%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP004_1 : TPTP v9.0.0. Bugfixed v7.5.0.
% 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 05:11:14 AM UTC 2025
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP004_1 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.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 : Thu Jun 19 18:04:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(p_type, type, (
% 0.20/0.46 p: mono_2Etyop_2Emin_2Ebool > $o)).
% 0.20/0.46 tff(j_mono_2Etyop_2Emin_2Ebool_type, type, (
% 0.20/0.46 j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool)).
% 0.20/0.46 tff(s_type, type, (
% 0.20/0.46 s: ( d * u ) > du)).
% 0.20/0.46 tff(c_2Ebool_2EIN_2E2_type, type, (
% 0.20/0.46 c_2Ebool_2EIN_2E2: ( du * du ) > u)).
% 0.20/0.46 tff(c_2Epred__set_2EDELETE_2E2_type, type, (
% 0.20/0.46 c_2Epred__set_2EDELETE_2E2: ( du * du ) > u)).
% 0.20/0.46 tff(c_2Epred__set_2ECHOICE_2E1_type, type, (
% 0.20/0.46 c_2Epred__set_2ECHOICE_2E1: du > u)).
% 0.20/0.46 tff(tptp_fun_V0s_2E0_4_type, type, (
% 0.20/0.46 tptp_fun_V0s_2E0_4: u)).
% 0.20/0.46 tff(tyop_2Emin_2Efun_type, type, (
% 0.20/0.46 tyop_2Emin_2Efun: ( d * d ) > d)).
% 0.20/0.46 tff(tyop_2Emin_2Ebool_type, type, (
% 0.20/0.46 tyop_2Emin_2Ebool: d)).
% 0.20/0.46 tff(tptp_fun_A_27a_5_type, type, (
% 0.20/0.46 tptp_fun_A_27a_5: d)).
% 0.20/0.46 tff(tptp_fun_V2x_2E0_3_type, type, (
% 0.20/0.46 tptp_fun_V2x_2E0_3: ( u * u * d ) > u)).
% 0.20/0.46 tff(c_2Epred__set_2EREST_2E1_type, type, (
% 0.20/0.46 c_2Epred__set_2EREST_2E1: du > u)).
% 0.20/0.46 tff(mono_2Ec_2Ebool_2ET_2E0_type, type, (
% 0.20/0.46 mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool)).
% 0.20/0.46 tff(inj_6_type, type, (
% 0.20/0.46 inj_6: $o > mono_2Etyop_2Emin_2Ebool)).
% 0.20/0.46 tff(c_2Epred__set_2ESUBSET_2E2_type, type, (
% 0.20/0.46 c_2Epred__set_2ESUBSET_2E2: ( du * du ) > u)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 ((p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))) <=> $true) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (p(mono_2Ec_2Ebool_2ET_2E0) <=> p(mono_2Ec_2Ebool_2ET_2E0)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(3,axiom,(p(mono_2Ec_2Ebool_2ET_2E0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reserved_2Eho_2Etruth')).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 (p(mono_2Ec_2Ebool_2ET_2E0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (p(mono_2Ec_2Ebool_2ET_2E0) <=> $true),
% 0.20/0.46 inference(iff_true,[status(thm)],[4])).
