%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ021-1 : TPTP v9.0.0. Released v1.0.0.
% 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 05:23:11 AM UTC 2025
% Result : Unsatisfiable 0.70s 0.86s
% Output : Proof 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : PUZ021-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 02:39:10 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.70/0.86 % SZS status Unsatisfiable
% 0.70/0.86 % SZS output start Proof
% 0.70/0.86 tff(a_truth_type, type, (
% 0.70/0.86 a_truth: ( $i * $i ) > $o)).
% 0.70/0.86 tff(and_type, type, (
% 0.70/0.86 and: ( $i * $i ) > $i)).
% 0.70/0.86 tff(knave_type, type, (
% 0.70/0.86 knave: $i > $i)).
% 0.70/0.86 tff(elem_0_type, type, (
% 0.70/0.86 elem_0: $i)).
% 0.70/0.86 tff(rich_type, type, (
% 0.70/0.86 rich: $i > $i)).
% 0.70/0.86 tff(poor_type, type, (
% 0.70/0.86 poor: $i > $i)).
% 0.70/0.86 tff(me_type, type, (
% 0.70/0.86 me: $i)).
% 0.70/0.86 tff(says_type, type, (
% 0.70/0.86 says: ( $i * $i ) > $o)).
% 0.70/0.86 tff(knight_type, type, (
% 0.70/0.86 knight: $i > $i)).
% 0.70/0.86 tff(1,assumption,(says(me, knave(me))), introduced(assumption)).
% 0.70/0.86 tff(2,plain,
% 0.70/0.86 (^[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))))),
% 0.70/0.86 inference(bind,[status(th)],[])).
% 0.70/0.86 tff(3,plain,
% 0.70/0.86 (![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)))),
% 0.70/0.86 inference(quant_intro,[status(thm)],[2])).
% 0.70/0.86 tff(4,plain,
% 0.70/0.86 (![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)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(5,plain,
% 0.70/0.86 (^[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)))))),
% 0.70/0.86 inference(bind,[status(th)],[])).
% 0.70/0.86 tff(6,plain,
% 0.70/0.86 (![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)))),
% 0.70/0.86 inference(quant_intro,[status(thm)],[5])).
% 0.70/0.86 tff(7,axiom,(![Z: $i, Y: $i, X: $i] : (((~a_truth(knave(X), Z)) | (~says(X, Y))) | (~a_truth(Y, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','knaves_lie1')).
% 0.70/0.86 tff(8,plain,
% 0.70/0.86 (![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.70/0.86 tff(9,plain,
% 0.70/0.86 (![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.70/0.86 tff(10,plain,(
% 0.70/0.86 ![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))),
% 0.70/0.86 inference(skolemize,[status(sab)],[9])).
% 0.70/0.86 tff(11,plain,
% 0.70/0.86 (![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.70/0.86 tff(12,plain,
% 0.70/0.86 (((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), rich(me))) | (~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), rich(me))) | (~says(me, knave(me))))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(13,plain,
% 0.70/0.86 (((~says(me, knave(me))) | (~a_truth(knave(me), rich(me))) | (~a_truth(knave(me), rich(me)))) <=> ((~a_truth(knave(me), rich(me))) | (~says(me, knave(me))))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(14,plain,
% 0.70/0.86 (((~![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), rich(me))) | (~a_truth(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), rich(me))) | (~says(me, knave(me)))))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[13])).
% 0.70/0.86 tff(15,plain,
% 0.70/0.86 (((~![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), rich(me))) | (~a_truth(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), rich(me))) | (~says(me, knave(me))))),
% 0.70/0.86 inference(transitivity,[status(thm)],[14, 12])).
% 0.70/0.86 tff(16,plain,
% 0.70/0.86 ((~![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), rich(me))) | (~a_truth(knave(me), rich(me))))),
% 0.70/0.86 inference(quant_inst,[status(thm)],[])).
% 0.70/0.86 tff(17,plain,
% 0.70/0.86 ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), rich(me))) | (~says(me, knave(me)))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.70/0.86 tff(18,plain,
% 0.70/0.86 ((~a_truth(knave(me), rich(me))) | (~says(me, knave(me)))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[17, 11])).
% 0.70/0.86 tff(19,plain,
% 0.70/0.86 (~a_truth(knave(me), rich(me))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[18, 1])).
% 0.70/0.86 tff(20,plain,
% 0.70/0.86 (^[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)))),
% 0.70/0.86 inference(bind,[status(th)],[])).
% 0.70/0.86 tff(21,plain,
% 0.70/0.86 (![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))),
% 0.70/0.86 inference(quant_intro,[status(thm)],[20])).
% 0.70/0.86 tff(22,plain,
% 0.70/0.86 (![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))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(23,plain,
% 0.70/0.86 (^[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)))),
% 0.70/0.86 inference(bind,[status(th)],[])).
% 0.70/0.86 tff(24,plain,
% 0.70/0.86 (![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))),
% 0.70/0.86 inference(quant_intro,[status(thm)],[23])).
% 0.70/0.86 tff(25,axiom,(![Y: $i, X: $i] : (a_truth(knight(X), Y) | a_truth(knave(X), Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','knight_or_knave')).
% 0.70/0.86 tff(26,plain,
% 0.70/0.86 (![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.70/0.86 tff(27,plain,
% 0.70/0.86 (![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.70/0.86 tff(28,plain,(
% 0.70/0.86 ![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))),
% 0.70/0.86 inference(skolemize,[status(sab)],[27])).
% 0.70/0.86 tff(29,plain,
% 0.70/0.86 (![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.70/0.86 tff(30,plain,
% 0.70/0.86 (((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | (a_truth(knave(me), rich(me)) | a_truth(knight(me), rich(me)))) <=> ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | a_truth(knave(me), rich(me)) | a_truth(knight(me), rich(me)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(31,plain,
% 0.70/0.86 ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | (a_truth(knave(me), rich(me)) | a_truth(knight(me), rich(me)))),
% 0.70/0.86 inference(quant_inst,[status(thm)],[])).
