%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ035-7 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:23:15 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : PUZ035-7 : TPTP v9.0.0. Released v2.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 02:40:25 EDT 2025
% 0.13/0.35 % CPUTime :
% 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(isa_type, type, (
% 0.21/0.40 isa: ( $i * $i ) > $i)).
% 0.21/0.40 tff(knave_type, type, (
% 0.21/0.40 knave: $i)).
% 0.21/0.40 tff(other_type, type, (
% 0.21/0.40 other: $i)).
% 0.21/0.40 tff(knight_type, type, (
% 0.21/0.40 knight: $i)).
% 0.21/0.40 tff(asked_type, type, (
% 0.21/0.40 asked: $i)).
% 0.21/0.40 tff(or_type, type, (
% 0.21/0.40 or: ( $i * $i ) > $i)).
% 0.21/0.40 tff(reply_type, type, (
% 0.21/0.40 reply: ( $i * $i * $i ) > $o)).
% 0.21/0.40 tff(yes_type, type, (
% 0.21/0.40 yes: $i)).
% 0.21/0.40 tff(no_type, type, (
% 0.21/0.40 no: $i)).
% 0.21/0.40 tff(1,assumption,(~truth(isa(asked, knight))), introduced(assumption)).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 (^[P: $i] : refl((truth(isa(P, knave)) | truth(isa(P, knight))) <=> (truth(isa(P, knave)) | truth(isa(P, knight))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight))) <=> ![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.40 tff(4,plain,
% 0.21/0.40 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight))) <=> ![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (^[P: $i] : rewrite((truth(isa(P, knight)) | truth(isa(P, knave))) <=> (truth(isa(P, knave)) | truth(isa(P, knight))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (![P: $i] : (truth(isa(P, knight)) | truth(isa(P, knave))) <=> ![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.40 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')).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.40 tff(10,plain,(
% 0.21/0.40 ![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[9])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 (![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (((~![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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 ((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))) | (truth(isa(asked, knave)) | truth(isa(asked, knight)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 ((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))) | truth(isa(asked, knave)) | truth(isa(asked, knight))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 (truth(isa(asked, knave)) | truth(isa(asked, knight))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (truth(isa(asked, knave))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[15, 1])).
% 0.21/0.40 tff(17,assumption,(~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)), introduced(assumption)).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 (^[Q: $i, P: $i] : refl((reply(P, Q, no) | reply(P, Q, yes)) <=> (reply(P, Q, no) | reply(P, Q, yes)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (![Q: $i, P: $i] : (reply(P, Q, no) | reply(P, Q, yes)) <=> ![Q: $i, P: $i] : (reply(P, Q, no) | reply(P, Q, yes))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 (![Q: $i, P: $i] : (reply(P, Q, no) | reply(P, Q, yes)) <=> ![Q: $i, P: $i] : (reply(P, Q, no) | reply(P, Q, yes))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (^[Q: $i, P: $i] : rewrite((reply(P, Q, yes) | reply(P, Q, no)) <=> (reply(P, Q, no) | reply(P, Q, yes)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (![Q: $i, P: $i] : (reply(P, Q, yes) | reply(P, Q, no)) <=> ![Q: $i, P: $i] : (reply(P, Q, no) | reply(P, Q, yes))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.40 tff(23,axiom,(![Q: $i, P: $i] : (reply(P, Q, yes) | reply(P, Q, no))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','yes_or_no')).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (![Q: $i, P: $i] : (reply(P, Q, no) | reply(P, Q, yes))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (![Q: $i, P: $i] : (reply(P, Q, no) | reply(P, Q, yes))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.21/0.41 tff(26,plain,(
% 0.21/0.41 ![Q: $i, P: $i] : (reply(P, Q, no) | reply(P, Q, yes))),
