TSTP Solution File: PUZ035-6 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ035-6 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 0.16s 0.35s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : PUZ035-6 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n012.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri Sep 2 18:23:49 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.30 Usage: tptp [options] [-file:]file
% 0.10/0.30 -h, -? prints this message.
% 0.10/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.30 -m, -model generate model.
% 0.10/0.30 -p, -proof generate proof.
% 0.10/0.30 -c, -core generate unsat core of named formulas.
% 0.10/0.30 -st, -statistics display statistics.
% 0.10/0.30 -t:timeout set timeout (in second).
% 0.10/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.30 -<param>:<value> configuration parameter and value.
% 0.10/0.30 -o:<output-file> file to place output in.
% 0.16/0.35 % SZS status Unsatisfiable
% 0.16/0.35 % SZS output start Proof
% 0.16/0.35 tff(truth_type, type, (
% 0.16/0.35 truth: $i > $o)).
% 0.16/0.35 tff(not_type, type, (
% 0.16/0.35 not: $i > $i)).
% 0.16/0.35 tff(or_type, type, (
% 0.16/0.35 or: ( $i * $i ) > $i)).
% 0.16/0.35 tff(isa_type, type, (
% 0.16/0.35 isa: ( $i * $i ) > $i)).
% 0.16/0.35 tff(knight_type, type, (
% 0.16/0.35 knight: $i)).
% 0.16/0.35 tff(other_type, type, (
% 0.16/0.35 other: $i)).
% 0.16/0.35 tff(asked_type, type, (
% 0.16/0.35 asked: $i)).
% 0.16/0.35 tff(knave_type, type, (
% 0.16/0.35 knave: $i)).
% 0.16/0.35 tff(says_type, type, (
% 0.16/0.35 says: ( $i * $i ) > $o)).
% 0.16/0.35 tff(1,assumption,(~truth(isa(asked, knight))), introduced(assumption)).
% 0.16/0.35 tff(2,plain,
% 0.16/0.35 (^[P: $i] : refl((truth(isa(P, knave)) | truth(isa(P, knight))) <=> (truth(isa(P, knave)) | truth(isa(P, knight))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(3,plain,
% 0.16/0.35 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight))) <=> ![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[2])).
% 0.16/0.35 tff(4,plain,
% 0.16/0.35 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight))) <=> ![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(5,plain,
% 0.16/0.35 (^[P: $i] : rewrite((truth(isa(P, knight)) | truth(isa(P, knave))) <=> (truth(isa(P, knave)) | truth(isa(P, knight))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(6,plain,
% 0.16/0.35 (![P: $i] : (truth(isa(P, knight)) | truth(isa(P, knave))) <=> ![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[5])).
% 0.16/0.35 tff(7,axiom,(![P: $i] : (truth(isa(P, knight)) | truth(isa(P, knave)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','everyone_a_knight_or_knave')).
% 0.16/0.35 tff(8,plain,
% 0.16/0.35 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.16/0.35 tff(9,plain,
% 0.16/0.35 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.16/0.35 tff(10,plain,(
% 0.16/0.35 ![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))),
% 0.16/0.35 inference(skolemize,[status(sab)],[9])).
% 0.16/0.35 tff(11,plain,
% 0.16/0.35 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.16/0.35 tff(12,plain,
% 0.16/0.35 (((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))) | (truth(isa(asked, knave)) | truth(isa(asked, knight)))) <=> ((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))) | truth(isa(asked, knave)) | truth(isa(asked, knight)))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(13,plain,
% 0.16/0.35 ((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))) | (truth(isa(asked, knave)) | truth(isa(asked, knight)))),
% 0.16/0.35 inference(quant_inst,[status(thm)],[])).
% 0.16/0.35 tff(14,plain,
% 0.16/0.35 ((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))) | truth(isa(asked, knave)) | truth(isa(asked, knight))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.16/0.35 tff(15,plain,
% 0.16/0.35 (truth(isa(asked, knave)) | truth(isa(asked, knight))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.16/0.35 tff(16,plain,
% 0.16/0.35 (truth(isa(asked, knave))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[15, 1])).
% 0.16/0.35 tff(17,plain,
% 0.16/0.35 (says(asked, not(or(isa(asked, knight), isa(other, knight)))) <=> says(asked, not(or(isa(asked, knight), isa(other, knight))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(18,axiom,(says(asked, not(or(isa(asked, knight), isa(other, knight))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','says_yes')).
% 0.16/0.35 tff(19,plain,
% 0.16/0.35 (says(asked, not(or(isa(asked, knight), isa(other, knight))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.16/0.35 tff(20,plain,
% 0.16/0.35 (^[S: $i, P: $i] : refl((truth(isa(P, knight)) | (~says(P, S)) | (~truth(S))) <=> (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(21,plain,
% 0.16/0.35 (![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)))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[20])).
