%------------------------------------------------------------------------------
% 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 : n015.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 2.24s 2.40s
% Output : Proof 2.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP004+1 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.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 18:04:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.24/2.40 % SZS status Theorem
% 2.24/2.40 % SZS output start Proof
% 2.24/2.40 tff(p_type, type, (
% 2.24/2.40 p: $i > $o)).
% 2.24/2.40 tff(s_type, type, (
% 2.24/2.40 s: ( $i * $i ) > $i)).
% 2.24/2.40 tff(c_2Ebool_2EIN_2E2_type, type, (
% 2.24/2.40 c_2Ebool_2EIN_2E2: ( $i * $i ) > $i)).
% 2.24/2.40 tff(c_2Epred__set_2EDELETE_2E2_type, type, (
% 2.24/2.40 c_2Epred__set_2EDELETE_2E2: ( $i * $i ) > $i)).
% 2.24/2.40 tff(c_2Epred__set_2ECHOICE_2E1_type, type, (
% 2.24/2.40 c_2Epred__set_2ECHOICE_2E1: $i > $i)).
% 2.24/2.40 tff(tptp_fun_V0s_2E0_4_type, type, (
% 2.24/2.40 tptp_fun_V0s_2E0_4: $i)).
% 2.24/2.40 tff(tyop_2Emin_2Efun_type, type, (
% 2.24/2.40 tyop_2Emin_2Efun: ( $i * $i ) > $i)).
% 2.24/2.40 tff(tyop_2Emin_2Ebool_type, type, (
% 2.24/2.40 tyop_2Emin_2Ebool: $i)).
% 2.24/2.40 tff(tptp_fun_A_27a_5_type, type, (
% 2.24/2.40 tptp_fun_A_27a_5: $i)).
% 2.24/2.40 tff(tptp_fun_V2x_2E0_3_type, type, (
% 2.24/2.40 tptp_fun_V2x_2E0_3: ( $i * $i * $i ) > $i)).
% 2.24/2.40 tff(c_2Epred__set_2EREST_2E1_type, type, (
% 2.24/2.40 c_2Epred__set_2EREST_2E1: $i > $i)).
% 2.24/2.40 tff(c_2Emin_2E_3D_2E2_type, type, (
% 2.24/2.40 c_2Emin_2E_3D_2E2: ( $i * $i ) > $i)).
% 2.24/2.40 tff(c_2Ebool_2ET_2E0_type, type, (
% 2.24/2.40 c_2Ebool_2ET_2E0: $i)).
% 2.24/2.40 tff(c_2Epred__set_2ESUBSET_2E2_type, type, (
% 2.24/2.40 c_2Epred__set_2ESUBSET_2E2: ( $i * $i ) > $i)).
% 2.24/2.40 tff(1,plain,
% 2.24/2.40 (^[A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : rewrite((~((~((~p(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: $i] : (p(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(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(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(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(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(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(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(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(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: $i] : (p(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(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))))))),
% 2.24/2.40 inference(bind,[status(th)],[])).
% 2.24/2.40 tff(2,plain,
% 2.24/2.40 (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(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: $i] : (p(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(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(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(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(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: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~(p(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(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(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(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: $i] : (p(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(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))),
% 2.24/2.40 inference(quant_intro,[status(thm)],[1])).
% 2.24/2.40 tff(3,plain,
% 2.24/2.40 (^[A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : refl((~((~((~p(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: $i] : (p(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(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(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(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(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(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: $i] : (p(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(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(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(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(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))))))))))))),
% 2.24/2.40 inference(bind,[status(th)],[])).
% 2.24/2.40 tff(4,plain,
% 2.24/2.40 (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(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: $i] : (p(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(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(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(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(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: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(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: $i] : (p(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(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(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(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(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)))))))))))),
% 2.24/2.40 inference(quant_intro,[status(thm)],[3])).
