, type, (
% 0.13/0.39 lies: $i > $o)).
% 0.13/0.39 tff(response_type, type, (
% 0.13/0.39 response: $i > $o)).
% 0.13/0.39 tff(other_type, type, (
% 0.13/0.39 other: $i)).
% 0.13/0.39 tff(yes_type, type, (
% 0.13/0.39 yes: $i)).
% 0.13/0.39 tff(person_type, type, (
% 0.13/0.39 person: $i > $o)).
% 0.13/0.39 tff(no_type, type, (
% 0.13/0.39 no: $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[Y: $i, A: $i, X: $i] : refl(((~isa(other, Y)) | (~isa(asked, X)) | (~response(A))) <=> ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A))) <=> ![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A))) <=> ![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (^[Y: $i, A: $i, X: $i] : rewrite((((~response(A)) | (~isa(asked, X))) | (~isa(other, Y))) <=> ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![Y: $i, A: $i, X: $i] : (((~response(A)) | (~isa(asked, X))) | (~isa(other, Y))) <=> ![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.13/0.39 tff(6,axiom,(![Y: $i, A: $i, X: $i] : (((~response(A)) | (~isa(asked, X))) | (~isa(other, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_answer')).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.39 tff(9,plain,(
% 0.13/0.39 ![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[8])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (^[Anyone: $i] : refl((response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked))) <=> (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked))) <=> ![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked))) <=> ![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (^[Anyone: $i] : rewrite(((response(yes) | (~tell_the_truth(asked))) | (~isa(Anyone, knight))) <=> (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (![Anyone: $i] : ((response(yes) | (~tell_the_truth(asked))) | (~isa(Anyone, knight))) <=> ![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.39 tff(16,axiom,(![Anyone: $i] : ((response(yes) | (~tell_the_truth(asked))) | (~isa(Anyone, knight)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','knight_answers3')).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.13/0.39 tff(19,plain,(
% 0.13/0.39 ![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[18])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.13/0.39 tff(21,assumption,(~lies(asked)), introduced(assumption)).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (person(asked) <=> person(asked)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(23,axiom,(person(asked)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','asked_person')).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (person(asked)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (^[X: $i] : refl((tell_the_truth(X) | (~person(X)) | lies(X)) <=> (tell_the_truth(X) | (~person(X)) | lies(X)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X)) <=> ![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X)) <=> ![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~person(X)) | tell_the_truth(X)) <=> (tell_the_truth(X) | (~person(X)))), ((((~person(X)) | tell_the_truth(X)) | lies(X)) <=> ((tell_the_truth(X) | (~person(X))) | lies(X)))), rewrite(((tell_the_truth(X) | (~person(X))) | lies(X)) <=> (tell_the_truth(X) | (~person(X)) | lies(X))), ((((~person(X)) | tell_the_truth(X)) | lies(X)) <=> (tell_the_truth(X) | (~person(X)) | lies(X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (![X: $i] : (((~person(X)) | tell_the_truth(X)) | lies(X)) <=> ![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.13/0.39 tff(30,axiom,(![X: $i] : (((~person(X)) | tell_the_truth(X)) | lies(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','statements_are_true_or_false2')).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.13/0.39 tff(33,plain,(
% 0.13/0.39 ![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))),
% 0.13/0.39 inference(skolemize,[status(sab)],[32])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (((~![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))) | (tell_the_truth(asked) | lies(asked) | (~person(asked)))) <=> ((~![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))) | tell_the_truth(asked) | lies(asked) | (~person(asked)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((tell_the_truth(asked) | (~person(asked)) | lies(asked)) <=> (tell_the_truth(asked) | lies(asked) | (~person(asked)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (((~![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))) | (tell_the_truth(asked) | (~person(asked)) | lies(asked))) <=> ((~![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))) | (tell_the_truth(asked) | lies(asked) | (~person(asked))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[36])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (((~![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))) | (tell_the_truth(asked) | (~person(asked)) | lies(asked))) <=> ((~![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))) | tell_the_truth(asked) | lies(asked) | (~person(asked)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[37, 