TSTP Solution File: PUZ021-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ021-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 14:10:54 EDT 2022
% Result : Unsatisfiable 1.11s 0.93s
% Output : Proof 1.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : PUZ021-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 18:17:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 1.11/0.93 % SZS status Unsatisfiable
% 1.11/0.93 % SZS output start Proof
% 1.11/0.93 tff(a_truth_type, type, (
% 1.11/0.93 a_truth: ( $i * $i ) > $o)).
% 1.11/0.93 tff(rich_type, type, (
% 1.11/0.93 rich: $i > $i)).
% 1.11/0.93 tff(elem_0_type, type, (
% 1.11/0.93 elem_0: $i)).
% 1.11/0.93 tff(and_type, type, (
% 1.11/0.93 and: ( $i * $i ) > $i)).
% 1.11/0.93 tff(knight_type, type, (
% 1.11/0.93 knight: $i > $i)).
% 1.11/0.93 tff(me_type, type, (
% 1.11/0.93 me: $i)).
% 1.11/0.93 tff(knave_type, type, (
% 1.11/0.93 knave: $i > $i)).
% 1.11/0.93 tff(says_type, type, (
% 1.11/0.93 says: ( $i * $i ) > $o)).
% 1.11/0.93 tff(poor_type, type, (
% 1.11/0.93 poor: $i > $i)).
% 1.11/0.93 tff(1,assumption,(~a_truth(and(knave(me), rich(me)), and(knight(me), knight(me)))), introduced(assumption)).
% 1.11/0.93 tff(2,assumption,(says(me, knave(me))), introduced(assumption)).
% 1.11/0.93 tff(3,assumption,(a_truth(knave(me), and(poor(me), rich(me)))), introduced(assumption)).
% 1.11/0.93 tff(4,plain,
% 1.11/0.93 (^[Z: $i, Y: $i, X: $i] : refl(((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z))) <=> ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z))))),
% 1.11/0.93 inference(bind,[status(th)],[])).
% 1.11/0.93 tff(5,plain,
% 1.11/0.93 (![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))),
% 1.11/0.93 inference(quant_intro,[status(thm)],[4])).
% 1.11/0.93 tff(6,plain,
% 1.11/0.93 (![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))),
% 1.11/0.93 inference(rewrite,[status(thm)],[])).
% 1.11/0.93 tff(7,plain,
% 1.11/0.93 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~a_truth(knave(X), Z)) | (~says(X, Y))) <=> ((~says(X, Y)) | (~a_truth(knave(X), Z)))), ((((~a_truth(knave(X), Z)) | (~says(X, Y))) | (~a_truth(Y, Z))) <=> (((~says(X, Y)) | (~a_truth(knave(X), Z))) | (~a_truth(Y, Z))))), rewrite((((~says(X, Y)) | (~a_truth(knave(X), Z))) | (~a_truth(Y, Z))) <=> ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))), ((((~a_truth(knave(X), Z)) | (~says(X, Y))) | (~a_truth(Y, Z))) <=> ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))))),
% 1.11/0.93 inference(bind,[status(th)],[])).
% 1.11/0.93 tff(8,plain,
% 1.11/0.93 (![Z: $i, Y: $i, X: $i] : (((~a_truth(knave(X), Z)) | (~says(X, Y))) | (~a_truth(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))),
% 1.11/0.93 inference(quant_intro,[status(thm)],[7])).
% 1.11/0.93 tff(9,axiom,(![Z: $i, Y: $i, X: $i] : (((~a_truth(knave(X), Z)) | (~says(X, Y))) | (~a_truth(Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','knaves_lie1')).
% 1.11/0.93 tff(10,plain,
% 1.11/0.93 (![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))),
% 1.11/0.93 inference(modus_ponens,[status(thm)],[9, 8])).
% 1.11/0.93 tff(11,plain,
% 1.11/0.93 (![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))),
% 1.11/0.93 inference(modus_ponens,[status(thm)],[10, 6])).
% 1.11/0.93 tff(12,plain,(
% 1.11/0.93 ![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))),
% 1.11/0.93 inference(skolemize,[status(sab)],[11])).
% 1.11/0.93 tff(13,plain,
% 1.11/0.93 (![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))),
% 1.11/0.93 inference(modus_ponens,[status(thm)],[12, 5])).
% 1.11/0.93 tff(14,plain,
% 1.11/0.93 (((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~says(me, knave(me))) | (~a_truth(knave(me), and(poor(me), rich(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | (~says(me, knave(me))) | (~a_truth(knave(me), and(poor(me), rich(me)))))),
% 1.11/0.93 inference(rewrite,[status(thm)],[])).
% 1.11/0.93 tff(15,plain,
% 1.11/0.93 (((~says(me, knave(me))) | (~a_truth(knave(me), and(poor(me), rich(me)))) | (~a_truth(knave(me), and(poor(me), rich(me))))) <=> ((~says(me, knave(me))) | (~a_truth(knave(me), and(poor(me), rich(me)))))),
% 1.11/0.93 inference(rewrite,[status(thm)],[])).
% 1.11/0.93 tff(16,plain,
% 1.11/0.93 (((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~says(me, knave(me))) | (~a_truth(knave(me), and(poor(me), rich(me)))) | (~a_truth(knave(me), and(poor(me), rich(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~says(me, knave(me))) | (~a_truth(knave(me), and(poor(me), rich(me))))))),
% 1.12/0.93 inference(monotonicity,[status(thm)],[15])).
% 1.12/0.93 tff(17,plain,
% 1.12/0.93 (((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~says(me, knave(me))) | (~a_truth(knave(me), and(poor(me), rich(me)))) | (~a_truth(knave(me), and(poor(me), rich(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | (~says(me, knave(me))) | (~a_truth(knave(me), and(poor(me), rich(me)))))),
% 1.12/0.93 inference(transitivity,[status(thm)],[16, 14])).
% 1.12/0.93 tff(18,plain,
% 1.12/0.93 ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~says(me, knave(me))) | (~a_truth(knave(me), and(poor(me), rich(me)))) | (~a_truth(knave(me), and(poor(me), rich(me)))))),
% 1.12/0.93 inference(quant_inst,[status(thm)],[])).
% 1.12/0.93 tff(19,plain,
% 1.12/0.93 ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | (~says(me, knave(me))) | (~a_truth(knave(me), and(poor(me), rich(me))))),
% 1.12/0.93 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.12/0.93 tff(20,plain,
% 1.12/0.93 ($false),
% 1.12/0.93 inference(unit_resolution,[status(thm)],[19, 13, 2, 3])).
% 1.12/0.93 tff(21,plain,((~says(me, knave(me))) | (~a_truth(knave(me), and(poor(me), rich(me))))), inference(lemma,lemma(discharge,[]))).
% 1.12/0.93 tff(22,plain,
% 1.12/0.93 (~a_truth(knave(me), and(poor(me), rich(me)))),
% 1.12/0.93 inference(unit_resolution,[status(thm)],[21, 2])).
% 1.12/0.93 tff(23,assumption,(a_truth(and(knave(me), rich(me)), and(poor(me), rich(me)))), introduced(assumption)).
% 1.12/0.93 tff(24,assumption,(~a_truth(knave(me), and(poor(me), rich(me)))), introduced(assumption)).
% 1.12/0.93 tff(25,plain,
% 1.12/0.93 (^[Z: $i, Y: $i, X: $i] : refl(((~a_truth(and(X, Y), Z)) | a_truth(X, Z)) <=> ((~a_truth(and(X, Y), Z)) | a_truth(X, Z)))),
% 1.12/0.93 inference(bind,[status(th)],[])).
% 1.12/0.93 tff(26,plain,
% 1.12/0.93 (![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))),
% 1.12/0.93 inference(quant_intro,[status(thm)],[25])).
% 1.12/0.93 tff(27,plain,
% 1.12/0.93 (![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))),
% 1.12/0.93 inference(rewrite,[status(thm)],[])).
% 1.12/0.93 tff(28,axiom,(![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjunction1')).
