TSTP Solution File: PUZ035-4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ035-4 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 14:11:01 EDT 2022
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : PUZ035-4 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Sep 2 18:36:16 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(truth_type, type, (
% 0.21/0.40 truth: $i > $o)).
% 0.21/0.40 tff(not_type, type, (
% 0.21/0.40 not: $i > $i)).
% 0.21/0.40 tff(or_type, type, (
% 0.21/0.40 or: ( $i * $i ) > $i)).
% 0.21/0.40 tff(isa_type, type, (
% 0.21/0.40 isa: ( $i * $i ) > $i)).
% 0.21/0.40 tff(knight_type, type, (
% 0.21/0.40 knight: $i)).
% 0.21/0.40 tff(other_type, type, (
% 0.21/0.40 other: $i)).
% 0.21/0.40 tff(asked_type, type, (
% 0.21/0.40 asked: $i)).
% 0.21/0.40 tff(knave_type, type, (
% 0.21/0.40 knave: $i)).
% 0.21/0.40 tff(says_type, type, (
% 0.21/0.40 says: ( $i * $i ) > $o)).
% 0.21/0.40 tff(person_type, type, (
% 0.21/0.40 person: $i > $o)).
% 0.21/0.40 tff(1,assumption,(truth(isa(other, knight))), introduced(assumption)).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 (^[S: $i, P2: $i, P1: $i] : refl(((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1)))) <=> ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1)))) <=> ![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.40 tff(4,plain,
% 0.21/0.40 (![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1)))) <=> ![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (^[S: $i, P2: $i, P1: $i] : rewrite((((~truth(isa(asked, P1))) | (~truth(isa(other, P2)))) | (~says(asked, S))) <=> ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (![S: $i, P2: $i, P1: $i] : (((~truth(isa(asked, P1))) | (~truth(isa(other, P2)))) | (~says(asked, S))) <=> ![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.40 tff(7,axiom,(![S: $i, P2: $i, P1: $i] : (((~truth(isa(asked, P1))) | (~truth(isa(other, P2)))) | (~says(asked, S)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_answer')).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.40 tff(10,plain,(
% 0.21/0.40 ![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[9])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 (![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.21/0.40 tff(12,assumption,(says(asked, or(isa(asked, knight), isa(other, knight)))), introduced(assumption)).
% 0.21/0.40 tff(13,assumption,(truth(isa(asked, knight))), introduced(assumption)).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knight))))) <=> ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knight))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knight))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knight)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 ((~truth(isa(other, knight))) | (~truth(isa(asked, knight)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[16, 12, 11])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 (~truth(isa(other, knight))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[17, 13])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (person(other) <=> person(other)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(20,axiom,(person(other)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','other_person')).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (person(other)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (^[P: $i] : refl((truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P))) <=> (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P))) <=> ![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P))) <=> ![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (^[P: $i] : rewrite((((~person(P)) | truth(isa(P, knight))) | truth(isa(P, knave))) <=> (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (![P: $i] : (((~person(P)) | truth(isa(P, knight))) | truth(isa(P, knave))) <=> ![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.41 tff(27,axiom,(![P: $i] : (((~person(P)) | truth(isa(P, knight))) | truth(isa(P, knave)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','everyone_a_knight_or_knave')).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.21/0.41 tff(30,plain,(
% 0.21/0.41 ![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[29])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))) | (truth(isa(other, knave)) | truth(isa(other, knight)) | (~person(other)))) <=> ((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))) | truth(isa(other, knave)) | truth(isa(other, knight)) | (~person(other)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 ((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))) | (truth(isa(other, knave)) | truth(isa(other, knight)) | (~person(other)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 ((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))) | truth(isa(other, knave)) | truth(isa(other, knight)) | (~person(other))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (truth(isa(other, knave)) | truth(isa(other, knight))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (truth(isa(other, knave))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[35, 18])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(asked, knight))) | (~truth(isa(other, knave))))) <=> ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(asked, knight))) | (~truth(isa(other, knave))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (((~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(other, knave))) | (~truth(isa(asked, knight)))) <=> ((~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(asked, knight))) | (~truth(isa(other, knave))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(other, knave))) | (~truth(isa(asked, knight))))) <=> ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(asked, knight))) | (~truth(isa(other, knave)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[38])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(other, knave))) | (~truth(isa(asked, knight))))) <=> ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(asked, knight))) | (~truth(isa(other, knave))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[39, 37])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(other, knave))) | (~truth(isa(asked, knight))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(asked, knight))) | (~truth(isa(other, knave)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[42, 12, 11, 13, 36])).
