%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ024-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:23:11 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : PUZ024-1 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.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 02:39:25 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(a_truth_type, type, (
% 0.19/0.38 a_truth: $i > $o)).
% 0.19/0.38 tff(truthteller_type, type, (
% 0.19/0.38 truthteller: $i > $i)).
% 0.19/0.38 tff(c_type, type, (
% 0.19/0.38 c: $i)).
% 0.19/0.38 tff(b_type, type, (
% 0.19/0.38 b: $i)).
% 0.19/0.38 tff(all_are_liars_type, type, (
% 0.19/0.38 all_are_liars: $i)).
% 0.19/0.38 tff(a_type, type, (
% 0.19/0.38 a: $i)).
% 0.19/0.38 tff(says_type, type, (
% 0.19/0.38 says: ( $i * $i ) > $i)).
% 0.19/0.38 tff(people_type, type, (
% 0.19/0.38 people: ( $i * $i * $i ) > $o)).
% 0.19/0.38 tff(one_truthteller_type, type, (
% 0.19/0.38 one_truthteller: $i)).
% 0.19/0.38 tff(liar_type, type, (
% 0.19/0.38 liar: $i > $i)).
% 0.19/0.38 tff(1,assumption,(a_truth(truthteller(b))), introduced(assumption)).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (^[Truthteller: $i] : refl((~a_truth(truthteller(Truthteller))) <=> (~a_truth(truthteller(Truthteller))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![Truthteller: $i] : (~a_truth(truthteller(Truthteller))) <=> ![Truthteller: $i] : (~a_truth(truthteller(Truthteller)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (![Truthteller: $i] : (~a_truth(truthteller(Truthteller))) <=> ![Truthteller: $i] : (~a_truth(truthteller(Truthteller)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(5,axiom,(![Truthteller: $i] : (~a_truth(truthteller(Truthteller)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_there_is_a_truthteller')).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (![Truthteller: $i] : (~a_truth(truthteller(Truthteller)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.38 tff(7,plain,(
% 0.19/0.38 ![Truthteller: $i] : (~a_truth(truthteller(Truthteller)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[6])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![Truthteller: $i] : (~a_truth(truthteller(Truthteller)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 ((~![Truthteller: $i] : (~a_truth(truthteller(Truthteller)))) | (~a_truth(truthteller(b)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.38 tff(11,plain,(~a_truth(truthteller(b))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (a_truth(says(a, all_are_liars)) <=> a_truth(says(a, all_are_liars))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(13,axiom,(a_truth(says(a, all_are_liars))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_says_all_are_liars')).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (a_truth(says(a, all_are_liars))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (people(a, c, b) <=> people(a, c, b)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(16,axiom,(people(a, c, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_c_b_people')).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (people(a, c, b)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (^[Z: $i, Y: $i, X: $i] : refl(((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z))) <=> ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z))) <=> ((~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))), ((((~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z))) | (~a_truth(truthteller(X)))) <=> (((~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z))) | (~a_truth(truthteller(X)))))), rewrite((((~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z))) | (~a_truth(truthteller(X)))) <=> ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))), ((((~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z))) | (~a_truth(truthteller(X)))) <=> ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (((~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z))) | (~a_truth(truthteller(X)))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.39 tff(23,axiom,(![Z: $i, Y: $i, X: $i] : (((~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z))) | (~a_truth(truthteller(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','speaker_is_lying')).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.39 tff(26,plain,(
% 0.19/0.39 ![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[25])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))) | ((~a_truth(says(a, all_are_liars))) | (~a_truth(truthteller(a))) | (~people(a, c, b)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))) | (~a_truth(says(a, all_are_liars))) | (~a_truth(truthteller(a))) | (~people(a, c, b)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (((~a_truth(truthteller(a))) | (~a_truth(says(a, all_are_liars))) | (~people(a, c, b))) <=> ((~a_truth(says(a, all_are_liars))) | (~a_truth(truthteller(a))) | (~people(a, c, b)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))) | ((~a_truth(truthteller(a))) | (~a_truth(says(a, all_are_liars))) | (~people(a, c, b)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))) | ((~a_truth(says(a, all_are_liars))) | (~a_truth(truthteller(a))) | (~people(a, c, b))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[29])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))) | ((~a_truth(truthteller(a))) | (~a_truth(says(a, all_are_liars))) | (~people(a, c, b)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))) | (~a_truth(says(a, all_are_liars))) | (~a_truth(truthteller(a))) | (~people(a, c, b)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[30, 