TSTP Solution File: PUZ026-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ026-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ026-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 17:44:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(a_truth_type, type, (
% 0.19/0.39 a_truth: $i > $o)).
% 0.19/0.39 tff(truthteller_type, type, (
% 0.19/0.39 truthteller: $i > $i)).
% 0.19/0.39 tff(b_type, type, (
% 0.19/0.39 b: $i)).
% 0.19/0.39 tff(normal_type, type, (
% 0.19/0.39 normal: $i > $i)).
% 0.19/0.39 tff(a_type, type, (
% 0.19/0.39 a: $i)).
% 0.19/0.39 tff(c_type, type, (
% 0.19/0.39 c: $i)).
% 0.19/0.39 tff(liar_type, type, (
% 0.19/0.39 liar: $i > $i)).
% 0.19/0.39 tff(says_type, type, (
% 0.19/0.39 says: ( $i * $i ) > $i)).
% 0.19/0.39 tff(people_type, type, (
% 0.19/0.39 people: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(not_normal_type, type, (
% 0.19/0.39 not_normal: $i > $i)).
% 0.19/0.39 tff(1,assumption,(~a_truth(normal(a))), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (a_truth(says(a, normal(a))) <=> a_truth(says(a, normal(a)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(3,axiom,(a_truth(says(a, normal(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_says_a_normal')).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (a_truth(says(a, normal(a)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.39 tff(10,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')).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.39 tff(13,plain,(
% 0.19/0.39 ![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[12])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (((~![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, normal(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, normal(a)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 ((a_truth(normal(a)) | (~a_truth(says(a, normal(a)))) | a_truth(normal(a)) | a_truth(liar(a))) <=> (a_truth(normal(a)) | a_truth(liar(a)) | (~a_truth(says(a, normal(a)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (((~![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, normal(a)))) | a_truth(normal(a)) | 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, normal(a))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[16])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (((~![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, normal(a)))) | a_truth(normal(a)) | 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, normal(a)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[17, 15])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 ((~![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, normal(a)))) | a_truth(normal(a)) | a_truth(liar(a)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 ((~![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, normal(a))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (a_truth(normal(a)) | a_truth(liar(a))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[20, 14, 4])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (a_truth(liar(a))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[21, 1])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (people(a, b, c) <=> people(a, b, c)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(24,axiom,(people(a, b, c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_b_c_are_people')).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (people(a, b, c)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (^[Z: $i, Y: $i, X: $i] : refl(((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y)))) <=> ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y)))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y)))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (^[Z: $i, Y: $i, X: $i] : rewrite((((~people(X, Y, Z)) | (~a_truth(liar(X)))) | (~a_truth(liar(Y)))) <=> ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : (((~people(X, Y, Z)) | (~a_truth(liar(X)))) | (~a_truth(liar(Y)))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.40 tff(31,axiom,(![Z: $i, Y: $i, X: $i] : (((~people(X, Y, Z)) | (~a_truth(liar(X)))) | (~a_truth(liar(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_two_liars1')).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.19/0.40 tff(34,plain,(
% 0.19/0.40 ![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[33])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))) | ((~a_truth(liar(a))) | (~a_truth(liar(b))) | (~people(a, b, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))) | (~a_truth(liar(a))) | (~a_truth(liar(b))) | (~people(a, b, c)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (((~a_truth(liar(a))) | (~people(a, b, c)) | (~a_truth(liar(b)))) <=> ((~a_truth(liar(a))) | (~a_truth(liar(b))) | (~people(a, b, c)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))) | ((~a_truth(liar(a))) | (~people(a, b, c)) | (~a_truth(liar(b))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))) | ((~a_truth(liar(a))) | (~a_truth(liar(b))) | (~people(a, b, c))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))) | ((~a_truth(liar(a))) | (~people(a, b, c)) | (~a_truth(liar(b))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))) | (~a_truth(liar(a))) | (~a_truth(liar(b))) | (~people(a, b, c)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[38, 36])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))) | ((~a_truth(liar(a))) | (~people(a, b, c)) | (~a_truth(liar(b))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Y))))) | (~a_truth(liar(a))) | (~a_truth(liar(b))) | (~people(a, b, c))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 ((~a_truth(liar(a))) | (~a_truth(liar(b)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[41, 35, 25])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (~a_truth(liar(b))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[42, 22])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (a_truth(says(b, normal(a))) <=> a_truth(says(b, normal(a)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(45,axiom,(a_truth(says(b, normal(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_says_a_normal')).