%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ027-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:23:11 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : PUZ027-1 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 02:42:01 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(a_truth_type, type, (
% 0.20/0.38 a_truth: $i > $o)).
% 0.20/0.38 tff(truthteller_type, type, (
% 0.20/0.38 truthteller: $i > $i)).
% 0.20/0.38 tff(a_type, type, (
% 0.20/0.38 a: $i)).
% 0.20/0.38 tff(normal_type, type, (
% 0.20/0.38 normal: $i > $i)).
% 0.20/0.38 tff(lower_type, type, (
% 0.20/0.38 lower: ( $i * $i ) > $i)).
% 0.20/0.38 tff(b_type, type, (
% 0.20/0.38 b: $i)).
% 0.20/0.38 tff(answer_type, type, (
% 0.20/0.38 answer: $i > $o)).
% 0.20/0.38 tff(a_normal_b_truthteller_type, type, (
% 0.20/0.38 a_normal_b_truthteller: $i)).
% 0.20/0.38 tff(not_lower_type, type, (
% 0.20/0.38 not_lower: ( $i * $i ) > $i)).
% 0.20/0.38 tff(a_and_b_normal_type, type, (
% 0.20/0.38 a_and_b_normal: $i)).
% 0.20/0.38 tff(says_type, type, (
% 0.20/0.38 says: ( $i * $i ) > $i)).
% 0.20/0.38 tff(liar_type, type, (
% 0.20/0.38 liar: $i > $i)).
% 0.20/0.38 tff(1,assumption,(a_truth(normal(a))), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (^[Answer: $i] : refl((~answer(Answer)) <=> (~answer(Answer)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![Answer: $i] : (~answer(Answer)) <=> ![Answer: $i] : (~answer(Answer))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![Answer: $i] : (~answer(Answer)) <=> ![Answer: $i] : (~answer(Answer))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(5,axiom,(![Answer: $i] : (~answer(Answer))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_there_is_an_answer')).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (![Answer: $i] : (~answer(Answer))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.38 tff(7,plain,(
% 0.20/0.38 ![Answer: $i] : (~answer(Answer))),
% 0.20/0.38 inference(skolemize,[status(sab)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![Answer: $i] : (~answer(Answer))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.38 tff(9,assumption,(answer(a_normal_b_truthteller)), introduced(assumption)).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 ((~![Answer: $i] : (~answer(Answer))) | (~answer(a_normal_b_truthteller))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[10, 9, 8])).
% 0.20/0.38 tff(12,plain,(~answer(a_normal_b_truthteller)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller)) <=> ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 ((((~a_truth(normal(a))) | (~a_truth(truthteller(b)))) | answer(a_normal_b_truthteller)) <=> ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(15,axiom,(((~a_truth(normal(a))) | (~a_truth(truthteller(b)))) | answer(a_normal_b_truthteller)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_normal_b_truthteller')).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (~a_truth(truthteller(b))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[20, 1, 12])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (^[Y: $i, X: $i] : refl(((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y)))) <=> ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y)))) <=> ![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y)))) <=> ![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((~a_truth(lower(X, Y))) | (~a_truth(normal(X)))) <=> ((~a_truth(normal(X))) | (~a_truth(lower(X, Y))))), ((((~a_truth(lower(X, Y))) | (~a_truth(normal(X)))) | a_truth(truthteller(Y))) <=> (((~a_truth(normal(X))) | (~a_truth(lower(X, Y)))) | a_truth(truthteller(Y))))), rewrite((((~a_truth(normal(X))) | (~a_truth(lower(X, Y)))) | a_truth(truthteller(Y))) <=> ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))), ((((~a_truth(lower(X, Y))) | (~a_truth(normal(X)))) | a_truth(truthteller(Y))) <=> ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (![Y: $i, X: $i] : (((~a_truth(lower(X, Y))) | (~a_truth(normal(X)))) | a_truth(truthteller(Y))) <=> ![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.38 tff(27,axiom,(![Y: $i, X: $i] : (((~a_truth(lower(X, Y))) | (~a_truth(normal(X)))) | a_truth(truthteller(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','truthtellers_highest')).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.38 tff(30,plain,(
% 0.20/0.38 ![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[29])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (((~![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))) | (a_truth(truthteller(b)) | (~a_truth(normal(a))) | (~a_truth(lower(a, b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))) | a_truth(truthteller(b)) | (~a_truth(normal(a))) | (~a_truth(lower(a, b))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (((~a_truth(normal(a))) | a_truth(truthteller(b)) | (~a_truth(lower(a, b)))) <=> (a_truth(truthteller(b)) | (~a_truth(normal(a))) | (~a_truth(lower(a, b))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (((~![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))) | ((~a_truth(normal(a))) | a_truth(truthteller(b)) | (~a_truth(lower(a, b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))) | (a_truth(truthteller(b)) | (~a_truth(normal(a))) | (~a_truth(lower(a, b)))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[33])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (((~![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))) | ((~a_truth(normal(a))) | a_truth(truthteller(b)) | (~a_truth(lower(a, b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))) | a_truth(truthteller(b)) | (~a_truth(normal(a))) | (~a_truth(lower(a, b))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[34, 32])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 ((~![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))) | ((~a_truth(normal(a))) | a_truth(truthteller(b)) | (~a_truth(lower(a, b))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 ((~![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))) | a_truth(truthteller(b)) | (~a_truth(normal(a))) | (~a_truth(lower(a, b)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (a_truth(truthteller(b)) | (~a_truth(normal(a))) | (~a_truth(lower(a, b)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[37, 31])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (~a_truth(lower(a, b))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[38, 21, 1])).
