%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN728+1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:39:55 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN728+1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n005.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 12:41:05 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(p_type, type, (
% 0.12/0.36 p: ( $i * $i ) > $o)).
% 0.12/0.36 tff(g_type, type, (
% 0.12/0.36 g: $i > $i)).
% 0.12/0.36 tff(tptp_fun_U_1_type, type, (
% 0.12/0.36 tptp_fun_U_1: $i)).
% 0.12/0.36 tff(tptp_fun_S_0_type, type, (
% 0.12/0.36 tptp_fun_S_0: $i > $i)).
% 0.12/0.36 tff(f_type, type, (
% 0.12/0.36 f: ( $i * $i ) > $i)).
% 0.12/0.36 tff(elem_2_type, type, (
% 0.12/0.36 elem_2: $i)).
% 0.12/0.36 tff(q_type, type, (
% 0.12/0.36 q: $i > $o)).
% 0.12/0.36 tff(m_type, type, (
% 0.12/0.36 m: $i > $o)).
% 0.12/0.36 tff(1,assumption,(~p(U!1, U!1)), introduced(assumption)).
% 0.12/0.36 tff(2,assumption,(p(elem!2, tptp_fun_S_0(elem!2))), introduced(assumption)).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (^[X: $i, Z: $i, Y: $i] : refl(((~p(X, Y)) | p(Z, Z)) <=> ((~p(X, Y)) | p(Z, Z)))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 (![X: $i] : ![Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))),
% 0.12/0.36 inference(pull_quant,[status(thm)],[])).
% 0.12/0.36 tff(6,plain,
% 0.12/0.37 (^[X: $i] : pull_quant((![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> ![Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![X: $i] : (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> ![X: $i] : ![Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![X: $i] : (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))),
% 0.12/0.37 inference(transitivity,[status(thm)],[7, 5])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (![X: $i] : (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))),
% 0.12/0.37 inference(transitivity,[status(thm)],[8, 4])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (^[X: $i] : rewrite((![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (![X: $i] : (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> ![X: $i] : (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (![X: $i] : (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))),
% 0.12/0.37 inference(transitivity,[status(thm)],[11, 9])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![X: $i] : ((~?[Y: $i] : p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> ![X: $i] : ((~?[Y: $i] : p(X, Y)) | ![Z: $i] : p(Z, Z))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 ((~(((![X: $i] : (?[Y: $i] : p(X, Y) => ![Z: $i] : p(Z, Z)) & ![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S))))) & ![W: $i] : (q(W) => (~m(g(W))))) => ![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U)))) <=> (~((~(![X: $i] : ((~?[Y: $i] : p(X, Y)) | ![Z: $i] : p(Z, Z)) & ![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S)))) & ![W: $i] : ((~q(W)) | (~m(g(W)))))) | ![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(15,axiom,(~(((![X: $i] : (?[Y: $i] : p(X, Y) => ![Z: $i] : p(Z, Z)) & ![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S))))) & ![W: $i] : (q(W) => (~m(g(W))))) => ![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm69')).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (~((~(![X: $i] : ((~?[Y: $i] : p(X, Y)) | ![Z: $i] : p(Z, Z)) & ![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S)))) & ![W: $i] : ((~q(W)) | (~m(g(W)))))) | ![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![X: $i] : ((~?[Y: $i] : p(X, Y)) | ![Z: $i] : p(Z, Z)) & ![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S)))) & ![W: $i] : ((~q(W)) | (~m(g(W))))),
% 0.12/0.37 inference(or_elim,[status(thm)],[16])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (![X: $i] : ((~?[Y: $i] : p(X, Y)) | ![Z: $i] : p(Z, Z))),
% 0.12/0.37 inference(and_elim,[status(thm)],[17])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![X: $i] : ((~?[Y: $i] : p(X, Y)) | ![Z: $i] : p(Z, Z))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.12/0.37 tff(20,plain,(
% 0.12/0.37 ![X: $i] : (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z))),
% 0.12/0.37 inference(skolemize,[status(sab)],[19])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(elem!2, tptp_fun_S_0(elem!2))) | p(U!1, U!1))) <=> ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(elem!2, tptp_fun_S_0(elem!2))) | p(U!1, U!1))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(elem!2, tptp_fun_S_0(elem!2))) | p(U!1, U!1))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(elem!2, tptp_fun_S_0(elem!2))) | p(U!1, U!1)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[24, 21, 2, 1])).
