TSTP Solution File: PUZ129+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ129+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 14:11:31 EDT 2022
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : PUZ129+2 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n003.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Sep 2 19:03:55 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(property1_type, type, (
% 0.11/0.38 property1: ( $i * $i * $i ) > $o)).
% 0.11/0.38 tff(pos_type, type, (
% 0.11/0.38 pos: $i)).
% 0.11/0.38 tff(healthy_type, type, (
% 0.11/0.38 healthy: $i)).
% 0.11/0.38 tff(tptp_fun_T_7_type, type, (
% 0.11/0.38 tptp_fun_T_7: $i)).
% 0.11/0.38 tff(tptp_fun_B_0_type, type, (
% 0.11/0.38 tptp_fun_B_0: $i > $i)).
% 0.11/0.38 tff(person_type, type, (
% 0.11/0.38 person: $i > $o)).
% 0.11/0.38 tff(tptp_fun_R_5_type, type, (
% 0.11/0.38 tptp_fun_R_5: $i > $i)).
% 0.11/0.38 tff(cyclist_type, type, (
% 0.11/0.38 cyclist: $i > $o)).
% 0.11/0.38 tff(tptp_fun_S_6_type, type, (
% 0.11/0.38 tptp_fun_S_6: $i)).
% 0.11/0.38 tff(grocer_type, type, (
% 0.11/0.38 grocer: $i > $o)).
% 0.11/0.38 tff(dishonest_type, type, (
% 0.11/0.38 dishonest: $i)).
% 0.11/0.38 tff(honest_type, type, (
% 0.11/0.38 honest: $i)).
% 0.11/0.38 tff(unhealthy_type, type, (
% 0.11/0.38 unhealthy: $i)).
% 0.11/0.38 tff(industrious_type, type, (
% 0.11/0.38 industrious: $i)).
% 0.11/0.38 tff(tptp_fun_F_1_type, type, (
% 0.11/0.38 tptp_fun_F_1: $i > $i)).
% 0.11/0.38 tff(tptp_fun_H_2_type, type, (
% 0.11/0.38 tptp_fun_H_2: $i > $i)).
% 0.11/0.38 tff(1,plain,
% 0.11/0.38 ((grocer(S!6) & (cyclist(T!7) & (S!6 = T!7))) <=> (grocer(S!6) & cyclist(T!7) & (S!6 = T!7))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 ((~(~grocer(S!6))) <=> grocer(S!6)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (((~(~grocer(S!6))) & (cyclist(T!7) & (S!6 = T!7))) <=> (grocer(S!6) & (cyclist(T!7) & (S!6 = T!7)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[2])).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 (((~(~grocer(S!6))) & (cyclist(T!7) & (S!6 = T!7))) <=> (grocer(S!6) & cyclist(T!7) & (S!6 = T!7))),
% 0.11/0.38 inference(transitivity,[status(thm)],[3, 1])).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 ((~![S: $i] : ((~grocer(S)) | (~?[T: $i] : (cyclist(T) & (S = T))))) <=> (~![S: $i] : ((~grocer(S)) | (~?[T: $i] : (cyclist(T) & (S = T)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(6,plain,
% 0.11/0.38 ((~(((((((((![A: $i] : (((person(A) & property1(A, honest, pos)) & property1(A, industrious, pos)) => ?[B: $i] : (property1(B, healthy, pos) & (A = B))) & ![C: $i] : (grocer(C) => (~?[D: $i] : (property1(D, healthy, pos) & (C = D))))) & ![E: $i] : ((grocer(E) & property1(E, industrious, pos)) => ?[F: $i] : (property1(F, honest, pos) & (E = F)))) & ![G: $i] : (cyclist(G) => ?[H: $i] : (property1(H, industrious, pos) & (G = H)))) & ![I: $i] : ((cyclist(I) & property1(I, unhealthy, pos)) => ?[J: $i] : (property1(J, dishonest, pos) & (I = J)))) & ![K: $i] : ((person(K) & property1(K, healthy, pos)) => (~?[L: $i] : (property1(L, unhealthy, pos) & (K = L))))) & ![M: $i] : ((person(M) & property1(M, honest, pos)) => (~?[N: $i] : (property1(N, dishonest, pos) & (M = N))))) & ![O: $i] : (grocer(O) => ?[P: $i] : (person(P) & (O = P)))) & ![Q: $i] : (cyclist(Q) => ?[R: $i] : (person(R) & (Q = R)))) => ![S: $i] : (grocer(S) => (~?[T: $i] : (cyclist(T) & (S = T)))))) <=> (~((~(![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | ?[B: $i] : (property1(B, healthy, pos) & (A = B))) & ![C: $i] : ((~grocer(C)) | (~?[D: $i] : (property1(D, healthy, pos) & (C = D)))) & ![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | ?[F: $i] : (property1(F, honest, pos) & (E = F))) & ![G: $i] : ((~cyclist(G)) | ?[H: $i] : (property1(H, industrious, pos) & (G = H))) & ![I: $i] : ((~(cyclist(I) & property1(I, unhealthy, pos))) | ?[J: $i] : (property1(J, dishonest, pos) & (I = J))) & ![K: $i] : ((~(person(K) & property1(K, healthy, pos))) | (~?[L: $i] : (property1(L, unhealthy, pos) & (K = L)))) & ![M: $i] : ((~(person(M) & property1(M, honest, pos))) | (~?[N: $i] : (property1(N, dishonest, pos) & (M = N)))) & ![O: $i] : ((~grocer(O)) | ?