% 2.24/2.40 tff(5,plain,
% 2.24/2.40 (^[A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : rewrite((~((~((~p(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: $i] : (p(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(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(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(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(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(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: $i] : (p(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(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(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(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(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))))))))))))),
% 2.24/2.40 inference(bind,[status(th)],[])).
% 2.24/2.40 tff(6,plain,
% 2.24/2.40 (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(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: $i] : (p(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(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(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(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(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: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(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: $i] : (p(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(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(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(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(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)))))))))))),
% 2.24/2.40 inference(quant_intro,[status(thm)],[5])).
% 2.24/2.40 tff(7,plain,
% 2.24/2.40 (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(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: $i] : (p(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(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(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(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(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: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(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: $i] : (p(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(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(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(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(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)))))))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[6, 4])).
% 2.24/2.40 tff(8,plain,
% 2.24/2.40 (^[A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : trans(monotonicity(rewrite(((~p(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: $i] : (p(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(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(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: $i] : (p(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(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(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: $i] : (p(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(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(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(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(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(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: $i] : (p(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(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(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(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(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(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: $i] : (p(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(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(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(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(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(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: $i] : (p(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(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(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(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(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(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: $i] : (p(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(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(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(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(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(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: $i] : (p(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(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(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(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(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)))))))))))))),
% 2.24/2.40 inference(bind,[status(th)],[])).
% 2.24/2.40 tff(9,plain,
% 2.24/2.40 (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (((~p(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: $i] : (p(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(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(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(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(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: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(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: $i] : (p(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(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(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(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(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)))))))))))),
% 2.24/2.40 inference(quant_intro,[status(thm)],[8])).
% 2.24/2.40 tff(10,plain,
% 2.24/2.40 (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (p(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: $i] : (p(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(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: $i, V0s_2E0: $i, V1t_2E0: $i] : (p(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: $i] : (p(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(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(11,plain,
% 2.24/2.40 (^[A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : rewrite((p(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: $i] : (p(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(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(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: $i] : (p(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(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))),
% 2.24/2.40 inference(bind,[status(th)],[])).
% 2.24/2.40 tff(12,plain,
% 2.24/2.40 (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (p(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: $i] : (p(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(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: $i, V0s_2E0: $i, V1t_2E0: $i] : (p(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: $i] : (p(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(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))),
% 2.24/2.40 inference(quant_intro,[status(thm)],[11])).
% 2.24/2.40 tff(13,axiom,(![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (p(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: $i] : (p(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(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/sandbox/benchmark/theBenchmark.p','thm_2Epred__set_2ESUBSET__DEF')).
% 2.24/2.40 tff(14,plain,
% 2.24/2.40 (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (p(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: $i] : (p(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(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 2.24/2.40 tff(15,plain,
% 2.24/2.40 (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (p(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: $i] : (p(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(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0)))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[14, 10])).
% 2.24/2.40 tff(16,plain,(
% 2.24/2.40 ![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (((~p(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: $i] : (p(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(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(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(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(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)))))))))),
% 2.24/2.40 inference(skolemize,[status(sab)],[15])).
% 2.24/2.40 tff(17,plain,
% 2.24/2.40 (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(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: $i] : (p(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(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(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(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(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)))))))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[16, 9])).
% 2.24/2.40 tff(18,plain,
% 2.24/2.40 (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~((~p(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: $i] : (p(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(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(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(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(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)))))))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[17, 7])).
% 2.24/2.40 tff(19,plain,
% 2.24/2.40 (![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~(p(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(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(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(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: $i] : (p(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(s(tyop_2Emin_2Ebool, c_2Ebool_2EIN_2E2(s(A_27a, V2x_2E0), s(tyop_2Emin_2Efun(A_27a, tyop_2Emin_2Ebool), V0s_2E0))))))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[18, 2])).
