TSTP Solution File: PUZ001+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ001+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 14:10:46 EDT 2022
% Result : Theorem 0.21s 0.57s
% Output : Proof 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : PUZ001+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 18:16:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.57 % SZS status Theorem
% 0.21/0.57 % SZS output start Proof
% 0.21/0.57 tff(predicate2_type, type, (
% 0.21/0.57 predicate2: ( $i * $i * $i * $i ) > $o)).
% 0.21/0.57 tff(tptp_fun_A1_8_type, type, (
% 0.21/0.57 tptp_fun_A1_8: $i > $i)).
% 0.21/0.57 tff(tptp_fun__Butler__type, type, (
% 0.21/0.57 tptp_fun__Butler_: $i)).
% 0.21/0.57 tff(hate_type, type, (
% 0.21/0.57 hate: $i)).
% 0.21/0.57 tff(tptp_fun_V_6_type, type, (
% 0.21/0.57 tptp_fun_V_6: $i > $i)).
% 0.21/0.57 tff(tptp_fun_A_2_type, type, (
% 0.21/0.57 tptp_fun_A_2: $i)).
% 0.21/0.57 tff(tptp_fun__AuntAgatha__type, type, (
% 0.21/0.57 tptp_fun__AuntAgatha_: $i)).
% 0.21/0.57 tff(kill_type, type, (
% 0.21/0.57 kill: $i)).
% 0.21/0.57 tff(tptp_fun_C_0_type, type, (
% 0.21/0.57 tptp_fun_C_0: $i)).
% 0.21/0.57 tff(tptp_fun_Y_7_type, type, (
% 0.21/0.57 tptp_fun_Y_7: $i > $i)).
% 0.21/0.57 tff(tptp_fun_U_5_type, type, (
% 0.21/0.57 tptp_fun_U_5: $i > $i)).
% 0.21/0.57 tff(property2_type, type, (
% 0.21/0.57 property2: ( $i * $i * $i * $i ) > $o)).
% 0.21/0.57 tff(comp_than_type, type, (
% 0.21/0.57 comp_than: $i)).
% 0.21/0.57 tff(rich_type, type, (
% 0.21/0.57 rich: $i)).
% 0.21/0.57 tff(tptp_fun_S_4_type, type, (
% 0.21/0.57 tptp_fun_S_4: $i > $i)).
% 0.21/0.57 tff(tptp_fun__Charles__type, type, (
% 0.21/0.57 tptp_fun__Charles_: $i)).
% 0.21/0.57 tff(tptp_fun_I_3_type, type, (
% 0.21/0.57 tptp_fun_I_3: ( $i * $i ) > $i)).
% 0.21/0.57 tff(modifier_pp_type, type, (
% 0.21/0.57 modifier_pp: ( $i * $i * $i ) > $o)).
% 0.21/0.57 tff(tptp_fun__DreadburyMansion__type, type, (
% 0.21/0.57 tptp_fun__DreadburyMansion_: $i)).
% 0.21/0.57 tff(in_type, type, (
% 0.21/0.57 in: $i)).
% 0.21/0.57 tff(predicate1_type, type, (
% 0.21/0.57 predicate1: ( $i * $i * $i ) > $o)).
% 0.21/0.57 tff(live_type, type, (
% 0.21/0.57 live: $i)).
% 0.21/0.57 tff(tptp_fun_B_1_type, type, (
% 0.21/0.57 tptp_fun_B_1: $i)).
% 0.21/0.57 tff(1,assumption,(A!2 = |'AuntAgatha'|), introduced(assumption)).
% 0.21/0.57 tff(2,plain,
% 0.21/0.57 (predicate2(C!0, kill, A!2, |'AuntAgatha'|) <=> predicate2(C!0, kill, |'AuntAgatha'|, |'AuntAgatha'|)),
% 0.21/0.57 inference(monotonicity,[status(thm)],[1])).
% 0.21/0.57 tff(3,plain,
% 0.21/0.57 (predicate2(C!0, kill, |'AuntAgatha'|, |'AuntAgatha'|) <=> predicate2(C!0, kill, A!2, |'AuntAgatha'|)),
% 0.21/0.57 inference(symmetry,[status(thm)],[2])).
% 0.21/0.57 tff(4,plain,
% 0.21/0.57 ((~predicate2(C!0, kill, |'AuntAgatha'|, |'AuntAgatha'|)) <=> (~predicate2(C!0, kill, A!2, |'AuntAgatha'|))),
% 0.21/0.57 inference(monotonicity,[status(thm)],[3])).
% 0.21/0.57 tff(5,plain,
% 0.21/0.57 (^[A: $i] : refl((~predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|)) <=> (~predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|)))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(6,plain,
% 0.21/0.57 (![A: $i] : (~predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|)) <=> ![A: $i] : (~predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.57 tff(7,plain,
% 0.21/0.57 ((~?[A: $i] : predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|)) <=> (~?[A: $i] : predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(8,axiom,(~?[A: $i] : predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove')).
% 0.21/0.57 tff(9,plain,
% 0.21/0.57 (~?[A: $i] : predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.21/0.57 tff(10,plain,
% 0.21/0.57 (~?[A: $i] : predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[9, 7])).
% 0.21/0.57 tff(11,plain,
% 0.21/0.57 (~?[A: $i] : predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.21/0.57 tff(12,plain,
% 0.21/0.57 (~?[A: $i] : predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.21/0.57 tff(13,plain,
% 0.21/0.57 (~?[A: $i] : predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.21/0.57 tff(14,plain,
% 0.21/0.57 (~?[A: $i] : predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[13, 7])).
% 0.21/0.57 tff(15,plain,
% 0.21/0.57 (~?[A: $i] : predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.57 tff(16,plain,
% 0.21/0.57 (^[A: $i] : refl($oeq((~predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|)), (~predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(17,plain,(
% 0.21/0.57 ![A: $i] : (~predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|))),
% 0.21/0.57 inference(nnf-neg,[status(sab)],[15, 16])).
% 0.21/0.57 tff(18,plain,
% 0.21/0.57 (![A: $i] : (~predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[17, 6])).
% 0.21/0.57 tff(19,plain,
% 0.21/0.57 ((~![A: $i] : (~predicate2(A, kill, |'AuntAgatha'|, |'AuntAgatha'|))) | (~predicate2(C!0, kill, |'AuntAgatha'|, |'AuntAgatha'|))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(20,plain,
% 0.21/0.57 (~predicate2(C!0, kill, |'AuntAgatha'|, |'AuntAgatha'|)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.21/0.57 tff(21,plain,
% 0.21/0.57 (~predicate2(C!0, kill, A!2, |'AuntAgatha'|)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[20, 4])).
