%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ023-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : PUZ023-1 : TPTP v9.0.0. Released v1.0.0.
% 0.13/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 20 02:40:25 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.21/0.38 % SZS status Unsatisfiable
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(an_answer_type, type, (
% 0.21/0.38 an_answer: $i > $o)).
% 0.21/0.38 tff(b_truthteller_and_c_liar_type, type, (
% 0.21/0.38 b_truthteller_and_c_liar: $i)).
% 0.21/0.38 tff(a_truth_type, type, (
% 0.21/0.38 a_truth: $i > $o)).
% 0.21/0.38 tff(truthteller_type, type, (
% 0.21/0.38 truthteller: $i > $i)).
% 0.21/0.38 tff(b_type, type, (
% 0.21/0.38 b: $i)).
% 0.21/0.38 tff(liar_type, type, (
% 0.21/0.38 liar: $i > $i)).
% 0.21/0.38 tff(b_liar_and_c_truthteller_type, type, (
% 0.21/0.38 b_liar_and_c_truthteller: $i)).
% 0.21/0.38 tff(c_type, type, (
% 0.21/0.38 c: $i)).
% 0.21/0.38 tff(says_type, type, (
% 0.21/0.38 says: ( $i * $i ) > $i)).
% 0.21/0.38 tff(1,plain,
% 0.21/0.38 (^[X: $i] : refl((~an_answer(X)) <=> (~an_answer(X)))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 (![X: $i] : (~an_answer(X)) <=> ![X: $i] : (~an_answer(X))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.38 tff(3,plain,
% 0.21/0.38 (![X: $i] : (~an_answer(X)) <=> ![X: $i] : (~an_answer(X))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(4,axiom,(![X: $i] : (~an_answer(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_there_is_an_answer')).
% 0.21/0.38 tff(5,plain,
% 0.21/0.38 (![X: $i] : (~an_answer(X))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.38 tff(6,plain,(
% 0.21/0.38 ![X: $i] : (~an_answer(X))),
% 0.21/0.38 inference(skolemize,[status(sab)],[5])).
% 0.21/0.38 tff(7,plain,
% 0.21/0.38 (![X: $i] : (~an_answer(X))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.38 tff(8,assumption,(an_answer(b_liar_and_c_truthteller)), introduced(assumption)).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 ((~![X: $i] : (~an_answer(X))) | (~an_answer(b_liar_and_c_truthteller))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[9, 8, 7])).
% 0.21/0.38 tff(11,plain,(~an_answer(b_liar_and_c_truthteller)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.38 tff(12,assumption,(a_truth(liar(b))), introduced(assumption)).
% 0.21/0.38 tff(13,plain,
% 0.21/0.38 (a_truth(says(c, liar(b))) <=> a_truth(says(c, liar(b)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(14,axiom,(a_truth(says(c, liar(b)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_says_b_lies')).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 (a_truth(says(c, liar(b)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.38 tff(16,plain,
% 0.21/0.38 (^[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))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.38 tff(18,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 (^[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))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(20,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.38 tff(21,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')).
% 0.21/0.38 tff(22,plain,
% 0.21/0.38 (![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.38 tff(23,plain,
% 0.21/0.38 (![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.21/0.38 tff(24,plain,(
% 0.21/0.38 ![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.21/0.38 inference(skolemize,[status(sab)],[23])).
% 0.21/0.38 tff(25,plain,
% 0.21/0.38 (![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.21/0.38 tff(26,plain,
% 0.21/0.38 (((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | ((~a_truth(liar(b))) | a_truth(truthteller(c)) | (~a_truth(says(c, liar(b)))))) <=> ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | (~a_truth(liar(b))) | a_truth(truthteller(c)) | (~a_truth(says(c, liar(b)))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(27,plain,
% 0.21/0.38 (((~a_truth(says(c, liar(b)))) | a_truth(truthteller(c)) | (~a_truth(liar(b)))) <=> ((~a_truth(liar(b))) | a_truth(truthteller(c)) | (~a_truth(says(c, liar(b)))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(28,plain,
% 0.21/0.38 (((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | ((~a_truth(says(c, liar(b)))) | a_truth(truthteller(c)) | (~a_truth(liar(b))))) <=> ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | ((~a_truth(liar(b))) | a_truth(truthteller(c)) | (~a_truth(says(c, liar(b))))))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[27])).