% 0.20/0.38 tff(40,assumption,(answer(a_and_b_normal)), introduced(assumption)).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 ((~![Answer: $i] : (~answer(Answer))) | (~answer(a_and_b_normal))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[41, 40, 8])).
% 0.20/0.38 tff(43,plain,(~answer(a_and_b_normal)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal)) <=> ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 ((((~a_truth(normal(a))) | (~a_truth(normal(b)))) | answer(a_and_b_normal)) <=> ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(46,axiom,(((~a_truth(normal(a))) | (~a_truth(normal(b)))) | answer(a_and_b_normal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_and_b_normal')).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 44])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[49, 44])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[50, 44])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (~a_truth(normal(b))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[51, 1, 43])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (a_truth(says(b, not_lower(a, b))) <=> a_truth(says(b, not_lower(a, b)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(54,axiom,(a_truth(says(b, not_lower(a, b)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_says_a_not_lower_than_b')).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (a_truth(says(b, not_lower(a, b)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (^[Y: $i, X: $i] : refl((a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X))) <=> (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X))) <=> ![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X))) <=> ![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (^[Y: $i, X: $i] : trans(monotonicity(rewrite((((~a_truth(X)) | (~a_truth(says(Y, X)))) | a_truth(truthteller(Y))) <=> (a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))), (((((~a_truth(X)) | (~a_truth(says(Y, X)))) | a_truth(truthteller(Y))) | a_truth(normal(Y))) <=> ((a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X))) | a_truth(normal(Y))))), rewrite(((a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X))) | a_truth(normal(Y))) <=> (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))), (((((~a_truth(X)) | (~a_truth(says(Y, X)))) | a_truth(truthteller(Y))) | a_truth(normal(Y))) <=> (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (![Y: $i, X: $i] : ((((~a_truth(X)) | (~a_truth(says(Y, X)))) | a_truth(truthteller(Y))) | a_truth(normal(Y))) <=> ![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.39 tff(61,axiom,(![Y: $i, X: $i] : ((((~a_truth(X)) | (~a_truth(says(Y, X)))) | a_truth(truthteller(Y))) | a_truth(normal(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ003-0.ax','truthtellers_and_normal_tell_truth')).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.20/0.39 tff(64,plain,(
% 0.20/0.39 ![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[63])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(truthteller(b)) | a_truth(normal(b)) | (~a_truth(says(b, not_lower(a, b)))) | (~a_truth(not_lower(a, b))))) <=> ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | a_truth(truthteller(b)) | a_truth(normal(b)) | (~a_truth(says(b, not_lower(a, b)))) | (~a_truth(not_lower(a, b))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 ((a_truth(normal(b)) | a_truth(truthteller(b)) | (~a_truth(says(b, not_lower(a, b)))) | (~a_truth(not_lower(a, b)))) <=> (a_truth(truthteller(b)) | a_truth(normal(b)) | (~a_truth(says(b, not_lower(a, b)))) | (~a_truth(not_lower(a, b))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(normal(b)) | a_truth(truthteller(b)) | (~a_truth(says(b, not_lower(a, b)))) | (~a_truth(not_lower(a, b))))) <=> ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(truthteller(b)) | a_truth(normal(b)) | (~a_truth(says(b, not_lower(a, b)))) | (~a_truth(not_lower(a, b)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[67])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(normal(b)) | a_truth(truthteller(b)) | (~a_truth(says(b, not_lower(a, b)))) | (~a_truth(not_lower(a, b))))) <=> ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | a_truth(truthteller(b)) | a_truth(normal(b)) | (~a_truth(says(b, not_lower(a, b)))) | (~a_truth(not_lower(a, b))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[68, 