%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ129+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:23:27 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : PUZ129+2 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n013.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 02:47:38 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(property1_type, type, (
% 0.12/0.36 property1: ( $i * $i * $i ) > $o)).
% 0.12/0.36 tff(pos_type, type, (
% 0.12/0.36 pos: $i)).
% 0.12/0.36 tff(industrious_type, type, (
% 0.12/0.36 industrious: $i)).
% 0.12/0.36 tff(tptp_fun_S_0_type, type, (
% 0.12/0.36 tptp_fun_S_0: $i)).
% 0.12/0.36 tff(cyclist_type, type, (
% 0.12/0.36 cyclist: $i > $o)).
% 0.12/0.36 tff(grocer_type, type, (
% 0.12/0.36 grocer: $i > $o)).
% 0.12/0.36 tff(person_type, type, (
% 0.12/0.36 person: $i > $o)).
% 0.12/0.36 tff(dishonest_type, type, (
% 0.12/0.36 dishonest: $i)).
% 0.12/0.36 tff(honest_type, type, (
% 0.12/0.36 honest: $i)).
% 0.12/0.36 tff(unhealthy_type, type, (
% 0.12/0.36 unhealthy: $i)).
% 0.12/0.36 tff(healthy_type, type, (
% 0.12/0.36 healthy: $i)).
% 0.12/0.36 tff(1,plain,
% 0.12/0.36 ((~((~grocer(S!0)) | (~cyclist(S!0)))) <=> (~((~grocer(S!0)) | (~cyclist(S!0))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 ((~![S: $i] : ((~grocer(S)) | (~cyclist(S)))) <=> (~![S: $i] : ((~grocer(S)) | (~cyclist(S))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 ((~(((((((((![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))) | property1(A, healthy, pos)) & ![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos))) & ![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | property1(E, honest, pos)) & ![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos)) & ![I: $i] : ((~(cyclist(I) & property1(I, unhealthy, pos))) | property1(I, dishonest, pos)) & ![K: $i] : ((~(person(K) & property1(K, healthy, pos))) | (~property1(K, unhealthy, pos))) & ![M: $i] : ((~(person(M) & property1(M, honest, pos))) | (~property1(M, dishonest, pos))) & ![O: $i] : (person(O) | (~grocer(O))) & ![Q: $i] : (person(Q) | (~cyclist(Q))))) | ![S: $i] : ((~grocer(S)) | (~cyclist(S)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(4,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/sandbox/benchmark/theBenchmark.p','prove')).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 (~((~(![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | property1(A, healthy, pos)) & ![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos))) & ![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | property1(E, honest, pos)) & ![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos)) & ![I: $i] : ((~(cyclist(I) & property1(I, unhealthy, pos))) | property1(I, dishonest, pos)) & ![K: $i] : ((~(person(K) & property1(K, healthy, pos))) | (~property1(K, unhealthy, pos))) & ![M: $i] : ((~(person(M) & property1(M, honest, pos))) | (~property1(M, dishonest, pos))) & ![O: $i] : (person(O) | (~grocer(O))) & ![Q: $i] : (person(Q) | (~cyclist(Q))))) | ![S: $i] : ((~grocer(S)) | (~cyclist(S))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~![S: $i] : ((~grocer(S)) | (~cyclist(S)))),
% 0.12/0.37 inference(or_elim,[status(thm)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~![S: $i] : ((~grocer(S)) | (~cyclist(S)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~![S: $i] : ((~grocer(S)) | (~cyclist(S)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~![S: $i] : ((~grocer(S)) | (~cyclist(S)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.12/0.37 tff(10,plain,(
% 0.12/0.37 ~((~grocer(S!0)) | (~cyclist(S!0)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (~((~grocer(S!0)) | (~cyclist(S!0)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (cyclist(S!0)),
% 0.12/0.37 inference(or_elim,[status(thm)],[11])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (^[G: $i] : refl(((~cyclist(G)) | property1(G, industrious, pos)) <=> ((~cyclist(G)) | property1(G, industrious, pos)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos)) <=> ![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos)) <=> ![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | property1(A, healthy, pos)) & ![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos))) & ![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | property1(E, honest, pos)) & ![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos)) & ![I: $i] : ((~(cyclist(I) & property1(I, unhealthy, pos))) | property1(I, dishonest, pos)) & ![K: $i] : ((~(person(K) & property1(K, healthy, pos))) | (~property1(K, unhealthy, pos))) & ![M: $i] : ((~(person(M) & property1(M, honest, pos))) | (~property1(M, dishonest, pos))) & ![O: $i] : (person(O) | (~grocer(O))) & ![Q: $i] : (person(Q) | (~cyclist(Q)))),
% 0.12/0.37 inference(or_elim,[status(thm)],[5])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos))),
% 0.12/0.37 inference(and_elim,[status(thm)],[16])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.12/0.37 tff(19,plain,(
% 0.12/0.37 ![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos))),