35])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 ((~![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))) | (tell_the_truth(asked) | (~person(asked)) | lies(asked))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 ((~![X: $i] : (tell_the_truth(X) | (~person(X)) | lies(X))) | tell_the_truth(asked) | lies(asked) | (~person(asked))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (tell_the_truth(asked) | lies(asked)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[40, 34, 24])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (tell_the_truth(asked)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[41, 21])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (^[X: $i] : refl(((~isa(X, knave)) | lies(X)) <=> ((~isa(X, knave)) | lies(X)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (![X: $i] : ((~isa(X, knave)) | lies(X)) <=> ![X: $i] : ((~isa(X, knave)) | lies(X))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (![X: $i] : ((~isa(X, knave)) | lies(X)) <=> ![X: $i] : ((~isa(X, knave)) | lies(X))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(46,axiom,(![X: $i] : ((~isa(X, knave)) | lies(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','knaves_make_false_statements')).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (![X: $i] : ((~isa(X, knave)) | lies(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.13/0.39 tff(48,plain,(
% 0.13/0.39 ![X: $i] : ((~isa(X, knave)) | lies(X))),
% 0.13/0.39 inference(skolemize,[status(sab)],[47])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (![X: $i] : ((~isa(X, knave)) | lies(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (((~![X: $i] : ((~isa(X, knave)) | lies(X))) | (lies(asked) | (~isa(asked, knave)))) <=> ((~![X: $i] : ((~isa(X, knave)) | lies(X))) | lies(asked) | (~isa(asked, knave)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (((~isa(asked, knave)) | lies(asked)) <=> (lies(asked) | (~isa(asked, knave)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 (((~![X: $i] : ((~isa(X, knave)) | lies(X))) | ((~isa(asked, knave)) | lies(asked))) <=> ((~![X: $i] : ((~isa(X, knave)) | lies(X))) | (lies(asked) | (~isa(asked, knave))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[51])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 (((~![X: $i] : ((~isa(X, knave)) | lies(X))) | ((~isa(asked, knave)) | lies(asked))) <=> ((~![X: $i] : ((~isa(X, knave)) | lies(X))) | lies(asked) | (~isa(asked, knave)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[52, 50])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 ((~![X: $i] : ((~isa(X, knave)) | lies(X))) | ((~isa(asked, knave)) | lies(asked))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 ((~![X: $i] : ((~isa(X, knave)) | lies(X))) | lies(asked) | (~isa(asked, knave))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 (~isa(asked, knave)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[55, 49, 21])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 (^[X: $i] : refl((isa(X, knave) | isa(X, knight) | (~person(X))) <=> (isa(X, knave) | isa(X, knight) | (~person(X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 (![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X))) <=> ![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 (![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X))) <=> ![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 (^[X: $i] : rewrite((((~person(X)) | isa(X, knight)) | isa(X, knave)) <=> (isa(X, knave) | isa(X, knight) | (~person(X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 (![X: $i] : (((~person(X)) | isa(X, knight)) | isa(X, knave)) <=> ![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[60])).
% 0.13/0.39 tff(62,axiom,(![X: $i] : (((~person(X)) | isa(X, knight)) | isa(X, knave))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','everyone_a_knight_or_knave')).
% 0.13/0.39 tff(63,plain,
% 0.13/0.39 (![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.13/0.39 tff(64,plain,
% 0.13/0.39 (![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.13/0.39 tff(65,plain,(
% 0.13/0.39 ![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[64])).
% 0.13/0.39 tff(66,plain,
% 0.13/0.39 (![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.13/0.39 tff(67,plain,
% 0.13/0.39 (((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | (isa(asked, knight) | isa(asked, knave) | (~person(asked)))) <=> ((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | isa(asked, knight) | isa(asked, knave) | (~person(asked)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(68,plain,
% 0.13/0.39 ((isa(asked, knave) | isa(asked, knight) | (~person(asked))) <=> (isa(asked, knight) | isa(asked, knave) | (~person(asked)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(69,plain,
% 0.13/0.39 (((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | (isa(asked, knave) | isa(asked, knight) | (~person(asked)))) <=> ((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | (isa(asked, knight) | isa(asked, knave) | (~person(asked))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[68])).