% 0.21/0.57 tff(22,plain,
% 0.21/0.57 ((predicate1(B!1, live, A!2) & modifier_pp(B!1, in, |'DreadburyMansion'|) & predicate2(C!0, kill, A!2, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | predicate2(tptp_fun_I_3(G, F), hate, F, G)) & ![J: $i] : ![K: $i, L: $i, M: $i] : (~(predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N))) & ![Q: $i] : (~predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | predicate2(tptp_fun_S_4(R), hate, |'AuntAgatha'|, R)) & ![T: $i] : ((property2(tptp_fun_U_5(T), rich, comp_than, |'AuntAgatha'|) & (T = tptp_fun_U_5(T))) | predicate2(tptp_fun_V_6(T), hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | predicate2(tptp_fun_Y_7(W), hate, |'Butler'|, W)) & ![Z: $i] : ![B1: $i] : (~predicate2(B1, hate, Z, tptp_fun_A1_8(Z))) & (~(|'AuntAgatha'| = |'Butler'|))) <=> (predicate1(B!1, live, A!2) & modifier_pp(B!1, in, |'DreadburyMansion'|) & predicate2(C!0, kill, A!2, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | predicate2(tptp_fun_I_3(G, F), hate, F, G)) & ![J: $i, K: $i, L: $i, M: $i] : (~(predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N))) & ![Q: $i] : (~predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | predicate2(tptp_fun_S_4(R), hate, |'AuntAgatha'|, R)) & ![T: $i] : ((property2(tptp_fun_U_5(T), rich, comp_than, |'AuntAgatha'|) & (T = tptp_fun_U_5(T))) | predicate2(tptp_fun_V_6(T), hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | predicate2(tptp_fun_Y_7(W), hate, |'Butler'|, W)) & ![Z: $i, B1: $i] : (~predicate2(B1, hate, Z, tptp_fun_A1_8(Z))) & (~(|'AuntAgatha'| = |'Butler'|)))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(23,plain,
% 0.21/0.57 (?[A: $i, B: $i, C: $i] : (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) & ![Z: $i] : (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1)) & (~(|'AuntAgatha'| = |'Butler'|))) <=> ?[A: $i, B: $i, C: $i] : (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) & ![Z: $i] : (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1)) & (~(|'AuntAgatha'| = |'Butler'|)))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(24,plain,
% 0.21/0.57 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|))), (((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) <=> ((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)))), rewrite(((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|))), (((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|)))), quant_intro(proof_bind(^[D: $i, E: $i] : trans(monotonicity(rewrite((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) <=> (predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|))), rewrite((((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)) <=> ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|))), (((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|))) <=> ((predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)) => ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|))))), rewrite(((predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)) => ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|))) <=> ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|))))), (((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|))) <=> ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|))))))), (![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|))) <=> ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))))), ((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) <=> ((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|))))))), rewrite(((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|))))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))))), ((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|))))))), trans(quant_intro(proof_bind(^[F: $i] : trans(monotonicity(quant_intro(proof_bind(^[G: $i, H: $i] : trans(monotonicity(rewrite(($true & predicate2(H, kill, F, G)) <=> predicate2(H, kill, F, G)), ((($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)) <=> (predicate2(H, kill, F, G) => ?[I: $i] : predicate2(I, hate, F, G)))), rewrite((predicate2(H, kill, F, G) => ?[I: $i] : predicate2(I, hate, F, G)) <=> ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G))), ((($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)) <=> ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G))))), (![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)) <=> ![G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)))), (($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G))) <=> ($true => ![G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G))))), rewrite(($true => ![G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G))) <=> ![G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G))), (($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G))) <=> ![G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G))))), (![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G))) <=> ![F: $i] : ![G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)))), pull_quant(![F: $i] : ![G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) <=> ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G))), (![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G))) <=> ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)))), (((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) <=> ((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|))))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G))))), rewrite(((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|))))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)))), (((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G))))), quant_intro(proof_bind(^[J: $i] : trans(monotonicity(rewrite((~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))) <=> (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M)))), (($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M)))) <=> ($true => (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M)))))), rewrite(($true => (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M)))) <=> (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M)))), (($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M)))) <=> (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M)))))), (![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M)))) <=> ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))))), ((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) <=> ((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G))) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M)))))), rewrite(((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G))) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M)))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))))), ((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M)))))), quant_intro(proof_bind(^[N: $i, O: $i] : trans(monotonicity(rewrite(($true & predicate2(O, hate, |'AuntAgatha'|, N)) <=> predicate2(O, hate, |'AuntAgatha'|, N)), rewrite((~?[P: $i] : predicate2(P, hate, |'Charles'|, N)) <=> (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))), ((($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) <=> (predicate2(O, hate, |'AuntAgatha'|, N) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))))), rewrite((predicate2(O, hate, |'AuntAgatha'|, N) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) <=> ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))), ((($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) <=> ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))))), (![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) <=> ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))))), (((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) <=> ((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M)))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))))), rewrite(((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M)))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))))), (((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))))), rewrite((~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) <=> (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))), ((((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) <=> ((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))))), rewrite(((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)))), ((((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))))), quant_intro(proof_bind(^[R: $i] : trans(monotonicity(rewrite(($true & (~(R = |'Butler'|))) <=> (~(R = |'Butler'|))), ((($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) <=> ((~(R = |'Butler'|)) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)))), rewrite(((~(R = |'Butler'|)) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) <=> ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))), ((($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) <=> ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))))), (![R: $i] : (($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) <=> ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)))), (((((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) & ![R: $i] : (($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) <=> ((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))))), rewrite(((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)))), (((((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) & ![R: $i] : (($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))))), quant_intro(proof_bind(^[T: $i] : trans(monotonicity(trans(monotonicity(rewrite((~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U))) <=> (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))), (($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) <=> ($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))))), rewrite(($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) <=> (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))), (($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) <=> (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U))))), ((($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) <=> ((~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T)))), rewrite(((~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) <=> (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T))), ((($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) <=> (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T))))), (![T: $i] : (($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) <=> ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)))), ((((((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) & ![R: $i] : (($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) & ![T: $i] : (($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T))) <=> ((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T))))), rewrite(((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)))), ((((((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) & ![R: $i] : (($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) & ![T: $i] : (($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T))))), quant_intro(proof_bind(^[W: $i, X: $i] : trans(monotonicity(rewrite(($true & predicate2(X, hate, |'AuntAgatha'|, W)) <=> predicate2(X, hate, |'AuntAgatha'|, W)), ((($true & predicate2(X, hate, |'AuntAgatha'|, W)) => ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) <=> (predicate2(X, hate, |'AuntAgatha'|, W) => ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)))), rewrite((predicate2(X, hate, |'AuntAgatha'|, W) => ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) <=> ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))), ((($true & predicate2(X, hate, |'AuntAgatha'|, W)) => ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) <=> ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))))), (![W: $i, X: $i] : (($true & predicate2(X, hate, |'AuntAgatha'|, W)) => ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) <=> ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)))), (((((((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) & ![R: $i] : (($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) & ![T: $i] : (($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T))) & ![W: $i, X: $i] : (($true & predicate2(X, hate, |'AuntAgatha'|, W)) => ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))) <=> ((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T))) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))))), rewrite(((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T))) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)))), (((((((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) & ![R: $i] : (($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) & ![T: $i] : (($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T))) & ![W: $i, X: $i] : (($true & predicate2(X, hate, |'AuntAgatha'|, W)) => ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))))), quant_intro(proof_bind(^[Z: $i] : trans(monotonicity(rewrite((~![A1: $i] : ($true => ?[B1: $i] : predicate2(B1, hate, Z, A1))) <=> (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1))), (($true => (~![A1: $i] : ($true => ?[B1: $i] : predicate2(B1, hate, Z, A1)))) <=> ($true => (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1))))), rewrite(($true => (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1))) <=> (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1))), (($true => (~![A1: $i] : ($true => ?[B1: $i] : predicate2(B1, hate, Z, A1)))) <=> (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1))))), (![Z: $i] : ($true => (~![A1: $i] : ($true => ?[B1: $i] : predicate2(B1, hate, Z, A1)))) <=> ![Z: $i] : (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1)))), ((((((((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) & ![R: $i] : (($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) & ![T: $i] : (($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T))) & ![W: $i, X: $i] : (($true & predicate2(X, hate, |'AuntAgatha'|, W)) => ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))) & ![Z: $i] : ($true => (~![A1: $i] : ($true => ?[B1: $i] : predicate2(B1, hate, Z, A1))))) <=> ((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))) & ![Z: $i] : (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1))))), rewrite(((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))) & ![Z: $i] : (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) & ![Z: $i] : (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1)))), ((((((((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) & ![R: $i] : (($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) & ![T: $i] : (($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T))) & ![W: $i, X: $i] : (($true & predicate2(X, hate, |'AuntAgatha'|, W)) => ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))) & ![Z: $i] : ($true => (~![A1: $i] : ($true => ?[B1: $i] : predicate2(B1, hate, Z, A1))))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) & ![Z: $i] : (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1))))), (((((((((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) & ![R: $i] : (($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) & ![T: $i] : (($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T))) & ![W: $i, X: $i] : (($true & predicate2(X, hate, |'AuntAgatha'|, W)) => ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))) & ![Z: $i] : ($true => (~![A1: $i] : ($true => ?[B1: $i] : predicate2(B1, hate, Z, A1))))) & (~(|'AuntAgatha'| = |'Butler'|))) <=> ((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) & ![Z: $i] : (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1))) & (~(|'AuntAgatha'| = |'Butler'|))))), rewrite(((predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) & ![Z: $i] : (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1))) & (~(|'AuntAgatha'| = |'Butler'|))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) & ![Z: $i] : (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1)) & (~(|'AuntAgatha'| = |'Butler'|)))), (((((((((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) & ![R: $i] : (($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) & ![T: $i] : (($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T))) & ![W: $i, X: $i] : (($true & predicate2(X, hate, |'AuntAgatha'|, W)) => ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))) & ![Z: $i] : ($true => (~![A1: $i] : ($true => ?[B1: $i] : predicate2(B1, hate, Z, A1))))) & (~(|'AuntAgatha'| = |'Butler'|))) <=> (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) & ![Z: $i] : (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1)) & (~(|'AuntAgatha'| = |'Butler'|)))))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(25,plain,
% 0.56/0.61 (?[A: $i, B: $i, C: $i] : ((((((((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) & ![R: $i] : (($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) & ![T: $i] : (($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T))) & ![W: $i, X: $i] : (($true & predicate2(X, hate, |'AuntAgatha'|, W)) => ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))) & ![Z: $i] : ($true => (~![A1: $i] : ($true => ?[B1: $i] : predicate2(B1, hate, Z, A1))))) & (~(|'AuntAgatha'| = |'Butler'|))) <=> ?[A: $i, B: $i, C: $i] : (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) & ![Z: $i] : (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1)) & (~(|'AuntAgatha'| = |'Butler'|)))),
% 0.56/0.61 inference(quant_intro,[status(thm)],[24])).
% 0.56/0.61 tff(26,axiom,(?[A: $i, B: $i, C: $i] : ((((((((((((($true & predicate1(B, live, A)) & modifier_pp(B, in, |'DreadburyMansion'|)) & predicate2(C, kill, A, |'AuntAgatha'|)) & ![D: $i, E: $i] : ((($true & predicate1(E, live, D)) & modifier_pp(E, in, |'DreadburyMansion'|)) => (((D = |'AuntAgatha'|) | (D = |'Butler'|)) | (D = |'Charles'|)))) & ![F: $i] : ($true => ![G: $i, H: $i] : (($true & predicate2(H, kill, F, G)) => ?[I: $i] : predicate2(I, hate, F, G)))) & ![J: $i] : ($true => (~?[K: $i, L: $i, M: $i] : ((($true & predicate2(L, kill, J, K)) & property2(M, rich, comp_than, K)) & (J = M))))) & ![N: $i, O: $i] : (($true & predicate2(O, hate, |'AuntAgatha'|, N)) => (~?[P: $i] : predicate2(P, hate, |'Charles'|, N)))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|))) & ![R: $i] : (($true & (~(R = |'Butler'|))) => ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R))) & ![T: $i] : (($true & (~?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)))) => ?[V: $i] : predicate2(V, hate, |'Butler'|, T))) & ![W: $i, X: $i] : (($true & predicate2(X, hate, |'AuntAgatha'|, W)) => ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W))) & ![Z: $i] : ($true => (~![A1: $i] : ($true => ?[B1: $i] : predicate2(B1, hate, Z, A1))))) & (~(|'AuntAgatha'| = |'Butler'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','background')).
% 0.56/0.61 tff(27,plain,
% 0.56/0.61 (?[A: $i, B: $i, C: $i] : (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) & ![Z: $i] : (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1)) & (~(|'AuntAgatha'| = |'Butler'|)))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.56/0.61 tff(28,plain,
% 0.56/0.61 (?[A: $i, B: $i, C: $i] : (predicate1(B, live, A) & modifier_pp(B, in, |'DreadburyMansion'|) & predicate2(C, kill, A, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | ?[I: $i] : predicate2(I, hate, F, G)) & ![J: $i] : (~?[K: $i, L: $i, M: $i] : (predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | (~?[P: $i] : predicate2(P, hate, |'Charles'|, N))) & (~?[Q: $i] : predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | ?[S: $i] : predicate2(S, hate, |'AuntAgatha'|, R)) & ![T: $i] : (?[U: $i] : (property2(U, rich, comp_than, |'AuntAgatha'|) & (T = U)) | ?[V: $i] : predicate2(V, hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | ?[Y: $i] : predicate2(Y, hate, |'Butler'|, W)) & ![Z: $i] : (~![A1: $i] : ?[B1: $i] : predicate2(B1, hate, Z, A1)) & (~(|'AuntAgatha'| = |'Butler'|)))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.56/0.61 tff(29,plain,
% 0.56/0.61 (predicate1(B!1, live, A!2) & modifier_pp(B!1, in, |'DreadburyMansion'|) & predicate2(C!0, kill, A!2, |'AuntAgatha'|) & ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) & ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | predicate2(tptp_fun_I_3(G, F), hate, F, G)) & ![J: $i, K: $i, L: $i, M: $i] : (~(predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) & ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N))) & ![Q: $i] : (~predicate2(Q, hate, |'AuntAgatha'|, |'Butler'|)) & ![R: $i] : ((R = |'Butler'|) | predicate2(tptp_fun_S_4(R), hate, |'AuntAgatha'|, R)) & ![T: $i] : ((property2(tptp_fun_U_5(T), rich, comp_than, |'AuntAgatha'|) & (T = tptp_fun_U_5(T))) | predicate2(tptp_fun_V_6(T), hate, |'Butler'|, T)) & ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | predicate2(tptp_fun_Y_7(W), hate, |'Butler'|, W)) & ![Z: $i, B1: $i] : (~predicate2(B1, hate, Z, tptp_fun_A1_8(Z))) & (~(|'AuntAgatha'| = |'Butler'|))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[28, 22])).