% 0.12/0.37 inference(skolemize,[status(sab)],[18])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (((~![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos))) | ((~cyclist(S!0)) | property1(S!0, industrious, pos))) <=> ((~![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos))) | (~cyclist(S!0)) | property1(S!0, industrious, pos))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos))) | ((~cyclist(S!0)) | property1(S!0, industrious, pos))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ((~![G: $i] : ((~cyclist(G)) | property1(G, industrious, pos))) | (~cyclist(S!0)) | property1(S!0, industrious, pos)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (property1(S!0, industrious, pos)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[23, 20, 12])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (grocer(S!0)),
% 0.12/0.37 inference(or_elim,[status(thm)],[11])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (^[E: $i] : refl((property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos))) <=> (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (![E: $i] : (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos))) <=> ![E: $i] : (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (^[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))))), (((~(grocer(E) & property1(E, industrious, pos))) | property1(E, honest, pos)) <=> (((~grocer(E)) | (~property1(E, industrious, pos))) | property1(E, honest, pos)))), rewrite((((~grocer(E)) | (~property1(E, industrious, pos))) | property1(E, honest, pos)) <=> (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos)))), (((~(grocer(E) & property1(E, industrious, pos))) | property1(E, honest, pos)) <=> (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | property1(E, honest, pos)) <=> ![E: $i] : (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | property1(E, honest, pos)) <=> ![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | property1(E, honest, pos))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | property1(E, honest, pos))),
% 0.12/0.37 inference(and_elim,[status(thm)],[16])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | property1(E, honest, pos))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.37 tff(33,plain,(
% 0.12/0.37 ![E: $i] : ((~(grocer(E) & property1(E, industrious, pos))) | property1(E, honest, pos))),
% 0.12/0.37 inference(skolemize,[status(sab)],[32])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (![E: $i] : (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (![E: $i] : (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (((~![E: $i] : (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos)))) | ((~grocer(S!0)) | property1(S!0, honest, pos) | (~property1(S!0, industrious, pos)))) <=> ((~![E: $i] : (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos)))) | (~grocer(S!0)) | property1(S!0, honest, pos) | (~property1(S!0, industrious, pos)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 ((property1(S!0, honest, pos) | (~grocer(S!0)) | (~property1(S!0, industrious, pos))) <=> ((~grocer(S!0)) | property1(S!0, honest, pos) | (~property1(S!0, industrious, pos)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (((~![E: $i] : (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos)))) | (property1(S!0, honest, pos) | (~grocer(S!0)) | (~property1(S!0, industrious, pos)))) <=> ((~![E: $i] : (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos)))) | ((~grocer(S!0)) | property1(S!0, honest, pos) | (~property1(S!0, industrious, pos))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[37])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (((~![E: $i] : (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos)))) | (property1(S!0, honest, pos) | (~grocer(S!0)) | (~property1(S!0, industrious, pos)))) <=> ((~![E: $i] : (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos)))) | (~grocer(S!0)) | property1(S!0, honest, pos) | (~property1(S!0, industrious, pos)))),
% 0.12/0.37 inference(transitivity,[status(thm)],[38, 36])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 ((~![E: $i] : (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos)))) | (property1(S!0, honest, pos) | (~grocer(S!0)) | (~property1(S!0, industrious, pos)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 ((~![E: $i] : (property1(E, honest, pos) | (~grocer(E)) | (~property1(E, industrious, pos)))) | (~grocer(S!0)) | property1(S!0, honest, pos) | (~property1(S!0, industrious, pos))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (property1(S!0, honest, pos) | (~property1(S!0, industrious, pos))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[41, 35, 25])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 (property1(S!0, honest, pos)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[42, 24])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (^[C: $i] : refl(((~grocer(C)) | (~property1(C, healthy, pos))) <=> ((~grocer(C)) | (~property1(C, healthy, pos))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 (![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos))) <=> ![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[44])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 (![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos))) <=> ![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 (![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos)))),
% 0.12/0.37 inference(and_elim,[status(thm)],[16])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 (![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.12/0.37 tff(49,plain,(
% 0.12/0.37 ![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[48])).