% 0.21/0.41 tff(44,plain,((~truth(isa(asked, knight))) | (~says(asked, or(isa(asked, knight), isa(other, knight))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (~truth(isa(asked, knight))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[44, 12])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (^[S: $i, P: $i] : refl((truth(isa(P, knight)) | (~says(P, S)) | (~truth(S))) <=> (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S))) <=> ![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S))) <=> ![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (^[S: $i, P: $i] : trans(monotonicity(rewrite((truth(isa(P, knight)) | (~says(P, S))) <=> (truth(isa(P, knight)) | (~says(P, S)))), (((truth(isa(P, knight)) | (~says(P, S))) | (~truth(S))) <=> ((truth(isa(P, knight)) | (~says(P, S))) | (~truth(S))))), rewrite(((truth(isa(P, knight)) | (~says(P, S))) | (~truth(S))) <=> (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))), (((truth(isa(P, knight)) | (~says(P, S))) | (~truth(S))) <=> (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (![S: $i, P: $i] : ((truth(isa(P, knight)) | (~says(P, S))) | (~truth(S))) <=> ![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.41 tff(51,axiom,(![S: $i, P: $i] : ((truth(isa(P, knight)) | (~says(P, S))) | (~truth(S)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','knights_make_true_statements2')).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.21/0.41 tff(54,plain,(
% 0.21/0.41 ![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[53])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (((~![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))) | (truth(isa(asked, knight)) | (~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(or(isa(asked, knight), isa(other, knight)))))) <=> ((~![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))) | truth(isa(asked, knight)) | (~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 ((~![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))) | (truth(isa(asked, knight)) | (~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 ((~![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))) | truth(isa(asked, knight)) | (~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (truth(isa(asked, knight)) | (~truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[58, 55, 12])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (~truth(or(isa(asked, knight), isa(other, knight)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[59, 45])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (^[Anyone: $i, S: $i] : refl(((~says(Anyone, S)) | truth(not(S)) | truth(S)) <=> ((~says(Anyone, S)) | truth(not(S)) | truth(S)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (![Anyone: $i, S: $i] : ((~says(Anyone, S)) | truth(not(S)) | truth(S)) <=> ![Anyone: $i, S: $i] : ((~says(Anyone, S)) | truth(not(S)) | truth(S))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (![Anyone: $i, S: $i] : ((~says(Anyone, S)) | truth(not(S)) | truth(S)) <=> ![Anyone: $i, S: $i] : ((~says(Anyone, S)) | truth(not(S)) | truth(S))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (^[Anyone: $i, S: $i] : rewrite(((truth(S) | truth(not(S))) | (~says(Anyone, S))) <=> ((~says(Anyone, S)) | truth(not(S)) | truth(S)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (![Anyone: $i, S: $i] : ((truth(S) | truth(not(S))) | (~says(Anyone, S))) <=> ![Anyone: $i, S: $i] : ((~says(Anyone, S)) | truth(not(S)) | truth(S))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.41 tff(66,axiom,(![Anyone: $i, S: $i] : ((truth(S) | truth(not(S))) | (~says(Anyone, S)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','statements_are_true_or_false')).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (![Anyone: $i, S: $i] : ((~says(Anyone, S)) | truth(not(S)) | truth(S))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (![Anyone: $i, S: $i] : ((~says(Anyone, S)) | truth(not(S)) | truth(S))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.21/0.41 tff(69,plain,(
% 0.21/0.41 ![Anyone: $i, S: $i] : ((~says(Anyone, S)) | truth(not(S)) | truth(S))),
% 0.21/0.41 inference(skolemize,[status(sab)],[68])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (![Anyone: $i, S: $i] : ((~says(Anyone, S)) | truth(not(S)) | truth(S))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (((~![Anyone: $i, S: $i] : ((~says(Anyone, S)) | truth(not(S)) | truth(S))) | ((~says(asked, or(isa(asked, knight), isa(other, knight)))) | truth(not(or(isa(asked, knight), isa(other, knight)))) | truth(or(isa(asked, knight), isa(other, knight))))) <=> ((~![Anyone: $i, S: $i] : ((~says(Anyone, S)) | truth(not(S)) | truth(S))) | (~says(asked, or(isa(asked, knight), isa(other, knight)))) | truth(not(or(isa(asked, knight), isa(other, knight)))) | truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 ((~![Anyone: $i, S: $i] : ((~says(Anyone, S)) | truth(not(S)) | truth(S))) | ((~says(asked, or(isa(asked, knight), isa(other, knight)))) | truth(not(or(isa(asked, knight), isa(other, knight)))) | truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 ((~![Anyone: $i, S: $i] : ((~says(Anyone, S)) | truth(not(S)) | truth(S))) | (~says(asked, or(isa(asked, knight), isa(other, knight)))) | truth(not(or(isa(asked, knight), isa(other, knight)))) | truth(or(isa(asked, knight), isa(other, knight)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (truth(not(or(isa(asked, knight), isa(other, knight)))) | truth(or(isa(asked, knight), isa(other, knight)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[73, 12, 70])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (truth(not(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[74, 60])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (^[S2: $i, Anything: $i] : refl(((~truth(S2)) | (~truth(not(or(Anything, S2))))) <=> ((~truth(S2)) | (~truth(not(or(Anything, S2))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 (![S2: $i, Anything: $i] : ((~truth(S2)) | (~truth(not(or(Anything, S2))))) <=> ![S2: $i, Anything: $i] : ((~truth(S2)) | (~truth(not(or(Anything, S2)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (![S2: $i, Anything: $i] : ((~truth(S2)) | (~truth(not(or(Anything, S2))))) <=> ![S2: $i, Anything: $i] : ((~truth(S2)) | (~truth(not(or(Anything, S2)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(79,axiom,(![S2: $i, Anything: $i] : ((~truth(S2)) | (~truth(not(or(Anything, S2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not2')).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (![S2: $i, Anything: $i] : ((~truth(S2)) | (~truth(not(or(Anything, S2)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.42 tff(81,plain,(
% 0.21/0.42 ![S2: $i, Anything: $i] : ((~truth(S2)) | (~truth(not(or(Anything, S2)))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[80])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (![S2: $i, Anything: $i] : ((~truth(S2)) | (~truth(not(or(Anything, S2)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (((~![S2: $i, Anything: $i] : ((~truth(S2)) | (~truth(not(or(Anything, S2)))))) | ((~truth(isa(other, knight))) | (~truth(not(or(isa(asked, knight), isa(other, knight))))))) <=> ((~![S2: $i, Anything: $i] : ((~truth(S2)) | (~truth(not(or(Anything, S2)))))) | (~truth(isa(other, knight))) | (~truth(not(or(isa(asked, knight), isa(other, knight))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 ((~![S2: $i, Anything: $i] : ((~truth(S2)) | (~truth(not(or(Anything, S2)))))) | ((~truth(isa(other, knight))) | (~truth(not(or(isa(asked, knight), isa(other, knight))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 ((~![S2: $i, Anything: $i] : ((~truth(S2)) | (~truth(not(or(Anything, S2)))))) | (~truth(isa(other, knight))) | (~truth(not(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 ((~truth(isa(other, knight))) | (~truth(not(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[85, 82])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (~truth(isa(other, knight))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[86, 75])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 (truth(isa(other, knave))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[35, 87])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (person(asked) <=> person(asked)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(90,axiom,(person(asked)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','asked_person')).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (person(asked)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))) | (truth(isa(asked, knave)) | truth(isa(asked, knight)) | (~person(asked)))) <=> ((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))) | truth(isa(asked, knave)) | truth(isa(asked, knight)) | (~person(asked)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 ((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))) | (truth(isa(asked, knave)) | truth(isa(asked, knight)) | (~person(asked)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 ((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)) | (~person(P)))) | truth(isa(asked, knave)) | truth(isa(asked, knight)) | (~person(asked))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (truth(isa(asked, knave)) | truth(isa(asked, knight))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[94, 31, 91])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (truth(isa(asked, knave))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[95, 45])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(other, knave))) | (~truth(isa(asked, knave))))) <=> ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(other, knave))) | (~truth(isa(asked, knave))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(other, knave))) | (~truth(isa(asked, knave))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~says(asked, or(isa(asked, knight), isa(other, knight)))) | (~truth(isa(other, knave))) | (~truth(isa(asked, knave)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[99, 12, 11, 96, 88])).