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (a_truth(says(b, normal(a)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (((~![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(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(liar(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(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(liar(b)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 ((a_truth(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(normal(a)) | a_truth(liar(b))) <=> (a_truth(normal(a)) | a_truth(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(liar(b)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | (a_truth(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(normal(a)) | a_truth(liar(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(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(liar(b))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[48])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | (a_truth(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(normal(a)) | a_truth(liar(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(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(liar(b)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[49, 47])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | (a_truth(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(normal(a)) | a_truth(liar(b)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 ((~![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(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(liar(b))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (a_truth(normal(a)) | a_truth(normal(b)) | a_truth(liar(b))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[52, 14, 46])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (a_truth(normal(b))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[53, 43, 1])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (people(b, c, a) <=> people(b, c, a)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(56,axiom,(people(b, c, a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_c_a_are_people')).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (people(b, c, a)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (^[Z: $i, Y: $i, X: $i] : refl(((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y)))) <=> ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y)))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y)))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (^[Z: $i, Y: $i, X: $i] : rewrite((((~people(X, Y, Z)) | (~a_truth(normal(X)))) | (~a_truth(normal(Y)))) <=> ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : (((~people(X, Y, Z)) | (~a_truth(normal(X)))) | (~a_truth(normal(Y)))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.40 tff(63,axiom,(![Z: $i, Y: $i, X: $i] : (((~people(X, Y, Z)) | (~a_truth(normal(X)))) | (~a_truth(normal(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_two_normal1')).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.19/0.40 tff(66,plain,(
% 0.19/0.40 ![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[65])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))) | ((~a_truth(normal(c))) | (~a_truth(normal(b))) | (~people(b, c, a)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))) | (~a_truth(normal(c))) | (~a_truth(normal(b))) | (~people(b, c, a)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (((~a_truth(normal(b))) | (~people(b, c, a)) | (~a_truth(normal(c)))) <=> ((~a_truth(normal(c))) | (~a_truth(normal(b))) | (~people(b, c, a)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))) | ((~a_truth(normal(b))) | (~people(b, c, a)) | (~a_truth(normal(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))) | ((~a_truth(normal(c))) | (~a_truth(normal(b))) | (~people(b, c, a))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))) | ((~a_truth(normal(b))) | (~people(b, c, a)) | (~a_truth(normal(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))) | (~a_truth(normal(c))) | (~a_truth(normal(b))) | (~people(b, c, a)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[70, 68])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))) | ((~a_truth(normal(b))) | (~people(b, c, a)) | (~a_truth(normal(c))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))) | (~a_truth(normal(c))) | (~a_truth(normal(b))) | (~people(b, c, a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 ((~a_truth(normal(c))) | (~a_truth(normal(b)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[73, 67, 57])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (~a_truth(normal(c))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[74, 54])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (^[Z: $i, Y: $i, X: $i] : refl(((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z)))) <=> ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z)))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z)))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (^[Z: $i, Y: $i, X: $i] : rewrite((((~people(X, Y, Z)) | (~a_truth(liar(X)))) | (~a_truth(liar(Z)))) <=> ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (![Z: $i, Y: $i, X: $i] : (((~people(X, Y, Z)) | (~a_truth(liar(X)))) | (~a_truth(liar(Z)))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.41 tff(81,axiom,(![Z: $i, Y: $i, X: $i] : (((~people(X, Y, Z)) | (~a_truth(liar(X)))) | (~a_truth(liar(Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_two_liars2')).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.19/0.41 tff(84,plain,(
