%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ025-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : PUZ025-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 02:40:03 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(a_truth_type, type, (
% 0.11/0.36 a_truth: $i > $o)).
% 0.11/0.36 tff(equal_type_type, type, (
% 0.11/0.36 equal_type: ( $i * $i ) > $i)).
% 0.11/0.36 tff(c_type, type, (
% 0.11/0.36 c: $i)).
% 0.11/0.36 tff(b_type, type, (
% 0.11/0.36 b: $i)).
% 0.11/0.36 tff(answer_type, type, (
% 0.11/0.36 answer: $i > $o)).
% 0.11/0.36 tff(yes_type, type, (
% 0.11/0.36 yes: $i)).
% 0.11/0.36 tff(truthteller_type, type, (
% 0.11/0.36 truthteller: $i > $i)).
% 0.11/0.36 tff(a_type, type, (
% 0.11/0.36 a: $i)).
% 0.11/0.36 tff(liar_type, type, (
% 0.11/0.36 liar: $i > $i)).
% 0.11/0.36 tff(ask_1_if_2_type, type, (
% 0.11/0.36 ask_1_if_2: ( $i * $i ) > $o)).
% 0.11/0.36 tff(says_type, type, (
% 0.11/0.36 says: ( $i * $i ) > $i)).
% 0.11/0.36 tff(1,assumption,(answer(yes)), introduced(assumption)).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (^[Answer: $i] : refl((~answer(Answer)) <=> (~answer(Answer)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![Answer: $i] : (~answer(Answer)) <=> ![Answer: $i] : (~answer(Answer))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (![Answer: $i] : (~answer(Answer)) <=> ![Answer: $i] : (~answer(Answer))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(5,axiom,(![Answer: $i] : (~answer(Answer))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_there_is_an_answer')).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (![Answer: $i] : (~answer(Answer))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.36 tff(7,plain,(
% 0.11/0.36 ![Answer: $i] : (~answer(Answer))),
% 0.11/0.36 inference(skolemize,[status(sab)],[6])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (![Answer: $i] : (~answer(Answer))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 ((~![Answer: $i] : (~answer(Answer))) | (~answer(yes))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.11/0.36 tff(11,plain,(~answer(yes)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(12,assumption,(~a_truth(equal_type(b, c))), introduced(assumption)).
% 0.11/0.36 tff(13,assumption,(~answer(yes)), introduced(assumption)).
% 0.11/0.36 tff(14,assumption,(~a_truth(equal_type(a, b))), introduced(assumption)).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (ask_1_if_2(c, equal_type(a, b)) <=> ask_1_if_2(c, equal_type(a, b))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(16,axiom,(ask_1_if_2(c, equal_type(a, b))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ask_c_if_a_and_b_equal')).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (ask_1_if_2(c, equal_type(a, b))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (^[Y: $i, X: $i] : refl(((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y))) <=> ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y))) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y))) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (^[Y: $i, X: $i] : trans(monotonicity(rewrite((((~ask_1_if_2(X, Y)) | (~a_truth(liar(X)))) | a_truth(Y)) <=> ((~a_truth(liar(X))) | a_truth(Y) | (~ask_1_if_2(X, Y)))), (((((~ask_1_if_2(X, Y)) | (~a_truth(liar(X)))) | a_truth(Y)) | answer(yes)) <=> (((~a_truth(liar(X))) | a_truth(Y) | (~ask_1_if_2(X, Y))) | answer(yes)))), rewrite((((~a_truth(liar(X))) | a_truth(Y) | (~ask_1_if_2(X, Y))) | answer(yes)) <=> ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))), (((((~ask_1_if_2(X, Y)) | (~a_truth(liar(X)))) | a_truth(Y)) | answer(yes)) <=> ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((((~ask_1_if_2(X, Y)) | (~a_truth(liar(X)))) | a_truth(Y)) | answer(yes)) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.11/0.37 tff(23,axiom,(![Y: $i, X: $i] : ((((~ask_1_if_2(X, Y)) | (~a_truth(liar(X)))) | a_truth(Y)) | answer(yes))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','liar_supports_lies')).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.11/0.37 tff(26,plain,(
