%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN364+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:38:54 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN364+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:31:10 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(big_p_type, type, (
% 0.12/0.38 big_p: ( $i * $i ) > $o)).
% 0.12/0.38 tff(g_type, type, (
% 0.12/0.38 g: $i > $i)).
% 0.12/0.38 tff(tptp_fun_U_1_type, type, (
% 0.12/0.38 tptp_fun_U_1: $i)).
% 0.12/0.38 tff(tptp_fun_V_0_type, type, (
% 0.12/0.38 tptp_fun_V_0: $i > $i)).
% 0.12/0.38 tff(f_type, type, (
% 0.12/0.38 f: ( $i * $i ) > $i)).
% 0.12/0.38 tff(big_q_type, type, (
% 0.12/0.38 big_q: $i > $o)).
% 0.12/0.38 tff(big_m_type, type, (
% 0.12/0.38 big_m: $i > $o)).
% 0.12/0.38 tff(1,assumption,(~big_p(U!1, U!1)), introduced(assumption)).
% 0.12/0.38 tff(2,assumption,(big_p(U!1, tptp_fun_V_0(U!1))), introduced(assumption)).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[X: $i, Z: $i, Y: $i] : refl(((~big_p(X, Y)) | big_p(Z, Z)) <=> ((~big_p(X, Y)) | big_p(Z, Z)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X: $i] : ![Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))),
% 0.12/0.38 inference(pull_quant,[status(thm)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (^[X: $i] : pull_quant((![Y: $i] : (~big_p(X, Y)) | ![Z: $i] : big_p(Z, Z)) <=> ![Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![X: $i] : (![Y: $i] : (~big_p(X, Y)) | ![Z: $i] : big_p(Z, Z)) <=> ![X: $i] : ![Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![X: $i] : (![Y: $i] : (~big_p(X, Y)) | ![Z: $i] : big_p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))),
% 0.12/0.38 inference(transitivity,[status(thm)],[7, 5])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![X: $i] : (![Y: $i] : (~big_p(X, Y)) | ![Z: $i] : big_p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))),
% 0.12/0.38 inference(transitivity,[status(thm)],[8, 4])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (^[X: $i] : rewrite((![Y: $i] : (~big_p(X, Y)) | ![Z: $i] : big_p(Z, Z)) <=> (![Y: $i] : (~big_p(X, Y)) | ![Z: $i] : big_p(Z, Z)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![X: $i] : (![Y: $i] : (~big_p(X, Y)) | ![Z: $i] : big_p(Z, Z)) <=> ![X: $i] : (![Y: $i] : (~big_p(X, Y)) | ![Z: $i] : big_p(Z, Z))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![X: $i] : (![Y: $i] : (~big_p(X, Y)) | ![Z: $i] : big_p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))),
% 0.12/0.38 inference(transitivity,[status(thm)],[11, 9])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![X: $i] : ((~?[Y: $i] : big_p(X, Y)) | ![Z: $i] : big_p(Z, Z)) <=> ![X: $i] : ((~?[Y: $i] : big_p(X, Y)) | ![Z: $i] : big_p(Z, Z))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 ((~(((![X: $i] : (?[Y: $i] : big_p(X, Y) => ![Z: $i] : big_p(Z, Z)) & ![U: $i] : ?[V: $i] : (big_p(U, V) | (big_m(U) & big_q(f(U, V))))) & ![W: $i] : (big_q(W) => (~big_m(g(W))))) => ![U: $i] : ?[V: $i] : (big_p(g(U), V) & big_p(U, U)))) <=> (~((~(![X: $i] : ((~?[Y: $i] : big_p(X, Y)) | ![Z: $i] : big_p(Z, Z)) & ![U: $i] : ?[V: $i] : (big_p(U, V) | (big_m(U) & big_q(f(U, V)))) & ![W: $i] : ((~big_q(W)) | (~big_m(g(W)))))) | ![U: $i] : ?[V: $i] : (big_p(g(U), V) & big_p(U, U))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(15,axiom,(~(((![X: $i] : (?[Y: $i] : big_p(X, Y) => ![Z: $i] : big_p(Z, Z)) & ![U: $i] : ?[V: $i] : (big_p(U, V) | (big_m(U) & big_q(f(U, V))))) & ![W: $i] : (big_q(W) => (~big_m(g(W))))) => ![U: $i] : ?[V: $i] : (big_p(g(U), V) & big_p(U, U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2115')).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (~((~(![X: $i] : ((~?[Y: $i] : big_p(X, Y)) | ![Z: $i] : big_p(Z, Z)) & ![U: $i] : ?[V: $i] : (big_p(U, V) | (big_m(U) & big_q(f(U, V)))) & ![W: $i] : ((~big_q(W)) | (~big_m(g(W)))))) | ![U: $i] : ?[V: $i] : (big_p(g(U), V) & big_p(U, U)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![X: $i] : ((~?[Y: $i] : big_p(X, Y)) | ![Z: $i] : big_p(Z, Z)) & ![U: $i] : ?[V: $i] : (big_p(U, V) | (big_m(U) & big_q(f(U, V)))) & ![W: $i] : ((~big_q(W)) | (~big_m(g(W))))),
% 0.12/0.38 inference(or_elim,[status(thm)],[16])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![X: $i] : ((~?[Y: $i] : big_p(X, Y)) | ![Z: $i] : big_p(Z, Z))),
% 0.12/0.38 inference(and_elim,[status(thm)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![X: $i] : ((~?[Y: $i] : big_p(X, Y)) | ![Z: $i] : big_p(Z, Z))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.12/0.38 tff(20,plain,(
% 0.12/0.38 ![X: $i] : (![Y: $i] : (~big_p(X, Y)) | ![Z: $i] : big_p(Z, Z))),