% 0.12/0.37 tff(26,plain,(p(U!1, U!1) | (~p(elem!2, tptp_fun_S_0(elem!2)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (~p(elem!2, tptp_fun_S_0(elem!2))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[26, 1])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (^[R: $i] : refl((p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R))))))) <=> (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R))))))) <=> ![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (^[R: $i] : trans(monotonicity(rewrite((m(R) & q(f(R, tptp_fun_S_0(R)))) <=> (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R))))))), ((p(R, tptp_fun_S_0(R)) | (m(R) & q(f(R, tptp_fun_S_0(R))))) <=> (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R))))))))), rewrite((p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R))))))) <=> (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))), ((p(R, tptp_fun_S_0(R)) | (m(R) & q(f(R, tptp_fun_S_0(R))))) <=> (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (![R: $i] : (p(R, tptp_fun_S_0(R)) | (m(R) & q(f(R, tptp_fun_S_0(R))))) <=> ![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S)))) <=> ![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S))))),
% 0.12/0.37 inference(and_elim,[status(thm)],[17])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.12/0.37 tff(35,plain,(
% 0.12/0.37 ![R: $i] : (p(R, tptp_fun_S_0(R)) | (m(R) & q(f(R, tptp_fun_S_0(R)))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[34])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | ((~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(elem!2, tptp_fun_S_0(elem!2)))) <=> ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(elem!2, tptp_fun_S_0(elem!2)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 ((p(elem!2, tptp_fun_S_0(elem!2)) | (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2))))))) <=> ((~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(elem!2, tptp_fun_S_0(elem!2)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 (((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (p(elem!2, tptp_fun_S_0(elem!2)) | (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))))) <=> ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | ((~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(elem!2, tptp_fun_S_0(elem!2))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[39])).
% 0.18/0.37 tff(41,plain,
% 0.18/0.37 (((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (p(elem!2, tptp_fun_S_0(elem!2)) | (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))))) <=> ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(elem!2, tptp_fun_S_0(elem!2)))),
% 0.18/0.37 inference(transitivity,[status(thm)],[40, 38])).
% 0.18/0.37 tff(42,plain,
% 0.18/0.37 ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (p(elem!2, tptp_fun_S_0(elem!2)) | (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(43,plain,
% 0.18/0.37 ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(elem!2, tptp_fun_S_0(elem!2))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.18/0.37 tff(44,plain,
% 0.18/0.37 ((~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(elem!2, tptp_fun_S_0(elem!2))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[43, 37])).
% 0.18/0.37 tff(45,plain,
% 0.18/0.37 (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[44, 27])).
% 0.18/0.37 tff(46,plain,
% 0.18/0.37 (((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2))))) | q(f(elem!2, tptp_fun_S_0(elem!2)))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(47,plain,
% 0.18/0.37 (q(f(elem!2, tptp_fun_S_0(elem!2)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.18/0.37 tff(48,plain,
% 0.18/0.37 (^[W: $i] : refl(((~q(W)) | (~m(g(W)))) <=> ((~q(W)) | (~m(g(W)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(49,plain,
% 0.18/0.37 (![W: $i] : ((~q(W)) | (~m(g(W)))) <=> ![W: $i] : ((~q(W)) | (~m(g(W))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[48])).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 (![W: $i] : ((~q(W)) | (~m(g(W)))) <=> ![W: $i] : ((~q(W)) | (~m(g(W))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(51,plain,
% 0.18/0.37 (![W: $i] : ((~q(W)) | (~m(g(W))))),
% 0.18/0.37 inference(and_elim,[status(thm)],[17])).
% 0.18/0.37 tff(52,plain,
% 0.18/0.37 (![W: $i] : ((~q(W)) | (~m(g(W))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.18/0.37 tff(53,plain,(
% 0.18/0.37 ![W: $i] : ((~q(W)) | (~m(g(W))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[52])).
% 0.18/0.37 tff(54,plain,
% 0.18/0.37 (![W: $i] : ((~q(W)) | (~m(g(W))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.18/0.37 tff(55,plain,
% 0.18/0.37 (((~![W: $i] : ((~q(W)) | (~m(g(W))))) | ((~q(f(elem!2, tptp_fun_S_0(elem!2)))) | (~m(g(f(elem!2, tptp_fun_S_0(elem!2))))))) <=> ((~![W: $i] : ((~q(W)) | (~m(g(W))))) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))) | (~m(g(f(elem!2, tptp_fun_S_0(elem!2))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(56,plain,
% 0.18/0.37 ((~![W: $i] : ((~q(W)) | (~m(g(W))))) | ((~q(f(elem!2, tptp_fun_S_0(elem!2)))) | (~m(g(f(elem!2, tptp_fun_S_0(elem!2))))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(57,plain,
% 0.18/0.37 ((~![W: $i] : ((~q(W)) | (~m(g(W))))) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))) | (~m(g(f(elem!2, tptp_fun_S_0(elem!2)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.37 tff(58,plain,
% 0.18/0.37 (~m(g(f(elem!2, tptp_fun_S_0(elem!2))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[57, 54, 47])).
% 0.18/0.37 tff(59,plain,
% 0.18/0.37 (((~m(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~q(f(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))) | m(g(f(elem!2, tptp_fun_S_0(elem!2))))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(60,plain,
% 0.18/0.37 ((~m(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~q(f(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.18/0.37 tff(61,plain,
% 0.18/0.37 (((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~((~m(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~q(f(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))) <=> ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~((~m(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~q(f(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(62,plain,
% 0.18/0.37 ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~((~m(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~q(f(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(63,plain,
% 0.18/0.37 ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~((~m(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~q(f(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.18/0.37 tff(64,plain,
% 0.18/0.37 (p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[63, 37, 60])).
