TSTP Solution File: PUZ027-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ027-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Sun Sep 18 14:10:55 EDT 2022
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : PUZ027-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 18:21:31 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(a_truth_type, type, (
% 0.13/0.40 a_truth: $i > $o)).
% 0.13/0.40 tff(truthteller_type, type, (
% 0.13/0.40 truthteller: $i > $i)).
% 0.13/0.40 tff(a_type, type, (
% 0.13/0.40 a: $i)).
% 0.13/0.40 tff(normal_type, type, (
% 0.13/0.40 normal: $i > $i)).
% 0.13/0.40 tff(lower_type, type, (
% 0.13/0.40 lower: ( $i * $i ) > $i)).
% 0.13/0.40 tff(b_type, type, (
% 0.13/0.40 b: $i)).
% 0.13/0.40 tff(answer_type, type, (
% 0.13/0.40 answer: $i > $o)).
% 0.13/0.40 tff(a_normal_b_truthteller_type, type, (
% 0.13/0.40 a_normal_b_truthteller: $i)).
% 0.13/0.40 tff(not_lower_type, type, (
% 0.13/0.40 not_lower: ( $i * $i ) > $i)).
% 0.13/0.40 tff(a_and_b_normal_type, type, (
% 0.13/0.40 a_and_b_normal: $i)).
% 0.13/0.40 tff(says_type, type, (
% 0.13/0.40 says: ( $i * $i ) > $i)).
% 0.13/0.40 tff(liar_type, type, (
% 0.13/0.40 liar: $i > $i)).
% 0.13/0.40 tff(1,assumption,(a_truth(normal(a))), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (^[Answer: $i] : refl((~answer(Answer)) <=> (~answer(Answer)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![Answer: $i] : (~answer(Answer)) <=> ![Answer: $i] : (~answer(Answer))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (![Answer: $i] : (~answer(Answer)) <=> ![Answer: $i] : (~answer(Answer))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(5,axiom,(![Answer: $i] : (~answer(Answer))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_there_is_an_answer')).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (![Answer: $i] : (~answer(Answer))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.40 tff(7,plain,(
% 0.13/0.40 ![Answer: $i] : (~answer(Answer))),
% 0.13/0.40 inference(skolemize,[status(sab)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (![Answer: $i] : (~answer(Answer))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.40 tff(9,assumption,(answer(a_normal_b_truthteller)), introduced(assumption)).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 ((~![Answer: $i] : (~answer(Answer))) | (~answer(a_normal_b_truthteller))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[10, 9, 8])).
% 0.13/0.40 tff(12,plain,(~answer(a_normal_b_truthteller)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (((~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))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 ((((~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))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(15,axiom,(((~a_truth(normal(a))) | (~a_truth(truthteller(b)))) | answer(a_normal_b_truthteller)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_normal_b_truthteller')).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 ((~a_truth(truthteller(b))) | (~a_truth(normal(a))) | answer(a_normal_b_truthteller)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (~a_truth(truthteller(b))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[23, 1, 12])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (![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))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (![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))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (^[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))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 (![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))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.13/0.41 tff(30,axiom,(![Y: $i, X: $i] : (((~a_truth(lower(X, Y))) | (~a_truth(normal(X)))) | a_truth(truthteller(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','truthtellers_highest')).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 (![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 (![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.13/0.41 tff(33,plain,(
% 0.13/0.41 ![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[32])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 (![Y: $i, X: $i] : ((~a_truth(normal(X))) | a_truth(truthteller(Y)) | (~a_truth(lower(X, Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 (((~![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))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 (((~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))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 (((~![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)))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[36])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 (((~![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))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[37, 35])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 ((~![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))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 ((~![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)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 (a_truth(truthteller(b)) | (~a_truth(normal(a))) | (~a_truth(lower(a, b)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[40, 34])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 (~a_truth(lower(a, b))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[41, 24, 1])).