% 0.20/0.46 tff(6,plain,
% 0.20/0.46 (![Xk!0: mono_2Etyop_2Emin_2Ebool] : (inj_6(p(Xk!0)) = Xk!0) <=> ![Xk!0: mono_2Etyop_2Emin_2Ebool] : (inj_6(p(Xk!0)) = Xk!0)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (![V0_2E0: mono_2Etyop_2Emin_2Ebool, V1_2E0: mono_2Etyop_2Emin_2Ebool] : ((~(p(V0_2E0) <=> p(V1_2E0))) | (V0_2E0 = V1_2E0)) <=> ![Xk!0: mono_2Etyop_2Emin_2Ebool] : (inj_6(p(Xk!0)) = Xk!0)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 (![V0_2E0: mono_2Etyop_2Emin_2Ebool, V1_2E0: mono_2Etyop_2Emin_2Ebool] : ((~(p(V0_2E0) <=> p(V1_2E0))) | (V0_2E0 = V1_2E0)) <=> ![V0_2E0: mono_2Etyop_2Emin_2Ebool, V1_2E0: mono_2Etyop_2Emin_2Ebool] : ((~(p(V0_2E0) <=> p(V1_2E0))) | (V0_2E0 = V1_2E0))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (^[V0_2E0: mono_2Etyop_2Emin_2Ebool, V1_2E0: mono_2Etyop_2Emin_2Ebool] : rewrite(((p(V0_2E0) <=> p(V1_2E0)) => (V0_2E0 = V1_2E0)) <=> ((~(p(V0_2E0) <=> p(V1_2E0))) | (V0_2E0 = V1_2E0)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (![V0_2E0: mono_2Etyop_2Emin_2Ebool, V1_2E0: mono_2Etyop_2Emin_2Ebool] : ((p(V0_2E0) <=> p(V1_2E0)) => (V0_2E0 = V1_2E0)) <=> ![V0_2E0: mono_2Etyop_2Emin_2Ebool, V1_2E0: mono_2Etyop_2Emin_2Ebool] : ((~(p(V0_2E0) <=> p(V1_2E0))) | (V0_2E0 = V1_2E0))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.46 tff(11,axiom,(![V0_2E0: mono_2Etyop_2Emin_2Ebool, V1_2E0: mono_2Etyop_2Emin_2Ebool] : ((p(V0_2E0) <=> p(V1_2E0)) => (V0_2E0 = V1_2E0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reserved_2Eho_2Eboolext')).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (![V0_2E0: mono_2Etyop_2Emin_2Ebool, V1_2E0: mono_2Etyop_2Emin_2Ebool] : ((~(p(V0_2E0) <=> p(V1_2E0))) | (V0_2E0 = V1_2E0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (![V0_2E0: mono_2Etyop_2Emin_2Ebool, V1_2E0: mono_2Etyop_2Emin_2Ebool] : ((~(p(V0_2E0) <=> p(V1_2E0))) | (V0_2E0 = V1_2E0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.46 tff(14,plain,(
% 0.20/0.46 ![V0_2E0: mono_2Etyop_2Emin_2Ebool, V1_2E0: mono_2Etyop_2Emin_2Ebool] : ((~(p(V0_2E0) <=> p(V1_2E0))) | (V0_2E0 = V1_2E0))),
% 0.20/0.46 inference(skolemize,[status(sab)],[13])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (![Xk!0: mono_2Etyop_2Emin_2Ebool] : (inj_6(p(Xk!0)) = Xk!0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (![Xk!0: mono_2Etyop_2Emin_2Ebool] : (inj_6(p(Xk!0)) = Xk!0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[15, 6])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 ((~![Xk!0: mono_2Etyop_2Emin_2Ebool] : (inj_6(p(Xk!0)) = Xk!0)) | (inj_6(p(mono_2Ec_2Ebool_2ET_2E0)) = mono_2Ec_2Ebool_2ET_2E0)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (inj_6(p(mono_2Ec_2Ebool_2ET_2E0)) = mono_2Ec_2Ebool_2ET_2E0),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 ($true <=> p(mono_2Ec_2Ebool_2ET_2E0)),
% 0.20/0.46 inference(symmetry,[status(thm)],[5])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 (^[A_27a: d, V0s_2E0: u, V1t_2E0: u] : rewrite((~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) <=> (~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 (![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) <=> ![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 (^[A_27a: d, V0s_2E0: u, V1t_2E0: u] : refl((~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) <=> (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(23,plain,
% 0.20/0.46 (![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) <=> ![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (^[A_27a: d, V0s_2E0: u, V1t_2E0: u] : rewrite((~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) <=> (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 (![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) <=> ![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.46 tff(26,plain,
% 0.20/0.46 (![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) <=> ![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[25, 23])).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (^[A_27a: d, V0s_2E0: u, V1t_2E0: u] : trans(monotonicity(rewrite(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) <=> ((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))), ((((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) & (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) <=> (((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) & (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))), rewrite((((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) & (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) <=> (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))))), ((((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) & (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) <=> (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(28,plain,
% 0.20/0.46 (![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) & (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) <=> ![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.46 tff(29,plain,
% 0.20/0.46 (![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) <=> ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) <=> ![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) <=> ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (^[A_27a: d, V0s_2E0: u, V1t_2E0: u] : rewrite((p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) <=> ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))))) <=> (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) <=> ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) <=> ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))))) <=> ![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) <=> ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.47 tff(32,axiom,(![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) <=> ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm_2Epred__set_2ESUBSET__DEF')).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 (![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) <=> ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) <=> ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.47 tff(35,plain,(
% 0.20/0.47 ![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))) & (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[34])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 (![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 (![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[37, 21])).