% 1.12/0.93 tff(29,plain,
% 1.12/0.93 (![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))),
% 1.12/0.93 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.12/0.93 tff(30,plain,(
% 1.12/0.93 ![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))),
% 1.12/0.93 inference(skolemize,[status(sab)],[29])).
% 1.12/0.93 tff(31,plain,
% 1.12/0.93 (![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))),
% 1.12/0.93 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.12/0.93 tff(32,plain,
% 1.12/0.93 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(knave(me), rich(me)), and(poor(me), rich(me)))) | a_truth(knave(me), and(poor(me), rich(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(knave(me), rich(me)), and(poor(me), rich(me)))) | a_truth(knave(me), and(poor(me), rich(me))))),
% 1.12/0.93 inference(rewrite,[status(thm)],[])).
% 1.12/0.93 tff(33,plain,
% 1.12/0.93 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(knave(me), rich(me)), and(poor(me), rich(me)))) | a_truth(knave(me), and(poor(me), rich(me))))),
% 1.12/0.93 inference(quant_inst,[status(thm)],[])).
% 1.12/0.93 tff(34,plain,
% 1.12/0.93 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(knave(me), rich(me)), and(poor(me), rich(me)))) | a_truth(knave(me), and(poor(me), rich(me)))),
% 1.12/0.93 inference(modus_ponens,[status(thm)],[33, 32])).
% 1.12/0.93 tff(35,plain,
% 1.12/0.93 ($false),
% 1.12/0.93 inference(unit_resolution,[status(thm)],[34, 31, 24, 23])).
% 1.12/0.93 tff(36,plain,((~a_truth(and(knave(me), rich(me)), and(poor(me), rich(me)))) | a_truth(knave(me), and(poor(me), rich(me)))), inference(lemma,lemma(discharge,[]))).
% 1.12/0.93 tff(37,plain,
% 1.12/0.93 (~a_truth(and(knave(me), rich(me)), and(poor(me), rich(me)))),
% 1.12/0.93 inference(unit_resolution,[status(thm)],[36, 22])).
% 1.12/0.94 tff(38,plain,
% 1.12/0.94 (^[X: $i] : refl((says(me, X) | a_truth(and(knave(me), rich(me)), X)) <=> (says(me, X) | a_truth(and(knave(me), rich(me)), X)))),
% 1.12/0.94 inference(bind,[status(th)],[])).
% 1.12/0.94 tff(39,plain,
% 1.12/0.94 (![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X)) <=> ![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))),
% 1.12/0.94 inference(quant_intro,[status(thm)],[38])).
% 1.12/0.94 tff(40,plain,
% 1.12/0.94 (![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X)) <=> ![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(41,axiom,(![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_statement_exists2')).
% 1.12/0.94 tff(42,plain,
% 1.12/0.94 (![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.12/0.94 tff(43,plain,(
% 1.12/0.94 ![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))),
% 1.12/0.94 inference(skolemize,[status(sab)],[42])).
% 1.12/0.94 tff(44,plain,
% 1.12/0.94 (![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[43, 39])).
% 1.12/0.94 tff(45,plain,
% 1.12/0.94 (((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | (a_truth(and(knave(me), rich(me)), and(poor(me), rich(me))) | says(me, and(poor(me), rich(me))))) <=> ((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | a_truth(and(knave(me), rich(me)), and(poor(me), rich(me))) | says(me, and(poor(me), rich(me))))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(46,plain,
% 1.12/0.94 ((says(me, and(poor(me), rich(me))) | a_truth(and(knave(me), rich(me)), and(poor(me), rich(me)))) <=> (a_truth(and(knave(me), rich(me)), and(poor(me), rich(me))) | says(me, and(poor(me), rich(me))))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(47,plain,
% 1.12/0.94 (((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | (says(me, and(poor(me), rich(me))) | a_truth(and(knave(me), rich(me)), and(poor(me), rich(me))))) <=> ((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | (a_truth(and(knave(me), rich(me)), and(poor(me), rich(me))) | says(me, and(poor(me), rich(me)))))),
% 1.12/0.94 inference(monotonicity,[status(thm)],[46])).
% 1.12/0.94 tff(48,plain,
% 1.12/0.94 (((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | (says(me, and(poor(me), rich(me))) | a_truth(and(knave(me), rich(me)), and(poor(me), rich(me))))) <=> ((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | a_truth(and(knave(me), rich(me)), and(poor(me), rich(me))) | says(me, and(poor(me), rich(me))))),
% 1.12/0.94 inference(transitivity,[status(thm)],[47, 45])).
% 1.12/0.94 tff(49,plain,
% 1.12/0.94 ((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | (says(me, and(poor(me), rich(me))) | a_truth(and(knave(me), rich(me)), and(poor(me), rich(me))))),
% 1.12/0.94 inference(quant_inst,[status(thm)],[])).
% 1.12/0.94 tff(50,plain,
% 1.12/0.94 ((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | a_truth(and(knave(me), rich(me)), and(poor(me), rich(me))) | says(me, and(poor(me), rich(me)))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.12/0.94 tff(51,plain,
% 1.12/0.94 (a_truth(and(knave(me), rich(me)), and(poor(me), rich(me))) | says(me, and(poor(me), rich(me)))),
% 1.12/0.94 inference(unit_resolution,[status(thm)],[50, 44])).
% 1.12/0.94 tff(52,plain,
% 1.12/0.94 (says(me, and(poor(me), rich(me)))),
% 1.12/0.94 inference(unit_resolution,[status(thm)],[51, 37])).
% 1.12/0.94 tff(53,assumption,(a_truth(and(poor(me), rich(me)), elem!0)), introduced(assumption)).
% 1.12/0.94 tff(54,plain,
% 1.12/0.94 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(poor(me), rich(me)), elem!0)) | a_truth(poor(me), elem!0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(poor(me), rich(me)), elem!0)) | a_truth(poor(me), elem!0))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(55,plain,
% 1.12/0.94 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(poor(me), rich(me)), elem!0)) | a_truth(poor(me), elem!0))),
% 1.12/0.94 inference(quant_inst,[status(thm)],[])).
% 1.12/0.94 tff(56,plain,
% 1.12/0.94 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(poor(me), rich(me)), elem!0)) | a_truth(poor(me), elem!0)),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.12/0.94 tff(57,plain,
% 1.12/0.94 ((~a_truth(and(poor(me), rich(me)), elem!0)) | a_truth(poor(me), elem!0)),
% 1.12/0.94 inference(unit_resolution,[status(thm)],[56, 31])).
% 1.12/0.94 tff(58,plain,
% 1.12/0.94 (a_truth(poor(me), elem!0)),
% 1.12/0.94 inference(unit_resolution,[status(thm)],[57, 53])).
% 1.12/0.94 tff(59,plain,
% 1.12/0.94 (^[Z: $i, Y: $i, X: $i] : refl(((~a_truth(and(X, Y), Z)) | a_truth(Y, Z)) <=> ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z)))),
% 1.12/0.94 inference(bind,[status(th)],[])).
% 1.12/0.94 tff(60,plain,
% 1.12/0.94 (![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))),
% 1.12/0.94 inference(quant_intro,[status(thm)],[59])).
% 1.12/0.94 tff(61,plain,
% 1.12/0.94 (![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(62,axiom,(![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjunction2')).
% 1.12/0.94 tff(63,plain,
% 1.12/0.94 (![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[62, 61])).
% 1.12/0.94 tff(64,plain,(
% 1.12/0.94 ![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))),
% 1.12/0.94 inference(skolemize,[status(sab)],[63])).
% 1.12/0.94 tff(65,plain,
% 1.12/0.94 (![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.12/0.94 tff(66,plain,
% 1.12/0.94 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(poor(me), rich(me)), elem!0)) | a_truth(rich(me), elem!0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(poor(me), rich(me)), elem!0)) | a_truth(rich(me), elem!0))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(67,plain,
% 1.12/0.94 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(poor(me), rich(me)), elem!0)) | a_truth(rich(me), elem!0))),
% 1.12/0.94 inference(quant_inst,[status(thm)],[])).