[P: $i] : (person(P) & (O = P))) & ![Q: $i] : ((~cyclist(Q)) | ?[R: $i] : (person(R) & (Q = R))))) | ![S: $i] : ((~grocer(S)) | (~?[T: $i] : (cyclist(T) & (S = T))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(7,axiom,(~(((((((((![A: $i] : (((person(A) & property1(A, honest, pos)) & property1(A, industrious, pos)) => ?[B: $i] : (property1(B, healthy, pos) & (A = B))) & ![C: $i] : (grocer(C) => (~?[D: $i] : (property1(D, healthy, pos) & (C = D))))) & ![E: $i] : ((grocer(E) & property1(E, industrious, pos)) => ?[F: $i] : (property1(F, honest, pos) & (E = F)))) & ![G: $i] : (cyclist(G) => ?[H: $i] : (property1(H, industrious, pos) & (G = H)))) & ![I: $i] : ((cyclist(I) & property1(I, unhealthy, pos)) => ?[J: $i] : (property1(J, dishonest, pos) & (I = J)))) & ![K: $i] : ((person(K) & property1(K, healthy, pos)) => (~?[L: $i] : (property1(L, unhealthy, pos) & (K = L))))) & ![M: $i] : ((person(M) & property1(M, honest, pos)) => (~?[N: $i] : (property1(N, dishonest, pos) & (M = N))))) & ![O: $i] : (grocer(O) => ?[P: $i] : (person(P) & (O = P)))) & ![Q: $i] : (cyclist(Q) => ?[R: $i] : (person(R) & (Q = R)))) => ![S: $i] : (grocer(S) => (~?[T: $i] : (cyclist(T) & (S = T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove')).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 (~((~(![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | ?[B: $i] : (property1(B, healthy, pos) & (A = B))) & ![C: $i] : ((~grocer(C)) | (~?[D: $i] : (property1(D, healthy, pos) & (C = D)))) & ![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | ?[F: $i] : (property1(F, honest, pos) & (E = F))) & ![G: $i] : ((~cyclist(G)) | ?[H: $i] : (property1(H, industrious, pos) & (G = H))) & ![I: $i] : ((~(cyclist(I) & property1(I, unhealthy, pos))) | ?[J: $i] : (property1(J, dishonest, pos) & (I = J))) & ![K: $i] : ((~(person(K) & property1(K, healthy, pos))) | (~?[L: $i] : (property1(L, unhealthy, pos) & (K = L)))) & ![M: $i] : ((~(person(M) & property1(M, honest, pos))) | (~?[N: $i] : (property1(N, dishonest, pos) & (M = N)))) & ![O: $i] : ((~grocer(O)) | ?[P: $i] : (person(P) & (O = P))) & ![Q: $i] : ((~cyclist(Q)) | ?[R: $i] : (person(R) & (Q = R))))) | ![S: $i] : ((~grocer(S)) | (~?[T: $i] : (cyclist(T) & (S = T)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (~![S: $i] : ((~grocer(S)) | (~?[T: $i] : (cyclist(T) & (S = T))))),
% 0.11/0.38 inference(or_elim,[status(thm)],[8])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (~![S: $i] : ((~grocer(S)) | (~?[T: $i] : (cyclist(T) & (S = T))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 (~![S: $i] : ((~grocer(S)) | (~?[T: $i] : (cyclist(T) & (S = T))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (~![S: $i] : ((~grocer(S)) | (~?[T: $i] : (cyclist(T) & (S = T))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (~![S: $i] : ((~grocer(S)) | (~?[T: $i] : (cyclist(T) & (S = T))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (~![S: $i] : ((~grocer(S)) | (~?[T: $i] : (cyclist(T) & (S = T))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 (~![S: $i] : ((~grocer(S)) | (~?[T: $i] : (cyclist(T) & (S = T))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[14, 5])).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (grocer(S!6) & cyclist(T!7) & (S!6 = T!7)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (cyclist(T!7)),
% 0.11/0.38 inference(and_elim,[status(thm)],[16])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (^[Q: $i] : refl(((~cyclist(Q)) | (~((~person(tptp_fun_R_5(Q))) | (~(Q = tptp_fun_R_5(Q)))))) <=> ((~cyclist(Q)) | (~((~person(tptp_fun_R_5(Q))) | (~(Q = tptp_fun_R_5(Q)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (![Q: $i] : ((~cyclist(Q)) | (~((~person(tptp_fun_R_5(Q))) | (~(Q = tptp_fun_R_5(Q)))))) <=> ![Q: $i] : ((~cyclist(Q)) | (~((~person(tptp_fun_R_5(Q))) | (~(Q = tptp_fun_R_5(Q))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (^[Q: $i] : rewrite(((~cyclist(Q)) | (person(tptp_fun_R_5(Q)) & (Q = tptp_fun_R_5(Q)))) <=> ((~cyclist(Q)) | (~((~person(tptp_fun_R_5(Q))) | (~(Q = tptp_fun_R_5(Q)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (![Q: $i] : ((~cyclist(Q)) | (person(tptp_fun_R_5(Q)) & (Q = tptp_fun_R_5(Q)))) <=> ![Q: $i] : ((~cyclist(Q)) | (~((~person(tptp_fun_R_5(Q))) | (~(Q = tptp_fun_R_5(Q))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (![Q: $i] : ((~cyclist(Q)) | ?