%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM926_1 : TPTP v9.2.1. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n006.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 08:41:06 AM UTC 2026 % Result : Theorem 0.38s 0.64s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM926_1 : TPTP v9.2.1. Released v5.3.0. % 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 : n006.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 12:33:49 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.64 % SZS status Theorem % 0.38/0.64 % SZS output start Proof % 0.38/0.64 ( % 0.38/0.64 (declare-sort tptp.nat 0) % 0.38/0.64 (declare-sort tptp.int 0) % 0.38/0.64 (declare-const tptp.ord_less_eq_nat (-> tptp.nat tptp.nat Bool)) % 0.38/0.64 (declare-const tptp.ord_less_nat (-> tptp.nat tptp.nat Bool)) % 0.38/0.64 (declare-const tptp.one_one_nat tptp.nat) % 0.38/0.64 (declare-const tptp.plus_plus_nat (-> tptp.nat tptp.nat tptp.nat)) % 0.38/0.64 (declare-const tptp.power_power_nat (-> tptp.nat tptp.nat tptp.nat)) % 0.38/0.64 (declare-const tptp.times_times_nat (-> tptp.nat tptp.nat tptp.nat)) % 0.38/0.64 (declare-const tptp.twoSqu1431725154sum2sq (-> tptp.int Bool)) % 0.38/0.64 (declare-const tptp.s tptp.int) % 0.38/0.64 (declare-const tptp.zprime (-> tptp.int Bool)) % 0.38/0.64 (declare-const tptp.plus_plus_int (-> tptp.int tptp.int tptp.int)) % 0.38/0.64 (declare-const tptp.number_number_of_nat (-> tptp.int tptp.nat)) % 0.38/0.64 (declare-const tptp.t tptp.int) % 0.38/0.64 (declare-const tptp.one_one_int tptp.int) % 0.38/0.64 (declare-const tptp.pls tptp.int) % 0.38/0.64 (declare-const tptp.ord_less_eq_int (-> tptp.int tptp.int Bool)) % 0.38/0.64 (declare-const tptp.m tptp.int) % 0.38/0.64 (declare-const tptp.number_number_of_int (-> tptp.int tptp.int)) % 0.38/0.64 (declare-const tptp.bit1 (-> tptp.int tptp.int)) % 0.38/0.64 (declare-const tptp.bit0 (-> tptp.int tptp.int)) % 0.38/0.64 (declare-const tptp.power_power_int (-> tptp.int tptp.nat tptp.int)) % 0.38/0.64 (declare-const tptp.times_times_int (-> tptp.int tptp.int tptp.int)) % 0.38/0.64 (declare-const tptp.ord_less_int (-> tptp.int tptp.int Bool)) % 0.38/0.64 (define @t1 () (tptp.ord_less_eq_int tptp.one_one_int tptp.t)) % 0.38/0.64 (define @t2 () (tptp.bit1 tptp.pls)) % 0.38/0.64 (define @t3 () (tptp.bit0 @t2)) % 0.38/0.64 (define @t4 () (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 @t3)) tptp.m) tptp.one_one_int)) % 0.38/0.64 (define @t5 () (tptp.number_number_of_nat @t3)) % 0.38/0.64 (define @t6 () (@var "Y" tptp.int)) % 0.38/0.64 (define @t7 () (@var "X" tptp.int)) % 0.38/0.64 (define @t8 () (= (tptp.plus_plus_int (tptp.power_power_int @t7 @t5) (tptp.power_power_int @t6 @t5)) @t4)) % 0.38/0.64 (define @t9 () (@list @t7 @t6)) % 0.38/0.64 (define @t10 () (exists @t9 @t8)) % 0.38/0.64 (define @t11 () (=> (= tptp.t tptp.one_one_int) @t10)) % 0.38/0.64 (define @t12 () (tptp.ord_less_int tptp.one_one_int tptp.t)) % 0.38/0.64 (define @t13 () (=> @t12 @t10)) % 0.38/0.64 (define @t14 () (tptp.times_times_int @t4 tptp.t)) % 0.38/0.64 (define @t15 () (tptp.plus_plus_int (tptp.power_power_int tptp.s @t5) tptp.one_one_int)) % 0.38/0.64 (define @t16 () (@var "B_4" tptp.int)) % 0.38/0.64 (define @t17 () (tptp.power_power_int @t16 @t5)) % 0.38/0.64 (define @t18 () (@var "A_8" tptp.int)) % 0.38/0.64 (define @t19 () (tptp.number_number_of_int @t3)) % 0.38/0.64 (define @t20 () (tptp.power_power_int @t18 @t5)) % 0.38/0.64 (define @t21 () (tptp.plus_plus_int @t18 @t16)) % 0.38/0.64 (define @t22 () (@list @t18 @t16)) % 0.38/0.64 (define @t23 () (tptp.bit1 @t2)) % 0.38/0.64 (define @t24 () (tptp.number_number_of_nat @t23)) % 0.38/0.64 (define @t25 () (tptp.number_number_of_int @t23)) % 0.38/0.64 (define @t26 () (tptp.power_power_int @t18 @t24)) % 0.38/0.64 (define @t27 () (@var "Y_2" tptp.nat)) % 0.38/0.64 (define @t28 () (@var "X_2" tptp.nat)) % 0.38/0.64 (define @t29 () (@var "Y_2" tptp.int)) % 0.38/0.64 (define @t30 () (@var "X_2" tptp.int)) % 0.38/0.64 (define @t31 () (@list @t30 @t29)) % 0.38/0.64 (define @t32 () (@var "W_4" tptp.int)) % 0.38/0.64 (define @t33 () (tptp.number_number_of_int @t32)) % 0.38/0.64 (define @t34 () (@list @t32)) % 0.38/0.64 (define @t35 () (tptp.number_number_of_nat @t32)) % 0.38/0.64 (define @t36 () (@var "X_7" tptp.int)) % 0.38/0.64 (define @t37 () (@var "X_7" tptp.nat)) % 0.38/0.64 (define @t38 () (@var "A_7" tptp.int)) % 0.38/0.64 (define @t39 () (@var "A_7" tptp.nat)) % 0.38/0.64 (define @t40 () (@var "N" tptp.nat)) % 0.38/0.64 (define @t41 () (@var "X_6" tptp.int)) % 0.38/0.64 (define @t42 () (tptp.power_power_int @t41 @t40)) % 0.38/0.64 (define @t43 () (tptp.times_times_nat @t5 @t40)) % 0.38/0.64 (define @t44 () (@var "X_6" tptp.nat)) % 0.38/0.64 (define @t45 () (tptp.power_power_nat @t44 @t40)) % 0.38/0.64 (define @t46 () (@var "W_3" tptp.int)) % 0.38/0.64 (define @t47 () (@var "V_3" tptp.int)) % 0.38/0.64 (define @t48 () (@var "T" tptp.int)) % 0.38/0.64 (define @t49 () (@var "W" tptp.int)) % 0.38/0.64 (define @t50 () (@var "Z" tptp.int)) % 0.38/0.64 (define @t51 () (tptp.ord_less_eq_int @t49 @t50)) % 0.38/0.64 (define @t52 () (tptp.ord_less_eq_int @t50 @t49)) % 0.38/0.64 (define @t53 () (@list @t50 @t49)) % 0.38/0.64 (define @t54 () (@var "W_1" tptp.int)) % 0.38/0.64 (define @t55 () (@var "Z_1" tptp.int)) % 0.38/0.64 (define @t56 () (@var "X_1" tptp.int)) % 0.38/0.64 (define @t57 () (@var "Y_1" tptp.int)) % 0.38/0.64 (define @t58 () (@var "K_1" tptp.int)) % 0.38/0.64 (define @t59 () (@var "I" tptp.int)) % 0.38/0.64 (define @t60 () (@var "J" tptp.int)) % 0.38/0.64 (define @t61 () (tptp.ord_less_eq_int @t59 @t60)) % 0.38/0.64 (define @t62 () (@list @t58 @t59 @t60)) % 0.38/0.64 (define @t63 () (@var "Q_1" tptp.nat)) % 0.38/0.64 (define @t64 () (@var "P_1" tptp.nat)) % 0.38/0.64 (define @t65 () (tptp.times_times_nat @t64 @t63)) % 0.38/0.64 (define @t66 () (@var "X_5" tptp.int)) % 0.38/0.64 (define @t67 () (@var "X_5" tptp.nat)) % 0.38/0.64 (define @t68 () (@var "X_4" tptp.int)) % 0.38/0.64 (define @t69 () (@var "X_4" tptp.nat)) % 0.38/0.64 (define @t70 () (@var "Z" tptp.nat)) % 0.38/0.64 (define @t71 () (@var "Y_1" tptp.nat)) % 0.38/0.64 (define @t72 () (tptp.power_power_int @t56 @t71)) % 0.38/0.64 (define @t73 () (@list @t56 @t71 @t70)) % 0.38/0.64 (define @t74 () (@var "V_2" tptp.int)) % 0.38/0.64 (define @t75 () (tptp.number_number_of_nat @t74)) % 0.38/0.64 (define @t76 () (tptp.number_number_of_nat @t54)) % 0.38/0.64 (define @t77 () (@list @t74 @t54)) % 0.38/0.64 (define @t78 () (tptp.number_number_of_int @t74)) % 0.38/0.64 (define @t79 () (tptp.number_number_of_int @t54)) % 0.38/0.64 (define @t80 () (tptp.number_number_of_int @t29)) % 0.38/0.64 (define @t81 () (tptp.number_number_of_int @t30)) % 0.38/0.64 (define @t82 () (tptp.plus_plus_int @t49 @t50)) % 0.38/0.64 (define @t83 () (@var "Z_2" tptp.int)) % 0.38/0.64 (define @t84 () (@var "W_2" tptp.int)) % 0.38/0.64 (define @t85 () (@var "Q" tptp.nat)) % 0.38/0.64 (define @t86 () (@var "P" tptp.nat)) % 0.38/0.64 (define @t87 () (tptp.plus_plus_nat @t86 @t85)) % 0.38/0.64 (define @t88 () (@var "X_3" tptp.int)) % 0.38/0.64 (define @t89 () (@var "X_3" tptp.nat)) % 0.38/0.64 (define @t90 () (tptp.plus_plus_nat @t70 @t70)) % 0.38/0.64 (define @t91 () (@list @t70)) % 0.38/0.64 (define @t92 () (@var "K2" tptp.int)) % 0.38/0.64 (define @t93 () (@var "K1" tptp.int)) % 0.38/0.64 (define @t94 () (tptp.ord_less_int @t93 @t92)) % 0.38/0.64 (define @t95 () (tptp.bit1 @t92)) % 0.38/0.64 (define @t96 () (tptp.bit1 @t93)) % 0.38/0.64 (define @t97 () (@list @t93 @t92)) % 0.38/0.64 (define @t98 () (@var "L" tptp.int)) % 0.38/0.64 (define @t99 () (@var "K" tptp.int)) % 0.38/0.64 (define @t100 () (tptp.ord_less_int @t99 @t98)) % 0.38/0.64 (define @t101 () (tptp.bit1 @t98)) % 0.38/0.64 (define @t102 () (tptp.bit1 @t99)) % 0.38/0.64 (define @t103 () (@list @t99 @t98)) % 0.38/0.64 (define @t104 () (tptp.ord_less_eq_int @t93 @t92)) % 0.38/0.64 (define @t105 () (tptp.ord_less_eq_int @t99 @t98)) % 0.38/0.64 (define @t106 () (tptp.bit0 @t92)) % 0.38/0.64 (define @t107 () (tptp.bit0 @t93)) % 0.38/0.64 (define @t108 () (tptp.bit0 @t98)) % 0.38/0.64 (define @t109 () (tptp.bit0 @t99)) % 0.38/0.64 (define @t110 () (tptp.number_number_of_int @t98)) % 0.38/0.64 (define @t111 () (tptp.number_number_of_int @t99)) % 0.38/0.64 (define @t112 () (@var "V_1" tptp.int)) % 0.38/0.64 (define @t113 () (@var "V" tptp.int)) % 0.38/0.64 (define @t114 () (tptp.number_number_of_nat @t112)) % 0.38/0.64 (define @t115 () (tptp.number_number_of_nat @t113)) % 0.38/0.64 (define @t116 () (tptp.plus_plus_nat @t115 @t114)) % 0.38/0.64 (define @t117 () (tptp.ord_less_int @t112 tptp.pls)) % 0.38/0.64 (define @t118 () (tptp.ord_less_int @t113 tptp.pls)) % 0.38/0.64 (define @t119 () (tptp.number_number_of_nat @t2)) % 0.38/0.64 (define @t120 () (tptp.ord_less_int @t99 tptp.pls)) % 0.38/0.64 (define @t121 () (@list @t99)) % 0.38/0.64 (define @t122 () (tptp.ord_less_eq_int tptp.pls @t99)) % 0.38/0.64 (define @t123 () (@list @t54 @t55)) % 0.38/0.64 (define @t124 () (@var "Ry_4" tptp.int)) % 0.38/0.64 (define @t125 () (@var "Ly_4" tptp.int)) % 0.38/0.64 (define @t126 () (@var "Rx_6" tptp.int)) % 0.38/0.64 (define @t127 () (@var "Lx_6" tptp.int)) % 0.38/0.64 (define @t128 () (@var "Ry_4" tptp.nat)) % 0.38/0.64 (define @t129 () (@var "Ly_4" tptp.nat)) % 0.38/0.64 (define @t130 () (@var "Rx_6" tptp.nat)) % 0.38/0.64 (define @t131 () (@var "Lx_6" tptp.nat)) % 0.38/0.64 (define @t132 () (@var "Ry_3" tptp.int)) % 0.38/0.64 (define @t133 () (@var "Ly_3" tptp.int)) % 0.38/0.64 (define @t134 () (@var "Lx_5" tptp.int)) % 0.38/0.64 (define @t135 () (tptp.times_times_int @t134 @t133)) % 0.38/0.64 (define @t136 () (@var "Rx_5" tptp.int)) % 0.38/0.64 (define @t137 () (@var "Ry_3" tptp.nat)) % 0.38/0.64 (define @t138 () (@var "Ly_3" tptp.nat)) % 0.38/0.64 (define @t139 () (@var "Lx_5" tptp.nat)) % 0.38/0.64 (define @t140 () (tptp.times_times_nat @t139 @t138)) % 0.38/0.64 (define @t141 () (@var "Rx_5" tptp.nat)) % 