% 1.12/0.94 tff(68,plain,
% 1.12/0.94 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(poor(me), rich(me)), elem!0)) | a_truth(rich(me), elem!0)),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.12/0.94 tff(69,plain,
% 1.12/0.94 (a_truth(rich(me), elem!0)),
% 1.12/0.94 inference(unit_resolution,[status(thm)],[68, 65, 53])).
% 1.12/0.94 tff(70,plain,
% 1.12/0.94 (^[Y: $i, X: $i] : refl(((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y))) <=> ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y))))),
% 1.12/0.94 inference(bind,[status(th)],[])).
% 1.12/0.94 tff(71,plain,
% 1.12/0.94 (![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y))) <=> ![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))),
% 1.12/0.94 inference(quant_intro,[status(thm)],[70])).
% 1.12/0.94 tff(72,plain,
% 1.12/0.94 (![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y))) <=> ![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(73,plain,
% 1.12/0.94 (^[Y: $i, X: $i] : rewrite(((~a_truth(rich(X), Y)) | (~a_truth(poor(X), Y))) <=> ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y))))),
% 1.12/0.94 inference(bind,[status(th)],[])).
% 1.12/0.94 tff(74,plain,
% 1.12/0.94 (![Y: $i, X: $i] : ((~a_truth(rich(X), Y)) | (~a_truth(poor(X), Y))) <=> ![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))),
% 1.12/0.94 inference(quant_intro,[status(thm)],[73])).
% 1.12/0.94 tff(75,axiom,(![Y: $i, X: $i] : ((~a_truth(rich(X), Y)) | (~a_truth(poor(X), Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_rich_and_poor')).
% 1.12/0.94 tff(76,plain,
% 1.12/0.94 (![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.12/0.94 tff(77,plain,
% 1.12/0.94 (![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[76, 72])).
% 1.12/0.94 tff(78,plain,(
% 1.12/0.94 ![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))),
% 1.12/0.94 inference(skolemize,[status(sab)],[77])).
% 1.12/0.94 tff(79,plain,
% 1.12/0.94 (![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[78, 71])).
% 1.12/0.94 tff(80,plain,
% 1.12/0.94 (((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | ((~a_truth(poor(me), elem!0)) | (~a_truth(rich(me), elem!0)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | (~a_truth(poor(me), elem!0)) | (~a_truth(rich(me), elem!0)))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(81,plain,
% 1.12/0.94 ((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | ((~a_truth(poor(me), elem!0)) | (~a_truth(rich(me), elem!0)))),
% 1.12/0.94 inference(quant_inst,[status(thm)],[])).
% 1.12/0.94 tff(82,plain,
% 1.12/0.94 ((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | (~a_truth(poor(me), elem!0)) | (~a_truth(rich(me), elem!0))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.12/0.94 tff(83,plain,
% 1.12/0.94 ($false),
% 1.12/0.94 inference(unit_resolution,[status(thm)],[82, 79, 69, 58])).
% 1.12/0.94 tff(84,plain,(~a_truth(and(poor(me), rich(me)), elem!0)), inference(lemma,lemma(discharge,[]))).
% 1.12/0.94 tff(85,assumption,(a_truth(knight(me), elem!0)), introduced(assumption)).
% 1.12/0.94 tff(86,assumption,(says(me, and(poor(me), rich(me)))), introduced(assumption)).
% 1.12/0.94 tff(87,assumption,(~a_truth(and(poor(me), rich(me)), elem!0)), introduced(assumption)).
% 1.12/0.94 tff(88,plain,
% 1.12/0.94 (^[Z: $i, Y: $i, X: $i] : refl((a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z))) <=> (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z))))),
% 1.12/0.94 inference(bind,[status(th)],[])).
% 1.12/0.94 tff(89,plain,
% 1.12/0.94 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z))) <=> ![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))),
% 1.12/0.94 inference(quant_intro,[status(thm)],[88])).
% 1.12/0.94 tff(90,plain,
% 1.12/0.94 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z))) <=> ![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(91,plain,
% 1.12/0.94 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~a_truth(knight(X), Z)) | (~says(X, Y))) <=> ((~says(X, Y)) | (~a_truth(knight(X), Z)))), ((((~a_truth(knight(X), Z)) | (~says(X, Y))) | a_truth(Y, Z)) <=> (((~says(X, Y)) | (~a_truth(knight(X), Z))) | a_truth(Y, Z)))), rewrite((((~says(X, Y)) | (~a_truth(knight(X), Z))) | a_truth(Y, Z)) <=> (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))), ((((~a_truth(knight(X), Z)) | (~says(X, Y))) | a_truth(Y, Z)) <=> (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))))),
% 1.12/0.94 inference(bind,[status(th)],[])).
% 1.12/0.94 tff(92,plain,
% 1.12/0.94 (![Z: $i, Y: $i, X: $i] : (((~a_truth(knight(X), Z)) | (~says(X, Y))) | a_truth(Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))),
% 1.12/0.94 inference(quant_intro,[status(thm)],[91])).
% 1.12/0.94 tff(93,axiom,(![Z: $i, Y: $i, X: $i] : (((~a_truth(knight(X), Z)) | (~says(X, Y))) | a_truth(Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','knights_tell_truth1')).
% 1.12/0.94 tff(94,plain,
% 1.12/0.94 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.12/0.94 tff(95,plain,
% 1.12/0.94 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[94, 90])).
% 1.12/0.94 tff(96,plain,(
% 1.12/0.94 ![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))),
% 1.12/0.94 inference(skolemize,[status(sab)],[95])).
% 1.12/0.94 tff(97,plain,
% 1.12/0.94 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[96, 89])).
% 1.12/0.94 tff(98,plain,
% 1.12/0.94 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | ((~a_truth(knight(me), elem!0)) | a_truth(and(poor(me), rich(me)), elem!0) | (~says(me, and(poor(me), rich(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (~a_truth(knight(me), elem!0)) | a_truth(and(poor(me), rich(me)), elem!0) | (~says(me, and(poor(me), rich(me)))))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(99,plain,
% 1.12/0.94 ((a_truth(and(poor(me), rich(me)), elem!0) | (~says(me, and(poor(me), rich(me)))) | (~a_truth(knight(me), elem!0))) <=> ((~a_truth(knight(me), elem!0)) | a_truth(and(poor(me), rich(me)), elem!0) | (~says(me, and(poor(me), rich(me)))))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(100,plain,
% 1.12/0.94 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(and(poor(me), rich(me)), elem!0) | (~says(me, and(poor(me), rich(me)))) | (~a_truth(knight(me), elem!0)))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | ((~a_truth(knight(me), elem!0)) | a_truth(and(poor(me), rich(me)), elem!0) | (~says(me, and(poor(me), rich(me))))))),
% 1.12/0.94 inference(monotonicity,[status(thm)],[99])).
% 1.12/0.94 tff(101,plain,
% 1.12/0.94 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(and(poor(me), rich(me)), elem!0) | (~says(me, and(poor(me), rich(me)))) | (~a_truth(knight(me), elem!0)))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (~a_truth(knight(me), elem!0)) | a_truth(and(poor(me), rich(me)), elem!0) | (~says(me, and(poor(me), rich(me)))))),
% 1.12/0.94 inference(transitivity,[status(thm)],[100, 98])).
% 1.12/0.94 tff(102,plain,
% 1.12/0.94 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(and(poor(me), rich(me)), elem!0) | (~says(me, and(poor(me), rich(me)))) | (~a_truth(knight(me), elem!0)))),
% 1.12/0.94 inference(quant_inst,[status(thm)],[])).
% 1.12/0.94 tff(103,plain,
% 1.12/0.94 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (~a_truth(knight(me), elem!0)) | a_truth(and(poor(me), rich(me)), elem!0) | (~says(me, and(poor(me), rich(me))))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.12/0.94 tff(104,plain,
% 1.12/0.94 ($false),
% 1.12/0.94 inference(unit_resolution,[status(thm)],[103, 97, 87, 86, 85])).