% 0.56/0.61 tff(30,plain,
% 0.56/0.61 (predicate2(C!0, kill, A!2, |'AuntAgatha'|)),
% 0.56/0.61 inference(and_elim,[status(thm)],[29])).
% 0.56/0.61 tff(31,plain,
% 0.56/0.61 ($false),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[30, 21])).
% 0.56/0.61 tff(32,plain,(~(A!2 = |'AuntAgatha'|)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.61 tff(33,assumption,(A!2 = |'Charles'|), introduced(assumption)).
% 0.56/0.61 tff(34,plain,
% 0.56/0.61 (|'Charles'| = A!2),
% 0.56/0.61 inference(symmetry,[status(thm)],[33])).
% 0.56/0.61 tff(35,plain,
% 0.56/0.61 (predicate2(tptp_fun_I_3(|'AuntAgatha'|, A!2), hate, |'Charles'|, |'AuntAgatha'|) <=> predicate2(tptp_fun_I_3(|'AuntAgatha'|, A!2), hate, A!2, |'AuntAgatha'|)),
% 0.56/0.61 inference(monotonicity,[status(thm)],[34])).
% 0.56/0.61 tff(36,plain,
% 0.56/0.61 (predicate2(tptp_fun_I_3(|'AuntAgatha'|, A!2), hate, A!2, |'AuntAgatha'|) <=> predicate2(tptp_fun_I_3(|'AuntAgatha'|, A!2), hate, |'Charles'|, |'AuntAgatha'|)),
% 0.56/0.61 inference(symmetry,[status(thm)],[35])).
% 0.56/0.61 tff(37,plain,
% 0.56/0.61 (^[F: $i, G: $i, H: $i] : refl(((~predicate2(H, kill, F, G)) | predicate2(tptp_fun_I_3(G, F), hate, F, G)) <=> ((~predicate2(H, kill, F, G)) | predicate2(tptp_fun_I_3(G, F), hate, F, G)))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(38,plain,
% 0.56/0.61 (![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | predicate2(tptp_fun_I_3(G, F), hate, F, G)) <=> ![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | predicate2(tptp_fun_I_3(G, F), hate, F, G))),
% 0.56/0.61 inference(quant_intro,[status(thm)],[37])).
% 0.56/0.61 tff(39,plain,
% 0.56/0.61 (![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | predicate2(tptp_fun_I_3(G, F), hate, F, G))),
% 0.56/0.61 inference(and_elim,[status(thm)],[29])).
% 0.56/0.61 tff(40,plain,
% 0.56/0.61 (![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | predicate2(tptp_fun_I_3(G, F), hate, F, G))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.56/0.61 tff(41,plain,
% 0.56/0.61 (((~![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | predicate2(tptp_fun_I_3(G, F), hate, F, G))) | ((~predicate2(C!0, kill, A!2, |'AuntAgatha'|)) | predicate2(tptp_fun_I_3(|'AuntAgatha'|, A!2), hate, A!2, |'AuntAgatha'|))) <=> ((~![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | predicate2(tptp_fun_I_3(G, F), hate, F, G))) | (~predicate2(C!0, kill, A!2, |'AuntAgatha'|)) | predicate2(tptp_fun_I_3(|'AuntAgatha'|, A!2), hate, A!2, |'AuntAgatha'|))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(42,plain,
% 0.56/0.61 ((~![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | predicate2(tptp_fun_I_3(G, F), hate, F, G))) | ((~predicate2(C!0, kill, A!2, |'AuntAgatha'|)) | predicate2(tptp_fun_I_3(|'AuntAgatha'|, A!2), hate, A!2, |'AuntAgatha'|))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(43,plain,
% 0.56/0.61 ((~![F: $i, G: $i, H: $i] : ((~predicate2(H, kill, F, G)) | predicate2(tptp_fun_I_3(G, F), hate, F, G))) | (~predicate2(C!0, kill, A!2, |'AuntAgatha'|)) | predicate2(tptp_fun_I_3(|'AuntAgatha'|, A!2), hate, A!2, |'AuntAgatha'|)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.56/0.61 tff(44,plain,
% 0.56/0.61 (predicate2(tptp_fun_I_3(|'AuntAgatha'|, A!2), hate, A!2, |'AuntAgatha'|)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[43, 30, 40])).
% 0.56/0.61 tff(45,plain,
% 0.56/0.61 (predicate2(tptp_fun_I_3(|'AuntAgatha'|, A!2), hate, |'Charles'|, |'AuntAgatha'|)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[44, 36])).
% 0.56/0.61 tff(46,plain,
% 0.56/0.61 (~(|'AuntAgatha'| = |'Butler'|)),
% 0.56/0.61 inference(and_elim,[status(thm)],[29])).
% 0.56/0.61 tff(47,plain,
% 0.56/0.61 (![R: $i] : ((R = |'Butler'|) | predicate2(tptp_fun_S_4(R), hate, |'AuntAgatha'|, R))),
% 0.56/0.61 inference(and_elim,[status(thm)],[29])).
% 0.56/0.61 tff(48,plain,
% 0.56/0.61 (((~![R: $i] : ((R = |'Butler'|) | predicate2(tptp_fun_S_4(R), hate, |'AuntAgatha'|, R))) | ((|'AuntAgatha'| = |'Butler'|) | predicate2(tptp_fun_S_4(|'AuntAgatha'|), hate, |'AuntAgatha'|, |'AuntAgatha'|))) <=> ((~![R: $i] : ((R = |'Butler'|) | predicate2(tptp_fun_S_4(R), hate, |'AuntAgatha'|, R))) | (|'AuntAgatha'| = |'Butler'|) | predicate2(tptp_fun_S_4(|'AuntAgatha'|), hate, |'AuntAgatha'|, |'AuntAgatha'|))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(49,plain,
% 0.56/0.61 ((~![R: $i] : ((R = |'Butler'|) | predicate2(tptp_fun_S_4(R), hate, |'AuntAgatha'|, R))) | ((|'AuntAgatha'| = |'Butler'|) | predicate2(tptp_fun_S_4(|'AuntAgatha'|), hate, |'AuntAgatha'|, |'AuntAgatha'|))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(50,plain,
% 0.56/0.61 ((~![R: $i] : ((R = |'Butler'|) | predicate2(tptp_fun_S_4(R), hate, |'AuntAgatha'|, R))) | (|'AuntAgatha'| = |'Butler'|) | predicate2(tptp_fun_S_4(|'AuntAgatha'|), hate, |'AuntAgatha'|, |'AuntAgatha'|)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.56/0.61 tff(51,plain,
% 0.56/0.61 (predicate2(tptp_fun_S_4(|'AuntAgatha'|), hate, |'AuntAgatha'|, |'AuntAgatha'|)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[50, 47, 46])).