66])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(normal(b)) | a_truth(truthteller(b)) | (~a_truth(says(b, not_lower(a, b)))) | (~a_truth(not_lower(a, b))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | a_truth(truthteller(b)) | a_truth(normal(b)) | (~a_truth(says(b, not_lower(a, b)))) | (~a_truth(not_lower(a, b)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (a_truth(truthteller(b)) | a_truth(normal(b)) | (~a_truth(not_lower(a, b)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[71, 65, 55])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (~a_truth(not_lower(a, b))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[72, 52, 21])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 (^[Y: $i, X: $i] : refl((a_truth(lower(X, Y)) | a_truth(not_lower(X, Y))) <=> (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y))) <=> ![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y))) <=> ![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (^[Y: $i, X: $i] : rewrite((a_truth(not_lower(X, Y)) | a_truth(lower(X, Y))) <=> (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(not_lower(X, Y)) | a_truth(lower(X, Y))) <=> ![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.39 tff(79,axiom,(![Y: $i, X: $i] : (a_truth(not_lower(X, Y)) | a_truth(lower(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_lower_or_lower')).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.39 tff(82,plain,(
% 0.20/0.39 ![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[81])).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 (((~![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))) | (a_truth(lower(a, b)) | a_truth(not_lower(a, b)))) <=> ((~![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))) | a_truth(lower(a, b)) | a_truth(not_lower(a, b)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 ((~![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))) | (a_truth(lower(a, b)) | a_truth(not_lower(a, b)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 ((~![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))) | a_truth(lower(a, b)) | a_truth(not_lower(a, b))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (a_truth(lower(a, b)) | a_truth(not_lower(a, b))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[86, 83])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[87, 73, 39])).
% 0.20/0.39 tff(89,plain,(~a_truth(normal(a))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(90,assumption,(~a_truth(normal(a))), introduced(assumption)).
% 0.20/0.39 tff(91,assumption,(~a_truth(liar(a))), introduced(assumption)).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 (a_truth(says(a, lower(a, b))) <=> a_truth(says(a, lower(a, b)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(93,axiom,(a_truth(says(a, lower(a, b)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_says_a_lower_than_b')).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 (a_truth(says(a, lower(a, b)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.39 tff(95,plain,
% 0.20/0.39 (^[Y: $i, X: $i] : refl((a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y))) <=> (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y))) <=> ![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.39 tff(97,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y))) <=> ![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((a_truth(X) | (~a_truth(says(Y, X)))) | a_truth(liar(Y))) <=> ((~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))), ((((a_truth(X) | (~a_truth(says(Y, X)))) | a_truth(liar(Y))) | a_truth(normal(Y))) <=> (((~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y))) | a_truth(normal(Y))))), rewrite((((~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y))) | a_truth(normal(Y))) <=> (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))), ((((a_truth(X) | (~a_truth(says(Y, X)))) | a_truth(liar(Y))) | a_truth(normal(Y))) <=> (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(99,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (((a_truth(X) | (~a_truth(says(Y, X)))) | a_truth(liar(Y))) | a_truth(normal(Y))) <=> ![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.39 tff(100,axiom,(![Y: $i, X: $i] : (((a_truth(X) | (~a_truth(says(Y, X)))) | a_truth(liar(Y))) | a_truth(normal(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ003-0.ax','liars_and_normal_lie')).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.39 tff(102,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.20/0.39 tff(103,plain,(
% 0.20/0.39 ![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[102])).