% 1.12/0.94 tff(105,plain,(a_truth(and(poor(me), rich(me)), elem!0) | (~says(me, and(poor(me), rich(me)))) | (~a_truth(knight(me), elem!0))), inference(lemma,lemma(discharge,[]))).
% 1.12/0.94 tff(106,plain,
% 1.12/0.94 ((~says(me, and(poor(me), rich(me)))) | (~a_truth(knight(me), elem!0))),
% 1.12/0.94 inference(unit_resolution,[status(thm)],[105, 84])).
% 1.12/0.94 tff(107,plain,
% 1.12/0.94 (~a_truth(knight(me), elem!0)),
% 1.12/0.94 inference(unit_resolution,[status(thm)],[106, 52])).
% 1.12/0.94 tff(108,assumption,(a_truth(knave(me), elem!0)), introduced(assumption)).
% 1.12/0.94 tff(109,plain,
% 1.12/0.94 (((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), elem!0)) | (~says(me, knave(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), elem!0)) | (~says(me, knave(me))))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(110,plain,
% 1.12/0.94 (((~says(me, knave(me))) | (~a_truth(knave(me), elem!0)) | (~a_truth(knave(me), elem!0))) <=> ((~a_truth(knave(me), elem!0)) | (~says(me, knave(me))))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(111,plain,
% 1.12/0.94 (((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~says(me, knave(me))) | (~a_truth(knave(me), elem!0)) | (~a_truth(knave(me), elem!0)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), elem!0)) | (~says(me, knave(me)))))),
% 1.12/0.94 inference(monotonicity,[status(thm)],[110])).
% 1.12/0.94 tff(112,plain,
% 1.12/0.94 (((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~says(me, knave(me))) | (~a_truth(knave(me), elem!0)) | (~a_truth(knave(me), elem!0)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), elem!0)) | (~says(me, knave(me))))),
% 1.12/0.94 inference(transitivity,[status(thm)],[111, 109])).
% 1.12/0.94 tff(113,plain,
% 1.12/0.94 ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~says(me, knave(me))) | (~a_truth(knave(me), elem!0)) | (~a_truth(knave(me), elem!0)))),
% 1.12/0.94 inference(quant_inst,[status(thm)],[])).
% 1.12/0.94 tff(114,plain,
% 1.12/0.94 ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), elem!0)) | (~says(me, knave(me)))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.12/0.94 tff(115,plain,
% 1.12/0.94 ($false),
% 1.12/0.94 inference(unit_resolution,[status(thm)],[114, 13, 108, 2])).
% 1.12/0.94 tff(116,plain,((~says(me, knave(me))) | (~a_truth(knave(me), elem!0))), inference(lemma,lemma(discharge,[]))).
% 1.12/0.94 tff(117,plain,
% 1.12/0.94 (~a_truth(knave(me), elem!0)),
% 1.12/0.94 inference(unit_resolution,[status(thm)],[116, 2])).
% 1.12/0.94 tff(118,plain,
% 1.12/0.94 (^[Y: $i, X: $i] : refl((a_truth(knave(X), Y) | a_truth(knight(X), Y)) <=> (a_truth(knave(X), Y) | a_truth(knight(X), Y)))),
% 1.12/0.94 inference(bind,[status(th)],[])).
% 1.12/0.94 tff(119,plain,
% 1.12/0.94 (![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y)) <=> ![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))),
% 1.12/0.94 inference(quant_intro,[status(thm)],[118])).
% 1.12/0.94 tff(120,plain,
% 1.12/0.94 (![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y)) <=> ![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(121,plain,
% 1.12/0.94 (^[Y: $i, X: $i] : rewrite((a_truth(knight(X), Y) | a_truth(knave(X), Y)) <=> (a_truth(knave(X), Y) | a_truth(knight(X), Y)))),
% 1.12/0.94 inference(bind,[status(th)],[])).
% 1.12/0.94 tff(122,plain,
% 1.12/0.94 (![Y: $i, X: $i] : (a_truth(knight(X), Y) | a_truth(knave(X), Y)) <=> ![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))),
% 1.12/0.94 inference(quant_intro,[status(thm)],[121])).
% 1.12/0.94 tff(123,axiom,(![Y: $i, X: $i] : (a_truth(knight(X), Y) | a_truth(knave(X), Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','knight_or_knave')).
% 1.12/0.94 tff(124,plain,
% 1.12/0.94 (![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.12/0.94 tff(125,plain,
% 1.12/0.94 (![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[124, 120])).
% 1.12/0.94 tff(126,plain,(
% 1.12/0.94 ![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))),
% 1.12/0.94 inference(skolemize,[status(sab)],[125])).
% 1.12/0.94 tff(127,plain,
% 1.12/0.94 (![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[126, 119])).
% 1.12/0.94 tff(128,plain,
% 1.12/0.94 (((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | (a_truth(knave(me), elem!0) | a_truth(knight(me), elem!0))) <=> ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | a_truth(knave(me), elem!0) | a_truth(knight(me), elem!0))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(129,plain,
% 1.12/0.94 ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | (a_truth(knave(me), elem!0) | a_truth(knight(me), elem!0))),
% 1.12/0.94 inference(quant_inst,[status(thm)],[])).
% 1.12/0.94 tff(130,plain,
% 1.12/0.94 ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | a_truth(knave(me), elem!0) | a_truth(knight(me), elem!0)),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[129, 128])).
% 1.12/0.94 tff(131,plain,
% 1.12/0.94 ($false),
% 1.12/0.94 inference(unit_resolution,[status(thm)],[130, 127, 117, 107])).
% 1.12/0.94 tff(132,plain,(~says(me, knave(me))), inference(lemma,lemma(discharge,[]))).
% 1.12/0.94 tff(133,plain,
% 1.12/0.94 (((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | (says(me, knave(me)) | a_truth(and(knave(me), rich(me)), knave(me)))) <=> ((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | says(me, knave(me)) | a_truth(and(knave(me), rich(me)), knave(me)))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(134,plain,
% 1.12/0.94 ((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | (says(me, knave(me)) | a_truth(and(knave(me), rich(me)), knave(me)))),
% 1.12/0.94 inference(quant_inst,[status(thm)],[])).
% 1.12/0.94 tff(135,plain,
% 1.12/0.94 ((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | says(me, knave(me)) | a_truth(and(knave(me), rich(me)), knave(me))),
% 1.12/0.94 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.12/0.94 tff(136,plain,
% 1.12/0.94 (says(me, knave(me)) | a_truth(and(knave(me), rich(me)), knave(me))),
% 1.12/0.94 inference(unit_resolution,[status(thm)],[135, 44])).
% 1.12/0.94 tff(137,plain,
% 1.12/0.94 (a_truth(and(knave(me), rich(me)), knave(me))),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[136, 132])).
% 1.12/0.95 tff(138,assumption,(~a_truth(knave(me), knave(me))), introduced(assumption)).
% 1.12/0.95 tff(139,assumption,(a_truth(and(knave(me), rich(me)), knave(me))), introduced(assumption)).
% 1.12/0.95 tff(140,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(knave(me), rich(me)), knave(me))) | a_truth(knave(me), knave(me)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | a_truth(knave(me), knave(me)))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(141,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(knave(me), rich(me)), knave(me))) | a_truth(knave(me), knave(me)))),
% 1.12/0.95 inference(quant_inst,[status(thm)],[])).
% 1.12/0.95 tff(142,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | a_truth(knave(me), knave(me))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[141, 140])).
% 1.12/0.95 tff(143,plain,
% 1.12/0.95 ($false),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[142, 31, 139, 138])).
% 1.12/0.95 tff(144,plain,((~a_truth(and(knave(me), rich(me)), knave(me))) | a_truth(knave(me), knave(me))), inference(lemma,lemma(discharge,[]))).
% 1.12/0.95 tff(145,plain,
% 1.12/0.95 (a_truth(knave(me), knave(me))),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[144, 137])).