% 0.11/0.37 ![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[25])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))) | (answer(yes) | (~a_truth(liar(c))) | a_truth(equal_type(a, b)) | (~ask_1_if_2(c, equal_type(a, b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))) | answer(yes) | (~a_truth(liar(c))) | a_truth(equal_type(a, b)) | (~ask_1_if_2(c, equal_type(a, b))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (((~a_truth(liar(c))) | answer(yes) | a_truth(equal_type(a, b)) | (~ask_1_if_2(c, equal_type(a, b)))) <=> (answer(yes) | (~a_truth(liar(c))) | a_truth(equal_type(a, b)) | (~ask_1_if_2(c, equal_type(a, b))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))) | ((~a_truth(liar(c))) | answer(yes) | a_truth(equal_type(a, b)) | (~ask_1_if_2(c, equal_type(a, b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))) | (answer(yes) | (~a_truth(liar(c))) | a_truth(equal_type(a, b)) | (~ask_1_if_2(c, equal_type(a, b)))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[29])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))) | ((~a_truth(liar(c))) | answer(yes) | a_truth(equal_type(a, b)) | (~ask_1_if_2(c, equal_type(a, b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))) | answer(yes) | (~a_truth(liar(c))) | a_truth(equal_type(a, b)) | (~ask_1_if_2(c, equal_type(a, b))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[30, 28])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))) | ((~a_truth(liar(c))) | answer(yes) | a_truth(equal_type(a, b)) | (~ask_1_if_2(c, equal_type(a, b))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | answer(yes) | a_truth(Y) | (~ask_1_if_2(X, Y)))) | answer(yes) | (~a_truth(liar(c))) | a_truth(equal_type(a, b)) | (~ask_1_if_2(c, equal_type(a, b)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (answer(yes) | (~a_truth(liar(c))) | a_truth(equal_type(a, b))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[33, 27, 17])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (~a_truth(liar(c))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[34, 14, 13])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (a_truth(says(a, equal_type(b, c))) <=> a_truth(says(a, equal_type(b, c)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(37,axiom,(a_truth(says(a, equal_type(b, c)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_says_b_and_c_equal')).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (a_truth(says(a, equal_type(b, c)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (^[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))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (![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)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[39])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (![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)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (^[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))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 (![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)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[42])).
% 0.11/0.37 tff(44,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')).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.11/0.37 tff(46,plain,
% 0.11/0.37 (![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.11/0.37 tff(47,plain,(
% 0.11/0.37 ![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[46])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 (![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 (((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | (a_truth(equal_type(b, c)) | (~a_truth(says(a, equal_type(b, c)))) | a_truth(liar(a)))) <=> ((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | a_truth(equal_type(b, c)) | (~a_truth(says(a, equal_type(b, c)))) | a_truth(liar(a)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 ((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | (a_truth(equal_type(b, c)) | (~a_truth(says(a, equal_type(b, c)))) | a_truth(liar(a)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 ((~![Liar: $i, Statement: $i] : (a_truth(Statement) | (~a_truth(says(Liar, Statement))) | a_truth(liar(Liar)))) | a_truth(equal_type(b, c)) | (~a_truth(says(a, equal_type(b, c)))) | a_truth(liar(a))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.11/0.37 tff(52,plain,
% 0.11/0.37 (a_truth(equal_type(b, c)) | a_truth(liar(a))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[51, 48, 38])).
% 0.11/0.37 tff(53,plain,
% 0.11/0.37 (a_truth(liar(a))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[52, 12])).
% 0.11/0.37 tff(54,plain,
% 0.11/0.37 (^[Y: $i, X: $i] : refl(((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y))) <=> ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(55,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y))) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[54])).