% 0.21/0.41 inference(skolemize,[status(sab)],[25])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (![Q: $i, P: $i] : (reply(P, Q, no) | reply(P, Q, yes))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (((~![Q: $i, P: $i] : (reply(P, Q, no) | reply(P, Q, yes))) | (reply(asked, or(isa(asked, knight), isa(other, knight)), no) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes))) <=> ((~![Q: $i, P: $i] : (reply(P, Q, no) | reply(P, Q, yes))) | reply(asked, or(isa(asked, knight), isa(other, knight)), no) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 ((~![Q: $i, P: $i] : (reply(P, Q, no) | reply(P, Q, yes))) | (reply(asked, or(isa(asked, knight), isa(other, knight)), no) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 ((~![Q: $i, P: $i] : (reply(P, Q, no) | reply(P, Q, yes))) | reply(asked, or(isa(asked, knight), isa(other, knight)), no) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (reply(asked, or(isa(asked, knight), isa(other, knight)), no)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[30, 27, 17])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (^[Q: $i, P: $i] : refl((truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q)) <=> (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q)) <=> ![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q)) <=> ![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (^[Q: $i, P: $i] : rewrite(((truth(Q) | truth(isa(P, knight))) | reply(P, Q, yes)) <=> (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (![Q: $i, P: $i] : ((truth(Q) | truth(isa(P, knight))) | reply(P, Q, yes)) <=> ![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.41 tff(37,axiom,(![Q: $i, P: $i] : ((truth(Q) | truth(isa(P, knight))) | reply(P, Q, yes))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','knights_make_true_statements4')).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.41 tff(40,plain,(
% 0.21/0.41 ![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))),
% 0.21/0.41 inference(skolemize,[status(sab)],[39])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (((~![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))) | (truth(isa(asked, knight)) | truth(or(isa(asked, knight), isa(other, knight))) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes))) <=> ((~![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))) | truth(isa(asked, knight)) | truth(or(isa(asked, knight), isa(other, knight))) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 ((truth(isa(asked, knight)) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes) | truth(or(isa(asked, knight), isa(other, knight)))) <=> (truth(isa(asked, knight)) | truth(or(isa(asked, knight), isa(other, knight))) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (((~![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))) | (truth(isa(asked, knight)) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes) | truth(or(isa(asked, knight), isa(other, knight))))) <=> ((~![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))) | (truth(isa(asked, knight)) | truth(or(isa(asked, knight), isa(other, knight))) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (((~![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))) | (truth(isa(asked, knight)) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes) | truth(or(isa(asked, knight), isa(other, knight))))) <=> ((~![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))) | truth(isa(asked, knight)) | truth(or(isa(asked, knight), isa(other, knight))) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes))),
% 0.21/0.41 inference(transitivity,[status(thm)],[44, 42])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 ((~![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))) | (truth(isa(asked, knight)) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes) | truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 ((~![Q: $i, P: $i] : (truth(isa(P, knight)) | reply(P, Q, yes) | truth(Q))) | truth(isa(asked, knight)) | truth(or(isa(asked, knight), isa(other, knight))) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.41 tff(48,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)],[47, 41, 17])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (truth(or(isa(asked, knight), isa(other, knight)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[48, 1])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (^[B: $i, A: $i] : refl((truth(B) | truth(A) | (~truth(or(A, B)))) <=> (truth(B) | truth(A) | (~truth(or(A, B)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (![B: $i, A: $i] : (truth(B) | truth(A) | (~truth(or(A, B)))) <=> ![B: $i, A: $i] : (truth(B) | truth(A) | (~truth(or(A, B))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (![B: $i, A: $i] : (truth(B) | truth(A) | (~truth(or(A, B)))) <=> ![B: $i, A: $i] : (truth(B) | truth(A) | (~truth(or(A, B))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (^[B: $i, A: $i] : rewrite(((truth(A) | truth(B)) | (~truth(or(A, B)))) <=> (truth(B) | truth(A) | (~truth(or(A, B)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (![B: $i, A: $i] : ((truth(A) | truth(B)) | (~truth(or(A, B)))) <=> ![B: $i, A: $i] : (truth(B) | truth(A) | (~truth(or(A, B))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.41 tff(55,axiom,(![B: $i, A: $i] : ((truth(A) | truth(B)) | (~truth(or(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','or1')).