% 0.12/0.38 inference(skolemize,[status(sab)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (((~![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))) | ((~big_p(U!1, tptp_fun_V_0(U!1))) | big_p(U!1, U!1))) <=> ((~![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))) | (~big_p(U!1, tptp_fun_V_0(U!1))) | big_p(U!1, U!1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ((~![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))) | ((~big_p(U!1, tptp_fun_V_0(U!1))) | big_p(U!1, U!1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((~![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))) | (~big_p(U!1, tptp_fun_V_0(U!1))) | big_p(U!1, U!1)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[24, 21, 1, 2])).
% 0.12/0.38 tff(26,plain,((~big_p(U!1, tptp_fun_V_0(U!1))) | big_p(U!1, U!1)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (~big_p(U!1, tptp_fun_V_0(U!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[26, 1])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (^[U: $i] : refl((big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U))))))) <=> (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U))))))) <=> ![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (^[U: $i] : trans(monotonicity(rewrite((big_m(U) & big_q(f(U, tptp_fun_V_0(U)))) <=> (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U))))))), ((big_p(U, tptp_fun_V_0(U)) | (big_m(U) & big_q(f(U, tptp_fun_V_0(U))))) <=> (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U))))))))), rewrite((big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U))))))) <=> (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))), ((big_p(U, tptp_fun_V_0(U)) | (big_m(U) & big_q(f(U, tptp_fun_V_0(U))))) <=> (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (big_m(U) & big_q(f(U, tptp_fun_V_0(U))))) <=> ![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (![U: $i] : ?[V: $i] : (big_p(U, V) | (big_m(U) & big_q(f(U, V)))) <=> ![U: $i] : ?[V: $i] : (big_p(U, V) | (big_m(U) & big_q(f(U, V))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![U: $i] : ?[V: $i] : (big_p(U, V) | (big_m(U) & big_q(f(U, V))))),
% 0.12/0.38 inference(and_elim,[status(thm)],[17])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (![U: $i] : ?[V: $i] : (big_p(U, V) | (big_m(U) & big_q(f(U, V))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.12/0.38 tff(35,plain,(
% 0.12/0.38 ![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (big_m(U) & big_q(f(U, tptp_fun_V_0(U)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[34])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (((~![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))) | ((~((~big_m(U!1)) | (~big_q(f(U!1, tptp_fun_V_0(U!1)))))) | big_p(U!1, tptp_fun_V_0(U!1)))) <=> ((~![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))) | (~((~big_m(U!1)) | (~big_q(f(U!1, tptp_fun_V_0(U!1)))))) | big_p(U!1, tptp_fun_V_0(U!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 ((big_p(U!1, tptp_fun_V_0(U!1)) | (~((~big_m(U!1)) | (~big_q(f(U!1, tptp_fun_V_0(U!1))))))) <=> ((~((~big_m(U!1)) | (~big_q(f(U!1, tptp_fun_V_0(U!1)))))) | big_p(U!1, tptp_fun_V_0(U!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (((~![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))) | (big_p(U!1, tptp_fun_V_0(U!1)) | (~((~big_m(U!1)) | (~big_q(f(U!1, tptp_fun_V_0(U!1)))))))) <=> ((~![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))) | ((~((~big_m(U!1)) | (~big_q(f(U!1, tptp_fun_V_0(U!1)))))) | big_p(U!1, tptp_fun_V_0(U!1))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[39])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (((~![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))) | (big_p(U!1, tptp_fun_V_0(U!1)) | (~((~big_m(U!1)) | (~big_q(f(U!1, tptp_fun_V_0(U!1)))))))) <=> ((~![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))) | (~((~big_m(U!1)) | (~big_q(f(U!1, tptp_fun_V_0(U!1)))))) | big_p(U!1, tptp_fun_V_0(U!1)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[40, 38])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 ((~![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))) | (big_p(U!1, tptp_fun_V_0(U!1)) | (~((~big_m(U!1)) | (~big_q(f(U!1, tptp_fun_V_0(U!1)))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ((~![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))) | (~((~big_m(U!1)) | (~big_q(f(U!1, tptp_fun_V_0(U!1)))))) | big_p(U!1, tptp_fun_V_0(U!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 ((~((~big_m(U!1)) | (~big_q(f(U!1, tptp_fun_V_0(U!1)))))) | big_p(U!1, tptp_fun_V_0(U!