% 0.13/0.39 tff(70,plain,
% 0.13/0.39 (((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | (isa(asked, knave) | isa(asked, knight) | (~person(asked)))) <=> ((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | isa(asked, knight) | isa(asked, knave) | (~person(asked)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[69, 67])).
% 0.13/0.39 tff(71,plain,
% 0.13/0.39 ((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | (isa(asked, knave) | isa(asked, knight) | (~person(asked)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(72,plain,
% 0.13/0.39 ((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | isa(asked, knight) | isa(asked, knave) | (~person(asked))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.13/0.39 tff(73,plain,
% 0.13/0.39 (isa(asked, knight) | isa(asked, knave)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[72, 66, 24])).
% 0.13/0.39 tff(74,plain,
% 0.13/0.39 (isa(asked, knight)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[73, 56])).
% 0.13/0.39 tff(75,plain,
% 0.13/0.39 (((~![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))) | (response(yes) | (~tell_the_truth(asked)) | (~isa(asked, knight)))) <=> ((~![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))) | response(yes) | (~tell_the_truth(asked)) | (~isa(asked, knight)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(76,plain,
% 0.13/0.39 ((response(yes) | (~isa(asked, knight)) | (~tell_the_truth(asked))) <=> (response(yes) | (~tell_the_truth(asked)) | (~isa(asked, knight)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(77,plain,
% 0.13/0.39 (((~![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))) | (response(yes) | (~isa(asked, knight)) | (~tell_the_truth(asked)))) <=> ((~![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))) | (response(yes) | (~tell_the_truth(asked)) | (~isa(asked, knight))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[76])).
% 0.13/0.39 tff(78,plain,
% 0.13/0.39 (((~![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))) | (response(yes) | (~isa(asked, knight)) | (~tell_the_truth(asked)))) <=> ((~![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))) | response(yes) | (~tell_the_truth(asked)) | (~isa(asked, knight)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[77, 75])).
% 0.13/0.39 tff(79,plain,
% 0.13/0.39 ((~![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))) | (response(yes) | (~isa(asked, knight)) | (~tell_the_truth(asked)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(80,plain,
% 0.13/0.39 ((~![Anyone: $i] : (response(yes) | (~isa(Anyone, knight)) | (~tell_the_truth(asked)))) | response(yes) | (~tell_the_truth(asked)) | (~isa(asked, knight))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.13/0.39 tff(81,plain,
% 0.13/0.39 (response(yes)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[80, 74, 42, 20])).
% 0.13/0.39 tff(82,assumption,(isa(other, knave)), introduced(assumption)).
% 0.13/0.39 tff(83,assumption,(response(yes)), introduced(assumption)).
% 0.13/0.39 tff(84,assumption,(isa(asked, knight)), introduced(assumption)).
% 0.13/0.39 tff(85,plain,
% 0.13/0.39 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~response(yes)) | (~isa(asked, knight)) | (~isa(other, knave)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(yes)) | (~isa(asked, knight)) | (~isa(other, knave)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(86,plain,
% 0.13/0.39 (((~isa(other, knave)) | (~isa(asked, knight)) | (~response(yes))) <=> ((~response(yes)) | (~isa(asked, knight)) | (~isa(other, knave)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(87,plain,
% 0.13/0.40 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knave)) | (~isa(asked, knight)) | (~response(yes)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~response(yes)) | (~isa(asked, knight)) | (~isa(other, knave))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[86])).
% 0.13/0.40 tff(88,plain,
% 0.13/0.40 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knave)) | (~isa(asked, knight)) | (~response(yes)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(yes)) | (~isa(asked, knight)) | (~isa(other, knave)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[87, 85])).
% 0.13/0.40 tff(89,plain,
% 0.13/0.40 ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knave)) | (~isa(asked, knight)) | (~response(yes)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(90,plain,
% 0.13/0.40 ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(yes)) | (~isa(asked, knight)) | (~isa(other, knave))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.13/0.40 tff(91,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[90, 84, 83, 10, 82])).