% 0.70/0.86 tff(32,plain,
% 0.70/0.86 ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | a_truth(knave(me), rich(me)) | a_truth(knight(me), rich(me))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.70/0.86 tff(33,plain,
% 0.70/0.86 (a_truth(knight(me), rich(me))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[32, 29, 19])).
% 0.70/0.86 tff(34,plain,
% 0.70/0.86 (^[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))))),
% 0.70/0.86 inference(bind,[status(th)],[])).
% 0.70/0.86 tff(35,plain,
% 0.70/0.86 (![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)))),
% 0.70/0.86 inference(quant_intro,[status(thm)],[34])).
% 0.70/0.86 tff(36,plain,
% 0.70/0.86 (![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)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(37,plain,
% 0.70/0.86 (^[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)))))),
% 0.70/0.86 inference(bind,[status(th)],[])).
% 0.70/0.86 tff(38,plain,
% 0.70/0.86 (![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)))),
% 0.70/0.86 inference(quant_intro,[status(thm)],[37])).
% 0.70/0.86 tff(39,axiom,(![Z: $i, Y: $i, X: $i] : (((~a_truth(knight(X), Z)) | (~says(X, Y))) | a_truth(Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','knights_tell_truth1')).
% 0.70/0.86 tff(40,plain,
% 0.70/0.86 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.70/0.86 tff(41,plain,
% 0.70/0.86 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.70/0.86 tff(42,plain,(
% 0.70/0.86 ![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))),
% 0.70/0.86 inference(skolemize,[status(sab)],[41])).
% 0.70/0.86 tff(43,plain,
% 0.70/0.86 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.70/0.86 tff(44,plain,
% 0.70/0.86 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(knave(me), rich(me)) | (~a_truth(knight(me), rich(me))) | (~says(me, knave(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | a_truth(knave(me), rich(me)) | (~a_truth(knight(me), rich(me))) | (~says(me, knave(me))))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(45,plain,
% 0.70/0.86 ((a_truth(knave(me), rich(me)) | (~says(me, knave(me))) | (~a_truth(knight(me), rich(me)))) <=> (a_truth(knave(me), rich(me)) | (~a_truth(knight(me), rich(me))) | (~says(me, knave(me))))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(46,plain,
% 0.70/0.86 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(knave(me), rich(me)) | (~says(me, knave(me))) | (~a_truth(knight(me), rich(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(knave(me), rich(me)) | (~a_truth(knight(me), rich(me))) | (~says(me, knave(me)))))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[45])).
% 0.70/0.86 tff(47,plain,
% 0.70/0.86 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(knave(me), rich(me)) | (~says(me, knave(me))) | (~a_truth(knight(me), rich(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | a_truth(knave(me), rich(me)) | (~a_truth(knight(me), rich(me))) | (~says(me, knave(me))))),
% 0.70/0.86 inference(transitivity,[status(thm)],[46, 44])).
% 0.70/0.86 tff(48,plain,
% 0.70/0.86 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(knave(me), rich(me)) | (~says(me, knave(me))) | (~a_truth(knight(me), rich(me))))),
% 0.70/0.86 inference(quant_inst,[status(thm)],[])).
% 0.70/0.86 tff(49,plain,
% 0.70/0.86 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | a_truth(knave(me), rich(me)) | (~a_truth(knight(me), rich(me))) | (~says(me, knave(me)))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.70/0.86 tff(50,plain,
% 0.70/0.86 ($false),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[49, 43, 19, 33, 1])).
% 0.70/0.86 tff(51,plain,(~says(me, knave(me))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.86 tff(52,plain,
% 0.70/0.86 (^[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)))),
% 0.70/0.86 inference(bind,[status(th)],[])).
% 0.70/0.86 tff(53,plain,
% 0.70/0.86 (![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))),
% 0.70/0.86 inference(quant_intro,[status(thm)],[52])).
% 0.70/0.86 tff(54,plain,
% 0.70/0.86 (![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))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(55,axiom,(![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_statement_exists2')).
% 0.70/0.86 tff(56,plain,
% 0.70/0.86 (![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.70/0.86 tff(57,plain,(
% 0.70/0.86 ![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))),
% 0.70/0.86 inference(skolemize,[status(sab)],[56])).
% 0.70/0.86 tff(58,plain,
% 0.70/0.86 (![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.70/0.86 tff(59,plain,
% 0.70/0.86 (((~![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)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(60,plain,
% 0.70/0.86 ((~![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)))),
% 0.70/0.86 inference(quant_inst,[status(thm)],[])).
% 0.70/0.86 tff(61,plain,
% 0.70/0.86 ((~![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))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.70/0.86 tff(62,plain,
% 0.70/0.86 (a_truth(and(knave(me), rich(me)), knave(me))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[61, 58, 51])).
% 0.70/0.86 tff(63,plain,
% 0.70/0.86 (^[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)))),
% 0.70/0.86 inference(bind,[status(th)],[])).
% 0.70/0.86 tff(64,plain,
% 0.70/0.86 (![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))),
% 0.70/0.86 inference(quant_intro,[status(thm)],[63])).
% 0.70/0.86 tff(65,plain,
% 0.70/0.86 (![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))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(66,axiom,(![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjunction1')).
% 0.70/0.86 tff(67,plain,
% 0.70/0.86 (![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.70/0.86 tff(68,plain,(
% 0.70/0.86 ![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))),
% 0.70/0.86 inference(skolemize,[status(sab)],[67])).
% 0.70/0.86 tff(69,plain,
% 0.70/0.86 (![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.70/0.86 tff(70,plain,
% 0.70/0.86 (((~![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)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(71,plain,
% 0.70/0.86 ((~![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)))),
% 0.70/0.86 inference(quant_inst,[status(thm)],[])).
% 0.70/0.86 tff(72,plain,
% 0.70/0.86 ((~![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))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.70/0.86 tff(73,plain,
% 0.70/0.86 (a_truth(knave(me), knave(me))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[72, 69, 62])).