[R: $i] : (person(R) & (Q = R))) <=> ![Q: $i] : ((~cyclist(Q)) | ?[R: $i] : (person(R) & (Q = R)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | ?[B: $i] : (property1(B, healthy, pos) & (A = B))) & ![C: $i] : ((~grocer(C)) | (~?[D: $i] : (property1(D, healthy, pos) & (C = D)))) & ![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | ?[F: $i] : (property1(F, honest, pos) & (E = F))) & ![G: $i] : ((~cyclist(G)) | ?[H: $i] : (property1(H, industrious, pos) & (G = H))) & ![I: $i] : ((~(cyclist(I) & property1(I, unhealthy, pos))) | ?[J: $i] : (property1(J, dishonest, pos) & (I = J))) & ![K: $i] : ((~(person(K) & property1(K, healthy, pos))) | (~?[L: $i] : (property1(L, unhealthy, pos) & (K = L)))) & ![M: $i] : ((~(person(M) & property1(M, honest, pos))) | (~?[N: $i] : (property1(N, dishonest, pos) & (M = N)))) & ![O: $i] : ((~grocer(O)) | ?[P: $i] : (person(P) & (O = P))) & ![Q: $i] : ((~cyclist(Q)) | ?[R: $i] : (person(R) & (Q = R)))),
% 0.11/0.38 inference(or_elim,[status(thm)],[8])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (![Q: $i] : ((~cyclist(Q)) | ?[R: $i] : (person(R) & (Q = R)))),
% 0.11/0.38 inference(and_elim,[status(thm)],[23])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (![Q: $i] : ((~cyclist(Q)) | ?[R: $i] : (person(R) & (Q = R)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[24, 22])).
% 0.11/0.38 tff(26,plain,(
% 0.11/0.38 ![Q: $i] : ((~cyclist(Q)) | (person(tptp_fun_R_5(Q)) & (Q = tptp_fun_R_5(Q))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[25])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 (![Q: $i] : ((~cyclist(Q)) | (~((~person(tptp_fun_R_5(Q))) | (~(Q = tptp_fun_R_5(Q))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (![Q: $i] : ((~cyclist(Q)) | (~((~person(tptp_fun_R_5(Q))) | (~(Q = tptp_fun_R_5(Q))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (((~![Q: $i] : ((~cyclist(Q)) | (~((~person(tptp_fun_R_5(Q))) | (~(Q = tptp_fun_R_5(Q))))))) | ((~cyclist(T!7)) | (~((~person(tptp_fun_R_5(T!7))) | (~(T!7 = tptp_fun_R_5(T!7))))))) <=> ((~![Q: $i] : ((~cyclist(Q)) | (~((~person(tptp_fun_R_5(Q))) | (~(Q = tptp_fun_R_5(Q))))))) | (~cyclist(T!7)) | (~((~person(tptp_fun_R_5(T!7))) | (~(T!7 = tptp_fun_R_5(T!7))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 ((~![Q: $i] : ((~cyclist(Q)) | (~((~person(tptp_fun_R_5(Q))) | (~(Q = tptp_fun_R_5(Q))))))) | ((~cyclist(T!7)) | (~((~person(tptp_fun_R_5(T!7))) | (~(T!7 = tptp_fun_R_5(T!7))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 ((~![Q: $i] : ((~cyclist(Q)) | (~((~person(tptp_fun_R_5(Q))) | (~(Q = tptp_fun_R_5(Q))))))) | (~cyclist(T!7)) | (~((~person(tptp_fun_R_5(T!7))) | (~(T!7 = tptp_fun_R_5(T!7)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (~((~person(tptp_fun_R_5(T!7))) | (~(T!7 = tptp_fun_R_5(T!7))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[31, 28, 17])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 (((~person(tptp_fun_R_5(T!7))) | (~(T!7 = tptp_fun_R_5(T!7)))) | (T!7 = tptp_fun_R_5(T!7))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 (T!7 = tptp_fun_R_5(T!7)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 (person(T!7) <=> person(tptp_fun_R_5(T!7))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[34])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (person(tptp_fun_R_5(T!7)) <=> person(T!7)),
% 0.11/0.38 inference(symmetry,[status(thm)],[35])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 (((~person(tptp_fun_R_5(T!7))) | (~(T!7 = tptp_fun_R_5(T!7)))) | person(tptp_fun_R_5(T!7))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (person(tptp_fun_R_5(T!7))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[37, 32])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (person(T!7)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[38, 36])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (S!6 = T!7),
% 0.11/0.38 inference(and_elim,[status(thm)],[16])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (T!7 = S!6),