% 0.21/0.42 tff(101,plain,(~says(asked, or(isa(asked, knight), isa(other, knight)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 ((says(asked, or(isa(asked, knight), isa(other, knight))) | says(asked, not(or(isa(asked, knight), isa(other, knight))))) <=> (says(asked, or(isa(asked, knight), isa(other, knight))) | says(asked, not(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(103,axiom,(says(asked, or(isa(asked, knight), isa(other, knight))) | says(asked, not(or(isa(asked, knight), isa(other, knight))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','one_is_knight_answer')).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (says(asked, or(isa(asked, knight), isa(other, knight))) | says(asked, not(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (says(asked, not(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~truth(isa(other, knight))) | (~truth(isa(asked, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))))) <=> ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (((~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knight)))) <=> ((~truth(isa(other, knight))) | (~truth(isa(asked, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knight))))) <=> ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~truth(isa(other, knight))) | (~truth(isa(asked, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight)))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[107])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knight))))) <=> ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[108, 106])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knight))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 ((~truth(isa(other, knight))) | (~truth(isa(asked, knight)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[111, 105, 11])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (~truth(isa(asked, knight))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[112, 1])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 (truth(isa(asked, knave))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[95, 113])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~truth(isa(other, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(asked, knave))))) <=> ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~truth(isa(other, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(asked, knave))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (((~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knave)))) <=> ((~truth(isa(other, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(asked, knave))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knave))))) <=> ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~truth(isa(other, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(asked, knave)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[116])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knave))))) <=> ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~truth(isa(other, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(asked, knave))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[117, 115])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knave))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~truth(isa(other, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(asked, knave)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[120, 105, 11, 114, 1])).
% 0.21/0.43 tff(122,plain,(~truth(isa(other, knight))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(123,plain,
% 0.21/0.43 (truth(isa(other, knave))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[35, 122])).
% 0.21/0.43 tff(124,plain,
% 0.21/0.43 (((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~truth(isa(asked, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knave))))) <=> ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~truth(isa(asked, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knave))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(125,plain,
% 0.21/0.43 (((~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knave))) | (~truth(isa(asked, knight)))) <=> ((~truth(isa(asked, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knave))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(126,plain,
% 0.21/0.43 (((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knave))) | (~truth(isa(asked, knight))))) <=> ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~truth(isa(asked, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knave)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[125])).
% 0.21/0.43 tff(127,plain,
% 0.21/0.43 (((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knave))) | (~truth(isa(asked, knight))))) <=> ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~truth(isa(asked, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knave))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[126, 124])).