% 0.70/0.86 tff(74,assumption,(says(me, and(knave(me), rich(me)))), introduced(assumption)).
% 0.70/0.86 tff(75,plain,
% 0.70/0.86 (((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~a_truth(and(knave(me), rich(me)), knave(me))) | (~says(me, and(knave(me), rich(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(and(knave(me), rich(me)), knave(me))) | (~says(me, and(knave(me), rich(me)))) | (~a_truth(knave(me), knave(me))))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(76,plain,
% 0.70/0.87 (((~says(me, and(knave(me), rich(me)))) | (~a_truth(and(knave(me), rich(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)))) | (~a_truth(knave(me), knave(me))))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(77,plain,
% 0.70/0.87 (((~![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(and(knave(me), rich(me)), knave(me))) | (~says(me, and(knave(me), rich(me)))) | (~a_truth(knave(me), knave(me)))))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[76])).
% 0.70/0.87 tff(78,plain,
% 0.70/0.87 (((~![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(and(knave(me), rich(me)), knave(me))) | (~says(me, and(knave(me), rich(me)))) | (~a_truth(knave(me), knave(me))))),
% 0.70/0.87 inference(transitivity,[status(thm)],[77, 75])).
% 0.70/0.87 tff(79,plain,
% 0.70/0.87 ((~![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))))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(80,plain,
% 0.70/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | (~a_truth(and(knave(me), rich(me)), knave(me))) | (~says(me, and(knave(me), rich(me)))) | (~a_truth(knave(me), knave(me)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.70/0.87 tff(81,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[80, 11, 74, 73, 62])).
% 0.70/0.87 tff(82,plain,(~says(me, and(knave(me), rich(me)))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(83,plain,
% 0.70/0.87 (((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | (says(me, and(knave(me), rich(me))) | a_truth(and(knave(me), rich(me)), and(knave(me), rich(me))))) <=> ((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | says(me, and(knave(me), rich(me))) | a_truth(and(knave(me), rich(me)), and(knave(me), rich(me))))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(84,plain,
% 0.70/0.87 ((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | (says(me, and(knave(me), rich(me))) | a_truth(and(knave(me), rich(me)), and(knave(me), rich(me))))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(85,plain,
% 0.70/0.87 ((~![X: $i] : (says(me, X) | a_truth(and(knave(me), rich(me)), X))) | says(me, and(knave(me), rich(me))) | a_truth(and(knave(me), rich(me)), and(knave(me), rich(me)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.70/0.87 tff(86,plain,
% 0.70/0.87 (a_truth(and(knave(me), rich(me)), and(knave(me), rich(me)))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[85, 58, 82])).
% 0.70/0.87 tff(87,plain,
% 0.70/0.87 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(knave(me), rich(me)), and(knave(me), rich(me)))) | a_truth(knave(me), and(knave(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(knave(me), rich(me)))) | a_truth(knave(me), and(knave(me), rich(me))))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(88,plain,
% 0.70/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(knave(me), rich(me)), and(knave(me), rich(me)))) | a_truth(knave(me), and(knave(me), rich(me))))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(89,plain,
% 0.70/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(knave(me), rich(me)), and(knave(me), rich(me)))) | a_truth(knave(me), and(knave(me), rich(me)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.70/0.87 tff(90,plain,
% 0.70/0.87 (a_truth(knave(me), and(knave(me), rich(me)))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[89, 69, 86])).
% 0.70/0.87 tff(91,assumption,(a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me)))), introduced(assumption)).
% 0.70/0.87 tff(92,plain,
% 0.70/0.87 (^[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)))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(93,plain,
% 0.70/0.87 (![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))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[92])).
% 0.70/0.87 tff(94,plain,
% 0.70/0.87 (![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))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(95,axiom,(![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjunction2')).
% 0.70/0.87 tff(96,plain,
% 0.70/0.87 (![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.70/0.87 tff(97,plain,(
% 0.70/0.87 ![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))),
% 0.70/0.87 inference(skolemize,[status(sab)],[96])).
% 0.70/0.87 tff(98,plain,
% 0.70/0.87 (![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.70/0.87 tff(99,plain,
% 0.70/0.87 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(knave(me), rich(me)), and(knave(me), rich(me)))) | a_truth(rich(me), and(knave(me), rich(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(knave(me), rich(me)), and(knave(me), rich(me)))) | a_truth(rich(me), and(knave(me), rich(me))))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(100,plain,
% 0.70/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(knave(me), rich(me)), and(knave(me), rich(me)))) | a_truth(rich(me), and(knave(me), rich(me))))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(101,plain,
% 0.70/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(knave(me), rich(me)), and(knave(me), rich(me)))) | a_truth(rich(me), and(knave(me), rich(me)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.70/0.87 tff(102,plain,
% 0.70/0.87 (a_truth(rich(me), and(knave(me), rich(me)))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[101, 98, 86])).
% 0.70/0.87 tff(103,plain,
% 0.70/0.87 (^[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))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(104,plain,
% 0.70/0.87 (![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)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[103])).
% 0.70/0.87 tff(105,plain,
% 0.70/0.87 (![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)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(106,plain,
% 0.70/0.87 (^[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))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(107,plain,
% 0.70/0.87 (![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)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[106])).
% 0.70/0.87 tff(108,axiom,(![Y: $i, X: $i] : ((~a_truth(rich(X), Y)) | (~a_truth(poor(X), Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_rich_and_poor')).
% 0.70/0.87 tff(109,plain,
% 0.70/0.87 (![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.71/0.87 tff(110,plain,
% 0.71/0.87 (![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.71/0.87 tff(111,plain,(
% 0.71/0.87 ![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))),
% 0.71/0.87 inference(skolemize,[status(sab)],[110])).