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (![B: $i, A: $i] : (truth(B) | truth(A) | (~truth(or(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (![B: $i, A: $i] : (truth(B) | truth(A) | (~truth(or(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.21/0.41 tff(58,plain,(
% 0.21/0.41 ![B: $i, A: $i] : (truth(B) | truth(A) | (~truth(or(A, B))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[57])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (![B: $i, A: $i] : (truth(B) | truth(A) | (~truth(or(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (((~![B: $i, A: $i] : (truth(B) | truth(A) | (~truth(or(A, B))))) | (truth(isa(other, knight)) | truth(isa(asked, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))))) <=> ((~![B: $i, A: $i] : (truth(B) | truth(A) | (~truth(or(A, B))))) | truth(isa(other, knight)) | truth(isa(asked, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 ((~![B: $i, A: $i] : (truth(B) | truth(A) | (~truth(or(A, B))))) | (truth(isa(other, knight)) | truth(isa(asked, knight)) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 ((~![B: $i, A: $i] : (truth(B) | truth(A) | (~truth(or(A, B))))) | truth(isa(other, knight)) | truth(isa(asked, knight)) | (~truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (truth(isa(other, knight)) | truth(isa(asked, knight)) | (~truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[62, 59])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (truth(isa(other, knight))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[63, 1, 49])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (^[R: $i, Y: $i, X: $i] : refl(((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R))) <=> ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R))) <=> ![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R))) <=> ![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (^[R: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~reply(asked, or(isa(asked, knight), isa(other, knight)), R)) | (~truth(isa(asked, X)))) <=> ((~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))), ((((~reply(asked, or(isa(asked, knight), isa(other, knight)), R)) | (~truth(isa(asked, X)))) | (~truth(isa(other, Y)))) <=> (((~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R))) | (~truth(isa(other, Y)))))), rewrite((((~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R))) | (~truth(isa(other, Y)))) <=> ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))), ((((~reply(asked, or(isa(asked, knight), isa(other, knight)), R)) | (~truth(isa(asked, X)))) | (~truth(isa(other, Y)))) <=> ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (![R: $i, Y: $i, X: $i] : (((~reply(asked, or(isa(asked, knight), isa(other, knight)), R)) | (~truth(isa(asked, X)))) | (~truth(isa(other, Y)))) <=> ![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.41 tff(70,axiom,(![R: $i, Y: $i, X: $i] : (((~reply(asked, or(isa(asked, knight), isa(other, knight)), R)) | (~truth(isa(asked, X)))) | (~truth(isa(other, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_answer')).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.21/0.41 tff(73,plain,(
% 0.21/0.41 ![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[72])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~truth(isa(other, knight))) | (~truth(isa(asked, knave))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), no)))) <=> ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knave))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), no)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~truth(isa(other, knight))) | (~truth(isa(asked, knave))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), no)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | (~truth(isa(other, knight))) | (~truth(isa(asked, knave))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), no))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[77, 74, 64, 31, 16])).