% 0.18/0.37 tff(65,plain,
% 0.18/0.37 (((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(U!1, U!1))) <=> ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(U!1, U!1))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(66,plain,
% 0.18/0.37 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(U!1, U!1))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(67,plain,
% 0.18/0.37 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(U!1, U!1)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.18/0.37 tff(68,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[67, 21, 1, 64])).
% 0.18/0.37 tff(69,plain,(p(U!1, U!1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(70,plain,
% 0.18/0.37 (^[V: $i] : refl(((~p(g(U!1), V)) | (~p(U!1, U!1))) <=> ((~p(g(U!1), V)) | (~p(U!1, U!1))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(71,plain,
% 0.18/0.37 (![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1))) <=> ![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[70])).
% 0.18/0.37 tff(72,plain,
% 0.18/0.37 (^[V: $i] : trans(monotonicity(rewrite((p(g(U!1), V) & p(U!1, U!1)) <=> (~((~p(g(U!1), V)) | (~p(U!1, U!1))))), ((~(p(g(U!1), V) & p(U!1, U!1))) <=> (~(~((~p(g(U!1), V)) | (~p(U!1, U!1))))))), rewrite((~(~((~p(g(U!1), V)) | (~p(U!1, U!1))))) <=> ((~p(g(U!1), V)) | (~p(U!1, U!1)))), ((~(p(g(U!1), V) & p(U!1, U!1))) <=> ((~p(g(U!1), V)) | (~p(U!1, U!1)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(73,plain,
% 0.18/0.37 (![V: $i] : (~(p(g(U!1), V) & p(U!1, U!1))) <=> ![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[72])).
% 0.18/0.37 tff(74,plain,
% 0.18/0.37 ((~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))) <=> (~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(75,plain,
% 0.18/0.37 (~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))),
% 0.18/0.37 inference(or_elim,[status(thm)],[16])).
% 0.18/0.37 tff(76,plain,
% 0.18/0.37 (~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.18/0.37 tff(77,plain,
% 0.18/0.37 (~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[76, 74])).
% 0.18/0.37 tff(78,plain,
% 0.18/0.37 (~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[77, 74])).
% 0.18/0.37 tff(79,plain,(
% 0.18/0.37 $oeq((~?[V: $i] : (p(g(U!1), V) & p(U!1, U!1))), ![V: $i] : (~(p(g(U!1), V) & p(U!1, U!1))))),
% 0.18/0.37 inference(transitivity,[status(sab)],[78])).
% 0.18/0.37 tff(80,plain,
% 0.18/0.37 (![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[79, 73])).
% 0.18/0.38 tff(81,plain,
% 0.18/0.38 (![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[80, 71])).
% 0.18/0.38 tff(82,plain,
% 0.18/0.38 (((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | ((~p(U!1, U!1)) | (~p(g(U!1), g(U!1))))) <=> ((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | (~p(U!1, U!1)) | (~p(g(U!1), g(U!1))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(83,plain,
% 0.18/0.38 (((~p(g(U!1), g(U!1))) | (~p(U!1, U!1))) <=> ((~p(U!1, U!1)) | (~p(g(U!1), g(U!1))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(84,plain,
% 0.18/0.38 (((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | ((~p(g(U!1), g(U!1))) | (~p(U!1, U!1)))) <=> ((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | ((~p(U!1, U!1)) | (~p(g(U!1), g(U!1)))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[83])).
% 0.18/0.38 tff(85,plain,
% 0.18/0.38 (((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | ((~p(g(U!1), g(U!1))) | (~p(U!1, U!1)))) <=> ((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | (~p(U!1, U!1)) | (~p(g(U!1), g(U!1))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[84, 82])).
% 0.18/0.38 tff(86,plain,
% 0.18/0.38 ((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | ((~p(g(U!1), g(U!1))) | (~p(U!1, U!1)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(87,plain,
% 0.18/0.38 ((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | (~p(U!1, U!1)) | (~p(g(U!1), g(U!1)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.18/0.38 tff(88,plain,
% 0.18/0.38 ((~p(U!1, U!1)) | (~p(g(U!1), g(U!1)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[87, 81])).
% 0.18/0.38 tff(89,plain,
% 0.18/0.38 (~p(g(U!1), g(U!1))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[88, 69])).
% 0.18/0.38 tff(90,plain,
% 0.18/0.38 (((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(U!1, U!1)) | p(g(U!1), g(U!1)))) <=> ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(U!1, U!1)) | p(g(U!1), g(U!1)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(91,plain,
% 0.18/0.38 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(U!1, U!1)) | p(g(U!1), g(U!1)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(92,plain,
% 0.18/0.38 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(U!1, U!1)) | p(g(U!1), g(U!1))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.18/0.38 tff(93,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[92, 21, 69, 89])).
% 0.18/0.38 % SZS output end Proof
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------