% 0.71/0.87 tff(112,plain,
% 0.71/0.87 (![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.71/0.87 tff(113,plain,
% 0.71/0.87 (((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | ((~a_truth(poor(me), and(knave(me), rich(me)))) | (~a_truth(rich(me), and(knave(me), rich(me)))))) <=> ((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | (~a_truth(poor(me), and(knave(me), rich(me)))) | (~a_truth(rich(me), and(knave(me), rich(me)))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(114,plain,
% 0.71/0.87 ((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | ((~a_truth(poor(me), and(knave(me), rich(me)))) | (~a_truth(rich(me), and(knave(me), rich(me)))))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(115,plain,
% 0.71/0.87 ((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | (~a_truth(poor(me), and(knave(me), rich(me)))) | (~a_truth(rich(me), and(knave(me), rich(me))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.71/0.87 tff(116,plain,
% 0.71/0.87 (~a_truth(poor(me), and(knave(me), rich(me)))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[115, 112, 102])).
% 0.71/0.87 tff(117,plain,
% 0.71/0.87 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me)))) | a_truth(poor(me), and(knave(me), rich(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me)))) | a_truth(poor(me), and(knave(me), rich(me))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(118,plain,
% 0.71/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me)))) | a_truth(poor(me), and(knave(me), rich(me))))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(119,plain,
% 0.71/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me)))) | a_truth(poor(me), and(knave(me), rich(me)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.71/0.87 tff(120,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[119, 69, 116, 91])).
% 0.71/0.87 tff(121,plain,(~a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(122,assumption,(a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me)))), introduced(assumption)).
% 0.71/0.87 tff(123,assumption,(~a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me)))), introduced(assumption)).
% 0.71/0.87 tff(124,plain,
% 0.71/0.87 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me)))) | a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me)))) | a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(125,plain,
% 0.71/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me)))) | a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me))))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(126,plain,
% 0.71/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me)))) | a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.71/0.87 tff(127,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[126, 69, 123, 122])).
% 0.71/0.87 tff(128,plain,((~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me)))) | a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(129,plain,
% 0.71/0.87 (~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me)))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[128, 121])).
% 0.71/0.87 tff(130,plain,
% 0.71/0.87 (^[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))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(131,plain,
% 0.71/0.87 (![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)))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[130])).
% 0.71/0.87 tff(132,plain,
% 0.71/0.87 (![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)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(133,plain,
% 0.71/0.87 (^[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))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(134,plain,
% 0.71/0.87 (![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)))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[133])).
% 0.71/0.87 tff(135,axiom,(![Z: $i, Y: $i, X: $i] : (((~a_truth(knave(X), Z)) | says(X, Y)) | a_truth(Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','knaves_lie2')).
% 0.71/0.87 tff(136,plain,
% 0.71/0.87 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.71/0.87 tff(137,plain,
% 0.71/0.87 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.71/0.87 tff(138,plain,(
% 0.71/0.87 ![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))),
% 0.71/0.87 inference(skolemize,[status(sab)],[137])).
% 0.71/0.87 tff(139,plain,
% 0.71/0.87 (![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.71/0.87 tff(140,plain,
% 0.71/0.87 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), poor(elem!0))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), poor(elem!0))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(141,plain,
% 0.71/0.87 ((a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), poor(elem!0))) | (~a_truth(knave(me), and(knave(me), rich(me))))) <=> ((~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), poor(elem!0))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(142,plain,
% 0.71/0.87 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), poor(elem!0))) | (~a_truth(knave(me), and(knave(me), rich(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), poor(elem!0)))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[141])).
% 0.71/0.87 tff(143,plain,
% 0.71/0.87 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), poor(elem!0))) | (~a_truth(knave(me), and(knave(me), rich(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), poor(elem!0))))),
% 0.71/0.87 inference(transitivity,[status(thm)],[142, 140])).
% 0.71/0.87 tff(144,plain,
% 0.71/0.87 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), poor(elem!0))) | (~a_truth(knave(me), and(knave(me), rich(me)))))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(145,plain,
% 0.71/0.87 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), poor(elem!0)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.71/0.87 tff(146,plain,
% 0.71/0.87 ((~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), poor(elem!0)))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[145, 139])).
% 0.71/0.87 tff(147,plain,
% 0.71/0.87 (says(me, and(and(poor(me), rich(elem!0)), poor(elem!0)))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[146, 129, 90])).
% 0.71/0.87 tff(148,assumption,(says(me, and(and(poor(me), rich(elem!0)), poor(elem!0)))), introduced(assumption)).
% 0.71/0.87 tff(149,assumption,(a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0)), introduced(assumption)).
% 0.71/0.87 tff(150,plain,
% 0.71/0.87 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0)) | a_truth(and(poor(me), rich(elem!0)), elem!0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0)) | a_truth(and(poor(me), rich(elem!0)), elem!0))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(151,plain,
% 0.71/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0)) | a_truth(and(poor(me), rich(elem!0)), elem!0))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(152,plain,
% 0.71/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0)) | a_truth(and(poor(me), rich(elem!0)), elem!0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.71/0.87 tff(153,plain,
% 0.71/0.87 ((~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0)) | a_truth(and(poor(me), rich(elem!0)), elem!0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[152, 69])).
% 0.71/0.87 tff(154,plain,
% 0.71/0.87 (a_truth(and(poor(me), rich(elem!0)), elem!0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[153, 149])).
% 0.71/0.87 tff(155,plain,
% 0.71/0.87 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(poor(me), rich(elem!0)), elem!0)) | a_truth(rich(elem!0), elem!0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(poor(me), rich(elem!0)), elem!0)) | a_truth(rich(elem!0), elem!0))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(156,plain,
% 0.71/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(poor(me), rich(elem!0)), elem!0)) | a_truth(rich(elem!0), elem!0))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(157,plain,
% 0.71/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(poor(me), rich(elem!0)), elem!0)) | a_truth(rich(elem!0), elem!0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.71/0.87 tff(158,plain,
% 0.71/0.87 ((~a_truth(and(poor(me), rich(elem!0)), elem!0)) | a_truth(rich(elem!0), elem!0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[157, 98])).
% 0.71/0.87 tff(159,plain,
% 0.71/0.87 (a_truth(rich(elem!0), elem!0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[158, 154])).