28])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))) | ((~a_truth(truthteller(a))) | (~a_truth(says(a, all_are_liars))) | (~people(a, c, b)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(says(X, all_are_liars))) | (~people(X, Y, Z)))) | (~a_truth(says(a, all_are_liars))) | (~a_truth(truthteller(a))) | (~people(a, c, b))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (~a_truth(truthteller(a))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[33, 27, 17, 14])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (^[Truthteller: $i, Statement: $i] : refl(((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement))) <=> ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement))) <=> ![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement))) <=> ![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (^[Truthteller: $i, Statement: $i] : rewrite((((~a_truth(Statement)) | (~a_truth(says(Truthteller, Statement)))) | a_truth(truthteller(Truthteller))) <=> ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (![Truthteller: $i, Statement: $i] : (((~a_truth(Statement)) | (~a_truth(says(Truthteller, Statement)))) | a_truth(truthteller(Truthteller))) <=> ![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.39 tff(40,axiom,(![Truthteller: $i, Statement: $i] : (((~a_truth(Statement)) | (~a_truth(says(Truthteller, Statement)))) | a_truth(truthteller(Truthteller)))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ002-0.ax','truths_are_told_by_truthtellers')).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.19/0.39 tff(43,plain,(
% 0.19/0.39 ![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[42])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | ((~a_truth(says(a, all_are_liars))) | a_truth(truthteller(a)) | (~a_truth(all_are_liars)))) <=> ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | (~a_truth(says(a, all_are_liars))) | a_truth(truthteller(a)) | (~a_truth(all_are_liars)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | ((~a_truth(says(a, all_are_liars))) | a_truth(truthteller(a)) | (~a_truth(all_are_liars)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | (~a_truth(says(a, all_are_liars))) | a_truth(truthteller(a)) | (~a_truth(all_are_liars))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (a_truth(truthteller(a)) | (~a_truth(all_are_liars))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[47, 44, 14])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (~a_truth(all_are_liars)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[48, 34])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (people(c, b, a) <=> people(c, b, a)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(51,axiom,(people(c, b, a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_b_a_people')).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (people(c, b, a)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (^[Z: $i, Y: $i, X: $i] : refl((a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z))) <=> (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((a_truth(all_are_liars) | (~people(X, Y, Z))) | a_truth(truthteller(X))) <=> (a_truth(truthteller(X)) | a_truth(all_are_liars) | (~people(X, Y, Z)))), ((((a_truth(all_are_liars) | (~people(X, Y, Z))) | a_truth(truthteller(X))) | a_truth(truthteller(Y))) <=> ((a_truth(truthteller(X)) | a_truth(all_are_liars) | (~people(X, Y, Z))) | a_truth(truthteller(Y))))), rewrite(((a_truth(truthteller(X)) | a_truth(all_are_liars) | (~people(X, Y, Z))) | a_truth(truthteller(Y))) <=> (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | (~people(X, Y, Z)))), ((((a_truth(all_are_liars) | (~people(X, Y, Z))) | a_truth(truthteller(X))) | a_truth(truthteller(Y))) <=> (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | (~people(X, Y, Z))))), (((((a_truth(all_are_liars) | (~people(X, Y, Z))) | a_truth(truthteller(X))) | a_truth(truthteller(Y))) | a_truth(truthteller(Z))) <=> ((a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | (~people(X, Y, Z))) | a_truth(truthteller(Z))))), rewrite(((a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | (~people(X, Y, Z))) | a_truth(truthteller(Z))) <=> (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))), (((((a_truth(all_are_liars) | (~people(X, Y, Z))) | a_truth(truthteller(X))) | a_truth(truthteller(Y))) | a_truth(truthteller(Z))) <=> (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : ((((a_truth(all_are_liars) | (~people(X, Y, Z))) | a_truth(truthteller(X))) | a_truth(truthteller(Y))) | a_truth(truthteller(Z))) <=> ![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.39 tff(58,axiom,(![Z: $i, Y: $i, X: $i] : ((((a_truth(all_are_liars) | (~people(X, Y, Z))) | a_truth(truthteller(X))) | a_truth(truthteller(Y))) | a_truth(truthteller(Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','all_truthtellers')).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.39 tff(61,plain,(