% 0.13/0.41 tff(43,assumption,(answer(a_and_b_normal)), introduced(assumption)).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 ((~![Answer: $i] : (~answer(Answer))) | (~answer(a_and_b_normal))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[44, 43, 8])).
% 0.13/0.41 tff(46,plain,(~answer(a_and_b_normal)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (((~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))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 ((((~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))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(49,axiom,(((~a_truth(normal(a))) | (~a_truth(normal(b)))) | answer(a_and_b_normal)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_and_b_normal')).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[50, 47])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[52, 47])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[53, 47])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[55, 47])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 ((~a_truth(normal(b))) | (~a_truth(normal(a))) | answer(a_and_b_normal)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[56, 47])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (~a_truth(normal(b))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[57, 1, 46])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (a_truth(says(b, not_lower(a, b))) <=> a_truth(says(b, not_lower(a, b)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(60,axiom,(a_truth(says(b, not_lower(a, b)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b_says_a_not_lower_than_b')).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (a_truth(says(b, not_lower(a, b)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[62])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 (^[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)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[65])).
% 0.13/0.41 tff(67,axiom,(![Y: $i, X: $i] : ((((~a_truth(X)) | (~a_truth(says(Y, X)))) | a_truth(truthteller(Y))) | a_truth(normal(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/PUZ003-0.ax','truthtellers_and_normal_tell_truth')).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 (![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 (![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.13/0.41 tff(70,plain,(
% 0.13/0.41 ![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[69])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 (![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 (((~![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))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 ((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))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 (((~![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)))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[73])).
% 0.13/0.41 tff(75,plain,
% 0.13/0.41 (((~![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))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[74, 72])).
% 0.13/0.41 tff(76,plain,
% 0.13/0.41 ((~![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))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(77,plain,
% 0.13/0.41 ((~![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)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.13/0.41 tff(78,plain,
% 0.13/0.41 (a_truth(truthteller(b)) | a_truth(normal(b)) | (~a_truth(not_lower(a, b)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[77, 71, 61])).
% 0.13/0.41 tff(79,plain,
% 0.13/0.41 (~a_truth(not_lower(a, b))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[78, 58, 24])).
% 0.13/0.41 tff(80,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(81,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.13/0.41 tff(82,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(83,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(84,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[83])).
% 0.13/0.41 tff(85,axiom,(![Y: $i, X: $i] : (a_truth(not_lower(X, Y)) | a_truth(lower(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_lower_or_lower')).
% 0.13/0.41 tff(86,plain,
% 0.13/0.41 (![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.13/0.41 tff(87,plain,
% 0.13/0.41 (![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.13/0.41 tff(88,plain,(
% 0.13/0.41 ![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[87])).
% 0.13/0.41 tff(89,plain,
% 0.13/0.41 (![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.13/0.41 tff(90,plain,
% 0.13/0.41 (((~![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)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(91,plain,
% 0.13/0.41 ((~![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)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(92,plain,
% 0.13/0.41 ((~![Y: $i, X: $i] : (a_truth(lower(X, Y)) | a_truth(not_lower(X, Y)))) | a_truth(lower(a, b)) | a_truth(not_lower(a, b))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.13/0.41 tff(93,plain,
% 0.13/0.41 (a_truth(lower(a, b)) | a_truth(not_lower(a, b))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[92, 89])).
% 0.13/0.41 tff(94,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[93, 79, 42])).
% 0.13/0.41 tff(95,plain,(~a_truth(normal(a))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(96,assumption,(~a_truth(normal(a))), introduced(assumption)).
% 0.13/0.41 tff(97,assumption,(~a_truth(liar(a))), introduced(assumption)).
% 0.13/0.41 tff(98,plain,
% 0.13/0.41 (a_truth(says(a, lower(a, b))) <=> a_truth(says(a, lower(a, b)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(99,axiom,(a_truth(says(a, lower(a, b)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_says_a_lower_than_b')).