% 0.11/0.37 tff(56,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y))) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(57,plain,
% 0.11/0.37 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((~a_truth(liar(X))) | a_truth(equal_type(X, Y))) <=> ((~a_truth(liar(X))) | a_truth(equal_type(X, Y)))), ((((~a_truth(liar(X))) | a_truth(equal_type(X, Y))) | a_truth(truthteller(Y))) <=> (((~a_truth(liar(X))) | a_truth(equal_type(X, Y))) | a_truth(truthteller(Y))))), rewrite((((~a_truth(liar(X))) | a_truth(equal_type(X, Y))) | a_truth(truthteller(Y))) <=> ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))), ((((~a_truth(liar(X))) | a_truth(equal_type(X, Y))) | a_truth(truthteller(Y))) <=> ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(58,plain,
% 0.11/0.37 (![Y: $i, X: $i] : (((~a_truth(liar(X))) | a_truth(equal_type(X, Y))) | a_truth(truthteller(Y))) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[57])).
% 0.11/0.37 tff(59,axiom,(![Y: $i, X: $i] : (((~a_truth(liar(X))) | a_truth(equal_type(X, Y))) | a_truth(truthteller(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','liar_not_equal_truthteller')).
% 0.11/0.37 tff(60,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.11/0.37 tff(61,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.11/0.37 tff(62,plain,(
% 0.11/0.37 ![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[61])).
% 0.11/0.37 tff(63,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.11/0.37 tff(64,plain,
% 0.11/0.37 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))) | ((~a_truth(liar(a))) | a_truth(truthteller(b)) | a_truth(equal_type(a, b)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))) | (~a_truth(liar(a))) | a_truth(truthteller(b)) | a_truth(equal_type(a, b)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(65,plain,
% 0.11/0.37 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))) | ((~a_truth(liar(a))) | a_truth(truthteller(b)) | a_truth(equal_type(a, b)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(66,plain,
% 0.11/0.37 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))) | (~a_truth(liar(a))) | a_truth(truthteller(b)) | a_truth(equal_type(a, b))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.11/0.37 tff(67,plain,
% 0.11/0.37 ((~a_truth(liar(a))) | a_truth(truthteller(b)) | a_truth(equal_type(a, b))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[66, 63])).
% 0.11/0.37 tff(68,plain,
% 0.11/0.37 (a_truth(truthteller(b))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[67, 14, 53])).
% 0.11/0.37 tff(69,plain,
% 0.11/0.37 (^[Y: $i, X: $i] : refl(((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y))) <=> ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(70,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y))) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[69])).
% 0.11/0.37 tff(71,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y))) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(72,plain,
% 0.11/0.37 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((~a_truth(truthteller(X))) | a_truth(equal_type(X, Y))) <=> ((~a_truth(truthteller(X))) | a_truth(equal_type(X, Y)))), ((((~a_truth(truthteller(X))) | a_truth(equal_type(X, Y))) | a_truth(liar(Y))) <=> (((~a_truth(truthteller(X))) | a_truth(equal_type(X, Y))) | a_truth(liar(Y))))), rewrite((((~a_truth(truthteller(X))) | a_truth(equal_type(X, Y))) | a_truth(liar(Y))) <=> ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))), ((((~a_truth(truthteller(X))) | a_truth(equal_type(X, Y))) | a_truth(liar(Y))) <=> ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(73,plain,
% 0.11/0.37 (![Y: $i, X: $i] : (((~a_truth(truthteller(X))) | a_truth(equal_type(X, Y))) | a_truth(liar(Y))) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[72])).
% 0.11/0.37 tff(74,axiom,(![Y: $i, X: $i] : (((~a_truth(truthteller(X))) | a_truth(equal_type(X, Y))) | a_truth(liar(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','truthteller_not_equal_liar')).
% 0.11/0.37 tff(75,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.11/0.37 tff(76,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.11/0.37 tff(77,plain,(
% 0.11/0.37 ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[76])).