% 0.20/0.39 tff(104,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.20/0.39 tff(105,plain,
% 0.20/0.39 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | (a_truth(normal(a)) | a_truth(liar(a)) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b)))) <=> ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | a_truth(normal(a)) | a_truth(liar(a)) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(106,plain,
% 0.20/0.39 ((a_truth(normal(a)) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b)) | a_truth(liar(a))) <=> (a_truth(normal(a)) | a_truth(liar(a)) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(107,plain,
% 0.20/0.39 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | (a_truth(normal(a)) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b)) | a_truth(liar(a)))) <=> ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | (a_truth(normal(a)) | a_truth(liar(a)) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.39 tff(108,plain,
% 0.20/0.39 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | (a_truth(normal(a)) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b)) | a_truth(liar(a)))) <=> ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | a_truth(normal(a)) | a_truth(liar(a)) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[107, 105])).
% 0.20/0.39 tff(109,plain,
% 0.20/0.39 ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | (a_truth(normal(a)) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b)) | a_truth(liar(a)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(110,plain,
% 0.20/0.39 ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | a_truth(normal(a)) | a_truth(liar(a)) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.39 tff(111,plain,
% 0.20/0.39 (a_truth(normal(a)) | a_truth(liar(a)) | a_truth(lower(a, b))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[110, 104, 94])).
% 0.20/0.39 tff(112,plain,
% 0.20/0.39 (a_truth(lower(a, b))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[111, 90, 91])).
% 0.20/0.39 tff(113,plain,
% 0.20/0.39 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(truthteller(a)) | a_truth(normal(a)) | (~a_truth(says(a, lower(a, b)))) | (~a_truth(lower(a, b))))) <=> ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | a_truth(truthteller(a)) | a_truth(normal(a)) | (~a_truth(says(a, lower(a, b)))) | (~a_truth(lower(a, b))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(114,plain,
% 0.20/0.40 ((a_truth(normal(a)) | a_truth(truthteller(a)) | (~a_truth(says(a, lower(a, b)))) | (~a_truth(lower(a, b)))) <=> (a_truth(truthteller(a)) | a_truth(normal(a)) | (~a_truth(says(a, lower(a, b)))) | (~a_truth(lower(a, b))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(115,plain,
% 0.20/0.40 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(normal(a)) | a_truth(truthteller(a)) | (~a_truth(says(a, lower(a, b)))) | (~a_truth(lower(a, b))))) <=> ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(truthteller(a)) | a_truth(normal(a)) | (~a_truth(says(a, lower(a, b)))) | (~a_truth(lower(a, b)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[114])).
% 0.20/0.40 tff(116,plain,
% 0.20/0.40 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(normal(a)) | a_truth(truthteller(a)) | (~a_truth(says(a, lower(a, b)))) | (~a_truth(lower(a, b))))) <=> ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | a_truth(truthteller(a)) | a_truth(normal(a)) | (~a_truth(says(a, lower(a, b)))) | (~a_truth(lower(a, b))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[115, 113])).
% 0.20/0.40 tff(117,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(normal(a)) | a_truth(truthteller(a)) | (~a_truth(says(a, lower(a, b)))) | (~a_truth(lower(a, b))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(118,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | a_truth(truthteller(a)) | a_truth(normal(a)) | (~a_truth(says(a, lower(a, b)))) | (~a_truth(lower(a, b)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.40 tff(119,plain,
% 0.20/0.40 (a_truth(truthteller(a)) | a_truth(normal(a)) | (~a_truth(lower(a, b)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[118, 65, 94])).
% 0.20/0.40 tff(120,plain,
% 0.20/0.40 (a_truth(truthteller(a))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[119, 90, 112])).
% 0.20/0.40 tff(121,plain,
% 0.20/0.40 (^[Y: $i, X: $i] : refl(((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y)))) <=> ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(122,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y)))) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[121])).
% 0.20/0.40 tff(123,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y)))) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(124,plain,
% 0.20/0.40 (^[Y: $i, X: $i] : rewrite(((~a_truth(lower(X, Y))) | (~a_truth(truthteller(X)))) <=> ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(125,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(truthteller(X)))) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.40 tff(126,axiom,(![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(truthteller(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','truthtellers_lower_than_no_one')).
% 0.20/0.40 tff(127,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.40 tff(128,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.20/0.40 tff(129,plain,(
% 0.20/0.40 ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[128])).