% 0.13/0.40 tff(92,plain,((~isa(other, knave)) | (~isa(asked, knight)) | (~response(yes))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(93,plain,
% 0.13/0.40 (~isa(other, knave)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[92, 74, 81])).
% 0.13/0.40 tff(94,plain,
% 0.13/0.40 (person(other) <=> person(other)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(95,axiom,(person(other)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','other_person')).
% 0.13/0.40 tff(96,plain,
% 0.13/0.40 (person(other)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.13/0.40 tff(97,plain,
% 0.13/0.40 (((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | (isa(other, knight) | isa(other, knave) | (~person(other)))) <=> ((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | isa(other, knight) | isa(other, knave) | (~person(other)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(98,plain,
% 0.13/0.40 ((isa(other, knave) | isa(other, knight) | (~person(other))) <=> (isa(other, knight) | isa(other, knave) | (~person(other)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(99,plain,
% 0.13/0.40 (((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | (isa(other, knave) | isa(other, knight) | (~person(other)))) <=> ((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | (isa(other, knight) | isa(other, knave) | (~person(other))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[98])).
% 0.13/0.40 tff(100,plain,
% 0.13/0.40 (((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | (isa(other, knave) | isa(other, knight) | (~person(other)))) <=> ((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | isa(other, knight) | isa(other, knave) | (~person(other)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[99, 97])).
% 0.13/0.40 tff(101,plain,
% 0.13/0.40 ((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | (isa(other, knave) | isa(other, knight) | (~person(other)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(102,plain,
% 0.13/0.40 ((~![X: $i] : (isa(X, knave) | isa(X, knight) | (~person(X)))) | isa(other, knight) | isa(other, knave) | (~person(other))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.13/0.40 tff(103,plain,
% 0.13/0.40 (isa(other, knight) | isa(other, knave)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[102, 66, 96])).
% 0.13/0.40 tff(104,plain,
% 0.13/0.40 (isa(other, knight)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[103, 93])).
% 0.13/0.40 tff(105,plain,
% 0.13/0.40 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~response(yes)) | (~isa(asked, knight)) | (~isa(other, knight)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(yes)) | (~isa(asked, knight)) | (~isa(other, knight)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(106,plain,
% 0.13/0.40 (((~isa(other, knight)) | (~isa(asked, knight)) | (~response(yes))) <=> ((~response(yes)) | (~isa(asked, knight)) | (~isa(other, knight)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(107,plain,
% 0.13/0.40 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knight)) | (~isa(asked, knight)) | (~response(yes)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~response(yes)) | (~isa(asked, knight)) | (~isa(other, knight))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[106])).
% 0.13/0.40 tff(108,plain,
% 0.13/0.40 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knight)) | (~isa(asked, knight)) | (~response(yes)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(yes)) | (~isa(asked, knight)) | (~isa(other, knight)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[107, 105])).
% 0.13/0.40 tff(109,plain,
% 0.13/0.40 ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knight)) | (~isa(asked, knight)) | (~response(yes)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(110,plain,
% 0.13/0.40 ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(yes)) | (~isa(asked, knight)) | (~isa(other, knight))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.13/0.40 tff(111,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[110, 74, 104, 81, 10])).
% 0.13/0.40 tff(112,plain,(lies(asked)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(113,plain,
% 0.13/0.40 (^[X: $i] : refl(((~lies(X)) | (~tell_the_truth(X))) <=> ((~lies(X)) | (~tell_the_truth(X))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(114,plain,
% 0.13/0.40 (![X: $i] : ((~lies(X)) | (~tell_the_truth(X))) <=> ![X: $i] : ((~lies(X)) | (~tell_the_truth(X)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[113])).
% 0.13/0.40 tff(115,plain,
% 0.13/0.40 (![X: $i] : ((~lies(X)) | (~tell_the_truth(X))) <=> ![X: $i] : ((~lies(X)) | (~tell_the_truth(X)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(116,plain,
% 0.13/0.40 (^[X: $i] : rewrite(((~tell_the_truth(X)) | (~lies(X))) <=> ((~lies(X)) | (~tell_the_truth(X))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(117,plain,
% 0.13/0.40 (![X: $i] : ((~tell_the_truth(X)) | (~lies(X))) <=> ![X: $i] : ((~lies(X)) | (~tell_the_truth(X)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[116])).
