%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ061+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:23:19 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : PUZ061+1 : TPTP v9.0.0. Released v3.1.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 02:42:20 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(not_killed_by_type, type, (
% 0.11/0.36 not_killed_by: ( $i * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_Peanuts_5_type, type, (
% 0.11/0.36 tptp_fun_Peanuts_5: $i)).
% 0.11/0.36 tff(tptp_fun_Bill_3_type, type, (
% 0.11/0.36 tptp_fun_Bill_3: $i)).
% 0.11/0.36 tff(eats_type, type, (
% 0.11/0.36 eats: ( $i * $i ) > $o)).
% 0.11/0.36 tff(food_type, type, (
% 0.11/0.36 food: $i > $o)).
% 0.11/0.36 tff(likes_type, type, (
% 0.11/0.36 likes: ( $i * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_John_4_type, type, (
% 0.11/0.36 tptp_fun_John_4: $i)).
% 0.11/0.36 tff(alive_type, type, (
% 0.11/0.36 alive: $i > $o)).
% 0.11/0.36 tff(tptp_fun_Sue_2_type, type, (
% 0.11/0.36 tptp_fun_Sue_2: $i)).
% 0.11/0.36 tff(tptp_fun_Chicken_0_type, type, (
% 0.11/0.36 tptp_fun_Chicken_0: $i)).
% 0.11/0.36 tff(tptp_fun_Apples_1_type, type, (
% 0.11/0.36 tptp_fun_Apples_1: $i)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 (((![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken!0))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John!4, X)) & food(Apples!1) & food(Chicken!0) & ![X: $i] : (food(X) | ![Y: $i] : (~(eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill!3, Peanuts!5) & alive(Bill!3) & ![X: $i] : ((~eats(Bill!3, X)) | eats(Sue!2, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X))) & (~likes(John!4, Peanuts!5))) <=> (![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken!0))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John!4, X)) & food(Apples!1) & food(Chicken!0) & ![X: $i] : (food(X) | ![Y: $i] : (~(eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill!3, Peanuts!5) & alive(Bill!3) & ![X: $i] : ((~eats(Bill!3, X)) | eats(Sue!2, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)) & (~likes(John!4, Peanuts!5)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 ((![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken!0))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John!4, X)) & food(Apples!1) & food(Chicken!0) & ![X: $i] : (food(X) | ![Y: $i] : (~(eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill!3, Peanuts!5) & alive(Bill!3) & ![X: $i] : ((~eats(Bill!3, X)) | eats(Sue!2, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X))) <=> (![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken!0))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John!4, X)) & food(Apples!1) & food(Chicken!0) & ![X: $i] : (food(X) | ![Y: $i] : (~(eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill!3, Peanuts!5) & alive(Bill!3) & ![X: $i] : ((~eats(Bill!3, X)) | eats(Sue!2, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (((![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken!0))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John!4, X)) & food(Apples!1) & food(Chicken!0) & ![X: $i] : (food(X) | ![Y: $i] : (~(eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill!3, Peanuts!5) & alive(Bill!3) & ![X: $i] : ((~eats(Bill!3, X)) | eats(Sue!2, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X))) & (~likes(John!4, Peanuts!5))) <=> ((![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken!0))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John!4, X)) & food(Apples!1) & food(Chicken!0) & ![X: $i] : (food(X) | ![Y: $i] : (~(eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill!3, Peanuts!5) & alive(Bill!3) & ![X: $i] : ((~eats(Bill!3, X)) | eats(Sue!2, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X))) & (~likes(John!4, Peanuts!5)))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[2])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (((![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken!0))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John!4, X)) & food(Apples!1) & food(Chicken!0) & ![X: $i] : (food(X) | ![Y: $i] : (~(eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill!3, Peanuts!5) & alive(Bill!3) & ![X: $i] : ((~eats(Bill!3, X)) | eats(Sue!2, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X))) & (~likes(John!4, Peanuts!5))) <=> (![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken!0))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John!4, X)) & food(Apples!1) & food(Chicken!0) & ![X: $i] : (food(X) | ![Y: $i] : (~(eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill!3, Peanuts!5) & alive(Bill!3) & ![X: $i] : ((~eats(Bill!3, X)) | eats(Sue!2, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)) & (~likes(John!4, Peanuts!5)))),