% 0.11/0.37 tff(78,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.11/0.37 tff(79,plain,
% 0.11/0.37 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))) | (a_truth(equal_type(b, c)) | a_truth(liar(c)) | (~a_truth(truthteller(b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))) | a_truth(equal_type(b, c)) | a_truth(liar(c)) | (~a_truth(truthteller(b))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(80,plain,
% 0.11/0.37 (((~a_truth(truthteller(b))) | a_truth(liar(c)) | a_truth(equal_type(b, c))) <=> (a_truth(equal_type(b, c)) | a_truth(liar(c)) | (~a_truth(truthteller(b))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(81,plain,
% 0.11/0.37 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))) | ((~a_truth(truthteller(b))) | a_truth(liar(c)) | a_truth(equal_type(b, c)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))) | (a_truth(equal_type(b, c)) | a_truth(liar(c)) | (~a_truth(truthteller(b)))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[80])).
% 0.11/0.37 tff(82,plain,
% 0.11/0.37 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))) | ((~a_truth(truthteller(b))) | a_truth(liar(c)) | a_truth(equal_type(b, c)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))) | a_truth(equal_type(b, c)) | a_truth(liar(c)) | (~a_truth(truthteller(b))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[81, 79])).
% 0.11/0.37 tff(83,plain,
% 0.11/0.37 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))) | ((~a_truth(truthteller(b))) | a_truth(liar(c)) | a_truth(equal_type(b, c)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(84,plain,
% 0.11/0.37 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))) | a_truth(equal_type(b, c)) | a_truth(liar(c)) | (~a_truth(truthteller(b)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.11/0.37 tff(85,plain,
% 0.11/0.37 (a_truth(equal_type(b, c)) | a_truth(liar(c)) | (~a_truth(truthteller(b)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[84, 78])).
% 0.11/0.37 tff(86,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[85, 68, 35, 12])).
% 0.11/0.37 tff(87,plain,(a_truth(equal_type(a, b)) | a_truth(equal_type(b, c)) | answer(yes)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(88,plain,
% 0.11/0.37 (a_truth(equal_type(a, b))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[87, 13, 12])).
% 0.11/0.37 tff(89,plain,
% 0.11/0.37 (^[Y: $i, X: $i] : refl(((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y))) <=> ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(90,plain,
% 0.11/0.37 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y))) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[89])).
% 0.11/0.38 tff(91,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y))) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(92,plain,
% 0.11/0.38 (^[Y: $i, X: $i] : trans(monotonicity(rewrite((((~ask_1_if_2(X, Y)) | (~a_truth(truthteller(X)))) | (~a_truth(Y))) <=> ((~a_truth(truthteller(X))) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))), (((((~ask_1_if_2(X, Y)) | (~a_truth(truthteller(X)))) | (~a_truth(Y))) | answer(yes)) <=> (((~a_truth(truthteller(X))) | (~a_truth(Y)) | (~ask_1_if_2(X, Y))) | answer(yes)))), rewrite((((~a_truth(truthteller(X))) | (~a_truth(Y)) | (~ask_1_if_2(X, Y))) | answer(yes)) <=> ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))), (((((~ask_1_if_2(X, Y)) | (~a_truth(truthteller(X)))) | (~a_truth(Y))) | answer(yes)) <=> ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(93,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((((~ask_1_if_2(X, Y)) | (~a_truth(truthteller(X)))) | (~a_truth(Y))) | answer(yes)) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[92])).
% 0.11/0.38 tff(94,axiom,(![Y: $i, X: $i] : ((((~ask_1_if_2(X, Y)) | (~a_truth(truthteller(X)))) | (~a_truth(Y))) | answer(yes))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','truthteller_identifies_truths')).
% 0.11/0.38 tff(95,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.11/0.38 tff(96,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.11/0.38 tff(97,plain,(
% 0.11/0.38 ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[96])).
% 0.11/0.38 tff(98,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.11/0.38 tff(99,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))) | (answer(yes) | (~a_truth(truthteller(c))) | (~a_truth(equal_type(a, b))) | (~ask_1_if_2(c, equal_type(a, b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))) | answer(yes) | (~a_truth(truthteller(c))) | (~a_truth(equal_type(a, b))) | (~ask_1_if_2(c, equal_type(a, b))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(100,plain,
% 0.11/0.38 (((~a_truth(truthteller(c))) | answer(yes) | (~a_truth(equal_type(a, b))) | (~ask_1_if_2(c, equal_type(a, b)))) <=> (answer(yes) | (~a_truth(truthteller(c))) | (~a_truth(equal_type(a, b))) | (~ask_1_if_2(c, equal_type(a, b))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(101,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))) | ((~a_truth(truthteller(c))) | answer(yes) | (~a_truth(equal_type(a, b))) | (~ask_1_if_2(c, equal_type(a, b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))) | (answer(yes) | (~a_truth(truthteller(c))) | (~a_truth(equal_type(a, b))) | (~ask_1_if_2(c, equal_type(a, b)))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[100])).