% 0.13/0.40 tff(118,axiom,(![X: $i] : ((~tell_the_truth(X)) | (~lies(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','statements_are_true_or_false')).
% 0.13/0.40 tff(119,plain,
% 0.13/0.40 (![X: $i] : ((~lies(X)) | (~tell_the_truth(X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.13/0.40 tff(120,plain,
% 0.13/0.40 (![X: $i] : ((~lies(X)) | (~tell_the_truth(X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.13/0.40 tff(121,plain,(
% 0.13/0.40 ![X: $i] : ((~lies(X)) | (~tell_the_truth(X)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[120])).
% 0.13/0.40 tff(122,plain,
% 0.13/0.40 (![X: $i] : ((~lies(X)) | (~tell_the_truth(X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.13/0.40 tff(123,plain,
% 0.13/0.40 (((~![X: $i] : ((~lies(X)) | (~tell_the_truth(X)))) | ((~lies(asked)) | (~tell_the_truth(asked)))) <=> ((~![X: $i] : ((~lies(X)) | (~tell_the_truth(X)))) | (~lies(asked)) | (~tell_the_truth(asked)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(124,plain,
% 0.13/0.40 ((~![X: $i] : ((~lies(X)) | (~tell_the_truth(X)))) | ((~lies(asked)) | (~tell_the_truth(asked)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(125,plain,
% 0.13/0.40 ((~![X: $i] : ((~lies(X)) | (~tell_the_truth(X)))) | (~lies(asked)) | (~tell_the_truth(asked))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.13/0.40 tff(126,plain,
% 0.13/0.40 (~tell_the_truth(asked)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[125, 122, 112])).
% 0.13/0.40 tff(127,plain,
% 0.13/0.40 (^[X: $i] : refl((tell_the_truth(X) | (~isa(X, knight))) <=> (tell_the_truth(X) | (~isa(X, knight))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(128,plain,
% 0.13/0.40 (![X: $i] : (tell_the_truth(X) | (~isa(X, knight))) <=> ![X: $i] : (tell_the_truth(X) | (~isa(X, knight)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[127])).
% 0.13/0.40 tff(129,plain,
% 0.13/0.40 (![X: $i] : (tell_the_truth(X) | (~isa(X, knight))) <=> ![X: $i] : (tell_the_truth(X) | (~isa(X, knight)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(130,plain,
% 0.13/0.40 (^[X: $i] : rewrite(((~isa(X, knight)) | tell_the_truth(X)) <=> (tell_the_truth(X) | (~isa(X, knight))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(131,plain,
% 0.13/0.40 (![X: $i] : ((~isa(X, knight)) | tell_the_truth(X)) <=> ![X: $i] : (tell_the_truth(X) | (~isa(X, knight)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[130])).
% 0.13/0.40 tff(132,axiom,(![X: $i] : ((~isa(X, knight)) | tell_the_truth(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','knights_make_true_statements')).
% 0.13/0.40 tff(133,plain,
% 0.13/0.40 (![X: $i] : (tell_the_truth(X) | (~isa(X, knight)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.13/0.40 tff(134,plain,
% 0.13/0.40 (![X: $i] : (tell_the_truth(X) | (~isa(X, knight)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.13/0.40 tff(135,plain,(
% 0.13/0.40 ![X: $i] : (tell_the_truth(X) | (~isa(X, knight)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[134])).