% 0.21/0.43 tff(128,plain,
% 0.21/0.43 ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | ((~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knave))) | (~truth(isa(asked, knight))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(129,plain,
% 0.21/0.43 ((~![S: $i, P2: $i, P1: $i] : ((~says(asked, S)) | (~truth(isa(other, P2))) | (~truth(isa(asked, P1))))) | (~truth(isa(asked, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(isa(other, knave)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.21/0.43 tff(130,plain,
% 0.21/0.43 (~truth(isa(asked, knight))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[129, 105, 11, 123])).
% 0.21/0.43 tff(131,plain,
% 0.21/0.43 (((~![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))) | (truth(isa(asked, knight)) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(not(or(isa(asked, knight), isa(other, knight))))))) <=> ((~![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))) | truth(isa(asked, knight)) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(not(or(isa(asked, knight), isa(other, knight))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 ((~![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))) | (truth(isa(asked, knight)) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(not(or(isa(asked, knight), isa(other, knight))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(133,plain,
% 0.21/0.43 ((~![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))) | truth(isa(asked, knight)) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))) | (~truth(not(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 (truth(isa(asked, knight)) | (~truth(not(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[133, 55, 105])).
% 0.21/0.43 tff(135,plain,
% 0.21/0.43 (~truth(not(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[134, 130])).
% 0.21/0.43 tff(136,plain,
% 0.21/0.43 (^[S2: $i, S1: $i] : refl((truth(S2) | truth(S1) | (~truth(or(S1, S2)))) <=> (truth(S2) | truth(S1) | (~truth(or(S1, S2)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(137,plain,
% 0.21/0.43 (![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2)))) <=> ![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[136])).
% 0.21/0.43 tff(138,plain,
% 0.21/0.43 (![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2)))) <=> ![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(139,plain,
% 0.21/0.43 (^[S2: $i, S1: $i] : rewrite(((truth(S1) | truth(S2)) | (~truth(or(S1, S2)))) <=> (truth(S2) | truth(S1) | (~truth(or(S1, S2)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 (![S2: $i, S1: $i] : ((truth(S1) | truth(S2)) | (~truth(or(S1, S2)))) <=> ![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[139])).
% 0.21/0.43 tff(141,axiom,(![S2: $i, S1: $i] : ((truth(S1) | truth(S2)) | (~truth(or(S1, S2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','or_def')).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 (![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 (![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.21/0.43 tff(144,plain,(
% 0.21/0.43 ![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[143])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 (![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[144, 137])).
% 0.21/0.43 tff(146,plain,
% 0.21/0.43 (((~![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))) | (truth(isa(asked, knight)) | truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))))) <=> ((~![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))) | truth(isa(asked, knight)) | truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 ((truth(isa(other, knight)) | truth(isa(asked, knight)) | (~truth(or(isa(asked, knight), isa(other, knight))))) <=> (truth(isa(asked, knight)) | truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(148,plain,
% 0.21/0.43 (((~![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))) | (truth(isa(other, knight)) | truth(isa(asked, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))))) <=> ((~![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))) | (truth(isa(asked, knight)) | truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 (((~![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))) | (truth(isa(other, knight)) | truth(isa(asked, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))))) <=> ((~![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))) | truth(isa(asked, knight)) | truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[148, 146])).
% 0.21/0.43 tff(150,plain,
% 0.21/0.43 ((~![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))) | (truth(isa(other, knight)) | truth(isa(asked, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(151,plain,
% 0.21/0.43 ((~![S2: $i, S1: $i] : (truth(S2) | truth(S1) | (~truth(or(S1, S2))))) | truth(isa(asked, knight)) | truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.44 tff(152,plain,
% 0.21/0.44 (truth(isa(asked, knight)) | truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[151, 145])).
% 0.21/0.44 tff(153,plain,
% 0.21/0.44 (~truth(or(isa(asked, knight), isa(other, knight)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[152, 130, 122])).