0.38/0.64 (define @t142 () (@var "Ry_2" tptp.int)) % 0.38/0.64 (define @t143 () (@var "Rx_4" tptp.int)) % 0.38/0.64 (define @t144 () (tptp.times_times_int @t143 @t142)) % 0.38/0.64 (define @t145 () (@var "Ly_2" tptp.int)) % 0.38/0.64 (define @t146 () (@var "Lx_4" tptp.int)) % 0.38/0.64 (define @t147 () (@var "Ry_2" tptp.nat)) % 0.38/0.64 (define @t148 () (@var "Rx_4" tptp.nat)) % 0.38/0.64 (define @t149 () (tptp.times_times_nat @t148 @t147)) % 0.38/0.64 (define @t150 () (@var "Ly_2" tptp.nat)) % 0.38/0.64 (define @t151 () (@var "Lx_4" tptp.nat)) % 0.38/0.64 (define @t152 () (@var "Ly_1" tptp.int)) % 0.38/0.64 (define @t153 () (@var "Rx_3" tptp.int)) % 0.38/0.64 (define @t154 () (@var "Lx_3" tptp.int)) % 0.38/0.64 (define @t155 () (@var "Ly_1" tptp.nat)) % 0.38/0.64 (define @t156 () (@var "Rx_3" tptp.nat)) % 0.38/0.64 (define @t157 () (@var "Lx_3" tptp.nat)) % 0.38/0.64 (define @t158 () (@var "Rx_2" tptp.int)) % 0.38/0.64 (define @t159 () (@var "Ly" tptp.int)) % 0.38/0.64 (define @t160 () (@var "Lx_2" tptp.int)) % 0.38/0.64 (define @t161 () (@var "Rx_2" tptp.nat)) % 0.38/0.64 (define @t162 () (@var "Ly" tptp.nat)) % 0.38/0.64 (define @t163 () (@var "Lx_2" tptp.nat)) % 0.38/0.64 (define @t164 () (@var "Ry_1" tptp.int)) % 0.38/0.64 (define @t165 () (@var "Rx_1" tptp.int)) % 0.38/0.64 (define @t166 () (@var "Lx_1" tptp.int)) % 0.38/0.64 (define @t167 () (@var "Ry_1" tptp.nat)) % 0.38/0.64 (define @t168 () (@var "Rx_1" tptp.nat)) % 0.38/0.64 (define @t169 () (@var "Lx_1" tptp.nat)) % 0.38/0.64 (define @t170 () (@var "Ry" tptp.int)) % 0.38/0.64 (define @t171 () (@var "Lx" tptp.int)) % 0.38/0.64 (define @t172 () (@var "Rx" tptp.int)) % 0.38/0.64 (define @t173 () (@var "Ry" tptp.nat)) % 0.38/0.64 (define @t174 () (@var "Lx" tptp.nat)) % 0.38/0.64 (define @t175 () (@var "Rx" tptp.nat)) % 0.38/0.64 (define @t176 () (@var "A_6" tptp.int)) % 0.38/0.64 (define @t177 () (@var "B_3" tptp.int)) % 0.38/0.64 (define @t178 () (@var "A_6" tptp.nat)) % 0.38/0.64 (define @t179 () (@var "B_3" tptp.nat)) % 0.38/0.64 (define @t180 () (@var "D_2" tptp.int)) % 0.38/0.64 (define @t181 () (@var "B_2" tptp.int)) % 0.38/0.64 (define @t182 () (@var "C_5" tptp.int)) % 0.38/0.64 (define @t183 () (@var "A_5" tptp.int)) % 0.38/0.64 (define @t184 () (@var "D_2" tptp.nat)) % 0.38/0.64 (define @t185 () (@var "B_2" tptp.nat)) % 0.38/0.64 (define @t186 () (@var "C_5" tptp.nat)) % 0.38/0.64 (define @t187 () (@var "A_5" tptp.nat)) % 0.38/0.64 (define @t188 () (@var "B_1" tptp.int)) % 0.38/0.64 (define @t189 () (@var "C_4" tptp.int)) % 0.38/0.64 (define @t190 () (@var "A_4" tptp.int)) % 0.38/0.64 (define @t191 () (@var "B_1" tptp.nat)) % 0.38/0.64 (define @t192 () (@var "C_4" tptp.nat)) % 0.38/0.64 (define @t193 () (@var "A_4" tptp.nat)) % 0.38/0.64 (define @t194 () (@var "C_3" tptp.int)) % 0.38/0.64 (define @t195 () (@var "B" tptp.int)) % 0.38/0.64 (define @t196 () (@var "A_3" tptp.int)) % 0.38/0.64 (define @t197 () (@var "C_3" tptp.nat)) % 0.38/0.64 (define @t198 () (@var "B" tptp.nat)) % 0.38/0.64 (define @t199 () (@var "A_3" tptp.nat)) % 0.38/0.64 (define @t200 () (@var "D_1" tptp.int)) % 0.38/0.64 (define @t201 () (@var "C_2" tptp.int)) % 0.38/0.64 (define @t202 () (@var "A_2" tptp.int)) % 0.38/0.64 (define @t203 () (@var "D_1" tptp.nat)) % 0.38/0.64 (define @t204 () (@var "C_2" tptp.nat)) % 