% 1.12/0.95 tff(146,assumption,(says(me, and(knave(me), rich(me)))), introduced(assumption)).
% 1.12/0.95 tff(147,assumption,(a_truth(knave(me), knave(me))), introduced(assumption)).
% 1.12/0.95 tff(148,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), knave(me))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | (~says(me, and(knave(me), rich(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), knave(me))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | (~says(me, and(knave(me), rich(me)))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(149,plain,
% 1.12/0.95 (((~says(me, and(knave(me), rich(me)))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | (~a_truth(knave(me), knave(me)))) <=> ((~a_truth(knave(me), knave(me))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | (~says(me, and(knave(me), rich(me)))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(150,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~says(me, and(knave(me), rich(me)))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | (~a_truth(knave(me), knave(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), knave(me))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | (~says(me, and(knave(me), rich(me))))))),
% 1.12/0.95 inference(monotonicity,[status(thm)],[149])).
% 1.12/0.95 tff(151,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~says(me, and(knave(me), rich(me)))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | (~a_truth(knave(me), knave(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), knave(me))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | (~says(me, and(knave(me), rich(me)))))),
% 1.12/0.95 inference(transitivity,[status(thm)],[150, 148])).
% 1.12/0.95 tff(152,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~says(me, and(knave(me), rich(me)))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | (~a_truth(knave(me), knave(me))))),
% 1.12/0.95 inference(quant_inst,[status(thm)],[])).
% 1.12/0.95 tff(153,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), knave(me))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | (~says(me, and(knave(me), rich(me))))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.12/0.95 tff(154,plain,
% 1.12/0.95 ($false),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[153, 13, 139, 147, 146])).
% 1.12/0.95 tff(155,plain,((~says(me, and(knave(me), rich(me)))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | (~a_truth(knave(me), knave(me)))), inference(lemma,lemma(discharge,[]))).
% 1.12/0.95 tff(156,plain,
% 1.12/0.95 (~says(me, and(knave(me), rich(me)))),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[155, 145, 137])).
% 1.12/0.95 tff(157,assumption,(~a_truth(knave(me), and(knight(me), knight(me)))), introduced(assumption)).
% 1.12/0.95 tff(158,plain,
% 1.12/0.95 (((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | (a_truth(knave(me), and(knight(me), knight(me))) | a_truth(knight(me), and(knight(me), knight(me))))) <=> ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | a_truth(knave(me), and(knight(me), knight(me))) | a_truth(knight(me), and(knight(me), knight(me))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(159,plain,
% 1.12/0.95 ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | (a_truth(knave(me), and(knight(me), knight(me))) | a_truth(knight(me), and(knight(me), knight(me))))),
% 1.12/0.95 inference(quant_inst,[status(thm)],[])).
% 1.12/0.95 tff(160,plain,
% 1.12/0.95 ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | a_truth(knave(me), and(knight(me), knight(me))) | a_truth(knight(me), and(knight(me), knight(me)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[159, 158])).
% 1.12/0.95 tff(161,plain,
% 1.12/0.95 (a_truth(knave(me), and(knight(me), knight(me))) | a_truth(knight(me), and(knight(me), knight(me)))),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[160, 127])).
% 1.12/0.95 tff(162,plain,
% 1.12/0.95 (a_truth(knight(me), and(knight(me), knight(me)))),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[161, 157])).
% 1.12/0.95 tff(163,assumption,(a_truth(and(poor(me), knave(me)), and(knight(me), knight(me)))), introduced(assumption)).
% 1.12/0.95 tff(164,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(poor(me), knave(me)), and(knight(me), knight(me)))) | a_truth(knave(me), and(knight(me), knight(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(poor(me), knave(me)), and(knight(me), knight(me)))) | a_truth(knave(me), and(knight(me), knight(me))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(165,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(poor(me), knave(me)), and(knight(me), knight(me)))) | a_truth(knave(me), and(knight(me), knight(me))))),
% 1.12/0.95 inference(quant_inst,[status(thm)],[])).
% 1.12/0.95 tff(166,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(poor(me), knave(me)), and(knight(me), knight(me)))) | a_truth(knave(me), and(knight(me), knight(me)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[165, 164])).
% 1.12/0.95 tff(167,plain,
% 1.12/0.95 ($false),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[166, 65, 157, 163])).
% 1.12/0.95 tff(168,plain,((~a_truth(and(poor(me), knave(me)), and(knight(me), knight(me)))) | a_truth(knave(me), and(knight(me), knight(me)))), inference(lemma,lemma(discharge,[]))).
% 1.12/0.95 tff(169,plain,
% 1.12/0.95 (~a_truth(and(poor(me), knave(me)), and(knight(me), knight(me)))),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[168, 157])).
% 1.12/0.95 tff(170,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(knave(me), rich(me)), knave(me))) | a_truth(rich(me), knave(me)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | a_truth(rich(me), knave(me)))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(171,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(knave(me), rich(me)), knave(me))) | a_truth(rich(me), knave(me)))),
% 1.12/0.95 inference(quant_inst,[status(thm)],[])).
% 1.12/0.95 tff(172,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | a_truth(rich(me), knave(me))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[171, 170])).
% 1.12/0.95 tff(173,plain,
% 1.12/0.95 (a_truth(rich(me), knave(me))),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[172, 65, 137])).
% 1.12/0.95 tff(174,plain,
% 1.12/0.95 (((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | ((~a_truth(poor(me), knave(me))) | (~a_truth(rich(me), knave(me))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | (~a_truth(poor(me), knave(me))) | (~a_truth(rich(me), knave(me))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(175,plain,
% 1.12/0.95 ((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | ((~a_truth(poor(me), knave(me))) | (~a_truth(rich(me), knave(me))))),
% 1.12/0.95 inference(quant_inst,[status(thm)],[])).
% 1.12/0.95 tff(176,plain,
% 1.12/0.95 ((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | (~a_truth(poor(me), knave(me))) | (~a_truth(rich(me), knave(me)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.12/0.95 tff(177,plain,
% 1.12/0.95 (~a_truth(poor(me), knave(me))),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[176, 79, 173])).
% 1.12/0.95 tff(178,assumption,(a_truth(and(poor(me), knave(me)), knave(me))), introduced(assumption)).
% 1.12/0.95 tff(179,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(poor(me), knave(me)), knave(me))) | a_truth(poor(me), knave(me)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(poor(me), knave(me)), knave(me))) | a_truth(poor(me), knave(me)))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(180,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(poor(me), knave(me)), knave(me))) | a_truth(poor(me), knave(me)))),
% 1.12/0.95 inference(quant_inst,[status(thm)],[])).
% 1.12/0.95 tff(181,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(poor(me), knave(me)), knave(me))) | a_truth(poor(me), knave(me))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[180, 179])).
% 1.12/0.95 tff(182,plain,
% 1.12/0.95 ($false),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[181, 31, 178, 177])).
% 1.12/0.95 tff(183,plain,(~a_truth(and(poor(me), knave(me)), knave(me))), inference(lemma,lemma(discharge,[]))).
% 1.12/0.95 tff(184,plain,
% 1.12/0.95 (^[Z: $i, Y: $i, X: $i] : refl((a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z))) <=> (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z))))),
% 1.12/0.95 inference(bind,[status(th)],[])).
% 1.12/0.95 tff(185,plain,
% 1.12/0.95 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z))) <=> ![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))),
% 1.12/0.95 inference(quant_intro,[status(thm)],[184])).
% 1.12/0.95 tff(186,plain,
% 1.12/0.95 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z))) <=> ![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(187,plain,
% 1.12/0.95 (^[Z: $i, Y: $i, X: $i] : rewrite((((~a_truth(knave(X), Z)) | says(X, Y)) | a_truth(Y, Z)) <=> (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z))))),
% 1.12/0.95 inference(bind,[status(th)],[])).
% 1.12/0.95 tff(188,plain,
% 1.12/0.95 (![Z: $i, Y: $i, X: $i] : (((~a_truth(knave(X), Z)) | says(X, Y)) | a_truth(Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))),
% 1.12/0.95 inference(quant_intro,[status(thm)],[187])).