% 0.16/0.35 tff(22,plain,
% 0.16/0.35 (![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)))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(23,plain,
% 0.16/0.35 (^[S: $i, P: $i] : trans(monotonicity(rewrite((truth(isa(P, knight)) | (~truth(S))) <=> (truth(isa(P, knight)) | (~truth(S)))), (((truth(isa(P, knight)) | (~truth(S))) | (~says(P, S))) <=> ((truth(isa(P, knight)) | (~truth(S))) | (~says(P, S))))), rewrite(((truth(isa(P, knight)) | (~truth(S))) | (~says(P, S))) <=> (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))), (((truth(isa(P, knight)) | (~truth(S))) | (~says(P, S))) <=> (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(24,plain,
% 0.16/0.35 (![S: $i, P: $i] : ((truth(isa(P, knight)) | (~truth(S))) | (~says(P, S))) <=> ![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[23])).
% 0.16/0.35 tff(25,axiom,(![S: $i, P: $i] : ((truth(isa(P, knight)) | (~truth(S))) | (~says(P, S)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','knights_make_true_statements2')).
% 0.16/0.35 tff(26,plain,
% 0.16/0.35 (![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.16/0.35 tff(27,plain,
% 0.16/0.35 (![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.16/0.35 tff(28,plain,(
% 0.16/0.35 ![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))),
% 0.16/0.35 inference(skolemize,[status(sab)],[27])).
% 0.16/0.35 tff(29,plain,
% 0.16/0.35 (![S: $i, P: $i] : (truth(isa(P, knight)) | (~says(P, S)) | (~truth(S)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.16/0.35 tff(30,plain,
% 0.16/0.35 (((~![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))))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(31,plain,
% 0.16/0.35 ((~![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))))))),
% 0.16/0.35 inference(quant_inst,[status(thm)],[])).
% 0.16/0.35 tff(32,plain,
% 0.16/0.35 ((~![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)))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.16/0.35 tff(33,plain,
% 0.16/0.35 (truth(isa(asked, knight)) | (~truth(not(or(isa(asked, knight), isa(other, knight)))))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[32, 29, 19])).
% 0.16/0.35 tff(34,plain,
% 0.16/0.35 (~truth(not(or(isa(asked, knight), isa(other, knight))))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[33, 1])).
% 0.16/0.35 tff(35,plain,
% 0.16/0.35 (^[C: $i] : refl((truth(C) | truth(not(C))) <=> (truth(C) | truth(not(C))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(36,plain,
% 0.16/0.35 (![C: $i] : (truth(C) | truth(not(C))) <=> ![C: $i] : (truth(C) | truth(not(C)))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[35])).
% 0.16/0.35 tff(37,plain,
% 0.16/0.35 (![C: $i] : (truth(C) | truth(not(C))) <=> ![C: $i] : (truth(C) | truth(not(C)))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(38,axiom,(![C: $i] : (truth(C) | truth(not(C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not1')).
% 0.16/0.35 tff(39,plain,
% 0.16/0.35 (![C: $i] : (truth(C) | truth(not(C)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.16/0.35 tff(40,plain,(
% 0.16/0.35 ![C: $i] : (truth(C) | truth(not(C)))),
% 0.16/0.35 inference(skolemize,[status(sab)],[39])).
% 0.16/0.35 tff(41,plain,
% 0.16/0.35 (![C: $i] : (truth(C) | truth(not(C)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.16/0.35 tff(42,plain,
% 0.16/0.35 (((~![C: $i] : (truth(C) | truth(not(C)))) | (truth(or(isa(asked, knight), isa(other, knight))) | truth(not(or(isa(asked, knight), isa(other, knight)))))) <=> ((~![C: $i] : (truth(C) | truth(not(C)))) | truth(or(isa(asked, knight), isa(other, knight))) | truth(not(or(isa(asked, knight), isa(other, knight)))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(43,plain,
% 0.16/0.35 ((~![C: $i] : (truth(C) | truth(not(C)))) | (truth(or(isa(asked, knight), isa(other, knight))) | truth(not(or(isa(asked, knight), isa(other, knight)))))),
% 0.16/0.35 inference(quant_inst,[status(thm)],[])).
% 0.16/0.35 tff(44,plain,
% 0.16/0.35 ((~![C: $i] : (truth(C) | truth(not(C)))) | truth(or(isa(asked, knight), isa(other, knight))) | truth(not(or(isa(asked, knight), isa(other, knight))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.16/0.35 tff(45,plain,
% 0.16/0.35 (truth(or(isa(asked, knight), isa(other, knight))) | truth(not(or(isa(asked, knight), isa(other, knight))))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[44, 41])).