% 0.71/0.87 tff(160,plain,
% 0.71/0.87 (((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | ((~a_truth(poor(elem!0), elem!0)) | (~a_truth(rich(elem!0), elem!0)))) <=> ((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | (~a_truth(poor(elem!0), elem!0)) | (~a_truth(rich(elem!0), elem!0)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(161,plain,
% 0.71/0.87 ((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | ((~a_truth(poor(elem!0), elem!0)) | (~a_truth(rich(elem!0), elem!0)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(162,plain,
% 0.71/0.87 ((~![Y: $i, X: $i] : ((~a_truth(poor(X), Y)) | (~a_truth(rich(X), Y)))) | (~a_truth(poor(elem!0), elem!0)) | (~a_truth(rich(elem!0), elem!0))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.71/0.87 tff(163,plain,
% 0.71/0.87 ((~a_truth(poor(elem!0), elem!0)) | (~a_truth(rich(elem!0), elem!0))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[162, 112])).
% 0.71/0.87 tff(164,plain,
% 0.71/0.87 (~a_truth(poor(elem!0), elem!0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[163, 159])).
% 0.71/0.87 tff(165,plain,
% 0.71/0.87 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0)) | a_truth(poor(elem!0), elem!0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0)) | a_truth(poor(elem!0), elem!0))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(166,plain,
% 0.71/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0)) | a_truth(poor(elem!0), elem!0))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(167,plain,
% 0.71/0.87 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0)) | a_truth(poor(elem!0), elem!0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.71/0.87 tff(168,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[167, 98, 164, 149])).
% 0.71/0.87 tff(169,plain,(~a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(170,assumption,(a_truth(knight(me), elem!0)), introduced(assumption)).
% 0.71/0.87 tff(171,plain,
% 0.71/0.87 (((~![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(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0) | (~says(me, and(and(poor(me), rich(elem!0)), poor(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(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0) | (~says(me, and(and(poor(me), rich(elem!0)), poor(elem!0)))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(172,plain,
% 0.71/0.87 ((a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0) | (~says(me, and(and(poor(me), rich(elem!0)), poor(elem!0)))) | (~a_truth(knight(me), elem!0))) <=> ((~a_truth(knight(me), elem!0)) | a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0) | (~says(me, and(and(poor(me), rich(elem!0)), poor(elem!0)))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(173,plain,
% 0.71/0.87 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0) | (~says(me, and(and(poor(me), rich(elem!0)), poor(elem!0)))) | (~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(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0) | (~says(me, and(and(poor(me), rich(elem!0)), poor(elem!0))))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[172])).
% 0.71/0.87 tff(174,plain,
% 0.71/0.87 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0) | (~says(me, and(and(poor(me), rich(elem!0)), poor(elem!0)))) | (~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(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0) | (~says(me, and(and(poor(me), rich(elem!0)), poor(elem!0)))))),
% 0.71/0.87 inference(transitivity,[status(thm)],[173, 171])).
% 0.71/0.87 tff(175,plain,
% 0.71/0.87 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0) | (~says(me, and(and(poor(me), rich(elem!0)), poor(elem!0)))) | (~a_truth(knight(me), elem!0)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(176,plain,
% 0.71/0.87 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (~a_truth(knight(me), elem!0)) | a_truth(and(and(poor(me), rich(elem!0)), poor(elem!0)), elem!0) | (~says(me, and(and(poor(me), rich(elem!0)), poor(elem!0))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.71/0.87 tff(177,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[176, 43, 170, 169, 148])).
% 0.71/0.87 tff(178,plain,((~says(me, and(and(poor(me), rich(elem!0)), poor(elem!0)))) | (~a_truth(knight(me), elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(179,plain,
% 0.71/0.87 (~a_truth(knight(me), elem!0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[178, 147])).
% 0.71/0.87 tff(180,plain,
% 0.71/0.87 (((~![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))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(181,plain,
% 0.71/0.87 ((~![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))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(182,plain,
% 0.71/0.87 ((~![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)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.71/0.87 tff(183,plain,
% 0.71/0.87 (a_truth(knave(me), elem!0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[182, 29, 179])).
% 0.71/0.87 tff(184,assumption,(a_truth(knave(me), elem!0)), introduced(assumption)).
% 0.71/0.87 tff(185,assumption,(~a_truth(and(knave(me), rich(me)), elem!0)), introduced(assumption)).
% 0.71/0.87 tff(186,plain,
% 0.71/0.87 (((~![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)), elem!0) | (~a_truth(knave(me), elem!0)) | says(me, and(knave(me), rich(me))))) <=> ((~![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)), elem!0) | (~a_truth(knave(me), elem!0)) | says(me, and(knave(me), rich(me))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(187,plain,
% 0.71/0.87 ((a_truth(and(knave(me), rich(me)), elem!0) | says(me, and(knave(me), rich(me))) | (~a_truth(knave(me), elem!0))) <=> (a_truth(and(knave(me), rich(me)), elem!0) | (~a_truth(knave(me), elem!0)) | says(me, and(knave(me), rich(me))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(188,plain,
% 0.71/0.87 (((~![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)), elem!0) | says(me, and(knave(me), rich(me))) | (~a_truth(knave(me), elem!0)))) <=> ((~![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)), elem!0) | (~a_truth(knave(me), elem!0)) | says(me, and(knave(me), rich(me)))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[187])).
% 0.71/0.87 tff(189,plain,
% 0.71/0.87 (((~![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)), elem!0) | says(me, and(knave(me), rich(me))) | (~a_truth(knave(me), elem!0)))) <=> ((~![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)), elem!0) | (~a_truth(knave(me), elem!0)) | says(me, and(knave(me), rich(me))))),
% 0.71/0.88 inference(transitivity,[status(thm)],[188, 186])).