% 0.19/0.41 ![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[83])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))) | ((~a_truth(liar(a))) | (~a_truth(liar(c))) | (~people(a, b, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))) | (~a_truth(liar(a))) | (~a_truth(liar(c))) | (~people(a, b, c)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (((~a_truth(liar(a))) | (~people(a, b, c)) | (~a_truth(liar(c)))) <=> ((~a_truth(liar(a))) | (~a_truth(liar(c))) | (~people(a, b, c)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))) | ((~a_truth(liar(a))) | (~people(a, b, c)) | (~a_truth(liar(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))) | ((~a_truth(liar(a))) | (~a_truth(liar(c))) | (~people(a, b, c))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[87])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))) | ((~a_truth(liar(a))) | (~people(a, b, c)) | (~a_truth(liar(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))) | (~a_truth(liar(a))) | (~a_truth(liar(c))) | (~people(a, b, c)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[88, 86])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))) | ((~a_truth(liar(a))) | (~people(a, b, c)) | (~a_truth(liar(c))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(liar(X))) | (~people(X, Y, Z)) | (~a_truth(liar(Z))))) | (~a_truth(liar(a))) | (~a_truth(liar(c))) | (~people(a, b, c))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 ((~a_truth(liar(a))) | (~a_truth(liar(c)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[91, 85, 25])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (~a_truth(liar(c))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[92, 22])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (a_truth(says(c, not_normal(c))) <=> a_truth(says(c, not_normal(c)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(95,axiom,(a_truth(says(c, not_normal(c)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_says_c_not_normal')).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (a_truth(says(c, not_normal(c)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | (a_truth(normal(c)) | (~a_truth(says(c, not_normal(c)))) | a_truth(not_normal(c)) | a_truth(liar(c)))) <=> ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | a_truth(normal(c)) | (~a_truth(says(c, not_normal(c)))) | a_truth(not_normal(c)) | a_truth(liar(c)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | (a_truth(normal(c)) | (~a_truth(says(c, not_normal(c)))) | a_truth(not_normal(c)) | a_truth(liar(c)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | (~a_truth(says(Y, X))) | a_truth(X) | a_truth(liar(Y)))) | a_truth(normal(c)) | (~a_truth(says(c, not_normal(c)))) | a_truth(not_normal(c)) | a_truth(liar(c))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (a_truth(normal(c)) | a_truth(not_normal(c)) | a_truth(liar(c))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[99, 14, 96])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (a_truth(not_normal(c))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[100, 75, 93])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.41 tff(107,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')).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.19/0.41 tff(110,plain,(
% 0.19/0.41 ![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[109])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(normal(c)) | (~a_truth(says(c, not_normal(c)))) | a_truth(truthteller(c)) | (~a_truth(not_normal(c))))) <=> ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | a_truth(normal(c)) | (~a_truth(says(c, not_normal(c)))) | a_truth(truthteller(c)) | (~a_truth(not_normal(c))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 ((a_truth(normal(c)) | a_truth(truthteller(c)) | (~a_truth(says(c, not_normal(c)))) | (~a_truth(not_normal(c)))) <=> (a_truth(normal(c)) | (~a_truth(says(c, not_normal(c)))) | a_truth(truthteller(c)) | (~a_truth(not_normal(c))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(normal(c)) | a_truth(truthteller(c)) | (~a_truth(says(c, not_normal(c)))) | (~a_truth(not_normal(c))))) <=> ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(normal(c)) | (~a_truth(says(c, not_normal(c)))) | a_truth(truthteller(c)) | (~a_truth(not_normal(c)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[113])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(normal(c)) | a_truth(truthteller(c)) | (~a_truth(says(c, not_normal(c)))) | (~a_truth(not_normal(c))))) <=> ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | a_truth(normal(c)) | (~a_truth(says(c, not_normal(c)))) | a_truth(truthteller(c)) | (~a_truth(not_normal(c))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[114, 112])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(normal(c)) | a_truth(truthteller(c)) | (~a_truth(says(c, not_normal(c)))) | (~a_truth(not_normal(c))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | a_truth(normal(c)) | (~a_truth(says(c, not_normal(c)))) | a_truth(truthteller(c)) | (~a_truth(not_normal(c)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (a_truth(normal(c)) | a_truth(truthteller(c)) | (~a_truth(not_normal(c)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[117, 111, 96])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 (a_truth(truthteller(c))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[118, 101, 75])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (^[Liar: $i, Truthteller: $i, Normal: $i] : refl(((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar)))) <=> ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar)))) <=> ![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[120])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar)))) <=> ![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (^[Liar: $i, Truthteller: $i, Normal: $i] : rewrite((((~a_truth(liar(Liar))) | (~a_truth(normal(Normal)))) | (~a_truth(truthteller(Truthteller)))) <=> ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (![Liar: $i, Truthteller: $i, Normal: $i] : (((~a_truth(liar(Liar))) | (~a_truth(normal(Normal)))) | (~a_truth(truthteller(Truthteller)))) <=> ![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.41 tff(125,axiom,(![Liar: $i, Truthteller: $i, Normal: $i] : (((~a_truth(liar(Liar))) | (~a_truth(normal(Normal)))) | (~a_truth(truthteller(Truthteller))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_one_of_each')).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.19/0.41 tff(128,plain,(