% 0.16/0.35 tff(46,plain,
% 0.16/0.35 (truth(or(isa(asked, knight), isa(other, knight)))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[45, 34])).
% 0.16/0.35 tff(47,plain,
% 0.16/0.35 (^[B: $i, A: $i] : refl((truth(B) | (~truth(or(A, B))) | truth(A)) <=> (truth(B) | (~truth(or(A, B))) | truth(A)))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(48,plain,
% 0.16/0.35 (![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A)) <=> ![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[47])).
% 0.16/0.35 tff(49,plain,
% 0.16/0.35 (![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A)) <=> ![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(50,plain,
% 0.16/0.35 (^[B: $i, A: $i] : rewrite(((truth(A) | truth(B)) | (~truth(or(A, B)))) <=> (truth(B) | (~truth(or(A, B))) | truth(A)))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(51,plain,
% 0.16/0.35 (![B: $i, A: $i] : ((truth(A) | truth(B)) | (~truth(or(A, B)))) <=> ![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[50])).
% 0.16/0.35 tff(52,axiom,(![B: $i, A: $i] : ((truth(A) | truth(B)) | (~truth(or(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','or1')).
% 0.16/0.35 tff(53,plain,
% 0.16/0.35 (![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.16/0.35 tff(54,plain,
% 0.16/0.35 (![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.16/0.35 tff(55,plain,(
% 0.16/0.35 ![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))),
% 0.16/0.35 inference(skolemize,[status(sab)],[54])).
% 0.16/0.35 tff(56,plain,
% 0.16/0.35 (![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.16/0.35 tff(57,plain,
% 0.16/0.35 (((~![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))) | (truth(isa(asked, knight)) | truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))))) <=> ((~![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))) | truth(isa(asked, knight)) | truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(58,plain,
% 0.16/0.35 ((truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))) | truth(isa(asked, knight))) <=> (truth(isa(asked, knight)) | truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(59,plain,
% 0.16/0.35 (((~![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))) | (truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))) | truth(isa(asked, knight)))) <=> ((~![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))) | (truth(isa(asked, knight)) | truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight))))))),
% 0.16/0.35 inference(monotonicity,[status(thm)],[58])).
% 0.16/0.35 tff(60,plain,
% 0.16/0.35 (((~![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))) | (truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))) | truth(isa(asked, knight)))) <=> ((~![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))) | truth(isa(asked, knight)) | truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.16/0.35 inference(transitivity,[status(thm)],[59, 57])).
% 0.16/0.35 tff(61,plain,
% 0.16/0.35 ((~![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))) | (truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))) | truth(isa(asked, knight)))),
% 0.16/0.35 inference(quant_inst,[status(thm)],[])).
% 0.16/0.35 tff(62,plain,
% 0.16/0.35 ((~![B: $i, A: $i] : (truth(B) | (~truth(or(A, B))) | truth(A))) | truth(isa(asked, knight)) | truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.16/0.35 tff(63,plain,
% 0.16/0.35 (truth(isa(asked, knight)) | truth(isa(other, knight)) | (~truth(or(isa(asked, knight), isa(other, knight))))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[62, 56])).
% 0.16/0.35 tff(64,plain,
% 0.16/0.35 (truth(isa(other, knight))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[63, 46, 1])).
% 0.16/0.35 tff(65,plain,
% 0.16/0.35 (^[Y: $i, X: $i] : refl(((~truth(isa(asked, X))) | (~truth(isa(other, Y)))) <=> ((~truth(isa(asked, X))) | (~truth(isa(other, Y)))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(66,plain,
% 0.16/0.35 (![Y: $i, X: $i] : ((~truth(isa(asked, X))) | (~truth(isa(other, Y)))) <=> ![Y: $i, X: $i] : ((~truth(isa(asked, X))) | (~truth(isa(other, Y))))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[65])).
% 0.16/0.35 tff(67,plain,
% 0.16/0.35 (![Y: $i, X: $i] : ((~truth(isa(asked, X))) | (~truth(isa(other, Y)))) <=> ![Y: $i, X: $i] : ((~truth(isa(asked, X))) | (~truth(isa(other, Y))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(68,axiom,(![Y: $i, X: $i] : ((~truth(isa(asked, X))) | (~truth(isa(other, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','query')).