% 0.21/0.42 tff(79,plain,(truth(isa(asked, knight)) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (truth(isa(asked, knight))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[79, 17])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (^[Q: $i, P: $i] : refl(((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q))) <=> ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q))) <=> ![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[81])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q))) <=> ![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (^[Q: $i, P: $i] : rewrite((((~truth(Q)) | (~truth(isa(P, knight)))) | reply(P, Q, yes)) <=> ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (![Q: $i, P: $i] : (((~truth(Q)) | (~truth(isa(P, knight)))) | reply(P, Q, yes)) <=> ![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.42 tff(86,axiom,(![Q: $i, P: $i] : (((~truth(Q)) | (~truth(isa(P, knight)))) | reply(P, Q, yes))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','knights_make_true_statements3')).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 (![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.21/0.42 tff(89,plain,(
% 0.21/0.42 ![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[88])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (((~![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))) | (reply(asked, or(isa(asked, knight), isa(other, knight)), yes) | (~truth(isa(asked, knight))) | (~truth(or(isa(asked, knight), isa(other, knight)))))) <=> ((~![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes) | (~truth(isa(asked, knight))) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (((~truth(isa(asked, knight))) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes) | (~truth(or(isa(asked, knight), isa(other, knight))))) <=> (reply(asked, or(isa(asked, knight), isa(other, knight)), yes) | (~truth(isa(asked, knight))) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 (((~![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))) | ((~truth(isa(asked, knight))) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes) | (~truth(or(isa(asked, knight), isa(other, knight)))))) <=> ((~![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))) | (reply(asked, or(isa(asked, knight), isa(other, knight)), yes) | (~truth(isa(asked, knight))) | (~truth(or(isa(asked, knight), isa(other, knight))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (((~![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))) | ((~truth(isa(asked, knight))) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes) | (~truth(or(isa(asked, knight), isa(other, knight)))))) <=> ((~![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes) | (~truth(isa(asked, knight))) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[93, 91])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 ((~![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))) | ((~truth(isa(asked, knight))) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 ((~![Q: $i, P: $i] : ((~truth(isa(P, knight))) | reply(P, Q, yes) | (~truth(Q)))) | reply(asked, or(isa(asked, knight), isa(other, knight)), yes) | (~truth(isa(asked, knight))) | (~truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 ((~truth(isa(asked, knight))) | (~truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[96, 90, 17])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (~truth(or(isa(asked, knight), isa(other, knight)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[97, 80])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (^[B: $i, A: $i] : refl(((~truth(A)) | truth(or(A, B))) <=> ((~truth(A)) | truth(or(A, B))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B))) <=> ![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[99])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B))) <=> ![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (^[B: $i, A: $i] : rewrite((truth(or(A, B)) | (~truth(A))) <=> ((~truth(A)) | truth(or(A, B))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (![B: $i, A: $i] : (truth(or(A, B)) | (~truth(A))) <=> ![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[102])).
% 0.21/0.42 tff(104,axiom,(![B: $i, A: $i] : (truth(or(A, B)) | (~truth(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','or2')).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.21/0.42 tff(107,plain,(
% 0.21/0.42 ![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[106])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (((~![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))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 ((~![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))) | ((~truth(isa(asked, knight))) | truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 ((~![B: $i, A: $i] : ((~truth(A)) | truth(or(A, B)))) | (~truth(isa(asked, knight))) | truth(or(isa(asked, knight), isa(other, knight)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 ((~truth(isa(asked, knight))) | truth(or(isa(asked, knight), isa(other, knight)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[111, 108])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[112, 98, 80])).
% 0.21/0.42 tff(114,plain,(reply(asked, or(isa(asked, knight), isa(other, knight)), yes)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (^[Q: $i, P: $i] : refl((truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q))) <=> (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (![Q: $i, P: $i] : (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q))) <=> ![Q: $i, P: $i] : (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[115])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (![Q: $i, P: $i] : (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q))) <=> ![Q: $i, P: $i] : (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (^[Q: $i, P: $i] : rewrite((((~truth(Q)) | truth(isa(P, knight))) | (~reply(P, Q, yes))) <=> (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (![Q: $i, P: $i] : (((~truth(Q)) | truth(isa(P, knight))) | (~reply(P, Q, yes))) <=> ![Q: $i, P: $i] : (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[118])).
% 0.21/0.42 tff(120,axiom,(![Q: $i, P: $i] : (((~truth(Q)) | truth(isa(P, knight))) | (~reply(P, Q, yes)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','knights_make_true_statements2')).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (![Q: $i, P: $i] : (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (![Q: $i, P: $i] : (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.21/0.42 tff(123,plain,(
% 0.21/0.42 ![Q: $i, P: $i] : (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[122])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 (![Q: $i, P: $i] : (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (((~![Q: $i, P: $i] : (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q)))) | (truth(isa(asked, knight)) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(or(isa(asked, knight), isa(other, knight)))))) <=> ((~![Q: $i, P: $i] : (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q)))) | truth(isa(asked, knight)) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 ((~![Q: $i, P: $i] : (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q)))) | (truth(isa(asked, knight)) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(or(isa(asked, knight), isa(other, knight)))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 ((~![Q: $i, P: $i] : (truth(isa(P, knight)) | (~reply(P, Q, yes)) | (~truth(Q)))) | truth(isa(asked, knight)) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.21/0.43 tff(128,plain,
% 0.21/0.43 (truth(isa(asked, knight)) | (~truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[127, 124, 114])).
