%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP001+4 : TPTP v9.2.1. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n022.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 08:24:20 AM UTC 2026 % Result : Theorem 0.36s 0.62s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP001+4 : TPTP v9.2.1. Bugfixed v7.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n022.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 03:32:53 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.62 % SZS status Theorem % 0.36/0.62 % SZS output start Proof % 0.36/0.62 ( % 0.36/0.62 (declare-sort $$unsorted 0) % 0.36/0.62 (declare-const tptp.c_2Ebool_2Eliteral__case_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2ERES__FORALL_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2ERES__EXISTS__UNIQUE_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2ERES__EXISTS_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2Eliteral__case_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2ERES__EXISTS_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2ETYPE__DEFINITION_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2ELET_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2EIN_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2ERES__SELECT_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2EIN_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2EONTO_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.tyop_2Emin_2Eind $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2EONE__ONE_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2EDATATYPE_2E1 (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2EDATATYPE_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.combin_s_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2ECOND_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.combin_k_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2E_3F_21_2E1 (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.combin_i_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.p (-> $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2ERES__SELECT_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2EBOUNDED_2E1 (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.tyop_2Emin_2Ebool $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Emin_2E_3D_3D_3E_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2E_7E_2E1 (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2EF_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.s (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2ETYPE__DEFINITION_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2ELET_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2E_3F_2E1 (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2ET_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2E_2F_5C_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2EONTO_2E1 (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2E_3F_21_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.tyop_2Emin_2Efun (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Emin_2E_3D_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2E_21_2E1 (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2EONE__ONE_2E1 (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.app_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2E_2F_5C_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2ERES__FORALL_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.c_2Ebool_2E_7E_2E0 $$unsorted) % 0.36/0.62 (declare-const tptp.c_2Ebool_2ECOND_2E3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.63 (declare-const tptp.c_2Ebool_2ERES__EXISTS__UNIQUE_2E0 $$unsorted) % 0.36/0.63 (declare-const tptp.c_2Emin_2E_3D_3D_3E_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.63 (declare-const tptp.c_2Ebool_2E_5C_2F_2E0 $$unsorted) % 0.36/0.63 (declare-const tptp.c_2Emin_2E_3D_2E0 $$unsorted) % 0.36/0.63 (declare-const tptp.c_2Ebool_2E_5C_2F_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.63 (declare-const tptp.c_2Ebool_2E_21_2E0 $$unsorted) % 0.36/0.63 (declare-const tptp.c_2Emin_2E_40_2E0 $$unsorted) % 0.36/0.63 (declare-const tptp.c_2Ebool_2E_3F_2E0 $$unsorted) % 0.36/0.63 (declare-const tptp.c_2Emin_2E_40_2E1 (-> $$unsorted $$unsorted)) % 0.36/0.63 (declare-const tptp.c_2Ebool_2EBOUNDED_2E0 $$unsorted) % 0.36/0.63 (define @t1 () (@var "V1g_2E0" $$unsorted)) % 0.36/0.63 (define @t2 () (@var "A_27b" $$unsorted)) % 0.36/0.63 (define @t3 () (@var "A_27a" $$unsorted)) % 0.36/0.63 (define @t4 () (tptp.tyop_2Emin_2Efun @t3 @t2)) % 0.36/0.63 (define @t5 () (tptp.s @t4 @t1)) % 0.36/0.63 (define @t6 () (@var "V0f_2E0" $$unsorted)) % 0.36/0.63 (define @t7 () (tptp.s @t4 @t6)) % 0.36/0.63 (define @t8 () (@var "V2x_2E0" $$unsorted)) % 0.36/0.63 (define @t9 () (tptp.s @t3 @t8)) % 0.36/0.63 (define @t10 () (tptp.s @t2 (tptp.app_2E2 @t5 @t9))) % 0.36/0.63 (define @t11 () (@list @t8)) % 0.36/0.63 (define @t12 () (@var "V1_2E0" $$unsorted)) % 0.36/0.63 (define @t13 () (tptp.s tptp.tyop_2Emin_2Ebool @t12)) % 0.36/0.63 (define @t14 () (@var "V0_2E0" $$unsorted)) % 0.36/0.63 (define @t15 () (tptp.s tptp.tyop_2Emin_2Ebool @t14)) % 0.36/0.63 (define @t16 () (tptp.p @t13)) % 0.36/0.63 (define @t17 () (tptp.p @t15)) % 0.36/0.63 (define @t18 () (@list @t14 @t12)) % 0.36/0.63 (define @t19 () (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0)) % 0.36/0.63 (define @t20 () (tptp.p @t19)) % 0.36/0.63 (define @t21 () (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0)) % 0.36/0.63 (define @t22 () (tptp.p @t21)) % 0.36/0.63 (define @t23 () (@var "V0t_2E0" $$unsorted)) % 0.36/0.63 (define @t24 () (tptp.s tptp.tyop_2Emin_2Ebool @t23)) % 0.36/0.63 (define @t25 () (@list @t23)) % 0.36/0.63 (define @t26 () (@var "V0x_2E0" $$unsorted)) % 0.36/0.63 (define @t27 () (tptp.s @t3 @t26)) % 0.36/0.63 (define @t28 () (tptp.tyop_2Emin_2Efun @t3 @t3)) % 0.36/0.63 (define @t29 () (@list @t3 @t26)) % 0.36/0.63 (define @t30 () (@var "V1y_2E0" $$unsorted)) % 0.36/0.63 (define @t31 () (tptp.s @t2 @t30)) % 0.36/0.63 (define @t32 () (tptp.tyop_2Emin_2Efun @t2 @t3)) % 0.36/0.63 (define @t33 () (@var "A_27c" $$unsorted)) % 0.36/0.63 (define @t34 () (tptp.tyop_2Emin_2Efun @t2 @t33)) % 0.36/0.63 (define @t35 () (tptp.tyop_2Emin_2Efun @t3 @t34)) % 0.36/0.63 (define @t36 () (tptp.s @t35 @t6)) % 0.36/0.63 (define @t37 () (tptp.tyop_2Emin_2Efun @t3 @t33)) % 0.36/0.63 (define @t38 () (tptp.tyop_2Emin_2Efun @t4 @t37)) % 0.36/0.63 (define @t39 () (tptp.s @t3 @t12)) % 0.36/0.63 (define @t40 () (tptp.s @t3 @t14)) % 0.36/0.63 (define @t41 () (@var "V1x_2E0" $$unsorted)) % 0.36/0.63 (define @t42 () (tptp.s @t3 @t41)) % 0.36/0.63 (define @t43 () (tptp.tyop_2Emin_2Efun @t3 tptp.tyop_2Emin_2Ebool)) % 0.36/0.63 (define @t44 () (tptp.s @t43 @t6)) % 0.36/0.63 (define @t45 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t44 @t42)))) % 0.36/0.63 (define @t46 () (@list @t41)) % 0.36/0.63 (define @t47 () (@list @t3 @t6)) % 0.36/0.63 (define @t48 () (@var "X1_2E0" $$unsorted)) % 0.36/0.63 (define @t49 () (tptp.s tptp.tyop_2Emin_2Ebool @t48)) % 0.36/0.63 (define @t50 () (@var "X0_2E0" $$unsorted)) % 0.36/0.63 (define @t51 () (tptp.s tptp.tyop_2Emin_2Ebool @t50)) % 0.36/0.63 (define @t52 () (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool)) % 0.36/0.63 (define @t53 () (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool @t52)) % 0.36/0.63 (define @t54 () (tptp.p @t49)) % 0.36/0.63 (define @t55 () (tptp.p @t51)) % 0.36/0.63 (define @t56 () (@list @t50 @t48)) % 0.36/0.63 (define @t57 () (@list @t50)) % 0.36/0.63 (define @t58 () (tptp.s @t3 @t48)) % 0.36/0.63 (define @t59 () (tptp.s @t3 @t50)) % 0.36/0.63 (define @t60 () (tptp.tyop_2Emin_2Efun @t3 @t43)) % 0.36/0.63 (define @t61 () (@list @t3 @t50 @t48)) % 0.36/0.63 (define @t62 () (tptp.s @t43 @t50)) % 0.36/0.63 (define @t63 () (tptp.tyop_2Emin_2Efun @t43 tptp.tyop_2Emin_2Ebool)) % 0.36/0.63 (define @t64 () (@list @t3 @t50)) % 0.36/0.63 (define @t65 () (tptp.tyop_2Emin_2Efun @t43 @t3)) % 0.36/0.63 (define @t66 () (tptp.s @t4 @t50)) % 0.36/0.63 (define @t67 () (tptp.tyop_2Emin_2Efun @t4 tptp.tyop_2Emin_2Ebool)) % 0.36/0.63 (define @t68 () (@list @t3 @t2 @t50)) % 0.36/0.63 (define @t69 () (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Eind tptp.tyop_2Emin_2Eind)) % 0.36/0.63 (define @t70 () (tptp.s @t69 @t50)) % 0.36/0.63 (define @t71 () (tptp.tyop_2Emin_2Efun @t69 tptp.tyop_2Emin_2Ebool)) % 0.36/0.63 (define @t72 () (tptp.s @t43 @t48)) % 0.36/0.63 (define @t73 () (tptp.tyop_2Emin_2Efun @t4 @t4)) % 0.36/0.63 (define @t74 () (@list @t3 @t2 @t50 @t48)) % 0.36/0.63 (define @t75 () (tptp.tyop_2Emin_2Efun @t43 @t63)) % 0.36/0.63 (define @t76 () (tptp.s @t32 @t48)) % 0.36/0.63 (define @t77 () (tptp.tyop_2Emin_2Efun @t32 tptp.tyop_2Emin_2Ebool)) % 0.36/0.63 (define @t78 () (@var "X2_2E0" $$unsorted)) % 0.36/0.63 (define @t79 () (tptp.s @t3 @t78)) % 0.36/0.63 (define @t80 () (tptp.tyop_2Emin_2Efun @t3 @t28)) % 0.36/0.63 (define @t81 () (@var "V0M_2E0" $$unsorted)) % 0.36/0.63 (define @t82 () (tptp.s @t2 (tptp.app_2E2 (tptp.s @t4 @t81) @t42))) % 0.36/0.63 (define @t83 () (@var "V0P_2E0" $$unsorted)) % 0.36/0.63 (define @t84 () (tptp.s @t43 @t83)) % 0.36/0.63 (define @t85 () (tptp.s @t69 @t6)) % 0.36/0.63 (define @t86 () (tptp.s tptp.tyop_2Emin_2Ebool @t26)) % 0.36/0.63 (define @t87 () (@list @t26)) % 0.36/0.63 (define @t88 () (tptp.s @t43 @t26)) % 0.36/0.63 (define @t89 () (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t88 @t42))) % 0.36/0.63 (define @t90 () (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_3F_2E1 @t88))) % 0.36/0.63 (define @t91 () (@var "V2t_2E0" $$unsorted)) % 0.36/0.63 (define @t92 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool @t91))) % 0.36/0.63 (define @t93 () (@var "V1x_27_2E0" $$unsorted)) % 0.36/0.63 (define @t94 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool @t93))) % 0.36/0.63 (define @t95 () (=> @t94 @t92)) % 0.36/0.63 (define @t96 () (tptp.p @t86)) % 0.36/0.63 (define @t97 () (@list @t91)) % 0.36/0.63 (define @t98 () (@list @t26 @t93)) % 0.36/0.63 (define @t99 () (@var "V2y_2E0" $$unsorted)) % 0.36/0.63 (define @t100 () (tptp.s @t3 @t99)) % 0.36/0.63 (define @t101 () (tptp.s @t3 @t93)) % 0.36/0.63 (define @t102 () (tptp.s @t4 @t26)) % 0.36/0.63 (define @t103 () (tptp.s @t2 (tptp.app_2E2 @t102 @t101))) % 0.36/0.63 (define @t104 () (@list @t3 @t2 @t26 @t93)) % 0.36/0.63 (define @t105 () (@var "V2x_27_27_2E0" $$unsorted)) % 0.36/0.63 (define @t106 () (tptp.s @t3 @t105)) % 0.36/0.63 (define @t107 () (@var "F0_2E0" $$unsorted)) % 0.36/0.63 (define @t108 () (tptp.tyop_2Emin_2Efun @t3 @t60)) % 0.36/0.63 (define @t109 () (tptp.s @t43 (tptp.app_2E2 (tptp.s @t60 (tptp.app_2E2 (tptp.s @t108 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool @t108) @t107) @t86)) @t101)) @t106))) % 