% 0.16/0.35 tff(69,plain,
% 0.16/0.35 (![Y: $i, X: $i] : ((~truth(isa(asked, X))) | (~truth(isa(other, Y))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.16/0.35 tff(70,plain,(
% 0.16/0.35 ![Y: $i, X: $i] : ((~truth(isa(asked, X))) | (~truth(isa(other, Y))))),
% 0.16/0.35 inference(skolemize,[status(sab)],[69])).
% 0.16/0.35 tff(71,plain,
% 0.16/0.35 (![Y: $i, X: $i] : ((~truth(isa(asked, X))) | (~truth(isa(other, Y))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.16/0.35 tff(72,plain,
% 0.16/0.35 (((~![Y: $i, X: $i] : ((~truth(isa(asked, X))) | (~truth(isa(other, Y))))) | ((~truth(isa(asked, knave))) | (~truth(isa(other, knight))))) <=> ((~![Y: $i, X: $i] : ((~truth(isa(asked, X))) | (~truth(isa(other, Y))))) | (~truth(isa(asked, knave))) | (~truth(isa(other, knight))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(73,plain,
% 0.16/0.35 ((~![Y: $i, X: $i] : ((~truth(isa(asked, X))) | (~truth(isa(other, Y))))) | ((~truth(isa(asked, knave))) | (~truth(isa(other, knight))))),
% 0.16/0.35 inference(quant_inst,[status(thm)],[])).
% 0.16/0.35 tff(74,plain,
% 0.16/0.35 ((~![Y: $i, X: $i] : ((~truth(isa(asked, X))) | (~truth(isa(other, Y))))) | (~truth(isa(asked, knave))) | (~truth(isa(other, knight)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.16/0.35 tff(75,plain,
% 0.16/0.35 ($false),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[74, 71, 64, 16])).
% 0.16/0.35 tff(76,plain,(truth(isa(asked, knight))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.35 tff(77,plain,
% 0.16/0.35 (^[S: $i, P: $i] : refl(((~truth(isa(P, knight))) | (~says(P, S)) | truth(S)) <=> ((~truth(isa(P, knight))) | (~says(P, S)) | truth(S)))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(78,plain,
% 0.16/0.35 (![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))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[77])).
% 0.16/0.35 tff(79,plain,
% 0.16/0.35 (![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))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(80,plain,
% 0.16/0.35 (^[S: $i, P: $i] : rewrite(((truth(S) | (~truth(isa(P, knight)))) | (~says(P, S))) <=> ((~truth(isa(P, knight))) | (~says(P, S)) | truth(S)))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(81,plain,
% 0.16/0.35 (![S: $i, P: $i] : ((truth(S) | (~truth(isa(P, knight)))) | (~says(P, S))) <=> ![S: $i, P: $i] : ((~truth(isa(P, knight))) | (~says(P, S)) | truth(S))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[80])).
% 0.16/0.35 tff(82,axiom,(![S: $i, P: $i] : ((truth(S) | (~truth(isa(P, knight)))) | (~says(P, S)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','knights_make_true_statements1')).
% 0.16/0.35 tff(83,plain,
% 0.16/0.36 (![S: $i, P: $i] : ((~truth(isa(P, knight))) | (~says(P, S)) | truth(S))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.16/0.36 tff(84,plain,
% 0.16/0.36 (![S: $i, P: $i] : ((~truth(isa(P, knight))) | (~says(P, S)) | truth(S))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.16/0.36 tff(85,plain,(
% 0.16/0.36 ![S: $i, P: $i] : ((~truth(isa(P, knight))) | (~says(P, S)) | truth(S))),
% 0.16/0.36 inference(skolemize,[status(sab)],[84])).
% 0.16/0.36 tff(86,plain,
% 0.16/0.36 (![S: $i, P: $i] : ((~truth(isa(P, knight))) | (~says(P, S)) | truth(S))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.16/0.36 tff(87,plain,
% 0.16/0.36 (((~![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)))))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(88,plain,
% 0.16/0.36 ((~![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)))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(89,plain,
% 0.16/0.36 ((~![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))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.16/0.36 tff(90,plain,
% 0.16/0.36 ((~truth(isa(asked, knight))) | truth(not(or(isa(asked, knight), isa(other, knight))))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[89, 86, 19])).
% 0.16/0.36 tff(91,plain,
% 0.16/0.36 (truth(not(or(isa(asked, knight), isa(other, knight))))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[90, 76])).
% 0.16/0.36 tff(92,plain,
% 0.16/0.36 (^[B: $i, A: $i] : refl(((~truth(A)) | truth(or(A, B))) <=> ((~truth(A)) | truth(or(A, B))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(93,plain,
% 0.16/0.36 (![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B))) <=> ![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[92])).