% 1.12/0.95 tff(189,axiom,(![Z: $i, Y: $i, X: $i] : (((~a_truth(knave(X), Z)) | says(X, Y)) | a_truth(Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','knaves_lie2')).
% 1.12/0.95 tff(190,plain,
% 1.12/0.95 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[189, 188])).
% 1.12/0.95 tff(191,plain,
% 1.12/0.95 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[190, 186])).
% 1.12/0.95 tff(192,plain,(
% 1.12/0.95 ![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))),
% 1.12/0.95 inference(skolemize,[status(sab)],[191])).
% 1.12/0.95 tff(193,plain,
% 1.12/0.95 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[192, 185])).
% 1.12/0.95 tff(194,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), knave(me))) | says(me, and(poor(me), knave(me))) | a_truth(and(poor(me), knave(me)), knave(me)))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), knave(me))) | says(me, and(poor(me), knave(me))) | a_truth(and(poor(me), knave(me)), knave(me)))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(195,plain,
% 1.12/0.95 ((a_truth(and(poor(me), knave(me)), knave(me)) | says(me, and(poor(me), knave(me))) | (~a_truth(knave(me), knave(me)))) <=> ((~a_truth(knave(me), knave(me))) | says(me, and(poor(me), knave(me))) | a_truth(and(poor(me), knave(me)), knave(me)))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(196,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(poor(me), knave(me)), knave(me)) | says(me, and(poor(me), knave(me))) | (~a_truth(knave(me), knave(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), knave(me))) | says(me, and(poor(me), knave(me))) | a_truth(and(poor(me), knave(me)), knave(me))))),
% 1.12/0.95 inference(monotonicity,[status(thm)],[195])).
% 1.12/0.95 tff(197,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(poor(me), knave(me)), knave(me)) | says(me, and(poor(me), knave(me))) | (~a_truth(knave(me), knave(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), knave(me))) | says(me, and(poor(me), knave(me))) | a_truth(and(poor(me), knave(me)), knave(me)))),
% 1.12/0.95 inference(transitivity,[status(thm)],[196, 194])).
% 1.12/0.95 tff(198,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(poor(me), knave(me)), knave(me)) | says(me, and(poor(me), knave(me))) | (~a_truth(knave(me), knave(me))))),
% 1.12/0.95 inference(quant_inst,[status(thm)],[])).
% 1.12/0.95 tff(199,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), knave(me))) | says(me, and(poor(me), knave(me))) | a_truth(and(poor(me), knave(me)), knave(me))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[198, 197])).
% 1.12/0.95 tff(200,plain,
% 1.12/0.95 ((~a_truth(knave(me), knave(me))) | says(me, and(poor(me), knave(me))) | a_truth(and(poor(me), knave(me)), knave(me))),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[199, 193])).
% 1.12/0.95 tff(201,plain,
% 1.12/0.95 (says(me, and(poor(me), knave(me))) | a_truth(and(poor(me), knave(me)), knave(me))),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[200, 145])).
% 1.12/0.95 tff(202,plain,
% 1.12/0.95 (says(me, and(poor(me), knave(me)))),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[201, 183])).
% 1.12/0.95 tff(203,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | ((~a_truth(knight(me), and(knight(me), knight(me)))) | a_truth(and(poor(me), knave(me)), and(knight(me), knight(me))) | (~says(me, and(poor(me), knave(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (~a_truth(knight(me), and(knight(me), knight(me)))) | a_truth(and(poor(me), knave(me)), and(knight(me), knight(me))) | (~says(me, and(poor(me), knave(me)))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(204,plain,
% 1.12/0.95 ((a_truth(and(poor(me), knave(me)), and(knight(me), knight(me))) | (~says(me, and(poor(me), knave(me)))) | (~a_truth(knight(me), and(knight(me), knight(me))))) <=> ((~a_truth(knight(me), and(knight(me), knight(me)))) | a_truth(and(poor(me), knave(me)), and(knight(me), knight(me))) | (~says(me, and(poor(me), knave(me)))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(205,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(and(poor(me), knave(me)), and(knight(me), knight(me))) | (~says(me, and(poor(me), knave(me)))) | (~a_truth(knight(me), and(knight(me), knight(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | ((~a_truth(knight(me), and(knight(me), knight(me)))) | a_truth(and(poor(me), knave(me)), and(knight(me), knight(me))) | (~says(me, and(poor(me), knave(me))))))),
% 1.12/0.95 inference(monotonicity,[status(thm)],[204])).
% 1.12/0.95 tff(206,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(and(poor(me), knave(me)), and(knight(me), knight(me))) | (~says(me, and(poor(me), knave(me)))) | (~a_truth(knight(me), and(knight(me), knight(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (~a_truth(knight(me), and(knight(me), knight(me)))) | a_truth(and(poor(me), knave(me)), and(knight(me), knight(me))) | (~says(me, and(poor(me), knave(me)))))),
% 1.12/0.95 inference(transitivity,[status(thm)],[205, 203])).
% 1.12/0.95 tff(207,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(and(poor(me), knave(me)), and(knight(me), knight(me))) | (~says(me, and(poor(me), knave(me)))) | (~a_truth(knight(me), and(knight(me), knight(me)))))),
% 1.12/0.95 inference(quant_inst,[status(thm)],[])).
% 1.12/0.95 tff(208,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (~a_truth(knight(me), and(knight(me), knight(me)))) | a_truth(and(poor(me), knave(me)), and(knight(me), knight(me))) | (~says(me, and(poor(me), knave(me))))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.12/0.95 tff(209,plain,
% 1.12/0.95 ((~a_truth(knight(me), and(knight(me), knight(me)))) | a_truth(and(poor(me), knave(me)), and(knight(me), knight(me))) | (~says(me, and(poor(me), knave(me))))),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[208, 97])).
% 1.12/0.95 tff(210,plain,
% 1.12/0.95 ((~a_truth(knight(me), and(knight(me), knight(me)))) | a_truth(and(poor(me), knave(me)), and(knight(me), knight(me)))),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[209, 202])).
% 1.12/0.95 tff(211,plain,
% 1.12/0.95 ($false),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[210, 169, 162])).
% 1.12/0.95 tff(212,plain,(a_truth(knave(me), and(knight(me), knight(me)))), inference(lemma,lemma(discharge,[]))).
% 1.12/0.95 tff(213,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (says(me, and(knave(me), rich(me))) | a_truth(and(knave(me), rich(me)), and(knight(me), knight(me))) | (~a_truth(knave(me), and(knight(me), knight(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | says(me, and(knave(me), rich(me))) | a_truth(and(knave(me), rich(me)), and(knight(me), knight(me))) | (~a_truth(knave(me), and(knight(me), knight(me)))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(214,plain,
% 1.12/0.95 ((a_truth(and(knave(me), rich(me)), and(knight(me), knight(me))) | says(me, and(knave(me), rich(me))) | (~a_truth(knave(me), and(knight(me), knight(me))))) <=> (says(me, and(knave(me), rich(me))) | a_truth(and(knave(me), rich(me)), and(knight(me), knight(me))) | (~a_truth(knave(me), and(knight(me), knight(me)))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(215,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(knave(me), rich(me)), and(knight(me), knight(me))) | says(me, and(knave(me), rich(me))) | (~a_truth(knave(me), and(knight(me), knight(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (says(me, and(knave(me), rich(me))) | a_truth(and(knave(me), rich(me)), and(knight(me), knight(me))) | (~a_truth(knave(me), and(knight(me), knight(me))))))),
% 1.12/0.95 inference(monotonicity,[status(thm)],[214])).
% 1.12/0.95 tff(216,plain,
% 1.12/0.95 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(knave(me), rich(me)), and(knight(me), knight(me))) | says(me, and(knave(me), rich(me))) | (~a_truth(knave(me), and(knight(me), knight(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | says(me, and(knave(me), rich(me))) | a_truth(and(knave(me), rich(me)), and(knight(me), knight(me))) | (~a_truth(knave(me), and(knight(me), knight(me)))))),
% 1.12/0.95 inference(transitivity,[status(thm)],[215, 213])).