% 0.56/0.61 tff(52,plain,
% 0.56/0.61 (^[N: $i, O: $i] : refl(((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N))) <=> ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N))))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(53,plain,
% 0.56/0.61 (![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N))) <=> ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N)))),
% 0.56/0.61 inference(quant_intro,[status(thm)],[52])).
% 0.56/0.61 tff(54,plain,
% 0.56/0.61 (^[N: $i, O: $i] : rewrite(((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N))) <=> ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N))))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(55,plain,
% 0.56/0.61 (![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N))) <=> ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N)))),
% 0.56/0.61 inference(quant_intro,[status(thm)],[54])).
% 0.56/0.61 tff(56,plain,
% 0.56/0.61 (![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N))) <=> ![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N)))),
% 0.56/0.61 inference(transitivity,[status(thm)],[55, 53])).
% 0.56/0.61 tff(57,plain,
% 0.56/0.61 (![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N)))),
% 0.56/0.61 inference(and_elim,[status(thm)],[29])).
% 0.56/0.61 tff(58,plain,
% 0.56/0.61 (![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N)))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.56/0.61 tff(59,plain,
% 0.56/0.61 (((~![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N)))) | ((~predicate2(tptp_fun_S_4(|'AuntAgatha'|), hate, |'AuntAgatha'|, |'AuntAgatha'|)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, |'AuntAgatha'|)))) <=> ((~![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N)))) | (~predicate2(tptp_fun_S_4(|'AuntAgatha'|), hate, |'AuntAgatha'|, |'AuntAgatha'|)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, |'AuntAgatha'|)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(60,plain,
% 0.56/0.61 ((~![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N)))) | ((~predicate2(tptp_fun_S_4(|'AuntAgatha'|), hate, |'AuntAgatha'|, |'AuntAgatha'|)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, |'AuntAgatha'|)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(61,plain,
% 0.56/0.61 ((~![N: $i, O: $i] : ((~predicate2(O, hate, |'AuntAgatha'|, N)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, N)))) | (~predicate2(tptp_fun_S_4(|'AuntAgatha'|), hate, |'AuntAgatha'|, |'AuntAgatha'|)) | ![P: $i] : (~predicate2(P, hate, |'Charles'|, |'AuntAgatha'|))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.56/0.61 tff(62,plain,
% 0.56/0.61 (![P: $i] : (~predicate2(P, hate, |'Charles'|, |'AuntAgatha'|))),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[61, 58, 51])).
% 0.56/0.61 tff(63,plain,
% 0.56/0.61 ((~![P: $i] : (~predicate2(P, hate, |'Charles'|, |'AuntAgatha'|))) | (~predicate2(tptp_fun_I_3(|'AuntAgatha'|, A!2), hate, |'Charles'|, |'AuntAgatha'|))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(64,plain,
% 0.56/0.61 (~predicate2(tptp_fun_I_3(|'AuntAgatha'|, A!2), hate, |'Charles'|, |'AuntAgatha'|)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.56/0.61 tff(65,plain,
% 0.56/0.61 ($false),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[64, 45])).
% 0.56/0.61 tff(66,plain,(~(A!2 = |'Charles'|)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.61 tff(67,plain,
% 0.56/0.61 (^[D: $i, E: $i] : refl(((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|))) <=> ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|))))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(68,plain,
% 0.56/0.61 (![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|))) <=> ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|)))),
% 0.56/0.61 inference(quant_intro,[status(thm)],[67])).
% 0.56/0.61 tff(69,plain,
% 0.56/0.61 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite((predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)) <=> (~((~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|))))), ((~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|))) <=> (~(~((~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|))))))), rewrite((~(~((~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|))))) <=> ((~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|)))), ((~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|))) <=> ((~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|))))), (((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) <=> ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | ((~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|)))))), rewrite(((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | ((~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|)))) <=> ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|)))), (((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) <=> ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|)))))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(70,plain,
% 0.56/0.61 (![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|)))) <=> ![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|)))),
% 0.56/0.61 inference(quant_intro,[status(thm)],[69])).
% 0.56/0.61 tff(71,plain,
% 0.56/0.61 (![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~(predicate1(E, live, D) & modifier_pp(E, in, |'DreadburyMansion'|))))),
% 0.56/0.61 inference(and_elim,[status(thm)],[29])).
% 0.56/0.61 tff(72,plain,
% 0.56/0.61 (![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|)))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.56/0.61 tff(73,plain,
% 0.56/0.61 (![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|)))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.56/0.61 tff(74,plain,
% 0.56/0.61 (modifier_pp(B!1, in, |'DreadburyMansion'|)),
% 0.56/0.61 inference(and_elim,[status(thm)],[29])).
% 0.56/0.61 tff(75,plain,
% 0.56/0.61 (predicate1(B!1, live, A!2)),
% 0.56/0.61 inference(and_elim,[status(thm)],[29])).
% 0.56/0.61 tff(76,plain,
% 0.56/0.61 (((~![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|)))) | ((A!2 = |'Charles'|) | (A!2 = |'Butler'|) | (A!2 = |'AuntAgatha'|) | (~predicate1(B!1, live, A!2)) | (~modifier_pp(B!1, in, |'DreadburyMansion'|)))) <=> ((~![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|)))) | (A!2 = |'Charles'|) | (A!2 = |'Butler'|) | (A!2 = |'AuntAgatha'|) | (~predicate1(B!1, live, A!2)) | (~modifier_pp(B!1, in, |'DreadburyMansion'|)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(77,plain,
% 0.56/0.61 ((~![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|)))) | ((A!2 = |'Charles'|) | (A!2 = |'Butler'|) | (A!2 = |'AuntAgatha'|) | (~predicate1(B!1, live, A!2)) | (~modifier_pp(B!1, in, |'DreadburyMansion'|)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(78,plain,
% 0.56/0.62 ((~![D: $i, E: $i] : ((D = |'Charles'|) | (D = |'Butler'|) | (D = |'AuntAgatha'|) | (~predicate1(E, live, D)) | (~modifier_pp(E, in, |'DreadburyMansion'|)))) | (A!2 = |'Charles'|) | (A!2 = |'Butler'|) | (A!2 = |'AuntAgatha'|) | (~predicate1(B!1, live, A!2)) | (~modifier_pp(B!1, in, |'DreadburyMansion'|))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.56/0.62 tff(79,plain,
% 0.56/0.62 ((A!2 = |'Charles'|) | (A!2 = |'Butler'|) | (A!2 = |'AuntAgatha'|)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[78, 75, 74, 73])).
% 0.56/0.62 tff(80,plain,
% 0.56/0.62 (A!2 = |'Butler'|),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[79, 66, 32])).
% 0.56/0.62 tff(81,plain,
% 0.56/0.62 (|'Butler'| = A!2),
% 0.56/0.62 inference(symmetry,[status(thm)],[80])).