% 2.24/2.40 tff(20,plain,
% 2.24/2.40 (((~![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~(p(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(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(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(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: $i] : (p(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(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(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: $i] : (p(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(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(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(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(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: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~(p(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(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(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(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: $i] : (p(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(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(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: $i] : (p(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(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(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(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(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))))))))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(21,plain,
% 2.24/2.40 ((~((~(p(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(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(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(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: $i] : (p(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(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(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: $i] : (p(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(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(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(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(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)))))))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(22,plain,
% 2.24/2.40 (((~![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~(p(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(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(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(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: $i] : (p(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(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(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(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(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(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: $i] : (p(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(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: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~(p(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(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(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(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: $i] : (p(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(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(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: $i] : (p(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(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(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(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(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))))))))))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[21])).
% 2.24/2.41 tff(23,plain,
% 2.24/2.41 (((~![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~(p(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(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(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(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: $i] : (p(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(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(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(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(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(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: $i] : (p(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(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: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~(p(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(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(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(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: $i] : (p(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(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(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: $i] : (p(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(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(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(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(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))))))))))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[22, 20])).
% 2.24/2.41 tff(24,plain,
% 2.24/2.41 ((~![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~(p(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(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(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(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: $i] : (p(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(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(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(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(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(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: $i] : (p(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(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))))))))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(25,plain,
% 2.24/2.41 ((~![A_27a: $i, V0s_2E0: $i, V1t_2E0: $i] : (~((~(p(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(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(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(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: $i] : (p(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(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(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: $i] : (p(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(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(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(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(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)))))))))))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 2.24/2.41 tff(26,plain,
% 2.24/2.41 (~((~((~p(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: $i] : (p(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(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(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(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(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))))))))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[25, 19])).
% 2.24/2.41 tff(27,plain,
% 2.24/2.41 (((~((~p(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: $i] : (p(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(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(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(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(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(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(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(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))))))))))),
% 2.24/2.41 inference(tautology,[status(thm)],[])).
% 2.24/2.41 tff(28,plain,
% 2.24/2.41 (p(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(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(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)))))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[27, 26])).
% 2.24/2.41 tff(29,plain,
% 2.24/2.41 ((~![A_27a: $i, V0s_2E0: $i] : p(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: $i, V0s_2E0: $i] : p(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)))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(30,axiom,(~![A_27a: $i, V0s_2E0: $i] : p(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/sandbox/benchmark/theBenchmark.p','thm_2Epred__set_2EREST__SUBSET')).
% 2.24/2.41 tff(31,plain,
% 2.24/2.41 (~![A_27a: $i, V0s_2E0: $i] : p(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))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 2.24/2.41 tff(32,plain,
% 2.24/2.41 (~![A_27a: $i, V0s_2E0: $i] : p(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))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[31, 29])).
% 2.24/2.41 tff(33,plain,
% 2.24/2.41 (~![A_27a: $i, V0s_2E0: $i] : p(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))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[32, 29])).
% 2.24/2.41 tff(34,plain,
% 2.24/2.41 (~![A_27a: $i, V0s_2E0: $i] : p(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))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 2.24/2.41 tff(35,plain,(
% 2.24/2.41 ~p(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))))),
% 2.24/2.41 inference(skolemize,[status(sab)],[34])).
% 2.24/2.41 tff(36,plain,
% 2.24/2.41 ((~(p(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(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(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(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(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(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)))))))))),
% 2.24/2.41 inference(tautology,[status(thm)],[])).
% 2.24/2.41 tff(37,plain,
% 2.24/2.41 ((~(p(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(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(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(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(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)))))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[36, 35])).
% 2.24/2.41 tff(38,plain,
% 2.24/2.41 (~(p(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(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))))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[37, 28])).
% 2.24/2.41 tff(39,plain,
% 2.24/2.41 ((p(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(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(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))))))),
% 2.24/2.41 inference(tautology,[status(thm)],[])).
% 2.24/2.41 tff(40,plain,
% 2.24/2.41 (p(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))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[39, 38])).