% 0.19/0.39 ![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[60])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (((~![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | (a_truth(all_are_liars) | a_truth(truthteller(a)) | a_truth(truthteller(b)) | a_truth(truthteller(c)) | (~people(c, b, a)))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | a_truth(all_are_liars) | a_truth(truthteller(a)) | a_truth(truthteller(b)) | a_truth(truthteller(c)) | (~people(c, b, a)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 ((a_truth(truthteller(c)) | a_truth(all_are_liars) | a_truth(truthteller(b)) | a_truth(truthteller(a)) | (~people(c, b, a))) <=> (a_truth(all_are_liars) | a_truth(truthteller(a)) | a_truth(truthteller(b)) | a_truth(truthteller(c)) | (~people(c, b, a)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (((~![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | (a_truth(truthteller(c)) | a_truth(all_are_liars) | a_truth(truthteller(b)) | a_truth(truthteller(a)) | (~people(c, b, a)))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | (a_truth(all_are_liars) | a_truth(truthteller(a)) | a_truth(truthteller(b)) | a_truth(truthteller(c)) | (~people(c, b, a))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[64])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (((~![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | (a_truth(truthteller(c)) | a_truth(all_are_liars) | a_truth(truthteller(b)) | a_truth(truthteller(a)) | (~people(c, b, a)))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | a_truth(all_are_liars) | a_truth(truthteller(a)) | a_truth(truthteller(b)) | a_truth(truthteller(c)) | (~people(c, b, a)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[65, 63])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 ((~![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | (a_truth(truthteller(c)) | a_truth(all_are_liars) | a_truth(truthteller(b)) | a_truth(truthteller(a)) | (~people(c, b, a)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 ((~![Z: $i, Y: $i, X: $i] : (a_truth(truthteller(X)) | a_truth(all_are_liars) | a_truth(truthteller(Y)) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | a_truth(all_are_liars) | a_truth(truthteller(a)) | a_truth(truthteller(b)) | a_truth(truthteller(c)) | (~people(c, b, a))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (a_truth(all_are_liars) | a_truth(truthteller(b)) | a_truth(truthteller(c))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[68, 62, 52, 34])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (a_truth(truthteller(b)) | a_truth(truthteller(c))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[69, 49])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (a_truth(truthteller(c))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[70, 11])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (a_truth(says(b, one_truthteller)) <=> a_truth(says(b, one_truthteller))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(73,axiom,(a_truth(says(b, one_truthteller))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_says_one_truthteller')).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (a_truth(says(b, one_truthteller))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 (((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | ((~a_truth(one_truthteller)) | (~a_truth(says(b, one_truthteller))) | a_truth(truthteller(b)))) <=> ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | (~a_truth(one_truthteller)) | (~a_truth(says(b, one_truthteller))) | a_truth(truthteller(b)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (((~a_truth(says(b, one_truthteller))) | a_truth(truthteller(b)) | (~a_truth(one_truthteller))) <=> ((~a_truth(one_truthteller)) | (~a_truth(says(b, one_truthteller))) | a_truth(truthteller(b)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | ((~a_truth(says(b, one_truthteller))) | a_truth(truthteller(b)) | (~a_truth(one_truthteller)))) <=> ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | ((~a_truth(one_truthteller)) | (~a_truth(says(b, one_truthteller))) | a_truth(truthteller(b))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[76])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 (((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | ((~a_truth(says(b, one_truthteller))) | a_truth(truthteller(b)) | (~a_truth(one_truthteller)))) <=> ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | (~a_truth(one_truthteller)) | (~a_truth(says(b, one_truthteller))) | a_truth(truthteller(b)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[77, 75])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | ((~a_truth(says(b, one_truthteller))) | a_truth(truthteller(b)) | (~a_truth(one_truthteller)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | (~a_truth(one_truthteller)) | (~a_truth(says(b, one_truthteller))) | a_truth(truthteller(b))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 ((~a_truth(one_truthteller)) | a_truth(truthteller(b))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[80, 44, 74])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (~a_truth(one_truthteller)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[81, 11])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (^[Liar: $i, Statement: $i] : refl((a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar))) <=> (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 (![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar))) <=> ![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 (![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar))) <=> ![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 (^[Liar: $i, Statement: $i] : rewrite(((a_truth(Statement) | (~a_truth(says(Liar, Statement)))) | a_truth(liar(Liar))) <=> (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 (![Liar: $i, Statement: $i] : ((a_truth(Statement) | (~a_truth(says(Liar, Statement)))) | a_truth(liar(Liar))) <=> ![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.39 tff(88,axiom,(![Liar: $i, Statement: $i] : ((a_truth(Statement) | (~a_truth(says(Liar, Statement)))) | a_truth(liar(Liar)))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ002-0.ax','liars_are_told_by_liars')).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.40 tff(91,plain,(