% 0.20/0.40 tff(130,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.20/0.40 tff(131,plain,
% 0.20/0.40 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))) | ((~a_truth(truthteller(a))) | (~a_truth(lower(a, b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))) | (~a_truth(truthteller(a))) | (~a_truth(lower(a, b))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(132,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))) | ((~a_truth(truthteller(a))) | (~a_truth(lower(a, b))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(133,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))) | (~a_truth(truthteller(a))) | (~a_truth(lower(a, b)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.40 tff(134,plain,
% 0.20/0.40 ((~a_truth(truthteller(a))) | (~a_truth(lower(a, b)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[133, 130])).
% 0.20/0.40 tff(135,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[134, 120, 112])).
% 0.20/0.40 tff(136,plain,(a_truth(normal(a)) | a_truth(liar(a))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(137,plain,
% 0.20/0.40 (a_truth(liar(a))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[136, 90])).
% 0.20/0.40 tff(138,assumption,(~a_truth(truthteller(a))), introduced(assumption)).
% 0.20/0.40 tff(139,plain,
% 0.20/0.40 (~a_truth(lower(a, b))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[119, 90, 138])).
% 0.20/0.40 tff(140,plain,
% 0.20/0.40 (a_truth(not_lower(a, b))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[87, 139])).
% 0.20/0.40 tff(141,plain,
% 0.20/0.40 (^[Y: $i, X: $i] : refl(((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y))) <=> ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(142,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y))) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[141])).
% 0.20/0.40 tff(143,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y))) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(144,plain,
% 0.20/0.40 (^[Y: $i, X: $i] : rewrite((((~a_truth(liar(X))) | (~a_truth(says(X, Y)))) | (~a_truth(Y))) <=> ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(145,plain,
% 0.20/0.40 (![Y: $i, X: $i] : (((~a_truth(liar(X))) | (~a_truth(says(X, Y)))) | (~a_truth(Y))) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[144])).
% 0.20/0.40 tff(146,axiom,(![Y: $i, X: $i] : (((~a_truth(liar(X))) | (~a_truth(says(X, Y)))) | (~a_truth(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ003-0.ax','liars_lie')).
% 0.20/0.40 tff(147,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.40 tff(148,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.20/0.40 tff(149,plain,(
% 0.20/0.40 ![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[148])).
% 0.20/0.40 tff(150,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.20/0.40 tff(151,plain,
% 0.20/0.40 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))) | ((~a_truth(liar(b))) | (~a_truth(says(b, not_lower(a, b)))) | (~a_truth(not_lower(a, b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))) | (~a_truth(liar(b))) | (~a_truth(says(b, not_lower(a, b)))) | (~a_truth(not_lower(a, b))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(152,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))) | ((~a_truth(liar(b))) | (~a_truth(says(b, not_lower(a, b)))) | (~a_truth(not_lower(a, b))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(153,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))) | (~a_truth(liar(b))) | (~a_truth(says(b, not_lower(a, b)))) | (~a_truth(not_lower(a, b)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.40 tff(154,plain,
% 0.20/0.40 ((~a_truth(liar(b))) | (~a_truth(not_lower(a, b)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[153, 150, 55])).
% 0.20/0.40 tff(155,plain,
% 0.20/0.40 (~a_truth(liar(b))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[154, 140])).
% 0.20/0.40 tff(156,plain,
% 0.20/0.40 (^[Y: $i, X: $i] : refl(((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X))) <=> ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(157,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X))) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.40 tff(158,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X))) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(159,plain,
% 0.20/0.40 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~a_truth(not_lower(X, Y))) | (~a_truth(liar(X)))) <=> ((~a_truth(liar(X))) | (~a_truth(not_lower(X, Y))))), ((((~a_truth(not_lower(X, Y))) | (~a_truth(liar(X)))) | a_truth(liar(Y))) <=> (((~a_truth(liar(X))) | (~a_truth(not_lower(X, Y)))) | a_truth(liar(Y))))), rewrite((((~a_truth(liar(X))) | (~a_truth(not_lower(X, Y)))) | a_truth(liar(Y))) <=> ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))))), ((((~a_truth(not_lower(X, Y))) | (~a_truth(liar(X)))) | a_truth(liar(Y))) <=> ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y)))))), (((((~a_truth(not_lower(X, Y))) | (~a_truth(liar(X)))) | a_truth(liar(Y))) | a_truth(lower(Y, X))) <=> (((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y)))) | a_truth(lower(Y, X))))), rewrite((((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y)))) | a_truth(lower(Y, X))) <=> ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))), (((((~a_truth(not_lower(X, Y))) | (~a_truth(liar(X)))) | a_truth(liar(Y))) | a_truth(lower(Y, X))) <=> ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(160,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((((~a_truth(not_lower(X, Y))) | (~a_truth(liar(X)))) | a_truth(liar(Y))) | a_truth(lower(Y, X))) <=> ![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[159])).