% 0.21/0.43 tff(129,plain,
% 0.21/0.43 (~truth(or(isa(asked, knight), isa(other, knight)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[128, 1])).
% 0.21/0.43 tff(130,plain,
% 0.21/0.43 (^[B: $i, A: $i] : refl(((~truth(B)) | truth(or(A, B))) <=> ((~truth(B)) | truth(or(A, B))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(131,plain,
% 0.21/0.43 (![B: $i, A: $i] : ((~truth(B)) | truth(or(A, B))) <=> ![B: $i, A: $i] : ((~truth(B)) | truth(or(A, B)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 (![B: $i, A: $i] : ((~truth(B)) | truth(or(A, B))) <=> ![B: $i, A: $i] : ((~truth(B)) | truth(or(A, B)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(133,plain,
% 0.21/0.43 (^[B: $i, A: $i] : rewrite((truth(or(A, B)) | (~truth(B))) <=> ((~truth(B)) | truth(or(A, B))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 (![B: $i, A: $i] : (truth(or(A, B)) | (~truth(B))) <=> ![B: $i, A: $i] : ((~truth(B)) | truth(or(A, B)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[133])).
% 0.21/0.43 tff(135,axiom,(![B: $i, A: $i] : (truth(or(A, B)) | (~truth(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','or3')).
% 0.21/0.43 tff(136,plain,
% 0.21/0.43 (![B: $i, A: $i] : ((~truth(B)) | truth(or(A, B)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.43 tff(137,plain,
% 0.21/0.43 (![B: $i, A: $i] : ((~truth(B)) | truth(or(A, B)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.21/0.43 tff(138,plain,(
% 0.21/0.43 ![B: $i, A: $i] : ((~truth(B)) | truth(or(A, B)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[137])).
% 0.21/0.43 tff(139,plain,
% 0.21/0.43 (![B: $i, A: $i] : ((~truth(B)) | truth(or(A, B)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 (((~![B: $i, A: $i] : ((~truth(B)) | truth(or(A, B)))) | ((~truth(isa(other, knight))) | truth(or(isa(asked, knight), isa(other, knight))))) <=> ((~![B: $i, A: $i] : ((~truth(B)) | truth(or(A, B)))) | (~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(141,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : ((~truth(B)) | truth(or(A, B)))) | ((~truth(isa(other, knight))) | truth(or(isa(asked, knight), isa(other, knight))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : ((~truth(B)) | truth(or(A, B)))) | (~truth(isa(other, knight))) | truth(or(isa(asked, knight), isa(other, knight)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 ((~truth(isa(other, knight))) | truth(or(isa(asked, knight), isa(other, knight)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[142, 139])).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 (~truth(isa(other, knight))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[143, 129])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 (((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))) | (truth(isa(other, knave)) | truth(isa(other, knight)))) <=> ((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))) | truth(isa(other, knave)) | truth(isa(other, knight)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(146,plain,
% 0.21/0.43 ((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))) | (truth(isa(other, knave)) | truth(isa(other, knight)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 ((~![P: $i] : (truth(isa(P, knave)) | truth(isa(P, knight)))) | truth(isa(other, knave)) | truth(isa(other, knight))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.21/0.43 tff(148,plain,
% 0.21/0.43 (truth(isa(other, knave)) | truth(isa(other, knight))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[147, 11])).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 (truth(isa(other, knave))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[148, 144])).
% 0.21/0.43 tff(150,plain,
% 0.21/0.43 (((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(other, knave))) | (~truth(isa(asked, knave))))) <=> ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(other, knave))) | (~truth(isa(asked, knave))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(151,plain,
% 0.21/0.43 (((~truth(isa(other, knave))) | (~truth(isa(asked, knave))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes))) <=> ((~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(other, knave))) | (~truth(isa(asked, knave))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(152,plain,
% 0.21/0.43 (((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~truth(isa(other, knave))) | (~truth(isa(asked, knave))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)))) <=> ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(other, knave))) | (~truth(isa(asked, knave)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[151])).