% 2.24/2.41 tff(41,plain,
% 2.24/2.41 (^[A_27a: $i, V0_2E0: $i, V1_2E0: $i] : refl((p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0))) <=> (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0))))),
% 2.24/2.41 inference(bind,[status(th)],[])).
% 2.24/2.41 tff(42,plain,
% 2.24/2.41 (![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0))) <=> ![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))),
% 2.24/2.41 inference(quant_intro,[status(thm)],[41])).
% 2.24/2.41 tff(43,plain,
% 2.24/2.41 (![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0))) <=> ![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(44,axiom,(![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reserved_2Elogic_2E_3D')).
% 2.24/2.41 tff(45,plain,
% 2.24/2.41 (![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 2.24/2.41 tff(46,plain,(
% 2.24/2.41 ![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))),
% 2.24/2.41 inference(skolemize,[status(sab)],[45])).
% 2.24/2.41 tff(47,plain,
% 2.24/2.41 (![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[46, 42])).
% 2.24/2.41 tff(48,plain,
% 2.24/2.41 (((~![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))))) <=> ((~![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(49,plain,
% 2.24/2.41 ((p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> $true) <=> p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(50,plain,
% 2.24/2.41 ((s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)) <=> $true),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(51,plain,
% 2.24/2.41 ((p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> (s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))) <=> (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> $true)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[50])).
% 2.24/2.41 tff(52,plain,
% 2.24/2.41 ((p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> (s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))) <=> p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[51, 49])).
% 2.24/2.41 tff(53,plain,
% 2.24/2.41 (((~![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> (s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> ((~![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[52])).
% 2.24/2.41 tff(54,plain,
% 2.24/2.41 (((~![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> (s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> ((~![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[53, 48])).
% 2.24/2.41 tff(55,plain,
% 2.24/2.41 ((~![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> (s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(56,plain,
% 2.24/2.41 ((~![A_27a: $i, V0_2E0: $i, V1_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0)))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[55, 54])).
% 2.24/2.42 tff(57,plain,
% 2.24/2.42 (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[56, 47])).
% 2.24/2.42 tff(58,plain,
% 2.24/2.42 ((p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> p(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(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))))) | (~p(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)))))))),
% 2.24/2.42 inference(tautology,[status(thm)],[])).
% 2.24/2.42 tff(59,plain,
% 2.24/2.42 (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> p(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))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[58, 57, 40])).
% 2.24/2.42 tff(60,plain,
% 2.24/2.42 (^[V0_2E0: $i, V1_2E0: $i] : refl(((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0))) <=> ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0))))),
% 2.24/2.42 inference(bind,[status(th)],[])).
% 2.24/2.42 tff(61,plain,
% 2.24/2.42 (![V0_2E0: $i, V1_2E0: $i] : ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0))) <=> ![V0_2E0: $i, V1_2E0: $i] : ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)))),
% 2.24/2.42 inference(quant_intro,[status(thm)],[60])).
% 2.24/2.42 tff(62,plain,
% 2.24/2.42 (![V0_2E0: $i, V1_2E0: $i] : ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0))) <=> ![V0_2E0: $i, V1_2E0: $i] : ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(63,plain,
% 2.24/2.42 (^[V0_2E0: $i, V1_2E0: $i] : rewrite(((p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))) => (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0))) <=> ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0))))),
% 2.24/2.42 inference(bind,[status(th)],[])).
% 2.24/2.42 tff(64,plain,
% 2.24/2.42 (![V0_2E0: $i, V1_2E0: $i] : ((p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))) => (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0))) <=> ![V0_2E0: $i, V1_2E0: $i] : ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)))),
% 2.24/2.42 inference(quant_intro,[status(thm)],[63])).
% 2.24/2.42 tff(65,axiom,(![V0_2E0: $i, V1_2E0: $i] : ((p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0))) => (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reserved_2Eho_2Eboolext')).
% 2.24/2.42 tff(66,plain,
% 2.24/2.42 (![V0_2E0: $i, V1_2E0: $i] : ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 2.24/2.42 tff(67,plain,
% 2.24/2.42 (![V0_2E0: $i, V1_2E0: $i] : ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[66, 62])).