% 0.21/0.44 tff(154,plain,
% 0.21/0.44 (^[Anyone: $i, S: $i] : refl((truth(not(S)) | truth(S) | (~says(Anyone, not(S)))) <=> (truth(not(S)) | truth(S) | (~says(Anyone, not(S)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(155,plain,
% 0.21/0.44 (![Anyone: $i, S: $i] : (truth(not(S)) | truth(S) | (~says(Anyone, not(S)))) <=> ![Anyone: $i, S: $i] : (truth(not(S)) | truth(S) | (~says(Anyone, not(S))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[154])).
% 0.21/0.44 tff(156,plain,
% 0.21/0.44 (![Anyone: $i, S: $i] : (truth(not(S)) | truth(S) | (~says(Anyone, not(S)))) <=> ![Anyone: $i, S: $i] : (truth(not(S)) | truth(S) | (~says(Anyone, not(S))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(157,plain,
% 0.21/0.44 (^[Anyone: $i, S: $i] : rewrite(((truth(S) | truth(not(S))) | (~says(Anyone, not(S)))) <=> (truth(not(S)) | truth(S) | (~says(Anyone, not(S)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(158,plain,
% 0.21/0.44 (![Anyone: $i, S: $i] : ((truth(S) | truth(not(S))) | (~says(Anyone, not(S)))) <=> ![Anyone: $i, S: $i] : (truth(not(S)) | truth(S) | (~says(Anyone, not(S))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[157])).
% 0.21/0.44 tff(159,axiom,(![Anyone: $i, S: $i] : ((truth(S) | truth(not(S))) | (~says(Anyone, not(S))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','statements_are_true_or_false2')).
% 0.21/0.44 tff(160,plain,
% 0.21/0.44 (![Anyone: $i, S: $i] : (truth(not(S)) | truth(S) | (~says(Anyone, not(S))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.21/0.44 tff(161,plain,
% 0.21/0.44 (![Anyone: $i, S: $i] : (truth(not(S)) | truth(S) | (~says(Anyone, not(S))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.21/0.44 tff(162,plain,(
% 0.21/0.44 ![Anyone: $i, S: $i] : (truth(not(S)) | truth(S) | (~says(Anyone, not(S))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[161])).
% 0.21/0.44 tff(163,plain,
% 0.21/0.44 (![Anyone: $i, S: $i] : (truth(not(S)) | truth(S) | (~says(Anyone, not(S))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.21/0.44 tff(164,plain,
% 0.21/0.44 (((~![Anyone: $i, S: $i] : (truth(not(S)) | truth(S) | (~says(Anyone, not(S))))) | (truth(not(or(isa(asked, knight), isa(other, knight)))) | truth(or(isa(asked, knight), isa(other, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))))) <=> ((~![Anyone: $i, S: $i] : (truth(not(S)) | truth(S) | (~says(Anyone, not(S))))) | truth(not(or(isa(asked, knight), isa(other, knight)))) | truth(or(isa(asked, knight), isa(other, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(165,plain,
% 0.21/0.44 ((~![Anyone: $i, S: $i] : (truth(not(S)) | truth(S) | (~says(Anyone, not(S))))) | (truth(not(or(isa(asked, knight), isa(other, knight)))) | truth(or(isa(asked, knight), isa(other, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(166,plain,
% 0.21/0.44 ((~![Anyone: $i, S: $i] : (truth(not(S)) | truth(S) | (~says(Anyone, not(S))))) | truth(not(or(isa(asked, knight), isa(other, knight)))) | truth(or(isa(asked, knight), isa(other, knight))) | (~says(asked, not(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.21/0.44 tff(167,plain,
% 0.21/0.44 (truth(not(or(isa(asked, knight), isa(other, knight)))) | truth(or(isa(asked, knight), isa(other, knight)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[166, 105, 163])).
% 0.21/0.44 tff(168,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[167, 153, 135])).
% 0.21/0.44 % SZS output end Proof
%------------------------------------------------------------------------------