% 0.11/0.38 tff(102,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))) | ((~a_truth(truthteller(c))) | answer(yes) | (~a_truth(equal_type(a, b))) | (~ask_1_if_2(c, equal_type(a, b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))) | answer(yes) | (~a_truth(truthteller(c))) | (~a_truth(equal_type(a, b))) | (~ask_1_if_2(c, equal_type(a, b))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[101, 99])).
% 0.11/0.38 tff(103,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))) | ((~a_truth(truthteller(c))) | answer(yes) | (~a_truth(equal_type(a, b))) | (~ask_1_if_2(c, equal_type(a, b))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(104,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | answer(yes) | (~a_truth(Y)) | (~ask_1_if_2(X, Y)))) | answer(yes) | (~a_truth(truthteller(c))) | (~a_truth(equal_type(a, b))) | (~ask_1_if_2(c, equal_type(a, b)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.11/0.38 tff(105,plain,
% 0.11/0.38 (answer(yes) | (~a_truth(truthteller(c))) | (~a_truth(equal_type(a, b)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[104, 98, 17])).
% 0.11/0.38 tff(106,plain,
% 0.11/0.38 (~a_truth(truthteller(c))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[105, 88, 13])).
% 0.11/0.38 tff(107,plain,
% 0.11/0.38 (^[Y: $i, X: $i] : refl(((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y)))) <=> ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(108,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y)))) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[107])).
% 0.11/0.38 tff(109,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y)))) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(110,plain,
% 0.11/0.38 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((~a_truth(equal_type(X, Y))) | (~a_truth(liar(X)))) <=> ((~a_truth(liar(X))) | (~a_truth(equal_type(X, Y))))), ((((~a_truth(equal_type(X, Y))) | (~a_truth(liar(X)))) | a_truth(liar(Y))) <=> (((~a_truth(liar(X))) | (~a_truth(equal_type(X, Y)))) | a_truth(liar(Y))))), rewrite((((~a_truth(liar(X))) | (~a_truth(equal_type(X, Y)))) | a_truth(liar(Y))) <=> ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))), ((((~a_truth(equal_type(X, Y))) | (~a_truth(liar(X)))) | a_truth(liar(Y))) <=> ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(111,plain,
% 0.11/0.38 (![Y: $i, X: $i] : (((~a_truth(equal_type(X, Y))) | (~a_truth(liar(X)))) | a_truth(liar(Y))) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[110])).
% 0.11/0.38 tff(112,axiom,(![Y: $i, X: $i] : (((~a_truth(equal_type(X, Y))) | (~a_truth(liar(X)))) | a_truth(liar(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','liar_equals_liar')).
% 0.11/0.38 tff(113,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.11/0.38 tff(114,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.11/0.38 tff(115,plain,(
% 0.11/0.38 ![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[114])).
% 0.11/0.38 tff(116,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.11/0.38 tff(117,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))) | ((~a_truth(liar(a))) | a_truth(liar(b)) | (~a_truth(equal_type(a, b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))) | (~a_truth(liar(a))) | a_truth(liar(b)) | (~a_truth(equal_type(a, b))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(118,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))) | ((~a_truth(liar(a))) | a_truth(liar(b)) | (~a_truth(equal_type(a, b))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(119,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))) | (~a_truth(liar(a))) | a_truth(liar(b)) | (~a_truth(equal_type(a, b)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.11/0.38 tff(120,plain,
% 0.11/0.38 ((~a_truth(liar(a))) | a_truth(liar(b)) | (~a_truth(equal_type(a, b)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[119, 116])).