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[43, 37])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (~((~big_m(U!1)) | (~big_q(f(U!1, tptp_fun_V_0(U!1)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[44, 27])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (((~big_m(U!1)) | (~big_q(f(U!1, tptp_fun_V_0(U!1))))) | big_q(f(U!1, tptp_fun_V_0(U!1)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (big_q(f(U!1, tptp_fun_V_0(U!1)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (^[W: $i] : refl(((~big_q(W)) | (~big_m(g(W)))) <=> ((~big_q(W)) | (~big_m(g(W)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (![W: $i] : ((~big_q(W)) | (~big_m(g(W)))) <=> ![W: $i] : ((~big_q(W)) | (~big_m(g(W))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (![W: $i] : ((~big_q(W)) | (~big_m(g(W)))) <=> ![W: $i] : ((~big_q(W)) | (~big_m(g(W))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (![W: $i] : ((~big_q(W)) | (~big_m(g(W))))),
% 0.20/0.39 inference(and_elim,[status(thm)],[17])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (![W: $i] : ((~big_q(W)) | (~big_m(g(W))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.39 tff(53,plain,(
% 0.20/0.39 ![W: $i] : ((~big_q(W)) | (~big_m(g(W))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[52])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (![W: $i] : ((~big_q(W)) | (~big_m(g(W))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (((~![W: $i] : ((~big_q(W)) | (~big_m(g(W))))) | ((~big_q(f(U!1, tptp_fun_V_0(U!1)))) | (~big_m(g(f(U!1, tptp_fun_V_0(U!1))))))) <=> ((~![W: $i] : ((~big_q(W)) | (~big_m(g(W))))) | (~big_q(f(U!1, tptp_fun_V_0(U!1)))) | (~big_m(g(f(U!1, tptp_fun_V_0(U!1))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 ((~![W: $i] : ((~big_q(W)) | (~big_m(g(W))))) | ((~big_q(f(U!1, tptp_fun_V_0(U!1)))) | (~big_m(g(f(U!1, tptp_fun_V_0(U!1))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 ((~![W: $i] : ((~big_q(W)) | (~big_m(g(W))))) | (~big_q(f(U!1, tptp_fun_V_0(U!1)))) | (~big_m(g(f(U!1, tptp_fun_V_0(U!1)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (~big_m(g(f(U!1, tptp_fun_V_0(U!1))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[57, 54, 47])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (((~big_m(g(f(U!1, tptp_fun_V_0(U!1))))) | (~big_q(f(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1)))))))) | big_m(g(f(U!1, tptp_fun_V_0(U!1))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 ((~big_m(g(f(U!1, tptp_fun_V_0(U!1))))) | (~big_q(f(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1)))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (((~![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))) | (big_p(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1))))) | (~((~big_m(g(f(U!1, tptp_fun_V_0(U!1))))) | (~big_q(f(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1))))))))))) <=> ((~![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))) | big_p(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1))))) | (~((~big_m(g(f(U!1, tptp_fun_V_0(U!1))))) | (~big_q(f(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1))))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((~![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))) | (big_p(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1))))) | (~((~big_m(g(f(U!1, tptp_fun_V_0(U!1))))) | (~big_q(f(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1))))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 ((~![U: $i] : (big_p(U, tptp_fun_V_0(U)) | (~((~big_m(U)) | (~big_q(f(U, tptp_fun_V_0(U)))))))) | big_p(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1))))) | (~((~big_m(g(f(U!1, tptp_fun_V_0(U!1))))) | (~big_q(f(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1)))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (big_p(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[63, 37, 60])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (((~![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))) | ((~big_p(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1)))))) | big_p(U!1, U!1))) <=> ((~![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))) | (~big_p(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1)))))) | big_p(U!1, U!1))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 ((~![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))) | ((~big_p(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1)))))) | big_p(U!1, U!1))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 ((~![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))) | (~big_p(g(f(U!1, tptp_fun_V_0(U!1))), tptp_fun_V_0(g(f(U!1, tptp_fun_V_0(U!1)))))) | big_p(U!1, U!1)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[67, 21, 1, 64])).