% 0.20/0.40 tff(161,axiom,(![Y: $i, X: $i] : ((((~a_truth(not_lower(X, Y))) | (~a_truth(liar(X)))) | a_truth(liar(Y))) | a_truth(lower(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_lower_than_liar')).
% 0.20/0.40 tff(162,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.40 tff(163,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.20/0.40 tff(164,plain,(
% 0.20/0.40 ![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[163])).
% 0.20/0.40 tff(165,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.20/0.40 tff(166,plain,
% 0.20/0.40 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))) | (a_truth(liar(b)) | (~a_truth(liar(a))) | (~a_truth(not_lower(a, b))) | a_truth(lower(b, a)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))) | a_truth(liar(b)) | (~a_truth(liar(a))) | (~a_truth(not_lower(a, b))) | a_truth(lower(b, a)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(167,plain,
% 0.20/0.40 (((~a_truth(liar(a))) | a_truth(liar(b)) | (~a_truth(not_lower(a, b))) | a_truth(lower(b, a))) <=> (a_truth(liar(b)) | (~a_truth(liar(a))) | (~a_truth(not_lower(a, b))) | a_truth(lower(b, a)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(168,plain,
% 0.20/0.40 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))) | ((~a_truth(liar(a))) | a_truth(liar(b)) | (~a_truth(not_lower(a, b))) | a_truth(lower(b, a)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))) | (a_truth(liar(b)) | (~a_truth(liar(a))) | (~a_truth(not_lower(a, b))) | a_truth(lower(b, a))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[167])).
% 0.20/0.40 tff(169,plain,
% 0.20/0.40 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))) | ((~a_truth(liar(a))) | a_truth(liar(b)) | (~a_truth(not_lower(a, b))) | a_truth(lower(b, a)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))) | a_truth(liar(b)) | (~a_truth(liar(a))) | (~a_truth(not_lower(a, b))) | a_truth(lower(b, a)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[168, 166])).
% 0.20/0.40 tff(170,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))) | ((~a_truth(liar(a))) | a_truth(liar(b)) | (~a_truth(not_lower(a, b))) | a_truth(lower(b, a)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(171,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))) | a_truth(liar(b)) | (~a_truth(liar(a))) | (~a_truth(not_lower(a, b))) | a_truth(lower(b, a))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.20/0.40 tff(172,plain,
% 0.20/0.40 (a_truth(liar(b)) | (~a_truth(liar(a))) | (~a_truth(not_lower(a, b))) | a_truth(lower(b, a))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[171, 165])).
% 0.20/0.40 tff(173,plain,
% 0.20/0.40 (a_truth(lower(b, a))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[172, 155, 140, 137])).
% 0.20/0.40 tff(174,plain,
% 0.20/0.40 (^[Y: $i, X: $i] : refl(((~a_truth(lower(X, Y))) | (~a_truth(liar(Y)))) <=> ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(175,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y)))) <=> ![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[174])).
% 0.20/0.40 tff(176,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y)))) <=> ![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(177,axiom,(![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_one_lower_than_liars')).
% 0.20/0.40 tff(178,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.40 tff(179,plain,(
% 0.20/0.40 ![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[178])).
% 0.20/0.40 tff(180,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.20/0.40 tff(181,plain,
% 0.20/0.40 (((~![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))) | ((~a_truth(liar(a))) | (~a_truth(lower(b, a))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))) | (~a_truth(liar(a))) | (~a_truth(lower(b, a))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(182,plain,
% 0.20/0.40 (((~a_truth(lower(b, a))) | (~a_truth(liar(a)))) <=> ((~a_truth(liar(a))) | (~a_truth(lower(b, a))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(183,plain,
% 0.20/0.40 (((~![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))) | ((~a_truth(lower(b, a))) | (~a_truth(liar(a))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))) | ((~a_truth(liar(a))) | (~a_truth(lower(b, a)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[182])).
% 0.20/0.40 tff(184,plain,
% 0.20/0.40 (((~![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))) | ((~a_truth(lower(b, a))) | (~a_truth(liar(a))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))) | (~a_truth(liar(a))) | (~a_truth(lower(b, a))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[183, 181])).