% 0.11/0.38 tff(121,plain,
% 0.11/0.38 (a_truth(liar(b))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[120, 88, 53])).
% 0.11/0.38 tff(122,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))) | (a_truth(equal_type(b, c)) | (~a_truth(liar(b))) | a_truth(truthteller(c)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))) | a_truth(equal_type(b, c)) | (~a_truth(liar(b))) | a_truth(truthteller(c)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(123,plain,
% 0.11/0.38 (((~a_truth(liar(b))) | a_truth(truthteller(c)) | a_truth(equal_type(b, c))) <=> (a_truth(equal_type(b, c)) | (~a_truth(liar(b))) | a_truth(truthteller(c)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(124,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))) | ((~a_truth(liar(b))) | a_truth(truthteller(c)) | a_truth(equal_type(b, c)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))) | (a_truth(equal_type(b, c)) | (~a_truth(liar(b))) | a_truth(truthteller(c))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[123])).
% 0.11/0.38 tff(125,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))) | ((~a_truth(liar(b))) | a_truth(truthteller(c)) | a_truth(equal_type(b, c)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))) | a_truth(equal_type(b, c)) | (~a_truth(liar(b))) | a_truth(truthteller(c)))),
% 0.11/0.38 inference(transitivity,[status(thm)],[124, 122])).
% 0.11/0.38 tff(126,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))) | ((~a_truth(liar(b))) | a_truth(truthteller(c)) | a_truth(equal_type(b, c)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(127,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(truthteller(Y)) | a_truth(equal_type(X, Y)))) | a_truth(equal_type(b, c)) | (~a_truth(liar(b))) | a_truth(truthteller(c))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.11/0.38 tff(128,plain,
% 0.11/0.38 (a_truth(equal_type(b, c)) | (~a_truth(liar(b))) | a_truth(truthteller(c))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[127, 63])).
% 0.11/0.38 tff(129,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[128, 121, 106, 12])).
% 0.11/0.38 tff(130,plain,(answer(yes) | a_truth(equal_type(b, c))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(131,plain,
% 0.11/0.38 (a_truth(equal_type(b, c))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[130, 11])).
% 0.11/0.38 tff(132,plain,
% 0.11/0.38 (~a_truth(liar(c))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[34, 14, 11])).
% 0.11/0.38 tff(133,plain,
% 0.11/0.38 (^[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))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(134,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[133])).
% 0.11/0.38 tff(135,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(136,plain,
% 0.11/0.38 (^[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))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(137,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[136])).
% 0.11/0.38 tff(138,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')).
% 0.11/0.38 tff(139,plain,
% 0.11/0.38 (![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.11/0.38 tff(140,plain,
% 0.11/0.38 (![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.11/0.38 tff(141,plain,(
% 0.11/0.38 ![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[140])).
% 0.11/0.38 tff(142,plain,
% 0.11/0.38 (![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.11/0.38 tff(143,plain,
% 0.11/0.38 (((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | ((~a_truth(says(a, equal_type(b, c)))) | a_truth(truthteller(a)) | (~a_truth(equal_type(b, c))))) <=> ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | (~a_truth(says(a, equal_type(b, c)))) | a_truth(truthteller(a)) | (~a_truth(equal_type(b, c))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(144,plain,
% 0.11/0.38 ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | ((~a_truth(says(a, equal_type(b, c)))) | a_truth(truthteller(a)) | (~a_truth(equal_type(b, c))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(145,plain,
% 0.11/0.38 ((~![Truthteller: $i, Statement: $i] : ((~a_truth(says(Truthteller, Statement))) | a_truth(truthteller(Truthteller)) | (~a_truth(Statement)))) | (~a_truth(says(a, equal_type(b, c)))) | a_truth(truthteller(a)) | (~a_truth(equal_type(b, c)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.11/0.38 tff(146,plain,
% 0.11/0.38 (a_truth(truthteller(a)) | (~a_truth(equal_type(b, c)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[145, 142, 38])).
% 0.11/0.38 tff(147,plain,
% 0.11/0.38 (a_truth(truthteller(a))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[146, 131])).