% 0.11/0.38 inference(symmetry,[status(thm)],[40])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (grocer(T!7) <=> grocer(S!6)),
% 0.11/0.38 inference(monotonicity,[status(thm)],[41])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (grocer(S!6) <=> grocer(T!7)),
% 0.11/0.38 inference(symmetry,[status(thm)],[42])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (grocer(S!6)),
% 0.11/0.38 inference(and_elim,[status(thm)],[16])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (grocer(T!7)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (^[G: $i] : refl(((~cyclist(G)) | (~((~property1(tptp_fun_H_2(G), industrious, pos)) | (~(G = tptp_fun_H_2(G)))))) <=> ((~cyclist(G)) | (~((~property1(tptp_fun_H_2(G), industrious, pos)) | (~(G = tptp_fun_H_2(G)))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(47,plain,
% 0.11/0.39 (![G: $i] : ((~cyclist(G)) | (~((~property1(tptp_fun_H_2(G), industrious, pos)) | (~(G = tptp_fun_H_2(G)))))) <=> ![G: $i] : ((~cyclist(G)) | (~((~property1(tptp_fun_H_2(G), industrious, pos)) | (~(G = tptp_fun_H_2(G))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.11/0.39 tff(48,plain,
% 0.11/0.39 (^[G: $i] : rewrite(((~cyclist(G)) | (property1(tptp_fun_H_2(G), industrious, pos) & (G = tptp_fun_H_2(G)))) <=> ((~cyclist(G)) | (~((~property1(tptp_fun_H_2(G), industrious, pos)) | (~(G = tptp_fun_H_2(G)))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(49,plain,
% 0.11/0.39 (![G: $i] : ((~cyclist(G)) | (property1(tptp_fun_H_2(G), industrious, pos) & (G = tptp_fun_H_2(G)))) <=> ![G: $i] : ((~cyclist(G)) | (~((~property1(tptp_fun_H_2(G), industrious, pos)) | (~(G = tptp_fun_H_2(G))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[48])).
% 0.11/0.39 tff(50,plain,
% 0.11/0.39 (![G: $i] : ((~cyclist(G)) | ?[H: $i] : (property1(H, industrious, pos) & (G = H))) <=> ![G: $i] : ((~cyclist(G)) | ?[H: $i] : (property1(H, industrious, pos) & (G = H)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(51,plain,
% 0.11/0.39 (![G: $i] : ((~cyclist(G)) | ?[H: $i] : (property1(H, industrious, pos) & (G = H)))),
% 0.11/0.39 inference(and_elim,[status(thm)],[23])).
% 0.11/0.39 tff(52,plain,
% 0.11/0.39 (![G: $i] : ((~cyclist(G)) | ?[H: $i] : (property1(H, industrious, pos) & (G = H)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.11/0.39 tff(53,plain,(
% 0.11/0.39 ![G: $i] : ((~cyclist(G)) | (property1(tptp_fun_H_2(G), industrious, pos) & (G = tptp_fun_H_2(G))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[52])).
% 0.11/0.39 tff(54,plain,
% 0.11/0.39 (![G: $i] : ((~cyclist(G)) | (~((~property1(tptp_fun_H_2(G), industrious, pos)) | (~(G = tptp_fun_H_2(G))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.11/0.39 tff(55,plain,
% 0.11/0.39 (![G: $i] : ((~cyclist(G)) | (~((~property1(tptp_fun_H_2(G), industrious, pos)) | (~(G = tptp_fun_H_2(G))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.11/0.39 tff(56,plain,
% 0.11/0.39 (((~![G: $i] : ((~cyclist(G)) | (~((~property1(tptp_fun_H_2(G), industrious, pos)) | (~(G = tptp_fun_H_2(G))))))) | ((~cyclist(T!7)) | (~((~property1(tptp_fun_H_2(T!7), industrious, pos)) | (~(T!7 = tptp_fun_H_2(T!7))))))) <=> ((~![G: $i] : ((~cyclist(G)) | (~((~property1(tptp_fun_H_2(G), industrious, pos)) | (~(G = tptp_fun_H_2(G))))))) | (~cyclist(T!7)) | (~((~property1(tptp_fun_H_2(T!7), industrious, pos)) | (~(T!7 = tptp_fun_H_2(T!7))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(57,plain,
% 0.11/0.39 ((~![G: $i] : ((~cyclist(G)) | (~((~property1(tptp_fun_H_2(G), industrious, pos)) | (~(G = tptp_fun_H_2(G))))))) | ((~cyclist(T!7)) | (~((~property1(tptp_fun_H_2(T!7), industrious, pos)) | (~(T!7 = tptp_fun_H_2(T!7))))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(58,plain,
% 0.11/0.39 ((~![G: $i] : ((~cyclist(G)) | (~((~property1(tptp_fun_H_2(G), industrious, pos)) | (~(G = tptp_fun_H_2(G))))))) | (~cyclist(T!7)) | (~((~property1(tptp_fun_H_2(T!7), industrious, pos)) | (~(T!7 = tptp_fun_H_2(T!7)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.11/0.39 tff(59,plain,
% 0.11/0.39 (~((~property1(tptp_fun_H_2(T!7), industrious, pos)) | (~(T!7 = tptp_fun_H_2(T!7))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[58, 55, 17])).