% 0.21/0.38 tff(29,plain,
% 0.21/0.38 (((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | ((~a_truth(says(c, liar(b)))) | a_truth(truthteller(c)) | (~a_truth(liar(b))))) <=> ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | (~a_truth(liar(b))) | a_truth(truthteller(c)) | (~a_truth(says(c, liar(b)))))),
% 0.21/0.38 inference(transitivity,[status(thm)],[28, 26])).
% 0.21/0.38 tff(30,plain,
% 0.21/0.38 ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | ((~a_truth(says(c, liar(b)))) | a_truth(truthteller(c)) | (~a_truth(liar(b))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(31,plain,
% 0.21/0.38 ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | (~a_truth(liar(b))) | a_truth(truthteller(c)) | (~a_truth(says(c, liar(b))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.21/0.38 tff(32,plain,
% 0.21/0.38 ((~a_truth(liar(b))) | a_truth(truthteller(c))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[31, 25, 15])).
% 0.21/0.38 tff(33,plain,
% 0.21/0.38 (a_truth(truthteller(c))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[32, 12])).
% 0.21/0.38 tff(34,plain,
% 0.21/0.38 (((~a_truth(liar(b))) | (~a_truth(truthteller(c))) | an_answer(b_liar_and_c_truthteller)) <=> ((~a_truth(liar(b))) | (~a_truth(truthteller(c))) | an_answer(b_liar_and_c_truthteller))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(35,plain,
% 0.21/0.38 ((((~a_truth(liar(b))) | (~a_truth(truthteller(c)))) | an_answer(b_liar_and_c_truthteller)) <=> ((~a_truth(liar(b))) | (~a_truth(truthteller(c))) | an_answer(b_liar_and_c_truthteller))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(36,axiom,(((~a_truth(liar(b))) | (~a_truth(truthteller(c)))) | an_answer(b_liar_and_c_truthteller)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_liar_and_c_truthteller')).
% 0.21/0.38 tff(37,plain,
% 0.21/0.38 ((~a_truth(liar(b))) | (~a_truth(truthteller(c))) | an_answer(b_liar_and_c_truthteller)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.38 tff(38,plain,
% 0.21/0.38 ((~a_truth(liar(b))) | (~a_truth(truthteller(c))) | an_answer(b_liar_and_c_truthteller)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.21/0.38 tff(39,plain,
% 0.21/0.38 ((~a_truth(liar(b))) | (~a_truth(truthteller(c))) | an_answer(b_liar_and_c_truthteller)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.38 tff(40,plain,
% 0.21/0.38 ((~a_truth(liar(b))) | (~a_truth(truthteller(c))) | an_answer(b_liar_and_c_truthteller)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.21/0.38 tff(41,plain,
% 0.21/0.38 ((~a_truth(liar(b))) | (~a_truth(truthteller(c))) | an_answer(b_liar_and_c_truthteller)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[40, 34])).
% 0.21/0.38 tff(42,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[41, 33, 12, 11])).
% 0.21/0.38 tff(43,plain,(~a_truth(liar(b))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.38 tff(44,plain,
% 0.21/0.38 (^[X: $i] : refl((a_truth(liar(X)) | a_truth(truthteller(X))) <=> (a_truth(liar(X)) | a_truth(truthteller(X))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(45,plain,
% 0.21/0.38 (![X: $i] : (a_truth(liar(X)) | a_truth(truthteller(X))) <=> ![X: $i] : (a_truth(liar(X)) | a_truth(truthteller(X)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.38 tff(46,plain,
% 0.21/0.38 (![X: $i] : (a_truth(liar(X)) | a_truth(truthteller(X))) <=> ![X: $i] : (a_truth(liar(X)) | a_truth(truthteller(X)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(47,plain,
% 0.21/0.38 (^[X: $i] : rewrite((a_truth(truthteller(X)) | a_truth(liar(X))) <=> (a_truth(liar(X)) | a_truth(truthteller(X))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(48,plain,
% 0.21/0.38 (![X: $i] : (a_truth(truthteller(X)) | a_truth(liar(X))) <=> ![X: $i] : (a_truth(liar(X)) | a_truth(truthteller(X)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.38 tff(49,axiom,(![X: $i] : (a_truth(truthteller(X)) | a_truth(liar(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ002-0.ax','truthteller_or_liar')).