% 0.11/0.38 tff(148,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))) | ((~a_truth(truthteller(a))) | a_truth(liar(b)) | a_truth(equal_type(a, b)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))) | (~a_truth(truthteller(a))) | a_truth(liar(b)) | a_truth(equal_type(a, b)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(149,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))) | ((~a_truth(truthteller(a))) | a_truth(liar(b)) | a_truth(equal_type(a, b)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(150,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(liar(Y)) | a_truth(equal_type(X, Y)))) | (~a_truth(truthteller(a))) | a_truth(liar(b)) | a_truth(equal_type(a, b))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.11/0.38 tff(151,plain,
% 0.11/0.38 ((~a_truth(truthteller(a))) | a_truth(liar(b)) | a_truth(equal_type(a, b))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[150, 78])).
% 0.11/0.38 tff(152,plain,
% 0.11/0.38 (a_truth(liar(b))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[151, 14, 147])).
% 0.11/0.39 tff(153,plain,
% 0.11/0.39 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))) | ((~a_truth(equal_type(b, c))) | (~a_truth(liar(b))) | a_truth(liar(c)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))) | (~a_truth(equal_type(b, c))) | (~a_truth(liar(b))) | a_truth(liar(c)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(154,plain,
% 0.11/0.39 (((~a_truth(liar(b))) | a_truth(liar(c)) | (~a_truth(equal_type(b, c)))) <=> ((~a_truth(equal_type(b, c))) | (~a_truth(liar(b))) | a_truth(liar(c)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(155,plain,
% 0.11/0.39 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))) | ((~a_truth(liar(b))) | a_truth(liar(c)) | (~a_truth(equal_type(b, c))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))) | ((~a_truth(equal_type(b, c))) | (~a_truth(liar(b))) | a_truth(liar(c))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[154])).
% 0.11/0.39 tff(156,plain,
% 0.11/0.39 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))) | ((~a_truth(liar(b))) | a_truth(liar(c)) | (~a_truth(equal_type(b, c))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))) | (~a_truth(equal_type(b, c))) | (~a_truth(liar(b))) | a_truth(liar(c)))),
% 0.11/0.39 inference(transitivity,[status(thm)],[155, 153])).
% 0.11/0.39 tff(157,plain,
% 0.11/0.39 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))) | ((~a_truth(liar(b))) | a_truth(liar(c)) | (~a_truth(equal_type(b, c))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(158,plain,
% 0.11/0.39 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(equal_type(X, Y))))) | (~a_truth(equal_type(b, c))) | (~a_truth(liar(b))) | a_truth(liar(c))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.11/0.39 tff(159,plain,
% 0.11/0.39 ((~a_truth(equal_type(b, c))) | (~a_truth(liar(b))) | a_truth(liar(c))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[158, 116])).
% 0.11/0.39 tff(160,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[159, 152, 132, 131])).
% 0.11/0.39 tff(161,plain,(a_truth(equal_type(a, b))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.39 tff(162,plain,
% 0.11/0.39 (~a_truth(truthteller(c))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[105, 161, 11])).
% 0.11/0.39 tff(163,plain,
% 0.11/0.39 (^[Y: $i, X: $i] : refl(((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y)))) <=> ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(164,plain,
% 0.11/0.39 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y)))) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[163])).
% 0.11/0.39 tff(165,plain,
% 0.11/0.39 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y)))) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(166,plain,
% 0.11/0.39 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((~a_truth(equal_type(X, Y))) | (~a_truth(truthteller(X)))) <=> ((~a_truth(truthteller(X))) | (~a_truth(equal_type(X, Y))))), ((((~a_truth(equal_type(X, Y))) | (~a_truth(truthteller(X)))) | a_truth(truthteller(Y))) <=> (((~a_truth(truthteller(X))) | (~a_truth(equal_type(X, Y)))) | a_truth(truthteller(Y))))), rewrite((((~a_truth(truthteller(X))) | (~a_truth(equal_type(X, Y)))) | a_truth(truthteller(Y))) <=> ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))), ((((~a_truth(equal_type(X, Y))) | (~a_truth(truthteller(X)))) | a_truth(truthteller(Y))) <=> ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(167,plain,
% 0.11/0.39 (![Y: $i, X: $i] : (((~a_truth(equal_type(X, Y))) | (~a_truth(truthteller(X)))) | a_truth(truthteller(Y))) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[166])).