% 0.13/0.41 tff(100,plain,
% 0.13/0.41 (a_truth(says(a, lower(a, b)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.13/0.41 tff(101,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(102,plain,
% 0.13/0.42 (![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)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[101])).
% 0.13/0.42 tff(103,plain,
% 0.13/0.42 (![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)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(104,plain,
% 0.13/0.42 (^[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)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(105,plain,
% 0.13/0.42 (![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)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[104])).
% 0.13/0.42 tff(106,axiom,(![Y: $i, X: $i] : (((a_truth(X) | (~a_truth(says(Y, X)))) | a_truth(liar(Y))) | a_truth(normal(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/PUZ003-0.ax','liars_and_normal_lie')).
% 0.13/0.42 tff(107,plain,
% 0.13/0.42 (![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.13/0.42 tff(108,plain,
% 0.13/0.42 (![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.13/0.42 tff(109,plain,(
% 0.13/0.42 ![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.13/0.42 inference(skolemize,[status(sab)],[108])).
% 0.13/0.42 tff(110,plain,
% 0.13/0.42 (![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.13/0.42 tff(111,plain,
% 0.13/0.42 (((~![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)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(112,plain,
% 0.13/0.42 ((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)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(113,plain,
% 0.13/0.42 (((~![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))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[112])).
% 0.13/0.42 tff(114,plain,
% 0.13/0.42 (((~![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)))),
% 0.13/0.42 inference(transitivity,[status(thm)],[113, 111])).
% 0.13/0.42 tff(115,plain,
% 0.13/0.42 ((~![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)))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(116,plain,
% 0.13/0.42 ((~![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))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.13/0.42 tff(117,plain,
% 0.13/0.42 (a_truth(normal(a)) | a_truth(liar(a)) | a_truth(lower(a, b))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[116, 110, 100])).
% 0.13/0.42 tff(118,plain,
% 0.13/0.42 (a_truth(lower(a, b))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[117, 96, 97])).
% 0.13/0.42 tff(119,plain,
% 0.13/0.42 (((~![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))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(120,plain,
% 0.13/0.42 ((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))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(121,plain,
% 0.13/0.42 (((~![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)))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[120])).
% 0.13/0.42 tff(122,plain,
% 0.13/0.42 (((~![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))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[121, 119])).
% 0.13/0.42 tff(123,plain,
% 0.13/0.42 ((~![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))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(124,plain,
% 0.13/0.42 ((~![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)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.13/0.42 tff(125,plain,
% 0.13/0.42 (a_truth(truthteller(a)) | a_truth(normal(a)) | (~a_truth(lower(a, b)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[124, 71, 100])).
% 0.13/0.42 tff(126,plain,
% 0.13/0.42 (a_truth(truthteller(a))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[125, 96, 118])).
% 0.13/0.42 tff(127,plain,
% 0.13/0.42 (^[Y: $i, X: $i] : refl(((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y)))) <=> ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(128,plain,
% 0.13/0.42 (![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))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[127])).
% 0.13/0.42 tff(129,plain,
% 0.13/0.42 (![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))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(130,plain,
% 0.13/0.42 (^[Y: $i, X: $i] : rewrite(((~a_truth(lower(X, Y))) | (~a_truth(truthteller(X)))) <=> ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(131,plain,
% 0.13/0.42 (![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))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[130])).
% 0.13/0.42 tff(132,axiom,(![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(truthteller(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','truthtellers_lower_than_no_one')).
% 0.13/0.42 tff(133,plain,
% 0.13/0.42 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.13/0.42 tff(134,plain,
% 0.13/0.42 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.13/0.42 tff(135,plain,(
% 0.13/0.42 ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[134])).