% 0.16/0.36 tff(94,plain,
% 0.16/0.36 (![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B))) <=> ![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(95,plain,
% 0.16/0.36 (^[B: $i, A: $i] : rewrite((truth(or(A, B)) | (~truth(A))) <=> ((~truth(A)) | truth(or(A, B))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(96,plain,
% 0.16/0.36 (![B: $i, A: $i] : (truth(or(A, B)) | (~truth(A))) <=> ![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[95])).
% 0.16/0.36 tff(97,axiom,(![B: $i, A: $i] : (truth(or(A, B)) | (~truth(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','or2')).
% 0.16/0.36 tff(98,plain,
% 0.16/0.36 (![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.16/0.36 tff(99,plain,
% 0.16/0.36 (![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.16/0.36 tff(100,plain,(
% 0.16/0.36 ![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))),
% 0.16/0.36 inference(skolemize,[status(sab)],[99])).
% 0.16/0.36 tff(101,plain,
% 0.16/0.36 (![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.16/0.36 tff(102,plain,
% 0.16/0.36 (((~![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))) | ((~truth(isa(asked, knight))) | truth(or(isa(asked, knight), isa(other, knight))))) <=> ((~![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))) | (~truth(isa(asked, knight))) | truth(or(isa(asked, knight), isa(other, knight))))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(103,plain,
% 0.16/0.36 ((~![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))) | ((~truth(isa(asked, knight))) | truth(or(isa(asked, knight), isa(other, knight))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(104,plain,
% 0.16/0.36 ((~![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))) | (~truth(isa(asked, knight))) | truth(or(isa(asked, knight), isa(other, knight)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.16/0.36 tff(105,plain,
% 0.16/0.36 ((~truth(isa(asked, knight))) | truth(or(isa(asked, knight), isa(other, knight)))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.16/0.36 tff(106,plain,
% 0.16/0.36 (truth(or(isa(asked, knight), isa(other, knight)))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[105, 76])).
% 0.16/0.36 tff(107,plain,
% 0.16/0.36 (^[C: $i] : refl(((~truth(C)) | (~truth(not(C)))) <=> ((~truth(C)) | (~truth(not(C)))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(108,plain,
% 0.16/0.36 (![C: $i] : ((~truth(C)) | (~truth(not(C)))) <=> ![C: $i] : ((~truth(C)) | (~truth(not(C))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[107])).
% 0.16/0.36 tff(109,plain,
% 0.16/0.36 (![C: $i] : ((~truth(C)) | (~truth(not(C)))) <=> ![C: $i] : ((~truth(C)) | (~truth(not(C))))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(110,axiom,(![C: $i] : ((~truth(C)) | (~truth(not(C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not2')).
% 0.16/0.36 tff(111,plain,
% 0.16/0.36 (![C: $i] : ((~truth(C)) | (~truth(not(C))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.16/0.36 tff(112,plain,(
% 0.16/0.36 ![C: $i] : ((~truth(C)) | (~truth(not(C))))),
% 0.16/0.36 inference(skolemize,[status(sab)],[111])).
% 0.16/0.36 tff(113,plain,
% 0.16/0.36 (![C: $i] : ((~truth(C)) | (~truth(not(C))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.16/0.36 tff(114,plain,
% 0.16/0.36 (((~![C: $i] : ((~truth(C)) | (~truth(not(C))))) | ((~truth(or(isa(asked, knight), isa(other, knight)))) | (~truth(not(or(isa(asked, knight), isa(other, knight))))))) <=> ((~![C: $i] : ((~truth(C)) | (~truth(not(C))))) | (~truth(or(isa(asked, knight), isa(other, knight)))) | (~truth(not(or(isa(asked, knight), isa(other, knight))))))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(115,plain,
% 0.16/0.36 ((~![C: $i] : ((~truth(C)) | (~truth(not(C))))) | ((~truth(or(isa(asked, knight), isa(other, knight)))) | (~truth(not(or(isa(asked, knight), isa(other, knight))))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(116,plain,
% 0.16/0.36 ((~![C: $i] : ((~truth(C)) | (~truth(not(C))))) | (~truth(or(isa(asked, knight), isa(other, knight)))) | (~truth(not(or(isa(asked, knight), isa(other, knight)))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.16/0.36 tff(117,plain,
% 0.16/0.36 ((~truth(or(isa(asked, knight), isa(other, knight)))) | (~truth(not(or(isa(asked, knight), isa(other, knight)))))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[116, 113])).
% 0.16/0.36 tff(118,plain,
% 0.16/0.36 ($false),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[117, 106, 91])).
% 0.16/0.36 % SZS output end Proof
%------------------------------------------------------------------------------