%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP004_1 : TPTP v9.2.1. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n016.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 : Wed Jun 3 08:24:23 AM UTC 2026 % Result : Theorem 0.38s 0.61s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP004_1 : TPTP v9.2.1. Bugfixed v7.5.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.33 % Computer : n016.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 03:37:24 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.61 % SZS status Theorem % 0.38/0.61 % SZS output start Proof % 0.38/0.61 ( % 0.38/0.61 (declare-sort tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 0) % 0.38/0.61 (declare-sort tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 0) % 0.38/0.61 (declare-sort tptp.mono_2Etyop_2Emin_2Ebool 0) % 0.38/0.61 (declare-sort tptp.d 0) % 0.38/0.61 (declare-sort tptp.u 0) % 0.38/0.61 (declare-sort tptp.du 0) % 0.38/0.61 (declare-const tptp.mono_2Ec_2Ebool_2E_7E_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) % 0.38/0.61 (declare-const tptp.mono_2Ec_2Ebool_2E_5C_2F_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) % 0.38/0.61 (declare-const tptp.c_2Epred__set_2ESUBSET_2E2 (-> tptp.du tptp.du tptp.u)) % 0.38/0.61 (declare-const tptp.c_2Epred__set_2ESUBSET_2E0 tptp.u) % 0.38/0.61 (declare-const tptp.c_2Epred__set_2EREST_2E1 (-> tptp.du tptp.u)) % 0.38/0.61 (declare-const tptp.c_2Epred__set_2EREST_2E0 tptp.u) % 0.38/0.61 (declare-const tptp.c_2Ebool_2EIN_2E2 (-> tptp.du tptp.du tptp.u)) % 0.38/0.61 (declare-const tptp.c_2Ebool_2EIN_2E0 tptp.u) % 0.38/0.61 (declare-const tptp.c_2Epred__set_2EDELETE_2E2 (-> tptp.du tptp.du tptp.u)) % 0.38/0.61 (declare-const tptp.c_2Epred__set_2EDELETE_2E0 tptp.u) % 0.38/0.61 (declare-const tptp.c_2Epred__set_2ECHOICE_2E1 (-> tptp.du tptp.u)) % 0.38/0.61 (declare-const tptp.c_2Epred__set_2ECHOICE_2E0 tptp.u) % 0.38/0.61 (declare-const tptp.c_2Ebool_2E_3F_2E0 tptp.u) % 0.38/0.61 (declare-const tptp.mono_2Ec_2Ebool_2E_5C_2F_2E2 (-> tptp.mono_2Etyop_2Emin_2Ebool tptp.mono_2Etyop_2Emin_2Ebool tptp.mono_2Etyop_2Emin_2Ebool)) % 0.38/0.61 (declare-const tptp.c_2Ebool_2E_3F_2E1 (-> tptp.du tptp.u)) % 0.38/0.61 (declare-const tptp.combin_s_2E0 tptp.u) % 0.38/0.61 (declare-const tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool (-> tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 tptp.mono_2Etyop_2Emin_2Ebool tptp.mono_2Etyop_2Emin_2Ebool)) % 0.38/0.61 (declare-const tptp.combin_i_2E0 tptp.u) % 0.38/0.61 (declare-const tptp.mono_2Ec_2Ebool_2EF_2E0 tptp.mono_2Etyop_2Emin_2Ebool) % 0.38/0.61 (declare-const tptp.combin_k_2E0 tptp.u) % 0.38/0.61 (declare-const tptp.mono_2Ec_2Ebool_2ET_2E0 tptp.mono_2Etyop_2Emin_2Ebool) % 0.38/0.61 (declare-const tptp.mono_2Ec_2Emin_2E_3D_3D_3E_2E2 (-> tptp.mono_2Etyop_2Emin_2Ebool tptp.mono_2Etyop_2Emin_2Ebool tptp.mono_2Etyop_2Emin_2Ebool)) % 0.38/0.61 (declare-const tptp.c_2Emin_2E_3D_2E2 (-> tptp.du tptp.du tptp.u)) % 0.38/0.61 (declare-const tptp.p (-> tptp.mono_2Etyop_2Emin_2Ebool Bool)) % 0.38/0.61 (declare-const tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (-> tptp.du tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29)) % 0.38/0.61 (declare-const tptp.mono_2Ec_2Ebool_2E_2F_5C_2E2 (-> tptp.mono_2Etyop_2Emin_2Ebool tptp.mono_2Etyop_2Emin_2Ebool tptp.mono_2Etyop_2Emin_2Ebool)) % 0.38/0.61 (declare-const tptp.app_2E2 (-> tptp.du tptp.du tptp.u)) % 0.38/0.61 (declare-const tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (-> tptp.du tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29)) % 0.38/0.61 (declare-const tptp.s (-> tptp.d tptp.u tptp.du)) % 0.38/0.61 (declare-const tptp.j_mono_2Etyop_2Emin_2Ebool (-> tptp.du tptp.mono_2Etyop_2Emin_2Ebool)) % 0.38/0.61 (declare-const tptp.mono_2Ec_2Ebool_2E_7E_2E1 (-> tptp.mono_2Etyop_2Emin_2Ebool tptp.mono_2Etyop_2Emin_2Ebool)) % 0.38/0.61 (declare-const tptp.tyop_2Emin_2Efun (-> tptp.d tptp.d tptp.d)) % 0.38/0.61 (declare-const tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (-> tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 tptp.u)) % 0.38/0.61 (declare-const tptp.tyop_2Emin_2Ebool tptp.d) % 0.38/0.61 (declare-const tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (-> tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 tptp.u)) % 0.38/0.61 (declare-const tptp.c_2Ebool_2E_21_2E1 (-> tptp.du tptp.u)) % 0.38/0.61 (declare-const tptp.mono_2Ec_2Ebool_2E_2F_5C_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) % 0.38/0.61 (declare-const tptp.i_mono_2Etyop_2Emin_2Ebool (-> tptp.mono_2Etyop_2Emin_2Ebool tptp.u)) % 0.38/0.61 (declare-const tptp.c_2Ebool_2E_21_2E0 tptp.u) % 0.38/0.61 (declare-const tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (-> tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 tptp.mono_2Etyop_2Emin_2Ebool tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29)) % 0.38/0.61 (declare-const tptp.c_2Emin_2E_3D_2E0 tptp.u) % 0.38/0.61 (declare-const tptp.mono_2Ec_2Emin_2E_3D_3D_3E_2E0 tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) % 0.38/0.61 (define @t1 () (@var "V1g_2E0" tptp.u)) % 0.38/0.61 (define @t2 () (@var "A_27b" tptp.d)) % 0.38/0.61 (define @t3 () (@var "A_27a" tptp.d)) % 0.38/0.61 (define @t4 () (tptp.tyop_2Emin_2Efun @t3 @t2)) % 0.38/0.61 (define @t5 () (tptp.s @t4 @t1)) % 0.38/0.61 (define @t6 () (@var "V0f_2E0" tptp.u)) % 0.38/0.61 (define @t7 () (tptp.s @t4 @t6)) % 0.38/0.61 (define @t8 () (@var "V2x_2E0" tptp.u)) % 0.38/0.61 (define @t9 () (tptp.s @t3 @t8)) % 0.38/0.61 (define @t10 () (tptp.s @t2 (tptp.app_2E2 @t5 @t9))) % 0.38/0.61 (define @t11 () (@list @t8)) % 0.38/0.61 (define @t12 () (@var "V1_2E0" tptp.mono_2Etyop_2Emin_2Ebool)) % 0.38/0.61 (define @t13 () (@var "V0_2E0" tptp.mono_2Etyop_2Emin_2Ebool)) % 0.38/0.61 (define @t14 () (tptp.p @t12)) % 0.38/0.61 (define @t15 () (tptp.p @t13)) % 0.38/0.61 (define @t16 () (@list @t13 @t12)) % 0.38/0.61 (define @t17 () (@var "V0t_2E0" tptp.mono_2Etyop_2Emin_2Ebool)) % 0.38/0.61 (define @t18 () (@var "V0x_2E0" tptp.u)) % 0.38/0.61 (define @t19 () (tptp.s @t3 @t18)) % 0.38/0.61 (define @t20 () (@var "V1y_2E0" tptp.u)) % 0.38/0.61 (define @t21 () (tptp.tyop_2Emin_2Efun @t2 @t3)) % 0.38/0.61 (define @t22 () (@var "A_27c" tptp.d)) % 0.38/0.61 (define @t23 () (tptp.tyop_2Emin_2Efun @t2 @t22)) % 0.38/0.61 (define @t24 () (tptp.tyop_2Emin_2Efun @t3 @t23)) % 0.38/0.61 (define @t25 () (tptp.s @t24 @t6)) % 0.38/0.61 (define @t26 () (tptp.tyop_2Emin_2Efun @t3 @t22)) % 0.38/0.61 (define @t27 () (tptp.tyop_2Emin_2Efun @t4 @t26)) % 0.38/0.61 (define @t28 () (@list @t13)) % 0.38/0.61 (define @t29 () (@var "V1_2E0" tptp.u)) % 0.38/0.61 (define @t30 () (tptp.s @t3 @t29)) % 0.38/0.61 (define @t31 () (@var "V0_2E0" tptp.u)) % 0.38/0.61 (define @t32 () (tptp.s @t3 @t31)) % 0.38/0.61 (define @t33 () (@var "V1x_2E0" tptp.u)) % 0.38/0.61 (define @t34 () (tptp.s @t3 @t33)) % 0.38/0.61 (define @t35 () (tptp.tyop_2Emin_2Efun @t3 tptp.tyop_2Emin_2Ebool)) % 0.38/0.61 (define @t36 () (tptp.s @t35 @t6)) % 0.38/0.61 (define @t37 () (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t36 @t34))))) % 0.38/0.61 (define @t38 () (@list @t33)) % 0.38/0.61 (define @t39 () (@list @t3 @t6)) % 0.38/0.61 (define @t40 () (tptp.s tptp.tyop_2Emin_2Ebool @t31)) % 0.38/0.61 (define @t41 () (@list @t31)) % 0.38/0.61 (define @t42 () (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool)) % 0.38/0.61 (define @t43 () (tptp.s @t42 @t31)) % 0.38/0.61 (define @t44 () (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool @t42)) % 0.38/0.61 (define @t45 () (tptp.s @t44 @t31)) % 0.38/0.61 (define @t46 () (@var "V0_2E0" tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29)) % 0.38/0.61 (define @t47 () (tptp.s @t42 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @t46))) % 0.38/0.61 (define @t48 () (@var "V0_2E0" tptp.mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29)) % 0.38/0.61 (define @t49 () (tptp.s @t44 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @t48))) % 0.38/0.61 (define @t50 () (@var "X0_2E0" tptp.u)) % 0.38/0.61 (define @t51 () (tptp.s @t35 @t50)) % 0.38/0.61 (define @t52 () (tptp.tyop_2Emin_2Efun @t35 tptp.tyop_2Emin_2Ebool)) % 0.38/0.61 (define @t53 () (@list @t3 @t50)) % 0.38/0.61 (define @t54 () (@var "X1_2E0" tptp.mono_2Etyop_2Emin_2Ebool)) % 0.38/0.61 (define @t55 () (@var "X0_2E0" tptp.mono_2Etyop_2Emin_2Ebool)) % 0.38/0.61 (define @t56 () (tptp.p @t54)) % 0.38/0.61 (define @t57 () (tptp.p @t55)) % 0.38/0.61 (define @t58 () (@list @t55 @t54)) % 0.38/0.61 (define @t59 () (@var "X1_2E0" tptp.u)) % 0.38/0.61 (define @t60 () (tptp.s @t3 @t59)) % 0.38/0.61 (define @t61 () (tptp.s @t3 @t50)) % 0.38/0.61 (define @t62 () (tptp.tyop_2Emin_2Efun @t3 @t35)) % 0.38/0.61 (define @t63 () (@list @t3 @t50 @t59)) % 0.38/0.61 (define @t64 () (tptp.s @t35 @t59)) % 0.38/0.61 (define @t65 () (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool @t12))) % 0.38/0.61 (define @t66 () (@var "V1t_2E0" tptp.u)) % 0.38/0.61 (define @t67 () (tptp.s @t35 @t66)) % 0.38/0.61 (define @t68 () (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EIN_2E2 @t9 @t67))))) % 0.38/0.61 (define @t69 () (@var "V0s_2E0" tptp.u)) % 0.38/0.61 (define @t70 () (tptp.s @t35 @t69)) % 0.38/0.61 (define @t71 () (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EIN_2E2 @t9 @t70))))) % 0.38/0.61 (define @t72 () (forall @t11 (=> @t71 @t68))) % 0.38/0.61 (define @t73 () (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Epred__set_2ESUBSET_2E2 @t70 @t67))))) % 0.38/0.61 (define @t74 () (= @t73 @t72)) % 0.38/0.61 (define @t75 () (forall (@list @t3 @t69 @t66) @t74)) % 0.38/0.61 (define @t76 () (@var "V2y_2E0" tptp.u)) % 