% 0.11/0.39 tff(60,plain,
% 0.11/0.39 (((~property1(tptp_fun_H_2(T!7), industrious, pos)) | (~(T!7 = tptp_fun_H_2(T!7)))) | (T!7 = tptp_fun_H_2(T!7))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(61,plain,
% 0.11/0.39 (T!7 = tptp_fun_H_2(T!7)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.11/0.39 tff(62,plain,
% 0.11/0.39 (tptp_fun_H_2(T!7) = T!7),
% 0.11/0.39 inference(symmetry,[status(thm)],[61])).
% 0.11/0.39 tff(63,plain,
% 0.11/0.39 (property1(tptp_fun_H_2(T!7), industrious, pos) <=> property1(T!7, industrious, pos)),
% 0.11/0.39 inference(monotonicity,[status(thm)],[62])).
% 0.11/0.39 tff(64,plain,
% 0.11/0.39 (((~property1(tptp_fun_H_2(T!7), industrious, pos)) | (~(T!7 = tptp_fun_H_2(T!7)))) | property1(tptp_fun_H_2(T!7), industrious, pos)),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(65,plain,
% 0.11/0.39 (property1(tptp_fun_H_2(T!7), industrious, pos)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[64, 59])).
% 0.11/0.39 tff(66,plain,
% 0.11/0.39 (property1(T!7, industrious, pos)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[65, 63])).
% 0.11/0.39 tff(67,plain,
% 0.11/0.39 (^[E: $i] : refl(((~grocer(E)) | (~property1(E, industrious, pos)) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E)))))) <=> ((~grocer(E)) | (~property1(E, industrious, pos)) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E)))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(68,plain,
% 0.11/0.39 (![E: $i] : ((~grocer(E)) | (~property1(E, industrious, pos)) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E)))))) <=> ![E: $i] : ((~grocer(E)) | (~property1(E, industrious, pos)) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[67])).
% 0.11/0.39 tff(69,plain,
% 0.11/0.39 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((grocer(E) & property1(E, industrious, pos)) <=> (~((~grocer(E)) | (~property1(E, industrious, pos))))), ((~(grocer(E) & property1(E, industrious, pos))) <=> (~(~((~grocer(E)) | (~property1(E, industrious, pos))))))), rewrite((~(~((~grocer(E)) | (~property1(E, industrious, pos))))) <=> ((~grocer(E)) | (~property1(E, industrious, pos)))), ((~(grocer(E) & property1(E, industrious, pos))) <=> ((~grocer(E)) | (~property1(E, industrious, pos))))), rewrite((property1(tptp_fun_F_1(E), honest, pos) & (E = tptp_fun_F_1(E))) <=> (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E)))))), (((~(grocer(E) & property1(E, industrious, pos))) | (property1(tptp_fun_F_1(E), honest, pos) & (E = tptp_fun_F_1(E)))) <=> (((~grocer(E)) | (~property1(E, industrious, pos))) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E)))))))), rewrite((((~grocer(E)) | (~property1(E, industrious, pos))) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E)))))) <=> ((~grocer(E)) | (~property1(E, industrious, pos)) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E))))))), (((~(grocer(E) & property1(E, industrious, pos))) | (property1(tptp_fun_F_1(E), honest, pos) & (E = tptp_fun_F_1(E)))) <=> ((~grocer(E)) | (~property1(E, industrious, pos)) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(70,plain,
% 0.11/0.39 (![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | (property1(tptp_fun_F_1(E), honest, pos) & (E = tptp_fun_F_1(E)))) <=> ![E: $i] : ((~grocer(E)) | (~property1(E, industrious, pos)) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[69])).
% 0.11/0.39 tff(71,plain,
% 0.11/0.39 (![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | ?[F: $i] : (property1(F, honest, pos) & (E = F))) <=> ![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | ?[F: $i] : (property1(F, honest, pos) & (E = F)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(72,plain,
% 0.11/0.39 (![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | ?[F: $i] : (property1(F, honest, pos) & (E = F)))),
% 0.11/0.39 inference(and_elim,[status(thm)],[23])).
% 0.11/0.39 tff(73,plain,
% 0.11/0.39 (![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | ?[F: $i] : (property1(F, honest, pos) & (E = F)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.11/0.39 tff(74,plain,(
% 0.11/0.39 ![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | (property1(tptp_fun_F_1(E), honest, pos) & (E = tptp_fun_F_1(E))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[73])).