% 0.20/0.47 tff(39,plain,
% 0.20/0.47 (((~![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) | (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))))))) <=> ((~![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) | (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 ((~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))))) <=> (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 (((~![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) | (~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))))) <=> ((~![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) | (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 (((~![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) | (~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))))) <=> ((~![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) | (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[41, 39])).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 ((~![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) | (~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 ((~![A_27a: d, V0s_2E0: u, V1t_2E0: u] : (~((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, tptp_fun_V2x_2E0_3(V1t_2E0, V0s_2E0, A_27a)), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))) | (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (~((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[44, 38])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (((~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | ![V2x_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, V2x_2E0), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))))) | (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 ((~![A_27a: d, V0s_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) <=> (~![A_27a: d, V0s_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(49,axiom,(~![A_27a: d, V0s_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm_2Epred__set_2EREST__SUBSET')).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (~![A_27a: d, V0s_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 (~![A_27a: d, V0s_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[50, 48])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 (~![A_27a: d, V0s_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[51, 48])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (~![A_27a: d, V0s_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.48 tff(54,plain,(
% 0.20/0.48 ~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[53])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 ((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 ((~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))) | (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 (~(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[56, 47])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 ((p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))) <=> $true),
% 0.20/0.48 inference(iff_true,[status(thm)],[59])).
% 0.20/0.48 tff(61,plain,
% 0.20/0.48 (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))) <=> p(mono_2Ec_2Ebool_2ET_2E0)),
% 0.20/0.48 inference(transitivity,[status(thm)],[60, 19])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (inj_6(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))) = inj_6(p(mono_2Ec_2Ebool_2ET_2E0))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 ((~![Xk!0: mono_2Etyop_2Emin_2Ebool] : (inj_6(p(Xk!0)) = Xk!0)) | (inj_6(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 (inj_6(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[63, 16])).
% 0.20/0.48 tff(65,plain,
% 0.20/0.48 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) = inj_6(p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))),
% 0.20/0.48 inference(symmetry,[status(thm)],[64])).
% 0.20/0.48 tff(66,plain,
% 0.20/0.48 (![A_27a: d, V0s_2E0: u] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) <=> ![A_27a: d, V0s_2E0: u] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 (^[A_27a: d, V0s_2E0: u] : refl((s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) <=> (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 (![A_27a: d, V0s_2E0: u] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) <=> ![A_27a: d, V0s_2E0: u] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 (![A_27a: d, V0s_2E0: u] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) <=> ![A_27a: d, V0s_2E0: u] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(70,axiom,(![A_27a: d, V0s_2E0: u] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm_2Epred__set_2EREST__DEF')).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 (![A_27a: d, V0s_2E0: u] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.48 tff(72,plain,(
% 0.20/0.48 ![A_27a: d, V0s_2E0: u] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[71])).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 (![A_27a: d, V0s_2E0: u] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.20/0.48 tff(74,plain,
% 0.20/0.48 (![A_27a: d, V0s_2E0: u] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.20/0.48 tff(75,plain,
% 0.20/0.48 ((~![A_27a: d, V0s_2E0: u] : (s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))) | (s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))) = s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(76,plain,
% 0.20/0.48 (s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))) = s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.48 tff(77,plain,
% 0.20/0.48 (s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) = s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))),
% 0.20/0.48 inference(symmetry,[status(thm)],[76])).