0.38/0.61 (define @t77 () (tptp.s @t3 @t76)) % 0.38/0.61 (define @t78 () (forall (@list @t3 @t69 @t33 @t76) (= (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EIN_2E2 @t34 (tptp.s @t35 (tptp.c_2Epred__set_2EDELETE_2E2 @t70 @t77)))))) (and (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EIN_2E2 @t34 @t70)))) (not (= @t34 @t77)))))) % 0.38/0.61 (define @t79 () (tptp.s @t35 (tptp.c_2Epred__set_2EREST_2E1 @t70))) % 0.38/0.61 (define @t80 () (@list @t3 @t69)) % 0.38/0.61 (define @t81 () (forall @t80 (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Epred__set_2ESUBSET_2E2 @t79 @t70)))))) % 0.38/0.61 (define @t82 () (@quantifiers_skolemize @t81 1)) % 0.38/0.61 (define @t83 () (@quantifiers_skolemize @t81 0)) % 0.38/0.61 (define @t84 () (tptp.tyop_2Emin_2Efun @t83 tptp.tyop_2Emin_2Ebool)) % 0.38/0.61 (define @t85 () (tptp.s @t84 @t82)) % 0.38/0.61 (define @t86 () (tptp.s @t83 @t8)) % 0.38/0.61 (define @t87 () (tptp.c_2Epred__set_2EREST_2E1 @t85)) % 0.38/0.61 (define @t88 () (tptp.s @t84 @t87)) % 0.38/0.61 (define @t89 () (forall @t11 (or (not (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EIN_2E2 @t86 @t88))))) (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EIN_2E2 @t86 @t85))))))) % 0.38/0.61 (define @t90 () (@quantifiers_skolemize @t89 0)) % 0.38/0.61 (define @t91 () (tptp.s @t83 @t90)) % 0.38/0.61 (define @t92 () (tptp.c_2Epred__set_2ECHOICE_2E1 @t85)) % 0.38/0.61 (define @t93 () (tptp.s @t83 @t92)) % 0.38/0.61 (define @t94 () (not (= @t91 @t93))) % 0.38/0.61 (define @t95 () (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EIN_2E2 @t91 @t85))))) % 0.38/0.61 (define @t96 () (and @t95 @t94)) % 0.38/0.61 (define @t97 () (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EIN_2E2 @t91 (tptp.s @t84 (tptp.c_2Epred__set_2EDELETE_2E2 @t85 @t93))))))) % 0.38/0.61 (define @t98 () (= @t97 @t96)) % 0.38/0.61 (define @t99 () (and @t95 (not (= @t93 @t91)))) % 0.38/0.61 (define @t100 () (= @t97 @t99)) % 0.38/0.61 (define @t101 () (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Epred__set_2ESUBSET_2E2 @t88 @t85))))) % 0.38/0.61 (define @t102 () (= @t101 @t89)) % 0.38/0.61 (define @t103 () (not @t89)) % 0.38/0.61 (define @t104 () (@list true false)) % 0.38/0.61 (define @t105 () (tptp.c_2Ebool_2EIN_2E2 @t91 @t88)) % 0.38/0.61 (define @t106 () (tptp.s tptp.tyop_2Emin_2Ebool @t105)) % 0.38/0.61 (define @t107 () (tptp.j_mono_2Etyop_2Emin_2Ebool @t106)) % 0.38/0.61 (define @t108 () (tptp.p @t107)) % 0.38/0.61 (define @t109 () (not @t108)) % 0.38/0.61 (define @t110 () (or @t109 @t95)) % 0.38/0.61 (define @t111 () (@list true)) % 0.38/0.61 (define @t112 () (@list @t110)) % 0.38/0.61 (define @t113 () (not @t99)) % 0.38/0.61 (define @t114 () (not @t97)) % 0.38/0.61 (assume @p1 (forall (@list @t3 @t2 @t6 @t1) (=> (forall @t11 (= (tptp.s @t2 (tptp.app_2E2 @t7 @t9)) @t10)) (= @t7 @t5)))) % 0.38/0.61 (assume @p2 (forall @t16 (=> (= @t15 @t14) (= @t13 @t12)))) % 0.38/0.61 (assume @p3 (tptp.p tptp.mono_2Ec_2Ebool_2ET_2E0)) % 0.38/0.61 (assume @p4 (not (tptp.p tptp.mono_2Ec_2Ebool_2EF_2E0))) % 0.38/0.61 (assume @p5 (forall (@list @t17) (or (= @t17 tptp.mono_2Ec_2Ebool_2ET_2E0) (= @t17 tptp.mono_2Ec_2Ebool_2EF_2E0)))) % 0.38/0.61 (assume @p6 (forall (@list @t3 @t18) (= (tptp.s @t3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t3 @t3) tptp.combin_i_2E0) @t19)) @t19))) % 0.38/0.61 (assume @p7 (forall (@list @t3 @t2 @t18 @t20) (= (tptp.s @t3 (tptp.app_2E2 (tptp.s @t21 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t3 @t21) tptp.combin_k_2E0) @t19)) (tptp.s @t2 @t20))) @t19))) % 0.38/0.61 (assume @p8 (forall (@list @t3 @t2 @t22 @t6 @t1 @t8) (= (tptp.s @t22 (tptp.app_2E2 (tptp.s @t26 (tptp.app_2E2 (tptp.s @t27 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t24 @t27) tptp.combin_s_2E0) @t25)) @t5)) @t9)) (tptp.s @t22 (tptp.app_2E2 (tptp.s @t23 (tptp.app_2E2 @t25 @t9)) @t10))))) % 0.38/0.61 (assume @p9 (forall @t16 (= (tptp.p (tptp.mono_2Ec_2Ebool_2E_2F_5C_2E2 @t13 @t12)) (and @t15 @t14)))) % 0.38/0.61 (assume @p10 (forall @t16 (= (tptp.p (tptp.mono_2Ec_2Ebool_2E_5C_2F_2E2 @t13 @t12)) (or @t15 @t14)))) % 0.38/0.61 (assume @p11 (forall @t28 (= (tptp.p (tptp.mono_2Ec_2Ebool_2E_7E_2E1 @t13)) (not @t15)))) % 0.38/0.61 (assume @p12 (forall @t16 (= (tptp.p (tptp.mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @t13 @t12)) (=> @t15 @t14)))) % 0.38/0.61 (assume @p13 (forall (@list @t3 @t31 @t29) (= (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Emin_2E_3D_2E2 @t32 @t30)))) (= @t32 @t30)))) % 0.38/0.61 (assume @p14 (forall @t39 (= (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_21_2E1 @t36)))) (forall @t38 @t37)))) % 0.38/0.61 (assume @p15 (forall @t39 (= (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_3F_2E1 @t36)))) (exists @t38 @t37)))) % 0.38/0.61 (assume @p16 (forall @t41 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool (tptp.j_mono_2Etyop_2Emin_2Ebool @t40))) @t40))) % 0.38/0.61 (assume @p17 (forall @t41 (= (tptp.s @t42 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @t43))) @t43))) % 0.38/0.61 (assume @p18 (forall @t41 (= (tptp.s @t44 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @t45))) @t45))) % 0.38/0.61 (assume @p19 (forall @t28 (= (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool @t13))) @t13))) % 0.38/0.61 (assume @p20 (forall (@list @t46) (= (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @t47) @t46))) % 0.38/0.61 (assume @p21 (forall (@list @t48) (= (tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @t49) @t48))) % 0.38/0.61 (assume @p22 (forall @t53 (= (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_21_2E1 @t51))) (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t52 tptp.c_2Ebool_2E_21_2E0) @t51)))))) % 0.38/0.61 (assume @p23 (forall @t58 (= (and @t57 @t56) (tptp.p (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 tptp.mono_2Ec_2Ebool_2E_2F_5C_2E0 @t55) @t54))))) % 0.38/0.61 (assume @p24 (forall @t63 (= (= @t61 @t60) (tptp.p (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t35 (tptp.app_2E2 (tptp.s @t62 tptp.c_2Emin_2E_3D_2E0) @t61)) @t60))))))) % 0.38/0.61 (assume @p25 (forall @t58 (= (=> @t57 @t56) (tptp.p (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 tptp.mono_2Ec_2Emin_2E_3D_3D_3E_2E0 @t55) @t54))))) % 0.38/0.61 (assume @p26 (forall @t53 (= (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_3F_2E1 @t51))) (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t52 