% 0.71/0.88 tff(190,plain,
% 0.71/0.88 ((~![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)), elem!0) | says(me, and(knave(me), rich(me))) | (~a_truth(knave(me), elem!0)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(191,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | a_truth(and(knave(me), rich(me)), elem!0) | (~a_truth(knave(me), elem!0)) | says(me, and(knave(me), rich(me)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.71/0.88 tff(192,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[191, 139, 185, 82, 184])).
% 0.71/0.88 tff(193,plain,(a_truth(and(knave(me), rich(me)), elem!0) | (~a_truth(knave(me), elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(194,plain,
% 0.71/0.88 (a_truth(and(knave(me), rich(me)), elem!0)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[193, 183])).
% 0.71/0.88 tff(195,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(knave(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(knave(me), rich(me)), elem!0)) | a_truth(rich(me), elem!0))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(196,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(knave(me), rich(me)), elem!0)) | a_truth(rich(me), elem!0))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(197,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(knave(me), rich(me)), elem!0)) | a_truth(rich(me), elem!0)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.71/0.88 tff(198,plain,
% 0.71/0.88 (a_truth(rich(me), elem!0)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[197, 98, 194])).
% 0.71/0.88 tff(199,plain,
% 0.71/0.88 (((~![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)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(200,plain,
% 0.71/0.88 ((~![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)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(201,plain,
% 0.71/0.88 ((~![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))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.71/0.88 tff(202,plain,
% 0.71/0.88 (~a_truth(poor(me), elem!0)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[201, 112, 198])).
% 0.71/0.88 tff(203,assumption,(a_truth(and(poor(me), rich(elem!0)), elem!0)), introduced(assumption)).
% 0.71/0.88 tff(204,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(poor(me), rich(elem!0)), 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(elem!0)), elem!0)) | a_truth(poor(me), elem!0))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(205,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(poor(me), rich(elem!0)), elem!0)) | a_truth(poor(me), elem!0))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(206,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(poor(me), rich(elem!0)), elem!0)) | a_truth(poor(me), elem!0)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.71/0.88 tff(207,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[206, 69, 203, 202])).
% 0.71/0.88 tff(208,plain,(~a_truth(and(poor(me), rich(elem!0)), elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(209,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0)) | a_truth(and(poor(me), rich(elem!0)), elem!0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0)) | a_truth(and(poor(me), rich(elem!0)), elem!0))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(210,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | ((~a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0)) | a_truth(and(poor(me), rich(elem!0)), elem!0))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(211,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(Y, Z))) | (~a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0)) | a_truth(and(poor(me), rich(elem!0)), elem!0)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.71/0.88 tff(212,plain,
% 0.71/0.88 ((~a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0)) | a_truth(and(poor(me), rich(elem!0)), elem!0)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[211, 98])).
% 0.71/0.88 tff(213,plain,
% 0.71/0.88 (~a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[212, 208])).
% 0.71/0.88 tff(214,assumption,(~says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))))), introduced(assumption)).
% 0.71/0.88 tff(215,assumption,(~a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0)), introduced(assumption)).
% 0.71/0.88 tff(216,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), elem!0)) | a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0) | says(me, and(and(knave(me), rich(me)), and(poor(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), elem!0)) | a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0) | says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0)))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(217,plain,
% 0.71/0.88 ((a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0) | says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0)))) | (~a_truth(knave(me), elem!0))) <=> ((~a_truth(knave(me), elem!0)) | a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0) | says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0)))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(218,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0) | says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0)))) | (~a_truth(knave(me), elem!0)))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), elem!0)) | a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0) | says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[217])).
% 0.71/0.88 tff(219,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0) | says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0)))) | (~a_truth(knave(me), elem!0)))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), elem!0)) | a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0) | says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0)))))),
% 0.71/0.88 inference(transitivity,[status(thm)],[218, 216])).
% 0.71/0.88 tff(220,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0) | says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0)))) | (~a_truth(knave(me), elem!0)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(221,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), elem!0)) | a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0) | says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.71/0.88 tff(222,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[221, 139, 184, 215, 214])).
% 0.71/0.88 tff(223,plain,(says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0)))) | (~a_truth(knave(me), elem!0)) | a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(224,plain,
% 0.71/0.88 (says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0)))) | a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), elem!0)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[223, 183])).
% 0.71/0.88 tff(225,plain,
% 0.71/0.88 (says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[224, 213])).
% 0.71/0.88 tff(226,assumption,(~a_truth(poor(me), and(knave(me), rich(me)))), introduced(assumption)).
% 0.71/0.88 tff(227,assumption,(a_truth(knave(me), and(knave(me), rich(me)))), introduced(assumption)).
% 0.71/0.88 tff(228,assumption,(~says(me, poor(me))), introduced(assumption)).
% 0.71/0.88 tff(229,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (says(me, poor(me)) | (~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(poor(me), and(knave(me), rich(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | says(me, poor(me)) | (~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(poor(me), and(knave(me), rich(me))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(230,plain,
% 0.71/0.88 ((a_truth(poor(me), and(knave(me), rich(me))) | says(me, poor(me)) | (~a_truth(knave(me), and(knave(me), rich(me))))) <=> (says(me, poor(me)) | (~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(poor(me), and(knave(me), rich(me))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(231,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(poor(me), and(knave(me), rich(me))) | says(me, poor(me)) | (~a_truth(knave(me), and(knave(me), rich(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (says(me, poor(me)) | (~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(poor(me), and(knave(me), rich(me)))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[230])).
% 0.71/0.88 tff(232,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(poor(me), and(knave(me), rich(me))) | says(me, poor(me)) | (~a_truth(knave(me), and(knave(me), rich(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | says(me, poor(me)) | (~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(poor(me), and(knave(me), rich(me))))),
% 0.71/0.88 inference(transitivity,[status(thm)],[231, 229])).
% 0.71/0.88 tff(233,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(poor(me), and(knave(me), rich(me))) | says(me, poor(me)) | (~a_truth(knave(me), and(knave(me), rich(me)))))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(234,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | says(me, poor(me)) | (~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(poor(me), and(knave(me), rich(me)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.71/0.88 tff(235,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[234, 139, 228, 227, 226])).