% 0.11/0.36 inference(transitivity,[status(thm)],[3, 1])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 ((~![Peanuts: $i, John: $i, Bill: $i, Sue: $i, Apples: $i, Chicken: $i] : ((~(![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John, X)) & food(Apples) & food(Chicken) & ![X: $i] : (food(X) | (~?[Y: $i] : (eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill, Peanuts) & alive(Bill) & ![X: $i] : ((~eats(Bill, X)) | eats(Sue, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)))) | likes(John, Peanuts))) <=> (~![Peanuts: $i, John: $i, Bill: $i, Sue: $i, Apples: $i, Chicken: $i] : ((~(![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John, X)) & food(Apples) & food(Chicken) & ![X: $i] : (food(X) | (~?[Y: $i] : (eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill, Peanuts) & alive(Bill) & ![X: $i] : ((~eats(Bill, X)) | eats(Sue, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)))) | likes(John, Peanuts)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 ((~![Peanuts: $i, John: $i, Bill: $i, Sue: $i, Apples: $i, Chicken: $i] : (((((((((![X: $i, Y: $i] : ((alive(Y) & eats(Y, Chicken)) => likes(Y, X)) & ![X: $i] : (food(X) => likes(John, X))) & food(Apples)) & food(Chicken)) & ![X: $i] : (?[Y: $i] : (eats(Y, X) & not_killed_by(Y, X)) => food(X))) & eats(Bill, Peanuts)) & alive(Bill)) & ![X: $i] : (eats(Bill, X) => eats(Sue, X))) & ![Y: $i] : (alive(Y) => ![X: $i] : not_killed_by(Y, X))) => likes(John, Peanuts))) <=> (~![Peanuts: $i, John: $i, Bill: $i, Sue: $i, Apples: $i, Chicken: $i] : ((~(![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John, X)) & food(Apples) & food(Chicken) & ![X: $i] : (food(X) | (~?[Y: $i] : (eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill, Peanuts) & alive(Bill) & ![X: $i] : ((~eats(Bill, X)) | eats(Sue, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)))) | likes(John, Peanuts)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(7,axiom,(~![Peanuts: $i, John: $i, Bill: $i, Sue: $i, Apples: $i, Chicken: $i] : (((((((((![X: $i, Y: $i] : ((alive(Y) & eats(Y, Chicken)) => likes(Y, X)) & ![X: $i] : (food(X) => likes(John, X))) & food(Apples)) & food(Chicken)) & ![X: $i] : (?[Y: $i] : (eats(Y, X) & not_killed_by(Y, X)) => food(X))) & eats(Bill, Peanuts)) & alive(Bill)) & ![X: $i] : (eats(Bill, X) => eats(Sue, X))) & ![Y: $i] : (alive(Y) => ![X: $i] : not_killed_by(Y, X))) => likes(John, Peanuts))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (~![Peanuts: $i, John: $i, Bill: $i, Sue: $i, Apples: $i, Chicken: $i] : ((~(![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John, X)) & food(Apples) & food(Chicken) & ![X: $i] : (food(X) | (~?[Y: $i] : (eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill, Peanuts) & alive(Bill) & ![X: $i] : ((~eats(Bill, X)) | eats(Sue, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)))) | likes(John, Peanuts))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (~![Peanuts: $i, John: $i, Bill: $i, Sue: $i, Apples: $i, Chicken: $i] : ((~(![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John, X)) & food(Apples) & food(Chicken) & ![X: $i] : (food(X) | (~?[Y: $i] : (eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill, Peanuts) & alive(Bill) & ![X: $i] : ((~eats(Bill, X)) | eats(Sue, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)))) | likes(John, Peanuts))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (~![Peanuts: $i, John: $i, Bill: $i, Sue: $i, Apples: $i, Chicken: $i] : ((~(![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John, X)) & food(Apples) & food(Chicken) & ![X: $i] : (food(X) | (~?[Y: $i] : (eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill, Peanuts) & alive(Bill) & ![X: $i] : ((~eats(Bill, X)) | eats(Sue, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)))) | likes(John, Peanuts))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (~![Peanuts: $i, John: $i, Bill: $i, Sue: $i, Apples: $i, Chicken: $i] : ((~(![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John, X)) & food(Apples) & food(Chicken) & ![X: $i] : (food(X) | (~?[Y: $i] : (eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill, Peanuts) & alive(Bill) & ![X: $i] : ((~eats(Bill, X)) | eats(Sue, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)))) | likes(John, Peanuts))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~(alive(Y) & eats(Y, Chicken!0))) | likes(Y, X)) & ![X: $i] : ((~food(X)) | likes(John!4, X)) & food(Apples!1) & food(Chicken!0) & ![X: $i] : (food(X) | ![Y: $i] : (~(eats(Y, X) & not_killed_by(Y, X)))) & eats(Bill!3, Peanuts!5) & alive(Bill!3) & ![X: $i] : ((~eats(Bill!3, X)) | eats(Sue!2, X)) & ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)) & (~likes(John!4, Peanuts!5))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (~likes(John!4, Peanuts!5)),
% 0.11/0.37 inference(and_elim,[status(thm)],[12])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (^[X: $i] : refl(((~food(X)) | likes(John!4, X)) <=> ((~food(X)) | likes(John!4, X)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (![X: $i] : ((~food(X)) | likes(John!4, X)) <=> ![X: $i] : ((~food(X)) | likes(John!4, X))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (![X: $i] : ((~food(X)) | likes(John!4, X))),
% 0.11/0.37 inference(and_elim,[status(thm)],[12])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![X: $i] : ((~food(X)) | likes(John!4, X))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (((~![X: $i] : ((~food(X)) | likes(John!4, X))) | ((~food(Peanuts!5)) | likes(John!4, Peanuts!5))) <=> ((~![X: $i] : ((~food(X)) | likes(John!4, X))) | (~food(Peanuts!5)) | likes(John!4, Peanuts!5))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 ((~![X: $i] : ((~food(X)) | likes(John!4, X))) | ((~food(Peanuts!5)) | likes(John!4, Peanuts!5))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 ((~![X: $i] : ((~food(X)) | likes(John!4, X))) | (~food(Peanuts!5)) | likes(John!4, Peanuts!5)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (~food(Peanuts!5)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[20, 17, 13])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (^[X: $i] : refl((food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X)))) <=> (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (![X: $i] : (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X)))) <=> ![X: $i] : (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (^[X: $i] : rewrite((food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X)))) <=> (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![X: $i] : (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X)))) <=> ![X: $i] : (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![X: $i] : (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X)))) <=> ![X: $i] : (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[25, 23])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (^[X: $i] : rewrite((food(X) | ![Y: $i] : (~(eats(Y, X) & not_killed_by(Y, X)))) <=> (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (![X: $i] : (food(X) | ![Y: $i] : (~(eats(Y, X) & not_killed_by(Y, X)))) <=> ![X: $i] : (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[27])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (![X: $i] : (food(X) | ![Y: $i] : (~(eats(Y, X) & not_killed_by(Y, X))))),
% 0.11/0.37 inference(and_elim,[status(thm)],[12])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (![X: $i] : (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (![X: $i] : (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (((~![X: $i] : (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X))))) | (food(Peanuts!5) | ![Y: $i] : ((~eats(Y, Peanuts!5)) | (~not_killed_by(Y, Peanuts!5))))) <=> ((~![X: $i] : (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X))))) | food(Peanuts!5) | ![Y: $i] : ((~eats(Y, Peanuts!5)) | (~not_killed_by(Y, Peanuts!5))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 ((~![X: $i] : (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X))))) | (food(Peanuts!5) | ![Y: $i] : ((~eats(Y, Peanuts!5)) | (~not_killed_by(Y, Peanuts!5))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 ((~![X: $i] : (food(X) | ![Y: $i] : ((~eats(Y, X)) | (~not_killed_by(Y, X))))) | food(Peanuts!5) | ![Y: $i] : ((~eats(Y, Peanuts!5)) | (~not_killed_by(Y, Peanuts!5)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (![Y: $i] : ((~eats(Y, Peanuts!5)) | (~not_killed_by(Y, Peanuts!5)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (eats(Bill!3, Peanuts!5)),
% 0.11/0.37 inference(and_elim,[status(thm)],[12])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (((~![Y: $i] : ((~eats(Y, Peanuts!5)) | (~not_killed_by(Y, Peanuts!5)))) | ((~eats(Bill!3, Peanuts!5)) | (~not_killed_by(Bill!3, Peanuts!5)))) <=> ((~![Y: $i] : ((~eats(Y, Peanuts!5)) | (~not_killed_by(Y, Peanuts!5)))) | (~eats(Bill!3, Peanuts!5)) | (~not_killed_by(Bill!3, Peanuts!5)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 ((~![Y: $i] : ((~eats(Y, Peanuts!5)) | (~not_killed_by(Y, Peanuts!5)))) | ((~eats(Bill!3, Peanuts!5)) | (~not_killed_by(Bill!3, Peanuts!5)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 ((~![Y: $i] : ((~eats(Y, Peanuts!5)) | (~not_killed_by(Y, Peanuts!5)))) | (~eats(Bill!3, Peanuts!5)) | (~not_killed_by(Bill!3, Peanuts!5))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (~not_killed_by(Bill!3, Peanuts!5)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[39, 36, 35])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (^[Y: $i] : refl(((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)) <=> ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)) <=> ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[41])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 (^[Y: $i] : rewrite(((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)) <=> ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)) <=> ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[43])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X)) <=> ![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X))),
% 0.11/0.37 inference(transitivity,[status(thm)],[44, 42])).
% 0.11/0.37 tff(46,plain,
% 0.11/0.37 (![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X))),
% 0.11/0.37 inference(and_elim,[status(thm)],[12])).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 (![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 (alive(Bill!3)),
% 0.11/0.37 inference(and_elim,[status(thm)],[12])).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 (((~![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X))) | ((~alive(Bill!3)) | ![X: $i] : not_killed_by(Bill!3, X))) <=> ((~![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X))) | (~alive(Bill!3)) | ![X: $i] : not_killed_by(Bill!3, X))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 ((~![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X))) | ((~alive(Bill!3)) | ![X: $i] : not_killed_by(Bill!3, X))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 ((~![Y: $i] : ((~alive(Y)) | ![X: $i] : not_killed_by(Y, X))) | (~alive(Bill!3)) | ![X: $i] : not_killed_by(Bill!3, X)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (![X: $i] : not_killed_by(Bill!3, X)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[51, 48, 47])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 ((~![X: $i] : not_killed_by(Bill!3, X)) | not_killed_by(Bill!3, Peanuts!5)),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(54,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[53, 52, 40])).
% 0.19/0.37 % SZS output end Proof
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------