% 0.19/0.41 ![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[127])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (((~![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))) | ((~a_truth(liar(a))) | (~a_truth(truthteller(c))) | (~a_truth(normal(b))))) <=> ((~![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))) | (~a_truth(liar(a))) | (~a_truth(truthteller(c))) | (~a_truth(normal(b))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 (((~a_truth(normal(b))) | (~a_truth(truthteller(c))) | (~a_truth(liar(a)))) <=> ((~a_truth(liar(a))) | (~a_truth(truthteller(c))) | (~a_truth(normal(b))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 (((~![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))) | ((~a_truth(normal(b))) | (~a_truth(truthteller(c))) | (~a_truth(liar(a))))) <=> ((~![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))) | ((~a_truth(liar(a))) | (~a_truth(truthteller(c))) | (~a_truth(normal(b)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[131])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (((~![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))) | ((~a_truth(normal(b))) | (~a_truth(truthteller(c))) | (~a_truth(liar(a))))) <=> ((~![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))) | (~a_truth(liar(a))) | (~a_truth(truthteller(c))) | (~a_truth(normal(b))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[132, 130])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 ((~![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))) | ((~a_truth(normal(b))) | (~a_truth(truthteller(c))) | (~a_truth(liar(a))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 ((~![Liar: $i, Truthteller: $i, Normal: $i] : ((~a_truth(normal(Normal))) | (~a_truth(truthteller(Truthteller))) | (~a_truth(liar(Liar))))) | (~a_truth(liar(a))) | (~a_truth(truthteller(c))) | (~a_truth(normal(b)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[135, 129, 22, 54, 119])).
% 0.19/0.42 tff(137,plain,(a_truth(normal(a))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))) | ((~a_truth(normal(a))) | (~people(a, b, c)) | (~a_truth(normal(b))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))) | (~a_truth(normal(a))) | (~people(a, b, c)) | (~a_truth(normal(b))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))) | ((~a_truth(normal(a))) | (~people(a, b, c)) | (~a_truth(normal(b))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Y))))) | (~a_truth(normal(a))) | (~people(a, b, c)) | (~a_truth(normal(b)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 ((~a_truth(normal(a))) | (~a_truth(normal(b)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[140, 67, 25])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (~a_truth(normal(b))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[141, 137])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (((~![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(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(truthteller(b)))) <=> ((~![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(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(truthteller(b)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 ((a_truth(normal(b)) | a_truth(truthteller(b)) | (~a_truth(says(b, normal(a)))) | (~a_truth(normal(a)))) <=> ((~a_truth(normal(a))) | a_truth(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(truthteller(b)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(normal(b)) | a_truth(truthteller(b)) | (~a_truth(says(b, normal(a)))) | (~a_truth(normal(a))))) <=> ((~![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(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(truthteller(b))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[144])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(normal(b)) | a_truth(truthteller(b)) | (~a_truth(says(b, normal(a)))) | (~a_truth(normal(a))))) <=> ((~![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(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(truthteller(b)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[145, 143])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 ((~![Y: $i, X: $i] : (a_truth(normal(Y)) | a_truth(truthteller(Y)) | (~a_truth(says(Y, X))) | (~a_truth(X)))) | (a_truth(normal(b)) | a_truth(truthteller(b)) | (~a_truth(says(b, normal(a)))) | (~a_truth(normal(a))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 ((~![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(normal(b)) | (~a_truth(says(b, normal(a)))) | a_truth(truthteller(b))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 ((~a_truth(normal(a))) | a_truth(normal(b)) | a_truth(truthteller(b))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[148, 111, 46])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (a_truth(truthteller(b))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[149, 142, 137])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 (^[Z: $i, Y: $i, X: $i] : refl(((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z)))) <=> ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 (![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z)))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[151])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 (![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z)))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 (^[Z: $i, Y: $i, X: $i] : rewrite((((~people(X, Y, Z)) | (~a_truth(normal(X)))) | (~a_truth(normal(Z)))) <=> ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 (![Z: $i, Y: $i, X: $i] : (((~people(X, Y, Z)) | (~a_truth(normal(X)))) | (~a_truth(normal(Z)))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[154])).