% 0.13/0.42 tff(136,plain,
% 0.13/0.42 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.13/0.42 tff(137,plain,
% 0.13/0.42 (((~![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))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(138,plain,
% 0.13/0.42 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))) | ((~a_truth(truthteller(a))) | (~a_truth(lower(a, b))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(139,plain,
% 0.13/0.42 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(lower(X, Y))))) | (~a_truth(truthteller(a))) | (~a_truth(lower(a, b)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.13/0.42 tff(140,plain,
% 0.13/0.42 ((~a_truth(truthteller(a))) | (~a_truth(lower(a, b)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[139, 136])).
% 0.13/0.42 tff(141,plain,
% 0.13/0.42 ($false),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[140, 126, 118])).
% 0.13/0.42 tff(142,plain,(a_truth(normal(a)) | a_truth(liar(a))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.42 tff(143,plain,
% 0.13/0.42 (a_truth(liar(a))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[142, 96])).
% 0.13/0.42 tff(144,assumption,(~a_truth(truthteller(a))), introduced(assumption)).
% 0.13/0.42 tff(145,plain,
% 0.13/0.42 (~a_truth(lower(a, b))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[125, 96, 144])).
% 0.13/0.42 tff(146,plain,
% 0.13/0.42 (a_truth(not_lower(a, b))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[93, 145])).
% 0.13/0.42 tff(147,plain,
% 0.13/0.42 (^[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))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(148,plain,
% 0.13/0.42 (![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)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[147])).
% 0.13/0.42 tff(149,plain,
% 0.13/0.42 (![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)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(150,plain,
% 0.13/0.42 (^[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))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(151,plain,
% 0.13/0.42 (![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)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[150])).
% 0.13/0.42 tff(152,axiom,(![Y: $i, X: $i] : (((~a_truth(liar(X))) | (~a_truth(says(X, Y)))) | (~a_truth(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/PUZ003-0.ax','liars_lie')).
% 0.13/0.42 tff(153,plain,
% 0.13/0.42 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.42 tff(154,plain,
% 0.20/0.42 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.20/0.42 tff(155,plain,(
% 0.20/0.42 ![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[154])).
% 0.20/0.42 tff(156,plain,
% 0.20/0.42 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | (~a_truth(says(X, Y))) | (~a_truth(Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.20/0.42 tff(157,plain,
% 0.20/0.42 (((~![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))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(158,plain,
% 0.20/0.42 ((~![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))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(159,plain,
% 0.20/0.42 ((~![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)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.42 tff(160,plain,
% 0.20/0.42 ((~a_truth(liar(b))) | (~a_truth(not_lower(a, b)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[159, 156, 61])).
% 0.20/0.42 tff(161,plain,
% 0.20/0.42 (~a_truth(liar(b))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[160, 146])).
% 0.20/0.42 tff(162,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(163,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[162])).
% 0.20/0.42 tff(164,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(165,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(166,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[165])).
% 0.20/0.43 tff(167,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/sandbox/benchmark/theBenchmark.p','not_lower_than_liar')).
% 0.20/0.43 tff(168,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.43 tff(169,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.20/0.43 tff(170,plain,(
% 0.20/0.43 ![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[169])).
% 0.20/0.43 tff(171,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((~a_truth(liar(X))) | a_truth(liar(Y)) | (~a_truth(not_lower(X, Y))) | a_truth(lower(Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.20/0.43 tff(172,plain,
% 0.20/0.43 (((~![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(173,plain,
% 0.20/0.43 (((~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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(174,plain,
% 0.20/0.43 (((~![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))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[173])).
% 0.20/0.43 tff(175,plain,
% 0.20/0.43 (((~![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)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[174, 172])).
% 0.20/0.43 tff(176,plain,
% 0.20/0.43 ((~![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)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(177,plain,
% 0.20/0.43 ((~![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))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.20/0.43 tff(178,plain,
% 0.20/0.43 (a_truth(liar(b)) | (~a_truth(liar(a))) | (~a_truth(not_lower(a, b))) | a_truth(lower(b, a))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[177, 171])).
% 0.20/0.43 tff(179,plain,
% 0.20/0.43 (a_truth(lower(b, a))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[178, 161, 146, 143])).