tptp.c_2Ebool_2E_3F_2E0) @t51)))))) % 0.38/0.61 (assume @p27 (forall @t53 (= (tptp.s @t3 (tptp.c_2Epred__set_2ECHOICE_2E1 @t51)) (tptp.s @t3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t35 @t3) tptp.c_2Epred__set_2ECHOICE_2E0) @t51))))) % 0.38/0.61 (assume @p28 (forall @t63 (= (tptp.s @t35 (tptp.c_2Epred__set_2EDELETE_2E2 @t51 @t60)) (tptp.s @t35 (tptp.app_2E2 (tptp.s @t62 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t35 @t62) tptp.c_2Epred__set_2EDELETE_2E0) @t51)) @t60))))) % 0.38/0.61 (assume @p29 (forall @t63 (= (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EIN_2E2 @t61 @t64))) (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t52 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t3 @t52) tptp.c_2Ebool_2EIN_2E0) @t61)) @t64)))))) % 0.38/0.61 (assume @p30 (forall @t53 (= (tptp.s @t35 (tptp.c_2Epred__set_2EREST_2E1 @t51)) (tptp.s @t35 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t35 @t35) tptp.c_2Epred__set_2EREST_2E0) @t51))))) % 0.38/0.61 (assume @p31 (forall @t63 (= (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Epred__set_2ESUBSET_2E2 @t51 @t64))) (tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t52 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t35 @t52) tptp.c_2Epred__set_2ESUBSET_2E0) @t51)) @t64)))))) % 0.38/0.61 (assume @p32 (forall @t58 (= (or @t57 @t56) (tptp.p (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 tptp.mono_2Ec_2Ebool_2E_5C_2F_2E0 @t55) @t54))))) % 0.38/0.61 (assume @p33 (forall (@list @t55) (= (not @t57) (tptp.p (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool tptp.mono_2Ec_2Ebool_2E_7E_2E0 @t55))))) % 0.38/0.61 (assume @p34 (forall (@list @t46 @t12) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.i_mono_2Etyop_2Emin_2Ebool (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @t46 @t12))) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t47 @t65))))) % 0.38/0.61 (assume @p35 (forall (@list @t48 @t12) (= (tptp.s @t42 (tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (tptp.mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @t48 @t12))) (tptp.s @t42 (tptp.app_2E2 @t49 @t65))))) % 0.38/0.61 (assume @p36 @t75) % 0.38/0.61 (assume @p37 @t78) % 0.38/0.61 (assume @p38 (forall @t80 (= @t79 (tptp.s @t35 (tptp.c_2Epred__set_2EDELETE_2E2 @t70 (tptp.s @t3 (tptp.c_2Epred__set_2ECHOICE_2E1 @t70))))))) % 0.38/0.61 (assume @p39 (not @t81)) % 0.38/0.61 (assume @p40 true) % 0.38/0.61 (step @p41 :rule evaluate :args ((= true false))) % 0.38/0.61 (step @p42 :rule eq-symm :args (@t91 @t93)) % 0.38/0.61 (step @p43 :rule cong :premises (@p42) :args (@t94)) % 0.38/0.61 (step @p44 :rule refl :args (@t95)) % 0.38/0.61 (step @p45 :rule nary_cong :premises (@p44 @p43) :args (@t96)) % 0.38/0.61 (step @p46 :rule refl :args (@t97)) % 0.38/0.61 (step @p47 :rule cong :premises (@p46 @p45) :args (@t98)) % 0.38/0.61 (step @p48 :rule refl :args (@t78)) % 0.38/0.61 (step @p49 :rule cong :premises (@p48 @p47) :args ((=> @t78 @t98))) % 0.38/0.61 (assume-push @p96 @t78) % 0.38/0.61 (step @p51 :rule instantiate :premises (@p37) :args ((@list @t83 @t82 @t90 @t92))) % 0.38/0.61 (step-pop @p97 :rule scope :premises (@p51)) % 0.38/0.61 (step @p52 :rule process_scope :premises (@p97) :args (@t98)) % 0.38/0.61 (step @p54 :rule eq_resolve :premises (@p52 @p49)) % 0.38/0.61 (step @p55 :rule implies_elim :premises (@p54)) % 0.38/0.61 (step @p56 :rule chain_m_resolution :premises (@p55 @p37) :args (@t100 (@list false) (@list @t78))) % 0.38/0.61 (step @p57 :rule bool-impl-elim :args (@t71 @t68)) % 0.38/0.61 (step @p58 :rule cong :premises (@p57) :args (@t72)) % 0.38/0.61 (step @p59 :rule refl :args (@t73)) % 0.38/0.61 (step @p60 :rule cong :premises (@p59 @p58) :args (@t74)) % 0.38/0.61 (step @p61 :rule cong :premises (@p60) :args (@t75)) % 0.38/0.61 (step @p62 :rule eq_resolve :premises (@p36 @p61)) % 0.38/0.61 (step @p63 :rule instantiate :premises (@p62) :args ((@list @t83 @t87 @t82))) % 0.38/0.61 (step @p64 :rule skolemize :premises (@p39)) % 0.38/0.61 (step @p65 :rule cnf_equiv_pos2 :args (@t102)) % 0.38/0.61 (step @p66 :rule reordering :premises (@p65) :args ((or @t101 @t103 (not @t102)))) % 0.38/0.61 (step @p67 :rule chain_m_resolution :premises (@p66 @p64 @p63) :args (@t103 @t104 (@list @t101 @t102))) % 0.38/0.61 (step @p68 :rule skolemize :premises (@p67)) % 0.38/0.61 (step @p69 :rule cnf_or_neg :args (@t110 1)) % 0.38/0.61 (step @p70 :rule chain_m_resolution :premises (@p69 @p68) :args ((not @t95) @t111 @t112)) % 0.38/0.61 (step @p71 :rule cnf_and_pos :args (@t99 0)) % 0.38/0.61 (step @p72 :rule reordering :premises (@p71) :args ((or @t95 @t113))) % 0.38/0.61 (step @p73 :rule chain_m_resolution :premises (@p72 @p70) :args (@t113 @t111 (@list @t95))) % 0.38/0.61 (step @p74 :rule cnf_equiv_pos1 :args (@t100)) % 0.38/0.61 (step @p75 :rule reordering :premises (@p74) :args ((or @t99 @t114 (not @t100)))) % 0.38/0.61 (step @p76 :rule chain_m_resolution :premises (@p75 @p73 @p56) :args (@t114 @t104 (@list @t99 @t100))) % 0.38/0.61 (step @p77 :rule false_intro :premises (@p76)) % 0.38/0.61 (step @p78 :rule instantiate :premises (@p38) :args ((@list @t83 @t82))) % 0.38/0.61 (step @p79 :rule refl :args (@t91)) % 0.38/0.61 (step @p80 :rule cong :premises (@p79 @p78) :args (@t105)) % 0.38/0.61 (step @p81 :rule refl :args (tptp.tyop_2Emin_2Ebool)) % 0.38/0.61 (step @p82 :rule cong :premises (@p81 @p80) :args (@t106)) % 0.38/0.61 (step @p83 :rule cong :premises (@p82) :args (@t107)) % 0.38/0.61 (step @p84 :rule cong :premises (@p83) :args (@t108)) % 0.38/0.61 (step @p85 :rule bool-double-not-elim :args (@t108)) % 0.38/0.61 (step @p86 :rule refl :args (@t110)) % 0.38/0.61 (step @p87 :rule nary_cong :premises (@p86 @p85) :args ((or @t110 (not @t109)))) % 0.38/0.61 (step @p88 :rule cnf_or_neg :args (@t110 0)) % 0.38/0.61 (step @p89 :rule eq_resolve :premises (@p88 @p87)) % 0.38/0.61 (step @p90 :rule reordering :premises (@p89) :args ((or @t108 @t110))) % 0.38/0.61 (step @p91 :rule chain_m_resolution :premises (@p90 @p68) :args (@t108 @t111 @t112)) % 0.38/0.61 (step @p92 :rule true_intro :premises (@p91)) % 0.38/0.61 (step @p93 :rule symm :premises (@p92)) % 0.38/0.61 (step @p94 :rule trans :premises (@p93 @p84 @p77)) % 0.38/0.61 (step @p95 false :rule eq_resolve :premises (@p94 @p41)) % 0.38/0.61 ) % 0.38/0.61 % SZS output end Proof % 0.38/0.61 % cvc5 exiting %------------------------------------------------------------------------------