% 0.13/0.40 tff(136,plain,
% 0.13/0.40 (![X: $i] : (tell_the_truth(X) | (~isa(X, knight)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.13/0.40 tff(137,plain,
% 0.13/0.40 (((~![X: $i] : (tell_the_truth(X) | (~isa(X, knight)))) | (tell_the_truth(asked) | (~isa(asked, knight)))) <=> ((~![X: $i] : (tell_the_truth(X) | (~isa(X, knight)))) | tell_the_truth(asked) | (~isa(asked, knight)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(138,plain,
% 0.13/0.40 ((~![X: $i] : (tell_the_truth(X) | (~isa(X, knight)))) | (tell_the_truth(asked) | (~isa(asked, knight)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(139,plain,
% 0.13/0.40 ((~![X: $i] : (tell_the_truth(X) | (~isa(X, knight)))) | tell_the_truth(asked) | (~isa(asked, knight))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.13/0.40 tff(140,plain,
% 0.13/0.40 (~isa(asked, knight)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[139, 136, 126])).
% 0.13/0.40 tff(141,plain,
% 0.13/0.40 (isa(asked, knave)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[73, 140])).
% 0.13/0.40 tff(142,assumption,(response(no)), introduced(assumption)).
% 0.13/0.40 tff(143,plain,
% 0.13/0.40 ((isa(asked, knight) | isa(other, knight) | (~response(no)) | (~lies(asked))) <=> (isa(asked, knight) | isa(other, knight) | (~response(no)) | (~lies(asked)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(144,plain,
% 0.13/0.40 (((isa(asked, knight) | isa(other, knight) | (~response(no))) | (~lies(asked))) <=> (isa(asked, knight) | isa(other, knight) | (~response(no)) | (~lies(asked)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(145,plain,
% 0.13/0.40 (((isa(asked, knight) | isa(other, knight)) | (~response(no))) <=> (isa(asked, knight) | isa(other, knight) | (~response(no)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(146,plain,
% 0.13/0.40 ((((isa(asked, knight) | isa(other, knight)) | (~response(no))) | (~lies(asked))) <=> ((isa(asked, knight) | isa(other, knight) | (~response(no))) | (~lies(asked)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[145])).
% 0.13/0.40 tff(147,plain,
% 0.13/0.40 ((((isa(asked, knight) | isa(other, knight)) | (~response(no))) | (~lies(asked))) <=> (isa(asked, knight) | isa(other, knight) | (~response(no)) | (~lies(asked)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[146, 144])).
% 0.13/0.40 tff(148,axiom,(((isa(asked, knight) | isa(other, knight)) | (~response(no))) | (~lies(asked))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lie_one_is_a_knight')).
% 0.13/0.40 tff(149,plain,
% 0.13/0.40 (isa(asked, knight) | isa(other, knight) | (~response(no)) | (~lies(asked))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.13/0.40 tff(150,plain,
% 0.13/0.40 (isa(asked, knight) | isa(other, knight) | (~response(no)) | (~lies(asked))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[149, 143])).
% 0.13/0.40 tff(151,plain,
% 0.13/0.40 (isa(asked, knight) | isa(other, knight) | (~response(no)) | (~lies(asked))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.13/0.40 tff(152,plain,
% 0.13/0.40 (isa(asked, knight) | isa(other, knight) | (~response(no)) | (~lies(asked))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[151, 143])).
% 0.13/0.40 tff(153,plain,
% 0.13/0.40 (isa(asked, knight) | isa(other, knight) | (~response(no)) | (~lies(asked))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[152, 143])).
% 0.13/0.41 tff(154,plain,
% 0.13/0.41 (isa(other, knight)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[153, 142, 140, 112])).
% 0.13/0.41 tff(155,plain,
% 0.13/0.41 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~response(no)) | (~isa(asked, knave)) | (~isa(other, knight)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(no)) | (~isa(asked, knave)) | (~isa(other, knight)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(156,plain,
% 0.13/0.41 (((~isa(other, knight)) | (~isa(asked, knave)) | (~response(no))) <=> ((~response(no)) | (~isa(asked, knave)) | (~isa(other, knight)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(157,plain,
% 0.13/0.41 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knight)) | (~isa(asked, knave)) | (~response(no)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~response(no)) | (~isa(asked, knave)) | (~isa(other, knight))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[156])).
% 0.13/0.41 tff(158,plain,
% 0.13/0.41 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knight)) | (~isa(asked, knave)) | (~response(no)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(no)) | (~isa(asked, knave)) | (~isa(other, knight)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[157, 155])).