% 0.19/0.40 ![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[90])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | (a_truth(all_are_liars) | (~a_truth(says(a, all_are_liars))) | a_truth(liar(a)))) <=> ((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | a_truth(all_are_liars) | (~a_truth(says(a, all_are_liars))) | a_truth(liar(a)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 ((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | (a_truth(all_are_liars) | (~a_truth(says(a, all_are_liars))) | a_truth(liar(a)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 ((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | a_truth(all_are_liars) | (~a_truth(says(a, all_are_liars))) | a_truth(liar(a))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (a_truth(all_are_liars) | a_truth(liar(a))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[95, 92, 14])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (a_truth(liar(a))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[96, 49])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (^[Z: $i, Y: $i, X: $i] : refl((a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z))) <=> (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((a_truth(one_truthteller) | (~people(X, Y, Z))) | (~a_truth(liar(X)))) <=> (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~people(X, Y, Z)))), ((((a_truth(one_truthteller) | (~people(X, Y, Z))) | (~a_truth(liar(X)))) | (~a_truth(truthteller(Y)))) <=> ((a_truth(one_truthteller) | (~a_truth(liar(X))) | (~people(X, Y, Z))) | (~a_truth(truthteller(Y)))))), rewrite(((a_truth(one_truthteller) | (~a_truth(liar(X))) | (~people(X, Y, Z))) | (~a_truth(truthteller(Y)))) <=> (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z)))), ((((a_truth(one_truthteller) | (~people(X, Y, Z))) | (~a_truth(liar(X)))) | (~a_truth(truthteller(Y)))) <=> (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z))))), (((((a_truth(one_truthteller) | (~people(X, Y, Z))) | (~a_truth(liar(X)))) | (~a_truth(truthteller(Y)))) | a_truth(truthteller(Z))) <=> ((a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z))) | a_truth(truthteller(Z))))), rewrite(((a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z))) | a_truth(truthteller(Z))) <=> (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))), (((((a_truth(one_truthteller) | (~people(X, Y, Z))) | (~a_truth(liar(X)))) | (~a_truth(truthteller(Y)))) | a_truth(truthteller(Z))) <=> (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : ((((a_truth(one_truthteller) | (~people(X, Y, Z))) | (~a_truth(liar(X)))) | (~a_truth(truthteller(Y)))) | a_truth(truthteller(Z))) <=> ![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[101])).
% 0.19/0.40 tff(103,axiom,(![Z: $i, Y: $i, X: $i] : ((((a_truth(one_truthteller) | (~people(X, Y, Z))) | (~a_truth(liar(X)))) | (~a_truth(truthteller(Y)))) | a_truth(truthteller(Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','two_truthtellers')).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.19/0.40 tff(106,plain,(
% 0.19/0.40 ![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[105])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | (a_truth(one_truthteller) | (~a_truth(liar(a))) | a_truth(truthteller(b)) | (~a_truth(truthteller(c))) | (~people(a, c, b)))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | a_truth(one_truthteller) | (~a_truth(liar(a))) | a_truth(truthteller(b)) | (~a_truth(truthteller(c))) | (~people(a, c, b)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 ((a_truth(one_truthteller) | (~a_truth(liar(a))) | (~a_truth(truthteller(c))) | a_truth(truthteller(b)) | (~people(a, c, b))) <=> (a_truth(one_truthteller) | (~a_truth(liar(a))) | a_truth(truthteller(b)) | (~a_truth(truthteller(c))) | (~people(a, c, b)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | (a_truth(one_truthteller) | (~a_truth(liar(a))) | (~a_truth(truthteller(c))) | a_truth(truthteller(b)) | (~people(a, c, b)))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | (a_truth(one_truthteller) | (~a_truth(liar(a))) | a_truth(truthteller(b)) | (~a_truth(truthteller(c))) | (~people(a, c, b))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[109])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | (a_truth(one_truthteller) | (~a_truth(liar(a))) | (~a_truth(truthteller(c))) | a_truth(truthteller(b)) | (~people(a, c, b)))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | a_truth(one_truthteller) | (~a_truth(liar(a))) | a_truth(truthteller(b)) | (~a_truth(truthteller(c))) | (~people(a, c, b)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[110, 108])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 ((~![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | (a_truth(one_truthteller) | (~a_truth(liar(a))) | (~a_truth(truthteller(c))) | a_truth(truthteller(b)) | (~people(a, c, b)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 ((~![Z: $i, Y: $i, X: $i] : (a_truth(one_truthteller) | (~a_truth(liar(X))) | (~a_truth(truthteller(Y))) | a_truth(truthteller(Z)) | (~people(X, Y, Z)))) | a_truth(one_truthteller) | (~a_truth(liar(a))) | a_truth(truthteller(b)) | (~a_truth(truthteller(c))) | (~people(a, c, b))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (a_truth(one_truthteller) | (~a_truth(liar(a))) | a_truth(truthteller(b)) | (~a_truth(truthteller(c)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[113, 107, 17])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (a_truth(one_truthteller) | a_truth(truthteller(b)) | (~a_truth(truthteller(c)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[114, 97])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[115, 82, 11, 71])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------