% 0.12/0.37 tff(50,plain,
% 0.12/0.37 (![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 (((~![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos)))) | ((~grocer(S!0)) | (~property1(S!0, healthy, pos)))) <=> ((~![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos)))) | (~grocer(S!0)) | (~property1(S!0, healthy, pos)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(52,plain,
% 0.12/0.37 ((~![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos)))) | ((~grocer(S!0)) | (~property1(S!0, healthy, pos)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(53,plain,
% 0.12/0.37 ((~![C: $i] : ((~grocer(C)) | (~property1(C, healthy, pos)))) | (~grocer(S!0)) | (~property1(S!0, healthy, pos))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.37 tff(54,plain,
% 0.12/0.37 (~property1(S!0, healthy, pos)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[53, 50, 25])).
% 0.12/0.37 tff(55,plain,
% 0.12/0.37 (^[O: $i] : refl((person(O) | (~grocer(O))) <=> (person(O) | (~grocer(O))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(56,plain,
% 0.12/0.37 (![O: $i] : (person(O) | (~grocer(O))) <=> ![O: $i] : (person(O) | (~grocer(O)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[55])).
% 0.12/0.37 tff(57,plain,
% 0.12/0.37 (![O: $i] : (person(O) | (~grocer(O))) <=> ![O: $i] : (person(O) | (~grocer(O)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(58,plain,
% 0.12/0.37 (![O: $i] : (person(O) | (~grocer(O)))),
% 0.12/0.37 inference(and_elim,[status(thm)],[16])).
% 0.12/0.37 tff(59,plain,
% 0.12/0.37 (![O: $i] : (person(O) | (~grocer(O)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.12/0.37 tff(60,plain,(
% 0.12/0.37 ![O: $i] : (person(O) | (~grocer(O)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[59])).
% 0.12/0.37 tff(61,plain,
% 0.12/0.37 (![O: $i] : (person(O) | (~grocer(O)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.12/0.37 tff(62,plain,
% 0.12/0.37 (((~![O: $i] : (person(O) | (~grocer(O)))) | (person(S!0) | (~grocer(S!0)))) <=> ((~![O: $i] : (person(O) | (~grocer(O)))) | person(S!0) | (~grocer(S!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(63,plain,
% 0.12/0.37 ((~![O: $i] : (person(O) | (~grocer(O)))) | (person(S!0) | (~grocer(S!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(64,plain,
% 0.12/0.37 ((~![O: $i] : (person(O) | (~grocer(O)))) | person(S!0) | (~grocer(S!0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.12/0.37 tff(65,plain,
% 0.12/0.37 (person(S!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[64, 61, 25])).
% 0.12/0.38 tff(66,plain,
% 0.12/0.38 (^[A: $i] : refl((property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos))) <=> (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(67,plain,
% 0.12/0.38 (![A: $i] : (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos))) <=> ![A: $i] : (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[66])).