% 0.56/0.62 tff(82,plain,
% 0.56/0.62 (predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, |'Butler'|, tptp_fun_A1_8(A!2)) <=> predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, A!2, tptp_fun_A1_8(A!2))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[81])).
% 0.56/0.62 tff(83,plain,
% 0.56/0.62 (predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, A!2, tptp_fun_A1_8(A!2)) <=> predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, |'Butler'|, tptp_fun_A1_8(A!2))),
% 0.56/0.62 inference(symmetry,[status(thm)],[82])).
% 0.56/0.62 tff(84,plain,
% 0.56/0.62 ((~predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, A!2, tptp_fun_A1_8(A!2))) <=> (~predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, |'Butler'|, tptp_fun_A1_8(A!2)))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[83])).
% 0.56/0.62 tff(85,plain,
% 0.56/0.62 (![Z: $i, B1: $i] : (~predicate2(B1, hate, Z, tptp_fun_A1_8(Z)))),
% 0.56/0.62 inference(and_elim,[status(thm)],[29])).
% 0.56/0.62 tff(86,plain,
% 0.56/0.62 ((~![Z: $i, B1: $i] : (~predicate2(B1, hate, Z, tptp_fun_A1_8(Z)))) | (~predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, A!2, tptp_fun_A1_8(A!2)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(87,plain,
% 0.56/0.62 (~predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, A!2, tptp_fun_A1_8(A!2))),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.56/0.62 tff(88,plain,
% 0.56/0.62 (~predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, |'Butler'|, tptp_fun_A1_8(A!2))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[87, 84])).
% 0.56/0.62 tff(89,assumption,(predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, |'Butler'|, tptp_fun_A1_8(A!2))), introduced(assumption)).
% 0.56/0.62 tff(90,plain,
% 0.56/0.62 ($false),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.56/0.62 tff(91,plain,(~predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, |'Butler'|, tptp_fun_A1_8(A!2))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.62 tff(92,assumption,(predicate2(tptp_fun_S_4(tptp_fun_A1_8(A!2)), hate, |'AuntAgatha'|, tptp_fun_A1_8(A!2))), introduced(assumption)).
% 0.56/0.62 tff(93,plain,
% 0.56/0.62 (^[W: $i, X: $i] : refl(((~predicate2(X, hate, |'AuntAgatha'|, W)) | predicate2(tptp_fun_Y_7(W), hate, |'Butler'|, W)) <=> ((~predicate2(X, hate, |'AuntAgatha'|, W)) | predicate2(tptp_fun_Y_7(W), hate, |'Butler'|, W)))),
% 0.56/0.62 inference(bind,[status(th)],[])).
% 0.56/0.62 tff(94,plain,
% 0.56/0.62 (![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | predicate2(tptp_fun_Y_7(W), hate, |'Butler'|, W)) <=> ![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | predicate2(tptp_fun_Y_7(W), hate, |'Butler'|, W))),
% 0.56/0.62 inference(quant_intro,[status(thm)],[93])).
% 0.56/0.62 tff(95,plain,
% 0.56/0.62 (![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | predicate2(tptp_fun_Y_7(W), hate, |'Butler'|, W))),
% 0.56/0.62 inference(and_elim,[status(thm)],[29])).
% 0.56/0.62 tff(96,plain,
% 0.56/0.62 (![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | predicate2(tptp_fun_Y_7(W), hate, |'Butler'|, W))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.56/0.62 tff(97,plain,
% 0.56/0.62 (((~![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | predicate2(tptp_fun_Y_7(W), hate, |'Butler'|, W))) | ((~predicate2(tptp_fun_S_4(tptp_fun_A1_8(A!2)), hate, |'AuntAgatha'|, tptp_fun_A1_8(A!2))) | predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, |'Butler'|, tptp_fun_A1_8(A!2)))) <=> ((~![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | predicate2(tptp_fun_Y_7(W), hate, |'Butler'|, W))) | (~predicate2(tptp_fun_S_4(tptp_fun_A1_8(A!2)), hate, |'AuntAgatha'|, tptp_fun_A1_8(A!2))) | predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, |'Butler'|, tptp_fun_A1_8(A!2)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(98,plain,
% 0.56/0.62 ((~![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | predicate2(tptp_fun_Y_7(W), hate, |'Butler'|, W))) | ((~predicate2(tptp_fun_S_4(tptp_fun_A1_8(A!2)), hate, |'AuntAgatha'|, tptp_fun_A1_8(A!2))) | predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, |'Butler'|, tptp_fun_A1_8(A!2)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(99,plain,
% 0.56/0.62 ((~![W: $i, X: $i] : ((~predicate2(X, hate, |'AuntAgatha'|, W)) | predicate2(tptp_fun_Y_7(W), hate, |'Butler'|, W))) | (~predicate2(tptp_fun_S_4(tptp_fun_A1_8(A!2)), hate, |'AuntAgatha'|, tptp_fun_A1_8(A!2))) | predicate2(tptp_fun_Y_7(tptp_fun_A1_8(A!2)), hate, |'Butler'|, tptp_fun_A1_8(A!2))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.56/0.62 tff(100,plain,
% 0.56/0.62 ($false),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[99, 96, 92, 91])).
% 0.56/0.62 tff(101,plain,(~predicate2(tptp_fun_S_4(tptp_fun_A1_8(A!2)), hate, |'AuntAgatha'|, tptp_fun_A1_8(A!2))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.62 tff(102,plain,
% 0.56/0.62 (((~![R: $i] : ((R = |'Butler'|) | predicate2(tptp_fun_S_4(R), hate, |'AuntAgatha'|, R))) | ((tptp_fun_A1_8(A!2) = |'Butler'|) | predicate2(tptp_fun_S_4(tptp_fun_A1_8(A!2)), hate, |'AuntAgatha'|, tptp_fun_A1_8(A!2)))) <=> ((~![R: $i] : ((R = |'Butler'|) | predicate2(tptp_fun_S_4(R), hate, |'AuntAgatha'|, R))) | (tptp_fun_A1_8(A!2) = |'Butler'|) | predicate2(tptp_fun_S_4(tptp_fun_A1_8(A!2)), hate, |'AuntAgatha'|, tptp_fun_A1_8(A!2)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(103,plain,
% 0.56/0.62 ((~![R: $i] : ((R = |'Butler'|) | predicate2(tptp_fun_S_4(R), hate, |'AuntAgatha'|, R))) | ((tptp_fun_A1_8(A!2) = |'Butler'|) | predicate2(tptp_fun_S_4(tptp_fun_A1_8(A!2)), hate, |'AuntAgatha'|, tptp_fun_A1_8(A!2)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(104,plain,
% 0.56/0.62 ((~![R: $i] : ((R = |'Butler'|) | predicate2(tptp_fun_S_4(R), hate, |'AuntAgatha'|, R))) | (tptp_fun_A1_8(A!2) = |'Butler'|) | predicate2(tptp_fun_S_4(tptp_fun_A1_8(A!2)), hate, |'AuntAgatha'|, tptp_fun_A1_8(A!2))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.56/0.62 tff(105,plain,
% 0.56/0.62 ((tptp_fun_A1_8(A!2) = |'Butler'|) | predicate2(tptp_fun_S_4(tptp_fun_A1_8(A!2)), hate, |'AuntAgatha'|, tptp_fun_A1_8(A!2))),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[104, 47])).