% 0.71/0.88 tff(236,plain,(says(me, poor(me)) | (~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(poor(me), and(knave(me), rich(me)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(237,plain,
% 0.71/0.88 (says(me, poor(me))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[236, 116, 90])).
% 0.71/0.88 tff(238,assumption,(a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me)))), introduced(assumption)).
% 0.71/0.88 tff(239,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me)))) | a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me)))) | a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(240,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me)))) | a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me))))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(241,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me)))) | a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.71/0.88 tff(242,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[241, 69, 238, 123])).
% 0.71/0.88 tff(243,plain,((~a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me)))) | a_truth(and(poor(me), rich(elem!0)), and(knave(me), rich(me)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(244,plain,
% 0.71/0.88 (~a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me)))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[243, 121])).
% 0.71/0.88 tff(245,assumption,(~says(me, and(and(poor(me), rich(elem!0)), knave(elem!0)))), introduced(assumption)).
% 0.71/0.88 tff(246,assumption,(~a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me)))), introduced(assumption)).
% 0.71/0.88 tff(247,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), knave(elem!0))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), knave(elem!0))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(248,plain,
% 0.71/0.88 ((a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~a_truth(knave(me), and(knave(me), rich(me))))) <=> ((~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), knave(elem!0))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(249,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~a_truth(knave(me), and(knave(me), rich(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), knave(elem!0)))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[248])).
% 0.71/0.88 tff(250,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~a_truth(knave(me), and(knave(me), rich(me)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), knave(elem!0))))),
% 0.71/0.88 inference(transitivity,[status(thm)],[249, 247])).
% 0.71/0.88 tff(251,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~a_truth(knave(me), and(knave(me), rich(me)))))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(252,plain,
% 0.71/0.88 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | says(X, Y) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), and(knave(me), rich(me)))) | a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me))) | says(me, and(and(poor(me), rich(elem!0)), knave(elem!0)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.71/0.88 tff(253,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[252, 139, 227, 246, 245])).
% 0.71/0.88 tff(254,plain,(a_truth(and(and(poor(me), rich(elem!0)), knave(elem!0)), and(knave(me), rich(me))) | (~a_truth(knave(me), and(knave(me), rich(me)))) | says(me, and(and(poor(me), rich(elem!0)), knave(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(255,plain,
% 0.71/0.88 (says(me, and(and(poor(me), rich(elem!0)), knave(elem!0)))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[254, 244, 90])).
% 0.71/0.88 tff(256,plain,
% 0.71/0.88 (^[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))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(257,plain,
% 0.71/0.88 (![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)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[256])).
% 0.71/0.88 tff(258,plain,
% 0.71/0.88 (![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)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(259,axiom,(![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_statement_exists1')).
% 0.71/0.88 tff(260,plain,
% 0.71/0.88 (![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.71/0.88 tff(261,plain,(
% 0.71/0.88 ![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))),
% 0.71/0.88 inference(skolemize,[status(sab)],[260])).
% 0.71/0.88 tff(262,plain,
% 0.71/0.88 (![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[261, 257])).
% 0.71/0.88 tff(263,plain,
% 0.71/0.88 (((~![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))) | ((~says(me, and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0)))))) <=> ((~![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))) | (~says(me, and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0)))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(264,plain,
% 0.71/0.88 ((~![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))) | ((~says(me, and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0)))))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(265,plain,
% 0.71/0.88 ((~![X: $i] : ((~says(me, X)) | (~a_truth(and(knave(me), rich(me)), X)))) | (~says(me, and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.71/0.88 tff(266,plain,
% 0.71/0.88 (~a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0)))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[265, 262, 255])).
% 0.71/0.88 tff(267,assumption,(a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))), introduced(assumption)).
% 0.71/0.88 tff(268,assumption,(~a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0)))), introduced(assumption)).
% 0.71/0.88 tff(269,plain,
% 0.71/0.88 (^[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))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(270,plain,
% 0.71/0.88 (![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)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[269])).
% 0.71/0.88 tff(271,plain,
% 0.71/0.88 (![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)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(272,plain,
% 0.71/0.88 (^[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)))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(273,plain,
% 0.71/0.88 (![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)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[272])).
% 0.71/0.88 tff(274,axiom,(![Z: $i, Y: $i, X: $i] : ((a_truth(and(X, Y), Z) | (~a_truth(X, Z))) | (~a_truth(Y, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjunction3')).
% 0.71/0.88 tff(275,plain,
% 0.71/0.88 (![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.71/0.88 tff(276,plain,
% 0.71/0.88 (![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[275, 271])).
% 0.71/0.88 tff(277,plain,(
% 0.71/0.88 ![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))),
% 0.71/0.88 inference(skolemize,[status(sab)],[276])).
% 0.71/0.88 tff(278,plain,
% 0.71/0.88 (![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[277, 270])).
% 0.71/0.88 tff(279,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | ((~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(280,plain,
% 0.71/0.88 (((~a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0))))) <=> ((~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(281,plain,
% 0.71/0.88 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | ((~a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | ((~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0))))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[280])).
% 0.71/0.89 tff(282,plain,
% 0.71/0.89 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | ((~a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))),
% 0.71/0.89 inference(transitivity,[status(thm)],[281, 279])).
% 0.71/0.89 tff(283,plain,
% 0.71/0.89 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | ((~a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(284,plain,
% 0.71/0.89 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(Y, Z)) | a_truth(and(X, Y), Z) | (~a_truth(X, Z)))) | (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.71/0.89 tff(285,plain,
% 0.71/0.89 ((~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0))))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[284, 278, 268])).
% 0.71/0.89 tff(286,plain,
% 0.71/0.89 (~a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[285, 267])).
% 0.71/0.89 tff(287,plain,
% 0.71/0.89 (^[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)))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(288,plain,
% 0.71/0.89 (![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))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[287])).
% 0.71/0.89 tff(289,plain,
% 0.71/0.89 (![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))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(290,plain,
% 0.71/0.89 (^[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)))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(291,plain,
% 0.71/0.89 (![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))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[290])).