% 0.19/0.42 tff(156,axiom,(![Z: $i, Y: $i, X: $i] : (((~people(X, Y, Z)) | (~a_truth(normal(X)))) | (~a_truth(normal(Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_two_normal2')).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 (![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.42 tff(158,plain,
% 0.19/0.42 (![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.19/0.42 tff(159,plain,(
% 0.19/0.42 ![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[158])).
% 0.19/0.42 tff(160,plain,
% 0.19/0.42 (![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[159, 152])).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))) | ((~a_truth(normal(a))) | (~a_truth(normal(c))) | (~people(a, b, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))) | (~a_truth(normal(a))) | (~a_truth(normal(c))) | (~people(a, b, c)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(162,plain,
% 0.19/0.42 (((~a_truth(normal(a))) | (~people(a, b, c)) | (~a_truth(normal(c)))) <=> ((~a_truth(normal(a))) | (~a_truth(normal(c))) | (~people(a, b, c)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(163,plain,
% 0.19/0.42 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))) | ((~a_truth(normal(a))) | (~people(a, b, c)) | (~a_truth(normal(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))) | ((~a_truth(normal(a))) | (~a_truth(normal(c))) | (~people(a, b, c))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[162])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))) | ((~a_truth(normal(a))) | (~people(a, b, c)) | (~a_truth(normal(c))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))) | (~a_truth(normal(a))) | (~a_truth(normal(c))) | (~people(a, b, c)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[163, 161])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))) | ((~a_truth(normal(a))) | (~people(a, b, c)) | (~a_truth(normal(c))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(166,plain,
% 0.19/0.42 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(normal(X))) | (~people(X, Y, Z)) | (~a_truth(normal(Z))))) | (~a_truth(normal(a))) | (~a_truth(normal(c))) | (~people(a, b, c))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.19/0.42 tff(167,plain,
% 0.19/0.42 ((~a_truth(normal(a))) | (~a_truth(normal(c)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[166, 160, 25])).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 (~a_truth(normal(c))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[167, 137])).
% 0.19/0.42 tff(169,plain,
% 0.19/0.42 (^[X: $i] : refl((a_truth(normal(X)) | a_truth(not_normal(X))) <=> (a_truth(normal(X)) | a_truth(not_normal(X))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(170,plain,
% 0.19/0.42 (![X: $i] : (a_truth(normal(X)) | a_truth(not_normal(X))) <=> ![X: $i] : (a_truth(normal(X)) | a_truth(not_normal(X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[169])).
% 0.19/0.42 tff(171,plain,
% 0.19/0.42 (![X: $i] : (a_truth(normal(X)) | a_truth(not_normal(X))) <=> ![X: $i] : (a_truth(normal(X)) | a_truth(not_normal(X)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(172,plain,
% 0.19/0.42 (^[X: $i] : rewrite((a_truth(not_normal(X)) | a_truth(normal(X))) <=> (a_truth(normal(X)) | a_truth(not_normal(X))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(173,plain,
% 0.19/0.42 (![X: $i] : (a_truth(not_normal(X)) | a_truth(normal(X))) <=> ![X: $i] : (a_truth(normal(X)) | a_truth(not_normal(X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[172])).
% 0.19/0.42 tff(174,axiom,(![X: $i] : (a_truth(not_normal(X)) | a_truth(normal(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','normal_or_not_normal')).