% 0.20/0.43 tff(180,plain,
% 0.20/0.43 (^[Y: $i, X: $i] : refl(((~a_truth(lower(X, Y))) | (~a_truth(liar(Y)))) <=> ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(181,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[180])).
% 0.20/0.43 tff(182,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(183,axiom,(![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','no_one_lower_than_liars')).
% 0.20/0.43 tff(184,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.20/0.43 tff(185,plain,(
% 0.20/0.43 ![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[184])).
% 0.20/0.43 tff(186,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.20/0.43 tff(187,plain,
% 0.20/0.43 (((~![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))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(188,plain,
% 0.20/0.43 (((~a_truth(lower(b, a))) | (~a_truth(liar(a)))) <=> ((~a_truth(liar(a))) | (~a_truth(lower(b, a))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(189,plain,
% 0.20/0.43 (((~![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)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[188])).
% 0.20/0.43 tff(190,plain,
% 0.20/0.43 (((~![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))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[189, 187])).
% 0.20/0.43 tff(191,plain,
% 0.20/0.43 ((~![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))) | ((~a_truth(lower(b, a))) | (~a_truth(liar(a))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(192,plain,
% 0.20/0.43 ((~![Y: $i, X: $i] : ((~a_truth(lower(X, Y))) | (~a_truth(liar(Y))))) | (~a_truth(liar(a))) | (~a_truth(lower(b, a)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.43 tff(193,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[192, 186, 143, 179])).
% 0.20/0.43 tff(194,plain,(a_truth(normal(a)) | a_truth(truthteller(a))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(195,plain,
% 0.20/0.43 (a_truth(truthteller(a))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[194, 95])).
% 0.20/0.43 tff(196,plain,
% 0.20/0.43 (a_truth(liar(a))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[142, 95])).
% 0.20/0.43 tff(197,plain,
% 0.20/0.43 (((~![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))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(198,plain,
% 0.20/0.43 ((~![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))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(199,plain,
% 0.20/0.43 ((~![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)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.43 tff(200,plain,
% 0.20/0.43 ((~a_truth(liar(a))) | (~a_truth(lower(a, b)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[199, 156, 100])).
% 0.20/0.43 tff(201,plain,
% 0.20/0.43 (~a_truth(lower(a, b))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[200, 196])).
% 0.20/0.43 tff(202,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(203,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[202])).
% 0.20/0.43 tff(204,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(205,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(206,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[205])).
% 0.20/0.43 tff(207,axiom,(![Y: $i, X: $i] : (((~a_truth(truthteller(X))) | (~a_truth(says(X, Y)))) | a_truth(Y))), file('/export/starexec/sandbox/benchmark/Axioms/PUZ003-0.ax','truthtellers_tell_truth')).
% 0.20/0.43 tff(208,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.20/0.43 tff(209,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.20/0.43 tff(210,plain,(
% 0.20/0.43 ![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[209])).
% 0.20/0.43 tff(211,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.20/0.43 tff(212,plain,
% 0.20/0.43 (((~![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(213,plain,
% 0.20/0.43 (((~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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(214,plain,
% 0.20/0.43 (((~![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))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[213])).
% 0.20/0.43 tff(215,plain,
% 0.20/0.43 (((~![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)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[214, 212])).
% 0.20/0.43 tff(216,plain,
% 0.20/0.43 ((~![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)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(217,plain,
% 0.20/0.43 ((~![Y: $i, X: $i] : ((~a_truth(truthteller(X))) | a_truth(Y) | (~a_truth(says(X, Y))))) | (~a_truth(truthteller(a))) | (~a_truth(says(a, lower(a, b)))) | a_truth(lower(a, b))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.20/0.43 tff(218,plain,
% 0.20/0.43 ((~a_truth(truthteller(a))) | a_truth(lower(a, b))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[217, 211, 100])).
% 0.20/0.43 tff(219,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[218, 201, 195])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------