% 2.24/2.42 tff(68,plain,(
% 2.24/2.42 ![V0_2E0: $i, V1_2E0: $i] : ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)))),
% 2.24/2.42 inference(skolemize,[status(sab)],[67])).
% 2.24/2.42 tff(69,plain,
% 2.24/2.42 (![V0_2E0: $i, V1_2E0: $i] : ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[68, 61])).
% 2.24/2.42 tff(70,plain,
% 2.24/2.42 (((~![V0_2E0: $i, V1_2E0: $i] : ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)))) | ((~(p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> p(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)))))))) | (s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))) = 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)))))))) <=> ((~![V0_2E0: $i, V1_2E0: $i] : ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> p(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)))))))) | (s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))) = 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)))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(71,plain,
% 2.24/2.42 ((~![V0_2E0: $i, V1_2E0: $i] : ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)))) | ((~(p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> p(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)))))))) | (s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))) = 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)))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(72,plain,
% 2.24/2.42 ((~![V0_2E0: $i, V1_2E0: $i] : ((~(p(s(tyop_2Emin_2Ebool, V0_2E0)) <=> p(s(tyop_2Emin_2Ebool, V1_2E0)))) | (s(tyop_2Emin_2Ebool, V0_2E0) = s(tyop_2Emin_2Ebool, V1_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> p(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)))))))) | (s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))) = 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))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[71, 70])).
% 2.24/2.42 tff(73,plain,
% 2.24/2.42 (s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))) = 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)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[72, 69, 59])).
% 2.24/2.42 tff(74,plain,
% 2.24/2.42 (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))))) = s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))),
% 2.24/2.42 inference(symmetry,[status(thm)],[73])).
% 2.24/2.42 tff(75,plain,
% 2.24/2.42 (![A_27a: $i, V0s_2E0: $i] : (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: $i, V0s_2E0: $i] : (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))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(76,plain,
% 2.24/2.42 (^[A_27a: $i, V0s_2E0: $i] : 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)))))))),
% 2.24/2.42 inference(bind,[status(th)],[])).
% 2.24/2.42 tff(77,plain,
% 2.24/2.42 (![A_27a: $i, V0s_2E0: $i] : (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: $i, V0s_2E0: $i] : (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))))))),
% 2.24/2.42 inference(quant_intro,[status(thm)],[76])).
% 2.24/2.42 tff(78,plain,
% 2.24/2.42 (![A_27a: $i, V0s_2E0: $i] : (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: $i, V0s_2E0: $i] : (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))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(79,axiom,(![A_27a: $i, V0s_2E0: $i] : (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/sandbox/benchmark/theBenchmark.p','thm_2Epred__set_2EREST__DEF')).
% 2.24/2.42 tff(80,plain,
% 2.24/2.42 (![A_27a: $i, V0s_2E0: $i] : (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))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[79, 78])).
% 2.24/2.42 tff(81,plain,(
% 2.24/2.42 ![A_27a: $i, V0s_2E0: $i] : (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))))))),
% 2.24/2.42 inference(skolemize,[status(sab)],[80])).
% 2.24/2.42 tff(82,plain,
% 2.24/2.42 (![A_27a: $i, V0s_2E0: $i] : (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))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[81, 77])).
% 2.24/2.42 tff(83,plain,
% 2.24/2.42 (![A_27a: $i, V0s_2E0: $i] : (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))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[82, 75])).
% 2.24/2.42 tff(84,plain,
% 2.24/2.42 ((~![A_27a: $i, V0s_2E0: $i] : (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))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(85,plain,
% 2.24/2.42 (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)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[84, 83])).
% 2.24/2.42 tff(86,plain,
% 2.24/2.42 (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)))),
% 2.24/2.42 inference(symmetry,[status(thm)],[85])).