% 0.21/0.38 tff(50,plain,
% 0.21/0.38 (![X: $i] : (a_truth(liar(X)) | a_truth(truthteller(X)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.38 tff(51,plain,
% 0.21/0.38 (![X: $i] : (a_truth(liar(X)) | a_truth(truthteller(X)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.38 tff(52,plain,(
% 0.21/0.38 ![X: $i] : (a_truth(liar(X)) | a_truth(truthteller(X)))),
% 0.21/0.38 inference(skolemize,[status(sab)],[51])).
% 0.21/0.38 tff(53,plain,
% 0.21/0.38 (![X: $i] : (a_truth(liar(X)) | a_truth(truthteller(X)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.21/0.38 tff(54,plain,
% 0.21/0.38 (((~![X: $i] : (a_truth(liar(X)) | a_truth(truthteller(X)))) | (a_truth(liar(b)) | a_truth(truthteller(b)))) <=> ((~![X: $i] : (a_truth(liar(X)) | a_truth(truthteller(X)))) | a_truth(liar(b)) | a_truth(truthteller(b)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(55,plain,
% 0.21/0.38 ((~![X: $i] : (a_truth(liar(X)) | a_truth(truthteller(X)))) | (a_truth(liar(b)) | a_truth(truthteller(b)))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(56,plain,
% 0.21/0.38 ((~![X: $i] : (a_truth(liar(X)) | a_truth(truthteller(X)))) | a_truth(liar(b)) | a_truth(truthteller(b))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.38 tff(57,plain,
% 0.21/0.38 (a_truth(liar(b)) | a_truth(truthteller(b))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.21/0.38 tff(58,plain,
% 0.21/0.38 (a_truth(truthteller(b))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[57, 43])).
% 0.21/0.38 tff(59,plain,
% 0.21/0.38 (^[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))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(60,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[59])).
% 0.21/0.38 tff(61,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(62,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(63,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.39 tff(64,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')).
% 0.21/0.39 tff(65,plain,
% 0.21/0.39 (![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.39 tff(66,plain,
% 0.21/0.39 (![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.21/0.39 tff(67,plain,(
% 0.21/0.39 ![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[66])).
% 0.21/0.39 tff(68,plain,
% 0.21/0.39 (![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.21/0.39 tff(69,plain,
% 0.21/0.39 (((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | (a_truth(liar(b)) | a_truth(liar(c)) | (~a_truth(says(c, liar(b)))))) <=> ((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | a_truth(liar(b)) | a_truth(liar(c)) | (~a_truth(says(c, liar(b)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(70,plain,
% 0.21/0.39 ((a_truth(liar(b)) | (~a_truth(says(c, liar(b)))) | a_truth(liar(c))) <=> (a_truth(liar(b)) | a_truth(liar(c)) | (~a_truth(says(c, liar(b)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(71,plain,
% 0.21/0.39 (((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | (a_truth(liar(b)) | (~a_truth(says(c, liar(b)))) | a_truth(liar(c)))) <=> ((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | (a_truth(liar(b)) | a_truth(liar(c)) | (~a_truth(says(c, liar(b))))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[70])).
% 0.21/0.39 tff(72,plain,
% 0.21/0.39 (((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | (a_truth(liar(b)) | (~a_truth(says(c, liar(b)))) | a_truth(liar(c)))) <=> ((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | a_truth(liar(b)) | a_truth(liar(c)) | (~a_truth(says(c, liar(b)))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[71, 69])).