% 0.71/0.89 tff(292,axiom,(![Y: $i, X: $i] : (a_truth(rich(X), Y) | a_truth(poor(X), Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rich_or_poor')).
% 0.71/0.89 tff(293,plain,
% 0.71/0.89 (![Y: $i, X: $i] : (a_truth(poor(X), Y) | a_truth(rich(X), Y))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.71/0.89 tff(294,plain,
% 0.71/0.89 (![Y: $i, X: $i] : (a_truth(poor(X), Y) | a_truth(rich(X), Y))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[293, 289])).
% 0.71/0.89 tff(295,plain,(
% 0.71/0.89 ![Y: $i, X: $i] : (a_truth(poor(X), Y) | a_truth(rich(X), Y))),
% 0.71/0.89 inference(skolemize,[status(sab)],[294])).
% 0.71/0.89 tff(296,plain,
% 0.71/0.89 (![Y: $i, X: $i] : (a_truth(poor(X), Y) | a_truth(rich(X), Y))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[295, 288])).
% 0.71/0.89 tff(297,plain,
% 0.71/0.89 (((~![Y: $i, X: $i] : (a_truth(poor(X), Y) | a_truth(rich(X), Y))) | (a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0))) | a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0))))) <=> ((~![Y: $i, X: $i] : (a_truth(poor(X), Y) | a_truth(rich(X), Y))) | a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0))) | a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(298,plain,
% 0.71/0.89 ((~![Y: $i, X: $i] : (a_truth(poor(X), Y) | a_truth(rich(X), Y))) | (a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0))) | a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(299,plain,
% 0.71/0.89 ((~![Y: $i, X: $i] : (a_truth(poor(X), Y) | a_truth(rich(X), Y))) | a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0))) | a_truth(rich(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.71/0.89 tff(300,plain,
% 0.71/0.89 (a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[299, 296, 286])).
% 0.71/0.89 tff(301,assumption,(says(me, poor(me))), introduced(assumption)).
% 0.71/0.89 tff(302,plain,
% 0.71/0.89 (((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~says(me, poor(me))) | (~a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~says(me, poor(me))) | (~a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(303,plain,
% 0.71/0.89 (((~says(me, poor(me))) | (~a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0))))) <=> ((~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~says(me, poor(me))) | (~a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(304,plain,
% 0.71/0.89 (((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~says(me, poor(me))) | (~a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~says(me, poor(me))) | (~a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0))))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[303])).
% 0.71/0.89 tff(305,plain,
% 0.71/0.89 (((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~says(me, poor(me))) | (~a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~says(me, poor(me))) | (~a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))),
% 0.71/0.89 inference(transitivity,[status(thm)],[304, 302])).
% 0.71/0.89 tff(306,plain,
% 0.71/0.89 ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | ((~says(me, poor(me))) | (~a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(307,plain,
% 0.71/0.89 ((~![Z: $i, Y: $i, X: $i] : ((~says(X, Y)) | (~a_truth(Y, Z)) | (~a_truth(knave(X), Z)))) | (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~says(me, poor(me))) | (~a_truth(poor(me), and(and(poor(me), rich(elem!0)), knave(elem!0))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.71/0.89 tff(308,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[307, 11, 301, 267, 300])).
% 0.71/0.89 tff(309,plain,((~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | (~says(me, poor(me))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(310,plain,
% 0.71/0.89 (~a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[309, 266, 237])).
% 0.71/0.89 tff(311,plain,
% 0.71/0.89 (((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | (a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0))) | a_truth(knight(me), and(and(poor(me), rich(elem!0)), knave(elem!0))))) <=> ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0))) | a_truth(knight(me), and(and(poor(me), rich(elem!0)), knave(elem!0))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(312,plain,
% 0.71/0.89 ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | (a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0))) | a_truth(knight(me), and(and(poor(me), rich(elem!0)), knave(elem!0))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(313,plain,
% 0.71/0.89 ((~![Y: $i, X: $i] : (a_truth(knave(X), Y) | a_truth(knight(X), Y))) | a_truth(knave(me), and(and(poor(me), rich(elem!0)), knave(elem!0))) | a_truth(knight(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.71/0.89 tff(314,plain,
% 0.71/0.89 (a_truth(knight(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[313, 29, 310])).
% 0.71/0.89 tff(315,plain,
% 0.71/0.89 (((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))))) | (~a_truth(knight(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))))) | (~a_truth(knight(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(316,plain,
% 0.71/0.89 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | (a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))))) | (~a_truth(knight(me), and(and(poor(me), rich(elem!0)), knave(elem!0)))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(317,plain,
% 0.71/0.89 ((~![Z: $i, Y: $i, X: $i] : (a_truth(Y, Z) | (~says(X, Y)) | (~a_truth(knight(X), Z)))) | a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), and(and(poor(me), rich(elem!0)), knave(elem!0))) | (~says(me, and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))))) | (~a_truth(knight(me), and(and(poor(me), rich(elem!0)), knave(elem!0))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.71/0.89 tff(318,plain,
% 0.71/0.89 (a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), and(and(poor(me), rich(elem!0)), knave(elem!0)))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[317, 43, 314, 225])).
% 0.71/0.89 tff(319,plain,
% 0.71/0.89 (((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(320,plain,
% 0.71/0.89 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | ((~a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(321,plain,
% 0.71/0.89 ((~![Z: $i, Y: $i, X: $i] : ((~a_truth(and(X, Y), Z)) | a_truth(X, Z))) | (~a_truth(and(and(knave(me), rich(me)), and(poor(me), rich(elem!0))), and(and(poor(me), rich(elem!0)), knave(elem!0)))) | a_truth(and(knave(me), rich(me)), and(and(poor(me), rich(elem!0)), knave(elem!0)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.71/0.89 tff(322,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[321, 69, 266, 318])).
% 0.71/0.89 % SZS output end Proof
% 0.71/0.89 % E exiting
%------------------------------------------------------------------------------