% 0.19/0.42 tff(175,plain,
% 0.19/0.42 (![X: $i] : (a_truth(normal(X)) | a_truth(not_normal(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.19/0.42 tff(176,plain,
% 0.19/0.42 (![X: $i] : (a_truth(normal(X)) | a_truth(not_normal(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.19/0.42 tff(177,plain,(
% 0.19/0.42 ![X: $i] : (a_truth(normal(X)) | a_truth(not_normal(X)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[176])).
% 0.19/0.42 tff(178,plain,
% 0.19/0.42 (![X: $i] : (a_truth(normal(X)) | a_truth(not_normal(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.19/0.42 tff(179,plain,
% 0.19/0.42 (((~![X: $i] : (a_truth(normal(X)) | a_truth(not_normal(X)))) | (a_truth(normal(c)) | a_truth(not_normal(c)))) <=> ((~![X: $i] : (a_truth(normal(X)) | a_truth(not_normal(X)))) | a_truth(normal(c)) | a_truth(not_normal(c)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(180,plain,
% 0.19/0.42 ((~![X: $i] : (a_truth(normal(X)) | a_truth(not_normal(X)))) | (a_truth(normal(c)) | a_truth(not_normal(c)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(181,plain,
% 0.19/0.42 ((~![X: $i] : (a_truth(normal(X)) | a_truth(not_normal(X)))) | a_truth(normal(c)) | a_truth(not_normal(c))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.42 tff(182,plain,
% 0.19/0.42 (a_truth(normal(c)) | a_truth(not_normal(c))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[181, 178])).
% 0.19/0.42 tff(183,plain,
% 0.19/0.42 (a_truth(not_normal(c))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[182, 168])).
% 0.19/0.42 tff(184,plain,
% 0.19/0.42 (a_truth(truthteller(c))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[118, 183, 168])).
% 0.19/0.42 tff(185,plain,
% 0.19/0.42 (^[Z: $i, Y: $i, X: $i] : refl(((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z))) <=> ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(186,plain,
% 0.19/0.42 (![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[185])).
% 0.19/0.42 tff(187,plain,
% 0.19/0.42 (![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(188,plain,
% 0.19/0.42 (^[Z: $i, Y: $i, X: $i] : rewrite((((~people(X, Y, Z)) | (~a_truth(truthteller(X)))) | (~a_truth(truthteller(Y)))) <=> ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(189,plain,
% 0.19/0.42 (![Z: $i, Y: $i, X: $i] : (((~people(X, Y, Z)) | (~a_truth(truthteller(X)))) | (~a_truth(truthteller(Y)))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[188])).
% 0.19/0.42 tff(190,axiom,(![Z: $i, Y: $i, X: $i] : (((~people(X, Y, Z)) | (~a_truth(truthteller(X)))) | (~a_truth(truthteller(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_two_truthtellers1')).
% 0.19/0.42 tff(191,plain,
% 0.19/0.42 (![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.19/0.42 tff(192,plain,
% 0.19/0.42 (![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[191, 187])).
% 0.19/0.42 tff(193,plain,(
% 0.19/0.42 ![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[192])).
% 0.19/0.42 tff(194,plain,
% 0.19/0.42 (![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[193, 186])).
% 0.19/0.42 tff(195,plain,
% 0.19/0.42 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z)))) | ((~a_truth(truthteller(b))) | (~a_truth(truthteller(c))) | (~people(b, c, a)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z)))) | (~a_truth(truthteller(b))) | (~a_truth(truthteller(c))) | (~people(b, c, a)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(196,plain,
% 0.19/0.42 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z)))) | ((~a_truth(truthteller(b))) | (~a_truth(truthteller(c))) | (~people(b, c, a)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(197,plain,
% 0.19/0.42 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(truthteller(X))) | (~a_truth(truthteller(Y))) | (~people(X, Y, Z)))) | (~a_truth(truthteller(b))) | (~a_truth(truthteller(c))) | (~people(b, c, a))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.19/0.42 tff(198,plain,
% 0.19/0.42 ((~a_truth(truthteller(b))) | (~a_truth(truthteller(c)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[197, 194, 57])).
% 0.19/0.42 tff(199,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[198, 184, 150])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------