% 0.20/0.40 tff(185,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))) | ((~a_truth(lower(b, a))) | (~a_truth(liar(a))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(186,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))) | (~a_truth(liar(a))) | (~a_truth(lower(b, a)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.20/0.40 tff(187,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[186, 180, 137, 173])).
% 0.20/0.40 tff(188,plain,(a_truth(normal(a)) | a_truth(truthteller(a))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(189,plain,
% 0.20/0.40 (a_truth(truthteller(a))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[188, 89])).
% 0.20/0.40 tff(190,plain,
% 0.20/0.40 (a_truth(liar(a))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[136, 89])).
% 0.20/0.40 tff(191,plain,
% 0.20/0.40 (((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))) | ((~a_truth(liar(a))) | (~a_truth(says(a, lower(a, b)))) | (~a_truth(lower(a, b))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))) | (~a_truth(liar(a))) | (~a_truth(says(a, lower(a, b)))) | (~a_truth(lower(a, b))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(192,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))) | ((~a_truth(liar(a))) | (~a_truth(says(a, lower(a, b)))) | (~a_truth(lower(a, b))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(193,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))) | (~a_truth(liar(a))) | (~a_truth(says(a, lower(a, b)))) | (~a_truth(lower(a, b)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.40 tff(194,plain,
% 0.20/0.40 ((~a_truth(liar(a))) | (~a_truth(lower(a, b)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[193, 150, 94])).
% 0.20/0.40 tff(195,plain,
% 0.20/0.40 (~a_truth(lower(a, b))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[194, 190])).
% 0.20/0.40 tff(196,plain,
% 0.20/0.40 (^[Y: $i, X: $i] : refl(((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y)))) <=> ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(197,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y)))) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[196])).
% 0.20/0.40 tff(198,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y)))) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(199,plain,
% 0.20/0.40 (^[Y: $i, X: $i] : rewrite((((~a_truth(truthteller(X))) | (~a_truth(says(X, Y)))) | a_truth(Y)) <=> ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(200,plain,
% 0.20/0.40 (![Y: $i, X: $i] : (((~a_truth(truthteller(X))) | (~a_truth(says(X, Y)))) | a_truth(Y)) <=> ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[199])).
% 0.20/0.40 tff(201,axiom,(![Y: $i, X: $i] : (((~a_truth(truthteller(X))) | (~a_truth(says(X, Y)))) | a_truth(Y))), file('/export/starexec/sandbox2/benchmark/Axioms/PUZ003-0.ax','truthtellers_tell_truth')).
% 0.20/0.41 tff(202,plain,
% 0.20/0.41 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.20/0.41 tff(203,plain,
% 0.20/0.41 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.20/0.41 tff(204,plain,(
% 0.20/0.41 ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[203])).
% 0.20/0.41 tff(205,plain,
% 0.20/0.41 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.20/0.41 tff(206,plain,
% 0.20/0.41 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))) | ((~a_truth(truthteller(a))) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))) | (~a_truth(truthteller(a))) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(207,plain,
% 0.20/0.41 (((~a_truth(truthteller(a))) | a_truth(lower(a, b)) | (~a_truth(says(a, lower(a, b))))) <=> ((~a_truth(truthteller(a))) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(208,plain,
% 0.20/0.41 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))) | ((~a_truth(truthteller(a))) | a_truth(lower(a, b)) | (~a_truth(says(a, lower(a, b)))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))) | ((~a_truth(truthteller(a))) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[207])).
% 0.20/0.41 tff(209,plain,
% 0.20/0.41 (((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))) | ((~a_truth(truthteller(a))) | a_truth(lower(a, b)) | (~a_truth(says(a, lower(a, b)))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))) | (~a_truth(truthteller(a))) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[208, 206])).
% 0.20/0.41 tff(210,plain,
% 0.20/0.41 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))) | ((~a_truth(truthteller(a))) | a_truth(lower(a, b)) | (~a_truth(says(a, lower(a, b)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(211,plain,
% 0.20/0.41 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))) | (~a_truth(truthteller(a))) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.20/0.41 tff(212,plain,
% 0.20/0.41 ((~a_truth(truthteller(a))) | a_truth(lower(a, b))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[211, 205, 94])).
% 0.20/0.41 tff(213,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[212, 195, 189])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------