% 1.12/0.95 tff(217,plain,
% 1.12/0.95 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(knave(me), rich(me)), and(knight(me), knight(me))) | says(me, and(knave(me), rich(me))) | (~a_truth(knave(me), and(knight(me), knight(me)))))),
% 1.12/0.96 inference(quant_inst,[status(thm)],[])).
% 1.12/0.96 tff(218,plain,
% 1.12/0.96 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | says(me, and(knave(me), rich(me))) | a_truth(and(knave(me), rich(me)), and(knight(me), knight(me))) | (~a_truth(knave(me), and(knight(me), knight(me))))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[217, 216])).
% 1.12/0.96 tff(219,plain,
% 1.12/0.96 ($false),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[218, 193, 212, 156, 1])).
% 1.12/0.96 tff(220,plain,(a_truth(and(knave(me), rich(me)), and(knight(me), knight(me)))), inference(lemma,lemma(discharge,[]))).
% 1.12/0.96 tff(221,plain,
% 1.12/0.96 (^[X: $i] : refl(((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X))) <=> ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X))))),
% 1.12/0.96 inference(bind,[status(th)],[])).
% 1.12/0.96 tff(222,plain,
% 1.12/0.96 (![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X))) <=> ![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))),
% 1.12/0.96 inference(quant_intro,[status(thm)],[221])).
% 1.12/0.96 tff(223,plain,
% 1.12/0.96 (![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X))) <=> ![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(224,axiom,(![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_statement_exists1')).
% 1.12/0.96 tff(225,plain,
% 1.12/0.96 (![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[224, 223])).
% 1.12/0.96 tff(226,plain,(
% 1.12/0.96 ![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))),
% 1.12/0.96 inference(skolemize,[status(sab)],[225])).
% 1.12/0.96 tff(227,plain,
% 1.12/0.96 (![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[226, 222])).
% 1.12/0.96 tff(228,plain,
% 1.12/0.96 (((~![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))) | ((~says(me, and(knight(me), knight(me)))) | (~a_truth(and(knave(me), rich(me)), and(knight(me), knight(me)))))) <=> ((~![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))) | (~says(me, and(knight(me), knight(me)))) | (~a_truth(and(knave(me), rich(me)), and(knight(me), knight(me)))))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(229,plain,
% 1.12/0.96 ((~![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))) | ((~says(me, and(knight(me), knight(me)))) | (~a_truth(and(knave(me), rich(me)), and(knight(me), knight(me)))))),
% 1.12/0.96 inference(quant_inst,[status(thm)],[])).
% 1.12/0.96 tff(230,plain,
% 1.12/0.96 ((~![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))) | (~says(me, and(knight(me), knight(me)))) | (~a_truth(and(knave(me), rich(me)), and(knight(me), knight(me))))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[229, 228])).
% 1.12/0.96 tff(231,plain,
% 1.12/0.96 (~says(me, and(knight(me), knight(me)))),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[230, 227, 220])).
% 1.12/0.96 tff(232,assumption,(a_truth(knight(me), rich(elem!0))), introduced(assumption)).
% 1.12/0.96 tff(233,plain,
% 1.12/0.96 (^[Z: $i, Y: $i, X: $i] : refl(((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z))) <=> ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z))))),
% 1.12/0.96 inference(bind,[status(th)],[])).
% 1.12/0.96 tff(234,plain,
% 1.12/0.96 (![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))),
% 1.12/0.96 inference(quant_intro,[status(thm)],[233])).
% 1.12/0.96 tff(235,plain,
% 1.12/0.96 (![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(236,plain,
% 1.12/0.96 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((a_truth(and(X, Y), Z) | (~a_truth(X, Z))) <=> (a_truth(and(X, Y), Z) | (~a_truth(X, Z)))), (((a_truth(and(X, Y), Z) | (~a_truth(X, Z))) | (~a_truth(Y, Z))) <=> ((a_truth(and(X, Y), Z) | (~a_truth(X, Z))) | (~a_truth(Y, Z))))), rewrite(((a_truth(and(X, Y), Z) | (~a_truth(X, Z))) | (~a_truth(Y, Z))) <=> ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))), (((a_truth(and(X, Y), Z) | (~a_truth(X, Z))) | (~a_truth(Y, Z))) <=> ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))))),
% 1.12/0.96 inference(bind,[status(th)],[])).
% 1.12/0.96 tff(237,plain,
% 1.12/0.96 (![Z: $i, Y: $i, X: $i] : ((a_truth(and(X, Y), Z) | (~a_truth(X, Z))) | (~a_truth(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))),
% 1.12/0.96 inference(quant_intro,[status(thm)],[236])).
% 1.12/0.96 tff(238,axiom,(![Z: $i, Y: $i, X: $i] : ((a_truth(and(X, Y), Z) | (~a_truth(X, Z))) | (~a_truth(Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjunction3')).
% 1.12/0.96 tff(239,plain,
% 1.12/0.96 (![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[238, 237])).
% 1.12/0.96 tff(240,plain,
% 1.12/0.96 (![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[239, 235])).
% 1.12/0.96 tff(241,plain,(
% 1.12/0.96 ![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))),
% 1.12/0.96 inference(skolemize,[status(sab)],[240])).
% 1.12/0.96 tff(242,plain,
% 1.12/0.96 (![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[241, 234])).
% 1.12/0.96 tff(243,plain,
% 1.12/0.96 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | ((~a_truth(knight(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | (~a_truth(knight(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0)))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(244,plain,
% 1.12/0.96 (((~a_truth(knight(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0)) | (~a_truth(knight(me), rich(elem!0)))) <=> ((~a_truth(knight(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0)))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(245,plain,
% 1.12/0.96 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | ((~a_truth(knight(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0)) | (~a_truth(knight(me), rich(elem!0))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | ((~a_truth(knight(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0))))),
% 1.12/0.96 inference(monotonicity,[status(thm)],[244])).
% 1.12/0.96 tff(246,plain,
% 1.12/0.96 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | ((~a_truth(knight(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0)) | (~a_truth(knight(me), rich(elem!0))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | (~a_truth(knight(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0)))),
% 1.12/0.96 inference(transitivity,[status(thm)],[245, 243])).
% 1.12/0.96 tff(247,plain,
% 1.12/0.96 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | ((~a_truth(knight(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0)) | (~a_truth(knight(me), rich(elem!0))))),
% 1.12/0.96 inference(quant_inst,[status(thm)],[])).
% 1.12/0.96 tff(248,plain,
% 1.12/0.96 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | (~a_truth(knight(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[247, 246])).
% 1.12/0.96 tff(249,plain,
% 1.12/0.96 ((~a_truth(knight(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0))),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[248, 242])).
% 1.12/0.96 tff(250,plain,
% 1.12/0.96 (a_truth(and(knight(me), knight(me)), rich(elem!0))),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[249, 232])).
% 1.12/0.96 tff(251,plain,
% 1.12/0.96 (^[Z: $i, Y: $i, X: $i] : refl((says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z))) <=> (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z))))),
% 1.12/0.96 inference(bind,[status(th)],[])).
% 1.12/0.96 tff(252,plain,
% 1.12/0.96 (![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))),
% 1.12/0.96 inference(quant_intro,[status(thm)],[251])).
% 1.12/0.96 tff(253,plain,
% 1.12/0.96 (![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(254,plain,
% 1.12/0.96 (^[Z: $i, Y: $i, X: $i] : rewrite((((~a_truth(knight(X), Z)) | says(X, Y)) | (~a_truth(Y, Z))) <=> (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z))))),
% 1.12/0.96 inference(bind,[status(th)],[])).
% 1.12/0.96 tff(255,plain,
% 1.12/0.96 (![Z: $i, Y: $i, X: $i] : (((~a_truth(knight(X), Z)) | says(X, Y)) | (~a_truth(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))),
% 1.12/0.96 inference(quant_intro,[status(thm)],[254])).