% 0.13/0.41 tff(159,plain,
% 0.13/0.41 ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knight)) | (~isa(asked, knave)) | (~response(no)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(160,plain,
% 0.13/0.41 ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(no)) | (~isa(asked, knave)) | (~isa(other, knight))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.13/0.41 tff(161,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[160, 154, 142, 10, 141])).
% 0.13/0.41 tff(162,plain,(~response(no)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(163,plain,
% 0.13/0.41 ((response(yes) | response(no)) <=> (response(yes) | response(no))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(164,axiom,(response(yes) | response(no)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','two_answers')).
% 0.13/0.41 tff(165,plain,
% 0.13/0.41 (response(yes) | response(no)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.13/0.41 tff(166,plain,
% 0.13/0.41 (response(yes) | response(no)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[165, 163])).
% 0.13/0.41 tff(167,plain,
% 0.13/0.41 (response(yes) | response(no)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[166, 163])).
% 0.13/0.41 tff(168,plain,
% 0.13/0.41 (response(yes) | response(no)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.13/0.41 tff(169,plain,
% 0.13/0.41 (response(yes) | response(no)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[168, 163])).
% 0.13/0.41 tff(170,plain,
% 0.13/0.41 (response(yes)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[169, 162])).
% 0.13/0.41 tff(171,plain,
% 0.13/0.41 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~response(yes)) | (~isa(asked, knave)) | (~isa(other, knave)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(yes)) | (~isa(asked, knave)) | (~isa(other, knave)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(172,plain,
% 0.13/0.41 (((~isa(other, knave)) | (~isa(asked, knave)) | (~response(yes))) <=> ((~response(yes)) | (~isa(asked, knave)) | (~isa(other, knave)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(173,plain,
% 0.13/0.41 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knave)) | (~isa(asked, knave)) | (~response(yes)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~response(yes)) | (~isa(asked, knave)) | (~isa(other, knave))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[172])).
% 0.13/0.41 tff(174,plain,
% 0.13/0.41 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knave)) | (~isa(asked, knave)) | (~response(yes)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(yes)) | (~isa(asked, knave)) | (~isa(other, knave)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[173, 171])).
% 0.21/0.41 tff(175,plain,
% 0.21/0.41 ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knave)) | (~isa(asked, knave)) | (~response(yes)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(176,plain,
% 0.21/0.41 ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(yes)) | (~isa(asked, knave)) | (~isa(other, knave))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.21/0.41 tff(177,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[176, 170, 10, 141, 82])).
% 0.21/0.41 tff(178,plain,(~isa(other, knave)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(179,plain,
% 0.21/0.41 (isa(other, knight)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[103, 178])).
% 0.21/0.41 tff(180,plain,
% 0.21/0.41 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~response(yes)) | (~isa(asked, knave)) | (~isa(other, knight)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(yes)) | (~isa(asked, knave)) | (~isa(other, knight)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(181,plain,
% 0.21/0.41 (((~isa(other, knight)) | (~isa(asked, knave)) | (~response(yes))) <=> ((~response(yes)) | (~isa(asked, knave)) | (~isa(other, knight)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(182,plain,
% 0.21/0.41 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knight)) | (~isa(asked, knave)) | (~response(yes)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~response(yes)) | (~isa(asked, knave)) | (~isa(other, knight))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[181])).
% 0.21/0.41 tff(183,plain,
% 0.21/0.41 (((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knight)) | (~isa(asked, knave)) | (~response(yes)))) <=> ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(yes)) | (~isa(asked, knave)) | (~isa(other, knight)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[182, 180])).
% 0.21/0.41 tff(184,plain,
% 0.21/0.41 ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | ((~isa(other, knight)) | (~isa(asked, knave)) | (~response(yes)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(185,plain,
% 0.21/0.41 ((~![Y: $i, A: $i, X: $i] : ((~isa(other, Y)) | (~isa(asked, X)) | (~response(A)))) | (~response(yes)) | (~isa(asked, knave)) | (~isa(other, knight))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.21/0.41 tff(186,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[185, 179, 170, 10, 141])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------