% 0.11/0.39 tff(75,plain,
% 0.11/0.39 (![E: $i] : ((~grocer(E)) | (~property1(E, industrious, pos)) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.11/0.39 tff(76,plain,
% 0.11/0.39 (![E: $i] : ((~grocer(E)) | (~property1(E, industrious, pos)) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.11/0.39 tff(77,plain,
% 0.11/0.39 (((~![E: $i] : ((~grocer(E)) | (~property1(E, industrious, pos)) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E))))))) | ((~grocer(T!7)) | (~property1(T!7, industrious, pos)) | (~((~property1(tptp_fun_F_1(T!7), honest, pos)) | (~(T!7 = tptp_fun_F_1(T!7))))))) <=> ((~![E: $i] : ((~grocer(E)) | (~property1(E, industrious, pos)) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E))))))) | (~grocer(T!7)) | (~property1(T!7, industrious, pos)) | (~((~property1(tptp_fun_F_1(T!7), honest, pos)) | (~(T!7 = tptp_fun_F_1(T!7))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(78,plain,
% 0.11/0.39 ((~![E: $i] : ((~grocer(E)) | (~property1(E, industrious, pos)) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E))))))) | ((~grocer(T!7)) | (~property1(T!7, industrious, pos)) | (~((~property1(tptp_fun_F_1(T!7), honest, pos)) | (~(T!7 = tptp_fun_F_1(T!7))))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(79,plain,
% 0.11/0.39 ((~![E: $i] : ((~grocer(E)) | (~property1(E, industrious, pos)) | (~((~property1(tptp_fun_F_1(E), honest, pos)) | (~(E = tptp_fun_F_1(E))))))) | (~grocer(T!7)) | (~property1(T!7, industrious, pos)) | (~((~property1(tptp_fun_F_1(T!7), honest, pos)) | (~(T!7 = tptp_fun_F_1(T!7)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.11/0.39 tff(80,plain,
% 0.11/0.39 ((~grocer(T!7)) | (~property1(T!7, industrious, pos)) | (~((~property1(tptp_fun_F_1(T!7), honest, pos)) | (~(T!7 = tptp_fun_F_1(T!7)))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[79, 76])).
% 0.11/0.39 tff(81,plain,
% 0.11/0.39 (~((~property1(tptp_fun_F_1(T!7), honest, pos)) | (~(T!7 = tptp_fun_F_1(T!7))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[80, 66, 45])).
% 0.11/0.39 tff(82,plain,
% 0.11/0.39 (((~property1(tptp_fun_F_1(T!7), honest, pos)) | (~(T!7 = tptp_fun_F_1(T!7)))) | (T!7 = tptp_fun_F_1(T!7))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(83,plain,
% 0.11/0.39 (T!7 = tptp_fun_F_1(T!7)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.11/0.39 tff(84,plain,
% 0.11/0.39 (tptp_fun_F_1(T!7) = T!7),
% 0.11/0.39 inference(symmetry,[status(thm)],[83])).
% 0.11/0.39 tff(85,plain,
% 0.11/0.39 (property1(tptp_fun_F_1(T!7), honest, pos) <=> property1(T!7, honest, pos)),
% 0.11/0.39 inference(monotonicity,[status(thm)],[84])).
% 0.11/0.39 tff(86,plain,
% 0.11/0.39 (((~property1(tptp_fun_F_1(T!7), honest, pos)) | (~(T!7 = tptp_fun_F_1(T!7)))) | property1(tptp_fun_F_1(T!7), honest, pos)),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(87,plain,
% 0.11/0.39 (property1(tptp_fun_F_1(T!7), honest, pos)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[86, 81])).
% 0.11/0.39 tff(88,plain,
% 0.11/0.39 (property1(T!7, honest, pos)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[87, 85])).
% 0.11/0.39 tff(89,plain,
% 0.11/0.39 (^[A: $i] : refl(((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A)))))) <=> ((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A)))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(90,plain,
% 0.11/0.39 (![A: $i] : ((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A)))))) <=> ![A: $i] : ((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[89])).
% 0.11/0.39 tff(91,plain,
% 0.11/0.39 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((person(A) & property1(A, honest, pos) & property1(A, industrious, pos)) <=> (~((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos))))), ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) <=> (~(~((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos))))))), rewrite((~(~((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos))))) <=> ((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))), ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) <=> ((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos))))), rewrite((property1(tptp_fun_B_0(A), healthy, pos) & (A = tptp_fun_B_0(A))) <=> (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A)))))), (((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | (property1(tptp_fun_B_0(A), healthy, pos) & (A = tptp_fun_B_0(A)))) <=> (((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos))) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A)))))))), rewrite((((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos))) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A)))))) <=> ((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A))))))), (((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | (property1(tptp_fun_B_0(A), healthy, pos) & (A = tptp_fun_B_0(A)))) <=> ((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A))))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(92,plain,
% 0.11/0.40 (![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | (property1(tptp_fun_B_0(A), healthy, pos) & (A = tptp_fun_B_0(A)))) <=> ![A: $i] : ((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A))))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[91])).
% 0.11/0.40 tff(93,plain,
% 0.11/0.40 (![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | ?[B: $i] : (property1(B, healthy, pos) & (A = B))) <=> ![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | ?[B: $i] : (property1(B, healthy, pos) & (A = B)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(94,plain,
% 0.11/0.40 (![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | ?[B: $i] : (property1(B, healthy, pos) & (A = B)))),
% 0.11/0.40 inference(and_elim,[status(thm)],[23])).