% 0.56/0.62 tff(106,plain,
% 0.56/0.62 (tptp_fun_A1_8(A!2) = |'Butler'|),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[105, 101])).
% 0.56/0.62 tff(107,plain,
% 0.56/0.62 (tptp_fun_A1_8(|'Butler'|) = tptp_fun_A1_8(A!2)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[81])).
% 0.56/0.62 tff(108,plain,
% 0.56/0.62 (tptp_fun_A1_8(|'Butler'|) = A!2),
% 0.56/0.62 inference(transitivity,[status(thm)],[107, 106, 81])).
% 0.56/0.62 tff(109,plain,
% 0.56/0.62 (predicate2(tptp_fun_V_6(A!2), hate, |'Butler'|, tptp_fun_A1_8(|'Butler'|)) <=> predicate2(tptp_fun_V_6(A!2), hate, |'Butler'|, A!2)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[108])).
% 0.56/0.62 tff(110,plain,
% 0.56/0.62 (predicate2(tptp_fun_V_6(A!2), hate, |'Butler'|, A!2) <=> predicate2(tptp_fun_V_6(A!2), hate, |'Butler'|, tptp_fun_A1_8(|'Butler'|))),
% 0.56/0.62 inference(symmetry,[status(thm)],[109])).
% 0.56/0.62 tff(111,assumption,(~((~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~(A!2 = tptp_fun_U_5(A!2))))), introduced(assumption)).
% 0.56/0.62 tff(112,plain,
% 0.56/0.62 (((~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~(A!2 = tptp_fun_U_5(A!2)))) | (A!2 = tptp_fun_U_5(A!2))),
% 0.56/0.62 inference(tautology,[status(thm)],[])).
% 0.56/0.62 tff(113,plain,
% 0.56/0.62 (A!2 = tptp_fun_U_5(A!2)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.56/0.62 tff(114,plain,
% 0.56/0.62 (tptp_fun_U_5(A!2) = A!2),
% 0.56/0.62 inference(symmetry,[status(thm)],[113])).
% 0.56/0.62 tff(115,plain,
% 0.56/0.62 (predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|) <=> predicate2(C!0, kill, A!2, |'AuntAgatha'|)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[114])).
% 0.56/0.62 tff(116,plain,
% 0.56/0.62 (predicate2(C!0, kill, A!2, |'AuntAgatha'|) <=> predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)),
% 0.56/0.62 inference(symmetry,[status(thm)],[115])).
% 0.56/0.62 tff(117,plain,
% 0.56/0.62 (predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[30, 116])).
% 0.56/0.62 tff(118,plain,
% 0.56/0.62 (((~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~(A!2 = tptp_fun_U_5(A!2)))) | property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)),
% 0.56/0.62 inference(tautology,[status(thm)],[])).
% 0.56/0.62 tff(119,plain,
% 0.56/0.62 (property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[118, 111])).
% 0.56/0.62 tff(120,plain,
% 0.56/0.62 (^[J: $i, K: $i, L: $i, M: $i] : refl(((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M))) <=> ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M))))),
% 0.56/0.62 inference(bind,[status(th)],[])).
% 0.56/0.62 tff(121,plain,
% 0.56/0.62 (![J: $i, K: $i, L: $i, M: $i] : ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M))) <=> ![J: $i, K: $i, L: $i, M: $i] : ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M)))),
% 0.56/0.62 inference(quant_intro,[status(thm)],[120])).
% 0.56/0.62 tff(122,plain,
% 0.56/0.62 (^[J: $i, K: $i, L: $i, M: $i] : trans(monotonicity(rewrite((predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M)) <=> (~((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M))))), ((~(predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) <=> (~(~((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M))))))), rewrite((~(~((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M))))) <=> ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M)))), ((~(predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) <=> ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M)))))),
% 0.56/0.62 inference(bind,[status(th)],[])).
% 0.56/0.62 tff(123,plain,
% 0.56/0.62 (![J: $i, K: $i, L: $i, M: $i] : (~(predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M))) <=> ![J: $i, K: $i, L: $i, M: $i] : ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M)))),
% 0.56/0.62 inference(quant_intro,[status(thm)],[122])).
% 0.56/0.62 tff(124,plain,
% 0.56/0.62 (![J: $i, K: $i, L: $i, M: $i] : (~(predicate2(L, kill, J, K) & property2(M, rich, comp_than, K) & (J = M)))),
% 0.56/0.62 inference(and_elim,[status(thm)],[29])).
% 0.56/0.62 tff(125,plain,
% 0.56/0.62 (![J: $i, K: $i, L: $i, M: $i] : ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M)))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.56/0.62 tff(126,plain,
% 0.56/0.62 (![J: $i, K: $i, L: $i, M: $i] : ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M)))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.56/0.62 tff(127,plain,
% 0.56/0.62 (((~![J: $i, K: $i, L: $i, M: $i] : ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M)))) | ((~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)))) <=> ((~![J: $i, K: $i, L: $i, M: $i] : ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M)))) | (~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(128,plain,
% 0.56/0.62 (((~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)) | (~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | $false) <=> ((~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(129,plain,
% 0.56/0.62 ((~$true) <=> $false),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(130,plain,
% 0.56/0.62 ((tptp_fun_U_5(A!2) = tptp_fun_U_5(A!2)) <=> $true),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(131,plain,
% 0.56/0.62 ((~(tptp_fun_U_5(A!2) = tptp_fun_U_5(A!2))) <=> (~$true)),
% 0.56/0.62 inference(monotonicity,[status(thm)],[130])).
% 0.56/0.62 tff(132,plain,
% 0.56/0.62 ((~(tptp_fun_U_5(A!2) = tptp_fun_U_5(A!2))) <=> $false),
% 0.56/0.62 inference(transitivity,[status(thm)],[131, 129])).
% 0.56/0.62 tff(133,plain,
% 0.56/0.62 (((~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)) | (~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~(tptp_fun_U_5(A!2) = tptp_fun_U_5(A!2)))) <=> ((~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)) | (~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | $false)),
% 0.59/0.62 inference(monotonicity,[status(thm)],[132])).
% 0.59/0.62 tff(134,plain,
% 0.59/0.62 (((~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)) | (~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~(tptp_fun_U_5(A!2) = tptp_fun_U_5(A!2)))) <=> ((~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)))),
% 0.59/0.62 inference(transitivity,[status(thm)],[133, 128])).
% 0.59/0.62 tff(135,plain,
% 0.59/0.62 (((~![J: $i, K: $i, L: $i, M: $i] : ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M)))) | ((~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)) | (~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~(tptp_fun_U_5(A!2) = tptp_fun_U_5(A!2))))) <=> ((~![J: $i, K: $i, L: $i, M: $i] : ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M)))) | ((~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|))))),
% 0.59/0.62 inference(monotonicity,[status(thm)],[134])).