% 0.21/0.39 tff(73,plain,
% 0.21/0.39 ((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | (a_truth(liar(b)) | (~a_truth(says(c, liar(b)))) | a_truth(liar(c)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(74,plain,
% 0.21/0.39 ((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | a_truth(liar(b)) | a_truth(liar(c)) | (~a_truth(says(c, liar(b))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.39 tff(75,plain,
% 0.21/0.39 (a_truth(liar(b)) | a_truth(liar(c))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[74, 68, 15])).
% 0.21/0.39 tff(76,plain,
% 0.21/0.39 (a_truth(liar(c))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[75, 43])).
% 0.21/0.39 tff(77,plain,
% 0.21/0.39 (((~a_truth(liar(c))) | (~a_truth(truthteller(b))) | an_answer(b_truthteller_and_c_liar)) <=> ((~a_truth(liar(c))) | (~a_truth(truthteller(b))) | an_answer(b_truthteller_and_c_liar))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(78,plain,
% 0.21/0.39 ((((~a_truth(liar(c))) | (~a_truth(truthteller(b)))) | an_answer(b_truthteller_and_c_liar)) <=> ((~a_truth(liar(c))) | (~a_truth(truthteller(b))) | an_answer(b_truthteller_and_c_liar))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(79,plain,
% 0.21/0.39 (((~a_truth(truthteller(b))) | (~a_truth(liar(c)))) <=> ((~a_truth(liar(c))) | (~a_truth(truthteller(b))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(80,plain,
% 0.21/0.39 ((((~a_truth(truthteller(b))) | (~a_truth(liar(c)))) | an_answer(b_truthteller_and_c_liar)) <=> (((~a_truth(liar(c))) | (~a_truth(truthteller(b)))) | an_answer(b_truthteller_and_c_liar))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.39 tff(81,plain,
% 0.21/0.39 ((((~a_truth(truthteller(b))) | (~a_truth(liar(c)))) | an_answer(b_truthteller_and_c_liar)) <=> ((~a_truth(liar(c))) | (~a_truth(truthteller(b))) | an_answer(b_truthteller_and_c_liar))),
% 0.21/0.39 inference(transitivity,[status(thm)],[80, 78])).
% 0.21/0.39 tff(82,axiom,(((~a_truth(truthteller(b))) | (~a_truth(liar(c)))) | an_answer(b_truthteller_and_c_liar)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_truthteller_and_c_liar')).
% 0.21/0.39 tff(83,plain,
% 0.21/0.39 ((~a_truth(liar(c))) | (~a_truth(truthteller(b))) | an_answer(b_truthteller_and_c_liar)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.39 tff(84,plain,
% 0.21/0.39 ((~a_truth(liar(c))) | (~a_truth(truthteller(b))) | an_answer(b_truthteller_and_c_liar)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[83, 77])).
% 0.21/0.39 tff(85,plain,
% 0.21/0.39 ((~a_truth(liar(c))) | (~a_truth(truthteller(b))) | an_answer(b_truthteller_and_c_liar)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.21/0.39 tff(86,plain,
% 0.21/0.39 ((~a_truth(liar(c))) | (~a_truth(truthteller(b))) | an_answer(b_truthteller_and_c_liar)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[85, 77])).
% 0.21/0.39 tff(87,plain,
% 0.21/0.39 ((~a_truth(liar(c))) | (~a_truth(truthteller(b))) | an_answer(b_truthteller_and_c_liar)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[86, 77])).
% 0.21/0.39 tff(88,plain,
% 0.21/0.39 (an_answer(b_truthteller_and_c_liar)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[87, 76, 58])).
% 0.21/0.39 tff(89,plain,
% 0.21/0.39 ((~![X: $i] : (~an_answer(X))) | (~an_answer(b_truthteller_and_c_liar))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(90,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[89, 88, 7])).
% 0.21/0.39 % SZS output end Proof
% 0.21/0.39 % E exiting
%------------------------------------------------------------------------------