% 2.24/2.42 tff(87,plain,
% 2.24/2.42 (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))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[86])).
% 2.24/2.42 tff(88,plain,
% 2.24/2.42 (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)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[87])).
% 2.24/2.42 tff(89,plain,
% 2.24/2.42 (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_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))),
% 2.24/2.42 inference(transitivity,[status(thm)],[88, 74])).
% 2.24/2.42 tff(90,plain,
% 2.24/2.42 (p(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(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[89])).
% 2.24/2.42 tff(91,plain,
% 2.24/2.42 (p(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)))) <=> p(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))))))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[90])).
% 2.24/2.42 tff(92,plain,
% 2.24/2.42 (p(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))))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[57, 91])).
% 2.24/2.42 tff(93,plain,
% 2.24/2.42 (^[A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : refl((~(((~p(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(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(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(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)))))))))),
% 2.24/2.42 inference(bind,[status(th)],[])).
% 2.24/2.42 tff(94,plain,
% 2.24/2.42 (![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (~(((~p(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(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: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (~(((~p(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(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))))))))),
% 2.24/2.42 inference(quant_intro,[status(thm)],[93])).
% 2.24/2.42 tff(95,plain,
% 2.24/2.42 (^[A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : trans(trans(monotonicity(rewrite((p(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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))))))))))),
% 2.24/2.42 inference(bind,[status(th)],[])).
% 2.24/2.42 tff(96,plain,
% 2.24/2.42 (![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(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(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: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (~(((~p(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(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))))))))),
% 2.24/2.42 inference(quant_intro,[status(thm)],[95])).
% 2.24/2.42 tff(97,plain,
% 2.24/2.42 (![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(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(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: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(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(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)))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(98,axiom,(![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(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(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/sandbox/benchmark/theBenchmark.p','thm_2Epred__set_2EIN__DELETE')).
% 2.24/2.42 tff(99,plain,
% 2.24/2.42 (![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(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(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)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[98, 97])).
% 2.24/2.42 tff(100,plain,(
% 2.24/2.42 ![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (p(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(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)))))),
% 2.24/2.42 inference(skolemize,[status(sab)],[99])).
% 2.24/2.42 tff(101,plain,
% 2.24/2.42 (![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (~(((~p(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(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))))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[100, 96])).
% 2.24/2.42 tff(102,plain,
% 2.24/2.42 (![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (~(((~p(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(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))))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[101, 94])).
% 2.24/2.42 tff(103,plain,
% 2.24/2.42 ((~![A_27a: $i, V0s_2E0: $i, V1x_2E0: $i, V2y_2E0: $i] : (~(((~p(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(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(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(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))))))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(104,plain,
% 2.24/2.42 (~(((~p(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(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)))))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[103, 102])).
% 2.24/2.42 tff(105,plain,
% 2.24/2.42 ((p(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(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(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)))))),
% 2.24/2.42 inference(tautology,[status(thm)],[])).
% 2.24/2.42 tff(106,plain,
% 2.24/2.42 (~p(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))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[105, 38])).
% 2.24/2.42 tff(107,plain,
% 2.24/2.42 (((~p(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(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))))),
% 2.24/2.42 inference(tautology,[status(thm)],[])).
% 2.24/2.42 tff(108,plain,
% 2.24/2.42 ((~p(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))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[107, 106])).
% 2.24/2.42 tff(109,plain,
% 2.24/2.42 ((((~p(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(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(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(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)))))))))),
% 2.24/2.42 inference(tautology,[status(thm)],[])).
% 2.24/2.42 tff(110,plain,
% 2.24/2.42 ((((~p(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(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(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)))))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[109, 108])).
% 2.24/2.42 tff(111,plain,
% 2.24/2.42 (~p(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))))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[110, 104])).
% 2.24/2.43 tff(112,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[111, 92])).
% 2.24/2.43 % SZS output end Proof
% 2.28/2.45 % E exiting
%------------------------------------------------------------------------------