% 0.59/0.62 tff(136,plain,
% 0.59/0.62 (((~![J: $i, K: $i, L: $i, M: $i] : ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M)))) | ((~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)) | (~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~(tptp_fun_U_5(A!2) = tptp_fun_U_5(A!2))))) <=> ((~![J: $i, K: $i, L: $i, M: $i] : ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M)))) | (~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)))),
% 0.59/0.62 inference(transitivity,[status(thm)],[135, 127])).
% 0.59/0.62 tff(137,plain,
% 0.59/0.62 ((~![J: $i, K: $i, L: $i, M: $i] : ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M)))) | ((~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)) | (~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~(tptp_fun_U_5(A!2) = tptp_fun_U_5(A!2))))),
% 0.59/0.62 inference(quant_inst,[status(thm)],[])).
% 0.59/0.62 tff(138,plain,
% 0.59/0.62 ((~![J: $i, K: $i, L: $i, M: $i] : ((~predicate2(L, kill, J, K)) | (~property2(M, rich, comp_than, K)) | (~(J = M)))) | (~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|))),
% 0.59/0.62 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.59/0.62 tff(139,plain,
% 0.59/0.62 (~predicate2(C!0, kill, tptp_fun_U_5(A!2), |'AuntAgatha'|)),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[138, 126, 119])).
% 0.59/0.62 tff(140,plain,
% 0.59/0.62 ($false),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[139, 117])).
% 0.59/0.62 tff(141,plain,((~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~(A!2 = tptp_fun_U_5(A!2)))), inference(lemma,lemma(discharge,[]))).
% 0.59/0.62 tff(142,plain,
% 0.59/0.62 (^[T: $i] : rewrite(((property2(tptp_fun_U_5(T), rich, comp_than, |'AuntAgatha'|) & (T = tptp_fun_U_5(T))) | predicate2(tptp_fun_V_6(T), hate, |'Butler'|, T)) <=> ((~((~property2(tptp_fun_U_5(T), rich, comp_than, |'AuntAgatha'|)) | (~(T = tptp_fun_U_5(T))))) | predicate2(tptp_fun_V_6(T), hate, |'Butler'|, T)))),
% 0.59/0.62 inference(bind,[status(th)],[])).
% 0.59/0.62 tff(143,plain,
% 0.59/0.62 (![T: $i] : ((property2(tptp_fun_U_5(T), rich, comp_than, |'AuntAgatha'|) & (T = tptp_fun_U_5(T))) | predicate2(tptp_fun_V_6(T), hate, |'Butler'|, T)) <=> ![T: $i] : ((~((~property2(tptp_fun_U_5(T), rich, comp_than, |'AuntAgatha'|)) | (~(T = tptp_fun_U_5(T))))) | predicate2(tptp_fun_V_6(T), hate, |'Butler'|, T))),
% 0.59/0.62 inference(quant_intro,[status(thm)],[142])).
% 0.59/0.62 tff(144,plain,
% 0.59/0.62 (![T: $i] : ((property2(tptp_fun_U_5(T), rich, comp_than, |'AuntAgatha'|) & (T = tptp_fun_U_5(T))) | predicate2(tptp_fun_V_6(T), hate, |'Butler'|, T))),
% 0.59/0.62 inference(and_elim,[status(thm)],[29])).
% 0.59/0.62 tff(145,plain,
% 0.59/0.62 (![T: $i] : ((~((~property2(tptp_fun_U_5(T), rich, comp_than, |'AuntAgatha'|)) | (~(T = tptp_fun_U_5(T))))) | predicate2(tptp_fun_V_6(T), hate, |'Butler'|, T))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.59/0.63 tff(146,plain,
% 0.59/0.63 (((~![T: $i] : ((~((~property2(tptp_fun_U_5(T), rich, comp_than, |'AuntAgatha'|)) | (~(T = tptp_fun_U_5(T))))) | predicate2(tptp_fun_V_6(T), hate, |'Butler'|, T))) | ((~((~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~(A!2 = tptp_fun_U_5(A!2))))) | predicate2(tptp_fun_V_6(A!2), hate, |'Butler'|, A!2))) <=> ((~![T: $i] : ((~((~property2(tptp_fun_U_5(T), rich, comp_than, |'AuntAgatha'|)) | (~(T = tptp_fun_U_5(T))))) | predicate2(tptp_fun_V_6(T), hate, |'Butler'|, T))) | (~((~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~(A!2 = tptp_fun_U_5(A!2))))) | predicate2(tptp_fun_V_6(A!2), hate, |'Butler'|, A!2))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(147,plain,
% 0.59/0.63 ((~![T: $i] : ((~((~property2(tptp_fun_U_5(T), rich, comp_than, |'AuntAgatha'|)) | (~(T = tptp_fun_U_5(T))))) | predicate2(tptp_fun_V_6(T), hate, |'Butler'|, T))) | ((~((~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~(A!2 = tptp_fun_U_5(A!2))))) | predicate2(tptp_fun_V_6(A!2), hate, |'Butler'|, A!2))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(148,plain,
% 0.59/0.63 ((~![T: $i] : ((~((~property2(tptp_fun_U_5(T), rich, comp_than, |'AuntAgatha'|)) | (~(T = tptp_fun_U_5(T))))) | predicate2(tptp_fun_V_6(T), hate, |'Butler'|, T))) | (~((~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~(A!2 = tptp_fun_U_5(A!2))))) | predicate2(tptp_fun_V_6(A!2), hate, |'Butler'|, A!2)),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.59/0.63 tff(149,plain,
% 0.59/0.63 ((~((~property2(tptp_fun_U_5(A!2), rich, comp_than, |'AuntAgatha'|)) | (~(A!2 = tptp_fun_U_5(A!2))))) | predicate2(tptp_fun_V_6(A!2), hate, |'Butler'|, A!2)),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[148, 145])).
% 0.59/0.63 tff(150,plain,
% 0.59/0.63 (predicate2(tptp_fun_V_6(A!2), hate, |'Butler'|, A!2)),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[149, 141])).
% 0.59/0.63 tff(151,plain,
% 0.59/0.63 (predicate2(tptp_fun_V_6(A!2), hate, |'Butler'|, tptp_fun_A1_8(|'Butler'|))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[150, 110])).
% 0.59/0.63 tff(152,plain,
% 0.59/0.63 ((~![Z: $i, B1: $i] : (~predicate2(B1, hate, Z, tptp_fun_A1_8(Z)))) | (~predicate2(tptp_fun_V_6(A!2), hate, |'Butler'|, tptp_fun_A1_8(|'Butler'|)))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(153,plain,
% 0.59/0.63 (~predicate2(tptp_fun_V_6(A!2), hate, |'Butler'|, tptp_fun_A1_8(|'Butler'|))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[152, 85])).
% 0.59/0.63 tff(154,plain,
% 0.59/0.63 ($false),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[153, 151])).
% 0.59/0.63 % SZS output end Proof
%------------------------------------------------------------------------------