% 0.11/0.40 tff(95,plain,
% 0.11/0.40 (![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | ?[B: $i] : (property1(B, healthy, pos) & (A = B)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.11/0.40 tff(96,plain,(
% 0.11/0.40 ![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | (property1(tptp_fun_B_0(A), healthy, pos) & (A = tptp_fun_B_0(A))))),
% 0.11/0.40 inference(skolemize,[status(sab)],[95])).
% 0.11/0.40 tff(97,plain,
% 0.11/0.40 (![A: $i] : ((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.11/0.40 tff(98,plain,
% 0.11/0.40 (![A: $i] : ((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.11/0.40 tff(99,plain,
% 0.11/0.40 (((~![A: $i] : ((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A))))))) | ((~person(T!7)) | (~property1(T!7, honest, pos)) | (~property1(T!7, industrious, pos)) | (~((~property1(tptp_fun_B_0(T!7), healthy, pos)) | (~(T!7 = tptp_fun_B_0(T!7))))))) <=> ((~![A: $i] : ((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A))))))) | (~person(T!7)) | (~property1(T!7, honest, pos)) | (~property1(T!7, industrious, pos)) | (~((~property1(tptp_fun_B_0(T!7), healthy, pos)) | (~(T!7 = tptp_fun_B_0(T!7))))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(100,plain,
% 0.11/0.40 ((~![A: $i] : ((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A))))))) | ((~person(T!7)) | (~property1(T!7, honest, pos)) | (~property1(T!7, industrious, pos)) | (~((~property1(tptp_fun_B_0(T!7), healthy, pos)) | (~(T!7 = tptp_fun_B_0(T!7))))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(101,plain,
% 0.11/0.40 ((~![A: $i] : ((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)) | (~((~property1(tptp_fun_B_0(A), healthy, pos)) | (~(A = tptp_fun_B_0(A))))))) | (~person(T!7)) | (~property1(T!7, honest, pos)) | (~property1(T!7, industrious, pos)) | (~((~property1(tptp_fun_B_0(T!7), healthy, pos)) | (~(T!7 = tptp_fun_B_0(T!7)))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.11/0.40 tff(102,plain,
% 0.11/0.40 ((~person(T!7)) | (~property1(T!7, honest, pos)) | (~((~property1(tptp_fun_B_0(T!7), healthy, pos)) | (~(T!7 = tptp_fun_B_0(T!7)))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[101, 98, 66])).
% 0.11/0.40 tff(103,plain,
% 0.11/0.40 (~((~property1(tptp_fun_B_0(T!7), healthy, pos)) | (~(T!7 = tptp_fun_B_0(T!7))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[102, 88, 39])).
% 0.11/0.40 tff(104,plain,
% 0.11/0.40 (((~property1(tptp_fun_B_0(T!7), healthy, pos)) | (~(T!7 = tptp_fun_B_0(T!7)))) | (T!7 = tptp_fun_B_0(T!7))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(105,plain,
% 0.11/0.40 (T!7 = tptp_fun_B_0(T!7)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.11/0.40 tff(106,plain,
% 0.11/0.40 (tptp_fun_B_0(T!7) = T!7),
% 0.11/0.40 inference(symmetry,[status(thm)],[105])).
% 0.11/0.40 tff(107,plain,
% 0.11/0.40 (property1(tptp_fun_B_0(T!7), healthy, pos) <=> property1(T!7, healthy, pos)),
% 0.11/0.40 inference(monotonicity,[status(thm)],[106])).
% 0.11/0.40 tff(108,plain,
% 0.11/0.40 (((~property1(tptp_fun_B_0(T!7), healthy, pos)) | (~(T!7 = tptp_fun_B_0(T!7)))) | property1(tptp_fun_B_0(T!7), healthy, pos)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(109,plain,
% 0.11/0.40 (property1(tptp_fun_B_0(T!7), healthy, pos)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[108, 103])).
% 0.11/0.40 tff(110,plain,
% 0.11/0.40 (property1(T!7, healthy, pos)),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[109, 107])).
% 0.11/0.40 tff(111,plain,
% 0.11/0.40 (^[C: $i] : refl(((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D)))) <=> ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(112,plain,
% 0.11/0.40 (![C: $i] : ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D)))) <=> ![C: $i] : ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[111])).
% 0.11/0.40 tff(113,plain,
% 0.11/0.40 (^[C: $i] : rewrite(((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D)))) <=> ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(114,plain,
% 0.11/0.40 (![C: $i] : ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D)))) <=> ![C: $i] : ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[113])).
% 0.11/0.40 tff(115,plain,
% 0.11/0.40 (![C: $i] : ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D)))) <=> ![C: $i] : ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D))))),
% 0.11/0.40 inference(transitivity,[status(thm)],[114, 112])).
% 0.11/0.40 tff(116,plain,
% 0.11/0.40 (^[C: $i] : rewrite(((~grocer(C)) | ![D: $i] : (~(property1(D, healthy, pos) & (C = D)))) <=> ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(117,plain,
% 0.11/0.40 (![C: $i] : ((~grocer(C)) | ![D: $i] : (~(property1(D, healthy, pos) & (C = D)))) <=> ![C: $i] : ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[116])).