% 0.12/0.38 tff(68,plain,
% 0.12/0.38 (^[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))))), (((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | property1(A, healthy, pos)) <=> (((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos))) | property1(A, healthy, pos)))), rewrite((((~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos))) | property1(A, healthy, pos)) <=> (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))), (((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | property1(A, healthy, pos)) <=> (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(69,plain,
% 0.12/0.38 (![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | property1(A, healthy, pos)) <=> ![A: $i] : (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[68])).
% 0.12/0.38 tff(70,plain,
% 0.12/0.38 (![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | property1(A, healthy, pos)) <=> ![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | property1(A, healthy, pos))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(71,plain,
% 0.12/0.38 (![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | property1(A, healthy, pos))),
% 0.12/0.38 inference(and_elim,[status(thm)],[16])).
% 0.12/0.38 tff(72,plain,
% 0.12/0.38 (![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | property1(A, healthy, pos))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.12/0.38 tff(73,plain,(
% 0.12/0.38 ![A: $i] : ((~(person(A) & property1(A, honest, pos) & property1(A, industrious, pos))) | property1(A, healthy, pos))),
% 0.12/0.38 inference(skolemize,[status(sab)],[72])).
% 0.12/0.38 tff(74,plain,
% 0.12/0.38 (![A: $i] : (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.12/0.38 tff(75,plain,
% 0.12/0.38 (![A: $i] : (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.12/0.38 tff(76,plain,
% 0.12/0.38 (((~![A: $i] : (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))) | (property1(S!0, healthy, pos) | (~property1(S!0, industrious, pos)) | (~person(S!0)) | (~property1(S!0, honest, pos)))) <=> ((~![A: $i] : (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))) | property1(S!0, healthy, pos) | (~property1(S!0, industrious, pos)) | (~person(S!0)) | (~property1(S!0, honest, pos)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(77,plain,
% 0.12/0.38 ((property1(S!0, healthy, pos) | (~person(S!0)) | (~property1(S!0, honest, pos)) | (~property1(S!0, industrious, pos))) <=> (property1(S!0, healthy, pos) | (~property1(S!0, industrious, pos)) | (~person(S!0)) | (~property1(S!0, honest, pos)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(78,plain,
% 0.12/0.38 (((~![A: $i] : (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))) | (property1(S!0, healthy, pos) | (~person(S!0)) | (~property1(S!0, honest, pos)) | (~property1(S!0, industrious, pos)))) <=> ((~![A: $i] : (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))) | (property1(S!0, healthy, pos) | (~property1(S!0, industrious, pos)) | (~person(S!0)) | (~property1(S!0, honest, pos))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[77])).
% 0.12/0.38 tff(79,plain,
% 0.12/0.38 (((~![A: $i] : (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))) | (property1(S!0, healthy, pos) | (~person(S!0)) | (~property1(S!0, honest, pos)) | (~property1(S!0, industrious, pos)))) <=> ((~![A: $i] : (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))) | property1(S!0, healthy, pos) | (~property1(S!0, industrious, pos)) | (~person(S!0)) | (~property1(S!0, honest, pos)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[78, 76])).
% 0.12/0.38 tff(80,plain,
% 0.12/0.38 ((~![A: $i] : (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))) | (property1(S!0, healthy, pos) | (~person(S!0)) | (~property1(S!0, honest, pos)) | (~property1(S!0, industrious, pos)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(81,plain,
% 0.12/0.38 ((~![A: $i] : (property1(A, healthy, pos) | (~person(A)) | (~property1(A, honest, pos)) | (~property1(A, industrious, pos)))) | property1(S!0, healthy, pos) | (~property1(S!0, industrious, pos)) | (~person(S!0)) | (~property1(S!0, honest, pos))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.12/0.38 tff(82,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[81, 75, 65, 54, 43, 24])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------