% 0.21/0.43 tff(153,plain,
% 0.21/0.43 (((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~truth(isa(other, knave))) | (~truth(isa(asked, knave))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)))) <=> ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(other, knave))) | (~truth(isa(asked, knave))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[152, 150])).
% 0.21/0.43 tff(154,plain,
% 0.21/0.43 ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~truth(isa(other, knave))) | (~truth(isa(asked, knave))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(155,plain,
% 0.21/0.43 ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(other, knave))) | (~truth(isa(asked, knave)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.21/0.43 tff(156,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[155, 74, 114, 149, 16])).
% 0.21/0.43 tff(157,plain,(truth(isa(asked, knight))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(158,plain,
% 0.21/0.43 (((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~truth(isa(other, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(asked, knight))))) <=> ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | (~truth(isa(other, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(asked, knight))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(159,plain,
% 0.21/0.43 (((~truth(isa(other, knight))) | (~truth(isa(asked, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes))) <=> ((~truth(isa(other, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(asked, knight))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(160,plain,
% 0.21/0.43 (((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~truth(isa(other, knight))) | (~truth(isa(asked, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)))) <=> ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~truth(isa(other, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(asked, knight)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[159])).
% 0.21/0.44 tff(161,plain,
% 0.21/0.44 (((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~truth(isa(other, knight))) | (~truth(isa(asked, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)))) <=> ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | (~truth(isa(other, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(asked, knight))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[160, 158])).
% 0.21/0.44 tff(162,plain,
% 0.21/0.44 ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~truth(isa(other, knight))) | (~truth(isa(asked, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(163,plain,
% 0.21/0.44 ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | (~truth(isa(other, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(asked, knight)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.21/0.44 tff(164,plain,
% 0.21/0.44 ((~truth(isa(other, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(asked, knight)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[163, 74])).
% 0.21/0.44 tff(165,plain,
% 0.21/0.44 ((~truth(isa(other, knight))) | (~truth(isa(asked, knight)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[164, 114])).
% 0.21/0.44 tff(166,plain,
% 0.21/0.44 (~truth(isa(other, knight))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[165, 157])).
% 0.21/0.44 tff(167,plain,
% 0.21/0.44 (truth(isa(other, knave))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[148, 166])).
% 0.21/0.44 tff(168,plain,
% 0.21/0.44 (((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(asked, knight))) | (~truth(isa(other, knave))))) <=> ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(asked, knight))) | (~truth(isa(other, knave))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(169,plain,
% 0.21/0.44 (((~truth(isa(other, knave))) | (~truth(isa(asked, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes))) <=> ((~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(asked, knight))) | (~truth(isa(other, knave))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(170,plain,
% 0.21/0.44 (((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~truth(isa(other, knave))) | (~truth(isa(asked, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)))) <=> ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(asked, knight))) | (~truth(isa(other, knave)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[169])).
% 0.21/0.44 tff(171,plain,
% 0.21/0.44 (((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~truth(isa(other, knave))) | (~truth(isa(asked, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)))) <=> ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(asked, knight))) | (~truth(isa(other, knave))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[170, 168])).
% 0.21/0.44 tff(172,plain,
% 0.21/0.44 ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | ((~truth(isa(other, knave))) | (~truth(isa(asked, knight))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(173,plain,
% 0.21/0.44 ((~![R: $i, Y: $i, X: $i] : ((~truth(isa(other, Y))) | (~truth(isa(asked, X))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), R)))) | (~reply(asked, or(isa(asked, knight), isa(other, knight)), yes)) | (~truth(isa(asked, knight))) | (~truth(isa(other, knave)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.21/0.44 tff(174,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[173, 74, 114, 157, 167])).
% 0.21/0.44 % SZS output end Proof
% 0.21/0.44 % E exiting
%------------------------------------------------------------------------------