% 0.11/0.40 tff(118,plain,
% 0.11/0.40 (![C: $i] : ((~grocer(C)) | (~?[D: $i] : (property1(D, healthy, pos) & (C = D)))) <=> ![C: $i] : ((~grocer(C)) | (~?[D: $i] : (property1(D, healthy, pos) & (C = D))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(119,plain,
% 0.11/0.40 (![C: $i] : ((~grocer(C)) | (~?[D: $i] : (property1(D, healthy, pos) & (C = D))))),
% 0.11/0.40 inference(and_elim,[status(thm)],[23])).
% 0.11/0.40 tff(120,plain,
% 0.11/0.40 (![C: $i] : ((~grocer(C)) | (~?[D: $i] : (property1(D, healthy, pos) & (C = D))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.11/0.40 tff(121,plain,(
% 0.11/0.40 ![C: $i] : ((~grocer(C)) | ![D: $i] : (~(property1(D, healthy, pos) & (C = D))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[120])).
% 0.18/0.41 tff(122,plain,
% 0.18/0.41 (![C: $i] : ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.18/0.41 tff(123,plain,
% 0.18/0.41 (![C: $i] : ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.18/0.41 tff(124,plain,
% 0.18/0.41 (((~![C: $i] : ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D))))) | ((~grocer(T!7)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(T!7 = D))))) <=> ((~![C: $i] : ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D))))) | (~grocer(T!7)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(T!7 = D))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(125,plain,
% 0.18/0.41 ((~![C: $i] : ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D))))) | ((~grocer(T!7)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(T!7 = D))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(126,plain,
% 0.18/0.41 ((~![C: $i] : ((~grocer(C)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(C = D))))) | (~grocer(T!7)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(T!7 = D)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.18/0.41 tff(127,plain,
% 0.18/0.41 ((~grocer(T!7)) | ![D: $i] : ((~property1(D, healthy, pos)) | (~(T!7 = D)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[126, 123])).
% 0.18/0.41 tff(128,plain,
% 0.18/0.41 (![D: $i] : ((~property1(D, healthy, pos)) | (~(T!7 = D)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[127, 45])).
% 0.18/0.41 tff(129,plain,
% 0.18/0.41 (((~![D: $i] : ((~property1(D, healthy, pos)) | (~(T!7 = D)))) | (~property1(T!7, healthy, pos))) <=> ((~![D: $i] : ((~property1(D, healthy, pos)) | (~(T!7 = D)))) | (~property1(T!7, healthy, pos)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(130,plain,
% 0.18/0.41 (((~property1(T!7, healthy, pos)) | $false) <=> (~property1(T!7, healthy, pos))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(131,plain,
% 0.18/0.41 ((~$true) <=> $false),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(132,plain,
% 0.18/0.41 ((T!7 = T!7) <=> $true),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(133,plain,
% 0.18/0.41 ((~(T!7 = T!7)) <=> (~$true)),
% 0.18/0.41 inference(monotonicity,[status(thm)],[132])).
% 0.18/0.41 tff(134,plain,
% 0.18/0.41 ((~(T!7 = T!7)) <=> $false),
% 0.18/0.41 inference(transitivity,[status(thm)],[133, 131])).
% 0.18/0.41 tff(135,plain,
% 0.18/0.41 (((~property1(T!7, healthy, pos)) | (~(T!7 = T!7))) <=> ((~property1(T!7, healthy, pos)) | $false)),
% 0.18/0.41 inference(monotonicity,[status(thm)],[134])).
% 0.18/0.41 tff(136,plain,
% 0.18/0.41 (((~property1(T!7, healthy, pos)) | (~(T!7 = T!7))) <=> (~property1(T!7, healthy, pos))),
% 0.18/0.41 inference(transitivity,[status(thm)],[135, 130])).
% 0.18/0.41 tff(137,plain,
% 0.18/0.41 (((~![D: $i] : ((~property1(D, healthy, pos)) | (~(T!7 = D)))) | ((~property1(T!7, healthy, pos)) | (~(T!7 = T!7)))) <=> ((~![D: $i] : ((~property1(D, healthy, pos)) | (~(T!7 = D)))) | (~property1(T!7, healthy, pos)))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[136])).
% 0.18/0.41 tff(138,plain,
% 0.18/0.41 (((~![D: $i] : ((~property1(D, healthy, pos)) | (~(T!7 = D)))) | ((~property1(T!7, healthy, pos)) | (~(T!7 = T!7)))) <=> ((~![D: $i] : ((~property1(D, healthy, pos)) | (~(T!7 = D)))) | (~property1(T!7, healthy, pos)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[137, 129])).
% 0.18/0.41 tff(139,plain,
% 0.18/0.41 ((~![D: $i] : ((~property1(D, healthy, pos)) | (~(T!7 = D)))) | ((~property1(T!7, healthy, pos)) | (~(T!7 = T!7)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(140,plain,
% 0.18/0.41 ((~![D: $i] : ((~property1(D, healthy, pos)) | (~(T!7 = D)))) | (~property1(T!7, healthy, pos))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.18/0.41 tff(141,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[140, 128, 110])).
% 0.18/0.41 % SZS output end Proof
%------------------------------------------------------------------------------