% 0.20/0.39 tff(69,plain,(big_p(U!1, U!1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (^[V: $i] : refl(((~big_p(g(U!1), V)) | (~big_p(U!1, U!1))) <=> ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (![V: $i] : ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1))) <=> ![V: $i] : ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (^[V: $i] : trans(monotonicity(rewrite((big_p(g(U!1), V) & big_p(U!1, U!1)) <=> (~((~big_p(g(U!1), V)) | (~big_p(U!1, U!1))))), ((~(big_p(g(U!1), V) & big_p(U!1, U!1))) <=> (~(~((~big_p(g(U!1), V)) | (~big_p(U!1, U!1))))))), rewrite((~(~((~big_p(g(U!1), V)) | (~big_p(U!1, U!1))))) <=> ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1)))), ((~(big_p(g(U!1), V) & big_p(U!1, U!1))) <=> ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (![V: $i] : (~(big_p(g(U!1), V) & big_p(U!1, U!1))) <=> ![V: $i] : ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 ((~![U: $i] : ?[V: $i] : (big_p(g(U), V) & big_p(U, U))) <=> (~![U: $i] : ?[V: $i] : (big_p(g(U), V) & big_p(U, U)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (~![U: $i] : ?[V: $i] : (big_p(g(U), V) & big_p(U, U))),
% 0.20/0.39 inference(or_elim,[status(thm)],[16])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 (~![U: $i] : ?[V: $i] : (big_p(g(U), V) & big_p(U, U))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (~![U: $i] : ?[V: $i] : (big_p(g(U), V) & big_p(U, U))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[76, 74])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 (~![U: $i] : ?[V: $i] : (big_p(g(U), V) & big_p(U, U))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[77, 74])).
% 0.20/0.39 tff(79,plain,(
% 0.20/0.39 $oeq((~?[V: $i] : (big_p(g(U!1), V) & big_p(U!1, U!1))), ![V: $i] : (~(big_p(g(U!1), V) & big_p(U!1, U!1))))),
% 0.20/0.39 inference(transitivity,[status(sab)],[78])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (![V: $i] : ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[79, 73])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 (![V: $i] : ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[80, 71])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (((~![V: $i] : ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1)))) | ((~big_p(U!1, U!1)) | (~big_p(g(U!1), g(U!1))))) <=> ((~![V: $i] : ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1)))) | (~big_p(U!1, U!1)) | (~big_p(g(U!1), g(U!1))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 (((~big_p(g(U!1), g(U!1))) | (~big_p(U!1, U!1))) <=> ((~big_p(U!1, U!1)) | (~big_p(g(U!1), g(U!1))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 (((~![V: $i] : ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1)))) | ((~big_p(g(U!1), g(U!1))) | (~big_p(U!1, U!1)))) <=> ((~![V: $i] : ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1)))) | ((~big_p(U!1, U!1)) | (~big_p(g(U!1), g(U!1)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 (((~![V: $i] : ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1)))) | ((~big_p(g(U!1), g(U!1))) | (~big_p(U!1, U!1)))) <=> ((~![V: $i] : ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1)))) | (~big_p(U!1, U!1)) | (~big_p(g(U!1), g(U!1))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[84, 82])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 ((~![V: $i] : ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1)))) | ((~big_p(g(U!1), g(U!1))) | (~big_p(U!1, U!1)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 ((~![V: $i] : ((~big_p(g(U!1), V)) | (~big_p(U!1, U!1)))) | (~big_p(U!1, U!1)) | (~big_p(g(U!1), g(U!1)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 (~big_p(g(U!1), g(U!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[87, 81, 69])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 (((~![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))) | ((~big_p(U!1, U!1)) | big_p(g(U!1), g(U!1)))) <=> ((~![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))) | (~big_p(U!1, U!1)) | big_p(g(U!1), g(U!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 ((~![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))) | ((~big_p(U!1, U!1)) | big_p(g(U!1), g(U!1)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 ((~![X: $i, Z: $i, Y: $i] : ((~big_p(X, Y)) | big_p(Z, Z))) | (~big_p(U!1, U!1)) | big_p(g(U!1), g(U!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[91, 21, 69, 88])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------