0.36/0.63 (define @t110 () (@var "V3x_2E0" $$unsorted)) % 0.36/0.63 (define @t111 () (tptp.s @t3 @t110)) % 0.36/0.63 (define @t112 () (@list @t3 @t107)) % 0.36/0.63 (define @t113 () (@var "V2x2_2E0" $$unsorted)) % 0.36/0.63 (define @t114 () (tptp.s @t3 @t113)) % 0.36/0.63 (define @t115 () (@var "V1x1_2E0" $$unsorted)) % 0.36/0.63 (define @t116 () (tptp.s @t3 @t115)) % 0.36/0.63 (define @t117 () (@list @t3 @t2 @t26)) % 0.36/0.63 (define @t118 () (@var "V5x_27_2E0" $$unsorted)) % 0.36/0.63 (define @t119 () (tptp.s @t32 @t93)) % 0.36/0.63 (define @t120 () (@var "V4x_2E0" $$unsorted)) % 0.36/0.63 (define @t121 () (tptp.s @t3 @t120)) % 0.36/0.63 (define @t122 () (@var "V3x_27_27_2E0" $$unsorted)) % 0.36/0.63 (define @t123 () (tptp.s @t2 @t122)) % 0.36/0.63 (define @t124 () (@var "V2x_27_2E0" $$unsorted)) % 0.36/0.63 (define @t125 () (tptp.s @t2 @t124)) % 0.36/0.63 (define @t126 () (tptp.s @t43 @t93)) % 0.36/0.63 (define @t127 () (@list @t3 @t26 @t93)) % 0.36/0.63 (define @t128 () (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t126 @t9))) % 0.36/0.63 (define @t129 () (tptp.p @t128)) % 0.36/0.63 (define @t130 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EIN_2E2 @t9 @t88)))) % 0.36/0.63 (define @t131 () (and @t130 @t129)) % 0.36/0.63 (define @t132 () (@var "F1_2E0" $$unsorted)) % 0.36/0.63 (define @t133 () (tptp.tyop_2Emin_2Efun @t43 @t43)) % 0.36/0.63 (define @t134 () (tptp.tyop_2Emin_2Efun @t43 @t133)) % 0.36/0.63 (define @t135 () (tptp.s @t43 (tptp.app_2E2 (tptp.s @t133 (tptp.app_2E2 (tptp.s @t134 @t132) @t88)) @t126))) % 0.36/0.63 (define @t136 () (tptp.s @t43 (tptp.app_2E2 (tptp.s @t133 @t107) @t126))) % 0.36/0.63 (define @t137 () (@var "F2_2E0" $$unsorted)) % 0.36/0.63 (define @t138 () (tptp.s @t43 (tptp.app_2E2 (tptp.s @t60 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t43 @t60) @t137) @t126)) @t111))) % 0.36/0.63 (define @t139 () (@var "V4y_2E0" $$unsorted)) % 0.36/0.63 (define @t140 () (tptp.s @t3 @t139)) % 0.36/0.63 (define @t141 () (tptp.s @t43 (tptp.app_2E2 (tptp.s @t133 (tptp.app_2E2 (tptp.s @t134 @t107) @t88)) @t126))) % 0.36/0.63 (assume @p1 (forall (@list @t3 @t2 @t6 @t1) (=> (forall @t11 (= (tptp.s @t2 (tptp.app_2E2 @t7 @t9)) @t10)) (= @t7 @t5)))) % 0.36/0.63 (assume @p2 (forall @t18 (=> (= @t17 @t16) (= @t15 @t13)))) % 0.36/0.63 (assume @p3 @t20) % 0.36/0.63 (assume @p4 (not @t22)) % 0.36/0.63 (assume @p5 (forall @t25 (or (= @t24 @t19) (= @t24 @t21)))) % 0.36/0.63 (assume @p6 (forall @t29 (= (tptp.s @t3 (tptp.app_2E2 (tptp.s @t28 tptp.combin_i_2E0) @t27)) @t27))) % 0.36/0.63 (assume @p7 (forall (@list @t3 @t2 @t26 @t30) (= (tptp.s @t3 (tptp.app_2E2 (tptp.s @t32 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t3 @t32) tptp.combin_k_2E0) @t27)) @t31)) @t27))) % 0.36/0.63 (assume @p8 (forall (@list @t3 @t2 @t33 @t6 @t1 @t8) (= (tptp.s @t33 (tptp.app_2E2 (tptp.s @t37 (tptp.app_2E2 (tptp.s @t38 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t35 @t38) tptp.combin_s_2E0) @t36)) @t5)) @t9)) (tptp.s @t33 (tptp.app_2E2 (tptp.s @t34 (tptp.app_2E2 @t36 @t9)) @t10))))) % 0.36/0.63 (assume @p9 (forall @t18 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_2F_5C_2E2 @t15 @t13))) (and @t17 @t16)))) % 0.36/0.63 (assume @p10 (forall @t18 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_5C_2F_2E2 @t15 @t13))) (or @t17 @t16)))) % 0.36/0.63 (assume @p11 (forall (@list @t14) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_7E_2E1 @t15))) (not @t17)))) % 0.36/0.63 (assume @p12 (forall @t18 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Emin_2E_3D_3D_3E_2E2 @t15 @t13))) (=> @t17 @t16)))) % 0.36/0.63 (assume @p13 (forall (@list @t3 @t14 @t12) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Emin_2E_3D_2E2 @t40 @t39))) (= @t40 @t39)))) % 0.36/0.63 (assume @p14 (forall @t47 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_21_2E1 @t44))) (forall @t46 @t45)))) % 0.36/0.63 (assume @p15 (forall @t47 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_3F_2E1 @t44))) (exists @t46 @t45)))) % 0.36/0.63 (assume @p16 (forall @t56 (= (and @t55 @t54) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t52 (tptp.app_2E2 (tptp.s @t53 tptp.c_2Ebool_2E_2F_5C_2E0) @t51)) @t49)))))) % 0.36/0.63 (assume @p17 (forall @t56 (= (or @t55 @t54) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t52 (tptp.app_2E2 (tptp.s @t53 tptp.c_2Ebool_2E_5C_2F_2E0) @t51)) @t49)))))) % 0.36/0.63 (assume @p18 (forall @t57 (= (not @t55) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t52 tptp.c_2Ebool_2E_7E_2E0) @t51)))))) % 0.36/0.63 (assume @p19 (forall @t56 (= (=> @t55 @t54) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t52 (tptp.app_2E2 (tptp.s @t53 tptp.c_2Emin_2E_3D_3D_3E_2E0) @t51)) @t49)))))) % 0.36/0.63 (assume @p20 (forall @t61 (= (= @t59 @t58) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t43 (tptp.app_2E2 (tptp.s @t60 tptp.c_2Emin_2E_3D_2E0) @t59)) @t58)))))) % 0.36/0.63 (assume @p21 (forall @t64 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_21_2E1 @t62)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t63 tptp.c_2Ebool_2E_21_2E0) @t62))))) % 0.36/0.63 (assume @p22 (forall @t64 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_3F_2E1 @t62)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t63 tptp.c_2Ebool_2E_3F_2E0) @t62))))) % 0.36/0.63 (assume @p23 (forall @t64 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_3F_21_2E1 @t62)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t63 tptp.c_2Ebool_2E_3F_21_2E0) @t62))))) % 0.36/0.63 (assume @p24 (forall @t64 (= (tptp.s @t3 (tptp.c_2Emin_2E_40_2E1 @t62)) (tptp.s @t3 (tptp.app_2E2 (tptp.s @t65 tptp.c_2Emin_2E_40_2E0) @t62))))) % 0.36/0.63 (assume @p25 (forall @t57 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EBOUNDED_2E1 @t51)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t52 tptp.c_2Ebool_2EBOUNDED_2E0) @t51))))) % 0.36/0.63 (assume @p26 (forall @t64 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EDATATYPE_2E1 @t59)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t43 tptp.c_2Ebool_2EDATATYPE_2E0) @t59))))) % 0.36/0.63 (assume @p27 (forall @t68 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EONE__ONE_2E1 @t66)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t67 tptp.c_2Ebool_2EONE__ONE_2E0) @t66))))) % 0.36/0.63 (assume @p28 (forall @t57 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EONE__ONE_2E1 @t70)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t71 tptp.c_2Ebool_2EONE__ONE_2E0) @t70))))) % 0.36/0.63 (assume @p29 (forall @t68 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EONTO_2E1 @t66)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t67 tptp.c_2Ebool_2EONTO_2E0) @t66))))) % 0.36/0.63 (assume @p30 (forall @t57 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EONTO_2E1 @t70)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t71 tptp.c_2Ebool_2EONTO_2E0) @t70))))) % 0.36/0.63 (assume @p31 (forall @t61 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EIN_2E2 @t59 @t72)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t63 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t3 @t63) tptp.c_2Ebool_2EIN_2E0) @t59)) @t72))))) % 0.36/0.63 (assume @p32 (forall @t74 (= (tptp.s @t2 (tptp.c_2Ebool_2ELET_2E2 @t66 @t58)) (tptp.s @t2 (tptp.app_2E2 (tptp.s @t4 (tptp.app_2E2 (tptp.s @t73 tptp.c_2Ebool_2ELET_2E0) @t66)) @t58))))) % 0.36/0.63 (assume @p33 (forall @t61 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2ERES__EXISTS_2E2 @t62 @t72)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t63 (tptp.app_2E2 (tptp.s @t75 tptp.c_2Ebool_2ERES__EXISTS_2E0) @t62)) @t72))))) % 0.36/0.63 (assume @p34 (forall @t61 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2ERES__EXISTS__UNIQUE_2E2 @t62 @t72)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t63 (tptp.app_2E2 (tptp.s @t75 tptp.c_2Ebool_2ERES__EXISTS__UNIQUE_2E0) @t62)) @t72))))) % 0.36/0.63 (assume @p35 (forall @t61 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2ERES__FORALL_2E2 @t62 @t72)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t63 (tptp.app_2E2 (tptp.s @t75 tptp.c_2Ebool_2ERES__FORALL_2E0) @t62)) @t72))))) % 0.36/0.63 (assume @p36 (forall @t61 (= (tptp.s @t3 (tptp.c_2Ebool_2ERES__SELECT_2E2 @t62 @t72)) (tptp.s @t3 (tptp.app_2E2 (tptp.s @t65 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t43 @t65) tptp.c_2Ebool_2ERES__SELECT_2E0) @t62)) @t72))))) % 0.36/0.63 (assume @p37 (forall @t74 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2ETYPE__DEFINITION_2E2 @t62 @t76)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t77 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t43 @t77) tptp.c_2Ebool_2ETYPE__DEFINITION_2E0) @t62)) @t76))))) % 0.36/0.63 (assume @p38 (forall @t74 (= (tptp.s @t2 (tptp.c_2Ebool_2Eliteral__case_2E2 @t66 @t58)) (tptp.s @t2 (tptp.app_2E2 (tptp.s @t4 (tptp.app_2E2 (tptp.s @t73 tptp.c_2Ebool_2Eliteral__case_2E0) @t66)) @t58))))) % 0.36/0.63 (assume @p39 (forall (@list @t3 @t50 @t48 @t78) (= (tptp.s @t3 (tptp.c_2Ebool_2ECOND_2E3 @t51 @t58 @t79)) (tptp.s @t3 (tptp.app_2E2 (tptp.s @t28 (tptp.app_2E2 (tptp.s @t80 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool @t80) tptp.c_2Ebool_2ECOND_2E0) @t51)) @t58)) @t79))))) % 0.36/0.63 (assume @p40 (forall (@list @t3 @t2 @t81 @t41) (= @t82 @t82))) % 0.36/0.63 (assume @p41 (forall (@list @t3 @t83 @t41) (=> (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t84 @t42))) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t84 (tptp.s @t3 (tptp.c_2Emin_2E_40_2E1 @t84)))))))) % 0.36/0.63 (assume @p42 (exists (@list @t6) (and (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EONE__ONE_2E1 @t85))) (not (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EONTO_2E1 @t85))))))) % 0.36/0.63 (assume @p43 (= @t20 (forall @t87 (= @t86 @t86)))) % 0.36/0.63 (assume @p44 (forall @t29 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_21_2E1 @t88))) (forall @t46 (= @t89 @t19))))) % 0.36/0.63 (assume @p45 (forall @t29 (= @t90 (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t88 (tptp.s @t3 (tptp.c_2Emin_2E_40_2E1 @t88))))))) % 0.36/0.63 (assume @p46 (forall @t98 (= (and @t96 @t94) (forall @t97 (=> (=> @t96 @t95) @t92))))) % 0.36/0.63 (assume @p47 (forall @t98 (= (or @t96 @t94) (forall @t97 (=> (=> @t96 @t92) (=> @t95 @t92)))))) % 0.36/0.63 (assume @p48 (= @t22 (forall @t25 (tptp.p @t24)))) % 0.36/0.63 (assume @p49 (forall @t87 (= (not @t96) (=> @t96 @t22)))) % 0.36/0.63 (assume @p50 (forall @t29 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_3F_21_2E1 @t88))) (and (tptp.p @t90) (forall (@list @t41 @t99) (=> (and (tptp.p @t89) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t88 @t100)))) (= @t42 @t100))))))) % 0.36/0.63 (assume @p51 (forall @t104 (= (tptp.s @t2 (tptp.c_2Ebool_2ELET_2E2 @t102 @t101)) @t103))) % 0.36/0.63 (assume @p52 (forall @t112 (=> (forall (@list @t26 @t93 @t105 @t110) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t109 @t111))) (and (=> (= @t86 @t19) (= @t111 @t101)) (=> (= @t86 @t21) (= @t111 @t106))))) (forall (@list @t26 @t93 @t105) (= (tptp.s @t3 (tptp.c_2Ebool_2ECOND_2E3 @t86 @t101 @t106)) (tptp.s @t3 (tptp.c_2Emin_2E_40_2E1 @t109))))))) % 0.36/0.63 (assume @p53 (forall @t117 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EONE__ONE_2E1 @t102))) (forall (@list @t115 @t113) (=> (= (tptp.s @t2 (tptp.app_2E2 @t102 @t116)) (tptp.s @t2 (tptp.app_2E2 @t102 @t114))) (= @t116 @t114)))))) % 0.36/0.63 (assume @p54 (forall @t117 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EONTO_2E1 @t102))) (forall (@list @t30) (exists @t11 (= @t31 (tptp.s @t2 (tptp.app_2E2 @t102 @t9)))))))) % 0.36/0.63 (assume @p55 (forall @t104 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2ETYPE__DEFINITION_2E2 @t88 @t119))) (and (forall (@list @t124 @t122) (=> (= (tptp.s @t3 (tptp.app_2E2 @t119 @t125)) (tptp.s @t3 (tptp.app_2E2 @t119 @t123))) (= @t125 @t123))) (forall (@list @t120) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t88 @t121))) (exists (@list @t118) (= @t121 (tptp.s @t3 (tptp.app_2E2 @t119 (tptp.s @t2 @t118))))))))))) % 0.36/0.63 (assume @p56 (forall @t104 (= (tptp.s @t2 (tptp.c_2Ebool_2Eliteral__case_2E2 @t102 @t101)) @t103))) % 0.36/0.63 (assume @p57 (forall @t127 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EIN_2E2 @t27 @t126)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t126 @t27))))) % 0.36/0.63 (assume @p58 (forall @t127 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2ERES__FORALL_2E2 @t88 @t126))) (forall @t11 (=> @t130 @t129))))) % 0.36/0.63 (assume @p59 (forall @t127 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2ERES__EXISTS_2E2 @t88 @t126))) (exists @t11 @t131)))) % 0.36/0.63 (assume @p60 (forall (@list @t3 @t137 @t132 @t107) (=> (forall (@list @t93 @t110 @t139) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t138 @t140))) (=> (and (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t126 @t111))) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t126 @t140)))) (= @t111 @t140)))) (=> (forall (@list @t26 @t93 @t110) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t135 @t111)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2ERES__FORALL_2E2 @t88 @t138)))) (=> (forall (@list @t93 @t8) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t136 @t9)) @t128)) (forall @t98 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2ERES__EXISTS__UNIQUE_2E2 @t88 @t126))) (and (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2ERES__EXISTS_2E2 @t88 @t136))) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2ERES__FORALL_2E2 @t88 @t135))))))))))) % 0.36/0.63 (assume @p61 (forall @t112 (=> (forall (@list @t26 @t93 @t8) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t141 @t9))) @t131)) (forall @t98 (= (tptp.s @t3 (tptp.c_2Ebool_2ERES__SELECT_2E2 @t88 @t126)) (tptp.s @t3 (tptp.c_2Emin_2E_40_2E1 @t141))))))) % 0.36/0.63 (assume @p62 (forall @t87 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EBOUNDED_2E1 @t86)) @t19))) % 0.36/0.63 (assume @p63 (forall @t29 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2EDATATYPE_2E1 @t27)) @t19))) % 0.36/0.63 (assume @p64 (not @t20)) % 0.36/0.63 (assume @p65 true) % 0.36/0.63 (step @p66 false :rule chain_m_resolution :premises (@p64 @p3) :args (false (@list false) (@list @t20))) % 0.36/0.63 ) % 0.36/0.63 % SZS output end Proof % 0.36/0.63 % cvc5 exiting %------------------------------------------------------------------------------