% 0.11/0.39 tff(168,axiom,(![Y: $i, X: $i] : (((~a_truth(equal_type(X, Y))) | (~a_truth(truthteller(X)))) | a_truth(truthteller(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','truthteller_equals_truthtller')).
% 0.11/0.39 tff(169,plain,
% 0.11/0.39 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.11/0.39 tff(170,plain,
% 0.11/0.39 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.11/0.39 tff(171,plain,(
% 0.11/0.39 ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[170])).
% 0.11/0.39 tff(172,plain,
% 0.11/0.39 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.11/0.39 tff(173,plain,
% 0.11/0.39 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))) | ((~a_truth(truthteller(a))) | a_truth(truthteller(b)) | (~a_truth(equal_type(a, b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))) | (~a_truth(truthteller(a))) | a_truth(truthteller(b)) | (~a_truth(equal_type(a, b))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(174,plain,
% 0.11/0.39 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))) | ((~a_truth(truthteller(a))) | a_truth(truthteller(b)) | (~a_truth(equal_type(a, b))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(175,plain,
% 0.11/0.39 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))) | (~a_truth(truthteller(a))) | a_truth(truthteller(b)) | (~a_truth(equal_type(a, b)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.11/0.39 tff(176,plain,
% 0.11/0.39 ((~a_truth(truthteller(a))) | a_truth(truthteller(b)) | (~a_truth(equal_type(a, b)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[175, 172])).
% 0.11/0.39 tff(177,plain,
% 0.11/0.39 (a_truth(truthteller(b))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[176, 161, 147])).
% 0.11/0.39 tff(178,plain,
% 0.11/0.39 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))) | ((~a_truth(equal_type(b, c))) | (~a_truth(truthteller(b))) | a_truth(truthteller(c)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))) | (~a_truth(equal_type(b, c))) | (~a_truth(truthteller(b))) | a_truth(truthteller(c)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(179,plain,
% 0.11/0.39 (((~a_truth(truthteller(b))) | a_truth(truthteller(c)) | (~a_truth(equal_type(b, c)))) <=> ((~a_truth(equal_type(b, c))) | (~a_truth(truthteller(b))) | a_truth(truthteller(c)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(180,plain,
% 0.11/0.39 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))) | ((~a_truth(truthteller(b))) | a_truth(truthteller(c)) | (~a_truth(equal_type(b, c))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))) | ((~a_truth(equal_type(b, c))) | (~a_truth(truthteller(b))) | a_truth(truthteller(c))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[179])).
% 0.11/0.39 tff(181,plain,
% 0.11/0.39 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))) | ((~a_truth(truthteller(b))) | a_truth(truthteller(c)) | (~a_truth(equal_type(b, c))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))) | (~a_truth(equal_type(b, c))) | (~a_truth(truthteller(b))) | a_truth(truthteller(c)))),
% 0.11/0.39 inference(transitivity,[status(thm)],[180, 178])).
% 0.11/0.39 tff(182,plain,
% 0.11/0.39 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))) | ((~a_truth(truthteller(b))) | a_truth(truthteller(c)) | (~a_truth(equal_type(b, c))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(183,plain,
% 0.11/0.39 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(truthteller(Y)) | (~a_truth(equal_type(X, Y))))) | (~a_truth(equal_type(b, c))) | (~a_truth(truthteller(b))) | a_truth(truthteller(c))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.11/0.39 tff(184,plain,
% 0.11/0.39 ((~a_truth(equal_type(b, c))) | (~a_truth(truthteller(b))) | a_truth(truthteller(c))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[183, 172])).
% 0.11/0.39 tff(185,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[184, 177, 162, 131])).
% 0.11/0.39 % SZS output end Proof
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------