% 1.12/0.96 tff(256,axiom,(![Z: $i, Y: $i, X: $i] : (((~a_truth(knight(X), Z)) | says(X, Y)) | (~a_truth(Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','knights_tell_truth2')).
% 1.12/0.96 tff(257,plain,
% 1.12/0.96 (![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[256, 255])).
% 1.12/0.96 tff(258,plain,
% 1.12/0.96 (![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[257, 253])).
% 1.12/0.96 tff(259,plain,(
% 1.12/0.96 ![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))),
% 1.12/0.96 inference(skolemize,[status(sab)],[258])).
% 1.12/0.96 tff(260,plain,
% 1.12/0.96 (![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[259, 252])).
% 1.12/0.96 tff(261,plain,
% 1.12/0.96 (((~![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))) | ((~a_truth(knight(me), rich(elem!0))) | (~a_truth(and(knight(me), knight(me)), rich(elem!0))) | says(me, and(knight(me), knight(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))) | (~a_truth(knight(me), rich(elem!0))) | (~a_truth(and(knight(me), knight(me)), rich(elem!0))) | says(me, and(knight(me), knight(me))))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(262,plain,
% 1.12/0.96 ((says(me, and(knight(me), knight(me))) | (~a_truth(knight(me), rich(elem!0))) | (~a_truth(and(knight(me), knight(me)), rich(elem!0)))) <=> ((~a_truth(knight(me), rich(elem!0))) | (~a_truth(and(knight(me), knight(me)), rich(elem!0))) | says(me, and(knight(me), knight(me))))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(263,plain,
% 1.12/0.96 (((~![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))) | (says(me, and(knight(me), knight(me))) | (~a_truth(knight(me), rich(elem!0))) | (~a_truth(and(knight(me), knight(me)), rich(elem!0))))) <=> ((~![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))) | ((~a_truth(knight(me), rich(elem!0))) | (~a_truth(and(knight(me), knight(me)), rich(elem!0))) | says(me, and(knight(me), knight(me)))))),
% 1.12/0.96 inference(monotonicity,[status(thm)],[262])).
% 1.12/0.96 tff(264,plain,
% 1.12/0.96 (((~![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))) | (says(me, and(knight(me), knight(me))) | (~a_truth(knight(me), rich(elem!0))) | (~a_truth(and(knight(me), knight(me)), rich(elem!0))))) <=> ((~![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))) | (~a_truth(knight(me), rich(elem!0))) | (~a_truth(and(knight(me), knight(me)), rich(elem!0))) | says(me, and(knight(me), knight(me))))),
% 1.12/0.96 inference(transitivity,[status(thm)],[263, 261])).
% 1.12/0.96 tff(265,plain,
% 1.12/0.96 ((~![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))) | (says(me, and(knight(me), knight(me))) | (~a_truth(knight(me), rich(elem!0))) | (~a_truth(and(knight(me), knight(me)), rich(elem!0))))),
% 1.12/0.96 inference(quant_inst,[status(thm)],[])).
% 1.12/0.96 tff(266,plain,
% 1.12/0.96 ((~![Z: $i, Y: $i, X: $i] : (says(X, Y) | (~a_truth(knight(X), Z)) | (~a_truth(Y, Z)))) | (~a_truth(knight(me), rich(elem!0))) | (~a_truth(and(knight(me), knight(me)), rich(elem!0))) | says(me, and(knight(me), knight(me)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[265, 264])).
% 1.12/0.96 tff(267,plain,
% 1.12/0.96 ((~a_truth(knight(me), rich(elem!0))) | (~a_truth(and(knight(me), knight(me)), rich(elem!0))) | says(me, and(knight(me), knight(me)))),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[266, 260])).
% 1.12/0.96 tff(268,plain,
% 1.12/0.96 ($false),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[267, 250, 232, 231])).
% 1.12/0.96 tff(269,plain,(~a_truth(knight(me), rich(elem!0))), inference(lemma,lemma(discharge,[]))).
% 1.12/0.96 tff(270,plain,
% 1.12/0.96 (((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | (a_truth(knave(me), rich(elem!0)) | a_truth(knight(me), rich(elem!0)))) <=> ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | a_truth(knave(me), rich(elem!0)) | a_truth(knight(me), rich(elem!0)))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(271,plain,
% 1.12/0.96 ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | (a_truth(knave(me), rich(elem!0)) | a_truth(knight(me), rich(elem!0)))),
% 1.12/0.96 inference(quant_inst,[status(thm)],[])).
% 1.12/0.96 tff(272,plain,
% 1.12/0.96 ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | a_truth(knave(me), rich(elem!0)) | a_truth(knight(me), rich(elem!0))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[271, 270])).
% 1.12/0.96 tff(273,plain,
% 1.12/0.96 (a_truth(knave(me), rich(elem!0))),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[272, 127, 269])).
% 1.12/0.96 tff(274,assumption,(~a_truth(and(knight(me), knight(me)), rich(elem!0))), introduced(assumption)).
% 1.12/0.96 tff(275,plain,
% 1.12/0.96 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0)) | says(me, and(knight(me), knight(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0)) | says(me, and(knight(me), knight(me))))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(276,plain,
% 1.12/0.96 ((a_truth(and(knight(me), knight(me)), rich(elem!0)) | says(me, and(knight(me), knight(me))) | (~a_truth(knave(me), rich(elem!0)))) <=> ((~a_truth(knave(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0)) | says(me, and(knight(me), knight(me))))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(277,plain,
% 1.12/0.96 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(knight(me), knight(me)), rich(elem!0)) | says(me, and(knight(me), knight(me))) | (~a_truth(knave(me), rich(elem!0))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0)) | says(me, and(knight(me), knight(me)))))),
% 1.12/0.96 inference(monotonicity,[status(thm)],[276])).
% 1.12/0.96 tff(278,plain,
% 1.12/0.96 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(knight(me), knight(me)), rich(elem!0)) | says(me, and(knight(me), knight(me))) | (~a_truth(knave(me), rich(elem!0))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0)) | says(me, and(knight(me), knight(me))))),
% 1.12/0.96 inference(transitivity,[status(thm)],[277, 275])).
% 1.12/0.96 tff(279,plain,
% 1.12/0.96 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(knight(me), knight(me)), rich(elem!0)) | says(me, and(knight(me), knight(me))) | (~a_truth(knave(me), rich(elem!0))))),
% 1.12/0.96 inference(quant_inst,[status(thm)],[])).
% 1.12/0.96 tff(280,plain,
% 1.12/0.96 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), rich(elem!0))) | a_truth(and(knight(me), knight(me)), rich(elem!0)) | says(me, and(knight(me), knight(me)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[279, 278])).
% 1.12/0.96 tff(281,plain,
% 1.12/0.96 ($false),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[280, 193, 274, 231, 273])).
% 1.12/0.96 tff(282,plain,(a_truth(and(knight(me), knight(me)), rich(elem!0))), inference(lemma,lemma(discharge,[]))).
% 1.12/0.96 tff(283,plain,
% 1.12/0.96 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(knight(me), knight(me)), rich(elem!0))) | a_truth(knight(me), rich(elem!0)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(knight(me), knight(me)), rich(elem!0))) | a_truth(knight(me), rich(elem!0)))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(284,plain,
% 1.12/0.96 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(knight(me), knight(me)), rich(elem!0))) | a_truth(knight(me), rich(elem!0)))),
% 1.12/0.96 inference(quant_inst,[status(thm)],[])).
% 1.12/0.96 tff(285,plain,
% 1.12/0.96 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(knight(me), knight(me)), rich(elem!0))) | a_truth(knight(me), rich(elem!0))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[284, 283])).
% 1.12/0.96 tff(286,plain,
% 1.12/0.96 ($false),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[285, 31, 269, 282])).
% 1.12/0.96 % SZS output end Proof
%------------------------------------------------------------------------------