% 0.20/0.48 tff(78,plain,
% 0.20/0.48 (c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) = c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[77])).
% 0.20/0.48 tff(79,plain,
% 0.20/0.48 (s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))) = s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[78])).
% 0.20/0.48 tff(80,plain,
% 0.20/0.48 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[79])).
% 0.20/0.48 tff(81,plain,
% 0.20/0.48 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))) = mono_2Ec_2Ebool_2ET_2E0),
% 0.20/0.48 inference(transitivity,[status(thm)],[80, 65, 62, 18])).
% 0.20/0.48 tff(82,plain,
% 0.20/0.48 (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))) <=> p(mono_2Ec_2Ebool_2ET_2E0)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[81])).
% 0.20/0.48 tff(83,plain,
% 0.20/0.48 (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))) <=> $true),
% 0.20/0.48 inference(transitivity,[status(thm)],[82, 5])).
% 0.20/0.48 tff(84,plain,
% 0.20/0.48 (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[83, 1])).
% 0.20/0.48 tff(85,plain,
% 0.20/0.48 (^[A_27a: d, V0s_2E0: u, V1x_2E0: u, V2y_2E0: u] : refl((~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))))) <=> (~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(86,plain,
% 0.20/0.48 (![A_27a: d, V0s_2E0: u, V1x_2E0: u, V2y_2E0: u] : (~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))))) <=> ![A_27a: d, V0s_2E0: u, V1x_2E0: u, V2y_2E0: u] : (~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.48 tff(87,plain,
% 0.20/0.48 (^[A_27a: d, V0s_2E0: u, V1x_2E0: u, V2y_2E0: u] : trans(trans(monotonicity(rewrite((p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0)))) <=> (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))), ((p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))) <=> (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))) <=> (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))) <=> (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))))), rewrite((p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))) <=> (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))) <=> (~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))))))), ((p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))) <=> (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))) <=> (~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))))))), rewrite((~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))))) <=> (~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))))))), ((p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))) <=> (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))) <=> (~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 (![A_27a: d, V0s_2E0: u, V1x_2E0: u, V2y_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))) <=> (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))) <=> ![A_27a: d, V0s_2E0: u, V1x_2E0: u, V2y_2E0: u] : (~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 (![A_27a: d, V0s_2E0: u, V1x_2E0: u, V2y_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))) <=> (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))))) <=> ![A_27a: d, V0s_2E0: u, V1x_2E0: u, V2y_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))) <=> (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(90,axiom,(![A_27a: d, V0s_2E0: u, V1x_2E0: u, V2y_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))) <=> (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm_2Epred__set_2EIN__DELETE')).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 (![A_27a: d, V0s_2E0: u, V1x_2E0: u, V2y_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))) <=> (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.49 tff(92,plain,(
% 0.20/0.49 ![A_27a: d, V0s_2E0: u, V1x_2E0: u, V2y_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0))))))) <=> (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))) & (~(s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0)))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[91])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 (![A_27a: d, V0s_2E0: u, V1x_2E0: u, V2y_2E0: u] : (~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 (![A_27a: d, V0s_2E0: u, V1x_2E0: u, V2y_2E0: u] : (~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 ((~![A_27a: d, V0s_2E0: u, V1x_2E0: u, V2y_2E0: u] : (~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))) | (s(A_27a, V1x_2E0) = s(A_27a, V2y_2E0))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V1x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0), s(A_27a, V2y_2E0)))))))))) | (~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | (s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)) = s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 (~(((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | (s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)) = s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 ((p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[97, 57])).
% 0.20/0.49 tff(99,plain,
% 0.20/0.49 (((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | (s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)) = s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 ((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | (s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)) = s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 ((((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | (s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)) = s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))) | (~((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | (s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)) = s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 ((((~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))) | (s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)) = s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4))))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a!5, tptp_fun_V2x_2E0_3(V0s_2E0!4, c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)), A_27a!5)), s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4), s(A_27a!5, c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a!5, tyop_2Emin_2Ebool), V0s_2E0!4)))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[102, 96])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[103, 84])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------