0.38/0.64 (define @t205 () (@var "A_2" tptp.nat)) % 0.38/0.64 (define @t206 () (@var "D" tptp.int)) % 0.38/0.64 (define @t207 () (@var "A_1" tptp.int)) % 0.38/0.64 (define @t208 () (@var "C_1" tptp.int)) % 0.38/0.64 (define @t209 () (@var "D" tptp.nat)) % 0.38/0.64 (define @t210 () (@var "A_1" tptp.nat)) % 0.38/0.64 (define @t211 () (@var "C_1" tptp.nat)) % 0.38/0.64 (define @t212 () (@var "A" tptp.int)) % 0.38/0.64 (define @t213 () (@var "C" tptp.int)) % 0.38/0.64 (define @t214 () (@var "A" tptp.nat)) % 0.38/0.64 (define @t215 () (@var "C" tptp.nat)) % 0.38/0.64 (define @t216 () (= @t99 @t98)) % 0.38/0.64 (define @t217 () (@var "Z3" tptp.int)) % 0.38/0.64 (define @t218 () (@var "Z2" tptp.int)) % 0.38/0.64 (define @t219 () (@var "Z1" tptp.int)) % 0.38/0.64 (define @t220 () (@list @t219 @t218 @t217)) % 0.38/0.64 (define @t221 () (not @t10)) % 0.38/0.64 (define @t222 () (forall @t9 (not @t8))) % 0.38/0.64 (define @t223 () (not @t222)) % 0.38/0.64 (define @t224 () (not @t12)) % 0.38/0.64 (define @t225 () (@list false)) % 0.38/0.64 (define @t226 () (@list @t222)) % 0.38/0.64 (define @t227 () (= tptp.one_one_int tptp.t)) % 0.38/0.64 (define @t228 () (not @t227)) % 0.38/0.64 (define @t229 () (not @t1)) % 0.38/0.64 (define @t230 () (and @t1 @t228)) % 0.38/0.64 (define @t231 () (= @t12 @t230)) % 0.38/0.64 (assume @p1 @t1) % 0.38/0.64 (assume @p2 @t11) % 0.38/0.64 (assume @p3 @t13) % 0.38/0.64 (assume @p4 (tptp.ord_less_int tptp.t @t4)) % 0.38/0.64 (assume @p5 (tptp.zprime @t4)) % 0.38/0.64 (assume @p6 (= @t15 @t14)) % 0.38/0.64 (assume @p7 (tptp.twoSqu1431725154sum2sq @t14)) % 0.38/0.64 (assume @p8 (forall @t22 (= (tptp.power_power_int @t21 @t5) (tptp.plus_plus_int (tptp.plus_plus_int @t20 (tptp.times_times_int (tptp.times_times_int @t19 @t18) @t16)) @t17)))) % 0.38/0.64 (assume @p9 (forall @t22 (= (tptp.power_power_int @t21 @t24) (tptp.plus_plus_int (tptp.plus_plus_int (tptp.plus_plus_int @t26 (tptp.times_times_int (tptp.times_times_int @t25 @t20) @t16)) (tptp.times_times_int (tptp.times_times_int @t25 @t18) @t17)) (tptp.power_power_int @t16 @t24))))) % 0.38/0.64 (assume @p10 (forall (@list @t28 @t27) (= (tptp.power_power_nat (tptp.plus_plus_nat @t28 @t27) @t5) (tptp.plus_plus_nat (tptp.plus_plus_nat (tptp.power_power_nat @t28 @t5) (tptp.power_power_nat @t27 @t5)) (tptp.times_times_nat (tptp.times_times_nat @t5 @t28) @t27))))) % 0.38/0.64 (assume @p11 (forall @t31 (= (tptp.power_power_int (tptp.plus_plus_int @t30 @t29) @t5) (tptp.plus_plus_int (tptp.plus_plus_int (tptp.power_power_int @t30 @t5) (tptp.power_power_int @t29 @t5)) (tptp.times_times_int (tptp.times_times_int @t19 @t30) @t29))))) % 0.38/0.64 (assume @p12 (forall @t34 (= (tptp.power_power_int @t33 @t5) (tptp.times_times_int @t33 @t33)))) % 0.38/0.64 (assume @p13 (forall @t34 (= (tptp.power_power_nat @t35 @t5) (tptp.times_times_nat @t35 @t35)))) % 0.38/0.64 (assume @p14 (forall (@list @t18) (= (tptp.times_times_int @t18 @t20) @t26))) % 0.38/0.64 (assume @p15 (= (tptp.power_power_nat tptp.one_one_nat @t5) tptp.one_one_nat)) % 0.38/0.64 (assume @p16 (= (tptp.power_power_int tptp.one_one_int @t5) tptp.one_one_int)) % 0.38/0.64 (assume @p17 (forall (@list @t36) (= (tptp.times_times_int @t36 @t36) (tptp.power_power_int @t36 @t5)))) % 0.38/0.64 (assume @p18 (forall (@list @t37) (= (tptp.times_times_nat @t37 @t37) (tptp.power_power_nat @t37 @t5)))) % 0.38/0.64 (assume @p19 (forall (@list @t38) (= (tptp.power_power_int @t38 @t5) (tptp.times_times_int @t38 @t38)))) % 0.38/0.64 (assume @p20 (forall (@list @t39) (= (tptp.power_power_nat @t39 @t5) (tptp.times_times_nat @t39 @t39)))) % 0.38/0.64 (assume @p21 (forall (@list @t41 @t40) (= (tptp.power_power_int @t41 @t43) (tptp.times_times_int @t42 @t42)))) % 0.38/0.64 (assume @p22 (forall (@list @t44 @t40) (= (tptp.power_power_nat @t44 @t43) (tptp.times_times_nat @t45 @t45)))) % 0.38/0.64 (assume @p23 (forall (@list @t46) (= (tptp.plus_plus_int tptp.one_one_int (tptp.number_number_of_int @t46)) (tptp.number_number_of_int (tptp.plus_plus_int @t2 @t46))))) % 0.38/0.64 (assume @p24 (forall (@list @t47) (= (tptp.plus_plus_int (tptp.number_number_of_int @t47) tptp.one_one_int) (tptp.number_number_of_int (tptp.plus_plus_int @t47 @t2))))) % 0.38/0.64 (assume @p25 (= (tptp.plus_plus_int tptp.one_one_int tptp.one_one_int) @t19)) % 0.38/0.64 (assume @p26 (not (forall (@list @t48) (not (= @t15 (tptp.times_times_int @t4 @t48)))))) % 0.38/0.64 (assume @p27 (forall (@list @t49) (tptp.ord_less_eq_int @t49 @t49))) % 0.38/0.64 (assume @p28 (forall @t53 (or @t52 @t51))) % 0.38/0.64 (assume @p29 (forall (@list @t55 @t54) (= (tptp.ord_less_int @t55 @t54) (and (tptp.ord_less_eq_int @t55 @t54) (not (= @t55 @t54)))))) % 0.38/0.64 (assume @p30 (forall (@list @t56 @t57) (or (tptp.ord_less_int @t56 @t57) (= @t56 @t57) (tptp.ord_less_int @t57 @t56)))) % 0.38/0.64 (assume @p31 (forall @t62 (=> @t61 (=> (tptp.ord_less_eq_int @t60 @t58) (tptp.ord_less_eq_int @t59 @t58))))) % 0.38/0.64 (assume @p32 (forall @t53 (=> @t52 (=> @t51 (= @t50 @t49))))) % 0.38/0.64 (assume @p33 (forall (@list @t66 @t64 @t63) (= (tptp.power_power_int (tptp.power_power_int @t66 @t64) @t63) (tptp.power_power_int @t66 @t65)))) % 0.38/0.64 (assume @p34 (forall (@list @t67 @t64 @t63) (= (tptp.power_power_nat (tptp.power_power_nat @t67 @t64) @t63) (tptp.power_power_nat @t67 @t65)))) % 0.38/0.64 (assume @p35 (forall (@list @t68) (= (tptp.power_power_int @t68 tptp.one_one_nat) @t68))) % 0.38/0.64 (assume @p36 (forall (@list @t69) (= (tptp.power_power_nat @t69 tptp.one_one_nat) @t69))) % 0.38/0.64 (assume @p37 (forall @t73 (= (tptp.power_power_int @t72 @t70) (tptp.power_power_int @t56 (tptp.times_times_nat @t71 @t70))))) % 0.38/0.64 (assume @p38 (forall @t77 (= (tptp.ord_less_eq_nat @t75 @t76) (not (tptp.ord_less_nat @t76 @t75))))) % 0.38/0.64 (assume @p39 (forall @t77 (= (tptp.ord_less_eq_int @t78 @t79) (not (tptp.ord_less_int @t79 @t78))))) % 0.38/0.64 (assume @p40 (forall @t31 (= (tptp.ord_less_int @t81 @t80) (tptp.ord_less_int @t30 @t29)))) % 0.38/0.64 (assume @p41 (forall @t31 (= (tptp.ord_less_eq_int @t81 @t80) (tptp.ord_less_eq_int @t30 @t29)))) % 0.38/0.64 (assume @p42 (forall (@list @t83 @t50 @t84 @t49) (=> (tptp.ord_less_int @t84 @t49) (=> (tptp.ord_less_eq_int @t83 @t50) (tptp.ord_less_int (tptp.plus_plus_int @t84 @t83) @t82))))) % 0.38/0.64 (assume @p43 (forall (@list @t88 @t86 @t85) (= (tptp.times_times_int (tptp.power_power_int @t88 @t86) (tptp.power_power_int @t88 @t85)) (tptp.power_power_int @t88 @t87)))) % 0.38/0.64 (assume @p44 (forall (@list @t89 @t86 @t85) (= (tptp.times_times_nat (tptp.power_power_nat @t89 @t86) (tptp.power_power_nat @t89 @t85)) (tptp.power_power_nat @t89 @t87)))) % 0.38/0.64 (assume @p45 (forall @t73 (= (tptp.power_power_int @t56 (tptp.plus_plus_nat @t71 @t70)) (tptp.times_times_int @t72 (tptp.power_power_int @t56 @t70))))) % 0.38/0.64 (assume @p46 (forall @t91 (= (tptp.times_times_nat @t5 @t70) @t90))) % 0.38/0.64 (assume @p47 (forall @t91 (= (tptp.times_times_nat @t70 @t5) @t90))) % 0.38/0.64 (assume @p48 (= (tptp.plus_plus_nat tptp.one_one_nat tptp.one_one_nat) @t5)) % 0.38/0.64 (assume @p49 (forall @t97 (= (tptp.ord_less_int @t96 @t95) @t94))) % 0.38/0.64 (assume @p50 (forall @t103 (= (tptp.ord_less_int @t102 @t101) @t100))) % 0.38/0.64 (assume @p51 (forall @t97 (= (tptp.ord_less_eq_int @t96 @t95) @t104))) % 0.38/0.64 (assume @p52 (forall @t103 (= (tptp.ord_less_eq_int @t102 @t101) @t105))) % 0.38/0.64 (assume @p53 (not (tptp.ord_less_int tptp.pls tptp.pls))) % 0.38/0.64 (assume @p54 (forall @t97 (= (tptp.ord_less_int @t107 @t106) @t94))) % 0.38/0.64 (assume @p55 (forall @t103 (= (tptp.ord_less_int @t109 @t108) @t100))) % 0.38/0.64 (assume @p56 (tptp.ord_less_eq_int tptp.pls tptp.pls)) % 0.38/0.64 (assume @p57 (forall @t97 (= (tptp.ord_less_eq_int @t107 @t106) @t104))) % 0.38/0.64 (assume @p58 (forall @t103 (= (tptp.ord_less_eq_int @t109 @t108) @t105))) % 0.38/0.64 (assume @p59 (forall @t103 (= (tptp.ord_less_int @t111 @t110) @t100))) % 0.38/0.64 (assume @p60 (forall @t103 (= (tptp.ord_less_eq_int @t111 @t110) @t105))) % 0.38/0.64 (assume @p61 (forall @t62 (=> (tptp.ord_less_int @t59 @t60) (tptp.ord_less_int (tptp.plus_plus_int @t59 @t58) (tptp.plus_plus_int @t60 @t58))))) % 0.38/0.64 (assume @p62 (forall @t62 (=> @t61 (tptp.ord_less_eq_int (tptp.plus_plus_int @t58 @t59) (tptp.plus_plus_int @t58 @t60))))) % 0.38/0.64 (assume @p63 (forall (@list @t112 @t113) (and (=> @t118 (= @t116 @t114)) (=> (not @t118) (and (=> @t117 (= @t116 @t115)) (=> (not @t117) (= @t116 (tptp.number_number_of_nat (tptp.plus_plus_int @t113 @t112))))))))) % 0.38/0.64 (assume @p64 (= @t119 tptp.one_one_nat)) % 0.38/0.64 (assume @p65 (= tptp.one_one_nat @t119)) % 0.38/0.64 (assume @p66 (forall @t121 (= (tptp.ord_less_eq_int @t102 tptp.pls) @t120))) % 0.38/0.64 (assume @p67 (forall @t121 (= (tptp.ord_less_int tptp.pls @t102) @t122))) % 0.38/0.64 (assume @p68 (forall @t97 (= (tptp.ord_less_eq_int @t96 @t106) @t94))) % 0.38/0.64 (assume @p69 (forall @t103 (= (tptp.ord_less_eq_int @t102 @t108) @t100))) % 0.38/0.64 (assume @p70 (forall @t97 (= (tptp.ord_less_int @t107 @t95) @t104))) % 0.38/0.64 (assume @p71 (forall @t103 (= (tptp.ord_less_int @t109 @t101) @t105))) % 0.38/0.64 (assume @p72 (forall (@list @t49 @t50) (=> (tptp.ord_less_int @t49 @t50) (tptp.ord_less_eq_int (tptp.plus_plus_int @t49 tptp.one_one_int) @t50)))) % 0.38/0.64 (assume @p73 (forall @t123 (= (tptp.ord_less_eq_int (tptp.plus_plus_int @t54 tptp.one_one_int) @t55) (tptp.ord_less_int @t54 @t55)))) % 0.38/0.64 (assume @p74 (forall @t123 (= (tptp.ord_less_int @t54 (tptp.plus_plus_int @t55 tptp.one_one_int)) (tptp.ord_less_eq_int @t54 @t55)))) % 0.38/0.64 (assume @p75 (tptp.zprime @t19)) % 0.38/0.64 (assume @p76 (forall (@list @t57 @t56) (=> (tptp.twoSqu1431725154sum2sq @t56) (=> (tptp.twoSqu1431725154sum2sq @t57) (tptp.twoSqu1431725154sum2sq (tptp.times_times_int @t56 @t57)))))) % 0.38/0.64 (assume @p77 (forall (@list @t127 @t125 @t126 @t124) (= (tptp.times_times_int (tptp.times_times_int @t127 @t125) (tptp.times_times_int @t126 @t124)) (tptp.times_times_int (tptp.times_times_int @t127 @t126) (tptp.times_times_int @t125 @t124))))) % 0.38/0.64 (assume @p78 (forall (@list @t131 @t129 @t130 @t128) (= (tptp.times_times_nat (tptp.times_times_nat @t131 @t129) (tptp.times_times_nat @t130 @t128)) (tptp.times_times_nat (tptp.times_times_nat @t131 @t130) (tptp.times_times_nat @t129 @t128))))) % 0.38/0.64 (assume @p79 (forall (@list @t134 @t133 @t136 @t132) (= (tptp.times_times_int @t135 (tptp.times_times_int @t136 @t132)) (tptp.times_times_int @t136 (tptp.times_times_int @t135 @t132))))) % 0.38/0.64 (assume @p80 (forall (@list @t139 @t138 @t141 @t137) (= (tptp.times_times_nat @t140 (tptp.times_times_nat @t141 @t137)) (tptp.times_times_nat @t141 (tptp.times_times_nat @t140 @t137))))) % 0.38/0.64 (assume @p81 (forall (@list @t146 @t145 @t143 @t142) (= (tptp.times_times_int (tptp.times_times_int @t146 @t145) @t144) (tptp.times_times_int @t146 (tptp.times_times_int @t145 @t144))))) % 0.38/0.64 (assume @p82 (forall (@list @t151 @t150 @t148 @t147) (= (tptp.times_times_nat (tptp.times_times_nat @t151 @t150) @t149) (tptp.times_times_nat @t151 (tptp.times_times_nat @t150 @t149))))) % 0.38/0.64 (assume @p83 (forall (@list @t154 @t152 @t153) (= (tptp.times_times_int (tptp.times_times_int @t154 @t152) @t153) (tptp.times_times_int (tptp.times_times_int @t154 @t153) @t152)))) % 0.38/0.64 (assume @p84 (forall (@list @t157 @t155 @t156) (= (tptp.times_times_nat (tptp.times_times_nat @t157 @t155) @t156) (tptp.times_times_nat (tptp.times_times_nat @t157 @t156) @t155)))) % 0.38/0.64 (assume @p85 (forall (@list @t160 @t159 @t158) (= (tptp.times_times_int (tptp.times_times_int @t160 @t159) @t158) (tptp.times_times_int @t160 (tptp.times_times_int @t159 @t158))))) % 0.38/0.64 (assume @p86 (forall (@list @t163 @t162 @t161) (= (tptp.times_times_nat (tptp.times_times_nat @t163 @t162) @t161) (tptp.times_times_nat @t163 (tptp.times_times_nat @t162 @t161))))) % 0.38/0.64 (assume @p87 (forall (@list @t166 @t165 @t164) (= (tptp.times_times_int @t166 (tptp.times_times_int @t165 @t164)) (tptp.times_times_int (tptp.times_times_int @t166 @t165) @t164)))) % 0.38/0.64 (assume @p88 (forall (@list @t169 @t168 @t167) (= (tptp.times_times_nat @t169 (tptp.times_times_nat @t168 @t167)) (tptp.times_times_nat (tptp.times_times_nat @t169 @t168) @t167)))) % 0.38/0.64 (assume @p89 (forall (@list @t171 @t172 @t170) (= (tptp.times_times_int @t171 (tptp.times_times_int @t172 @t170)) (tptp.times_times_int @t172 (tptp.times_times_int @t171 @t170))))) % 0.38/0.64 (assume @p90 (forall (@list @t174 @t175 @t173) (= (tptp.times_times_nat @t174 (tptp.times_times_nat @t175 @t173)) (tptp.times_times_nat @t175 (tptp.times_times_nat @t174 @t173))))) % 0.38/0.64 (assume @p91 (forall (@list @t176 @t177) (= (tptp.times_times_int @t176 @t177) (tptp.times_times_int @t177 @t176)))) % 0.38/0.64 (assume @p92 (forall (@list @t178 @t179) (= (tptp.times_times_nat @t178 @t179) (tptp.times_times_nat @t179 @t178)))) % 0.38/0.64 (assume @p93 (forall (@list @t183 @t181 @t182 @t180) (= (tptp.plus_plus_int (tptp.plus_plus_int @t183 @t181) (tptp.plus_plus_int @t182 @t180)) (tptp.plus_plus_int (tptp.plus_plus_int @t183 @t182) (tptp.plus_plus_int @t181 @t180))))) % 0.38/0.64 (assume @p94 (forall (@list @t187 @t185 @t186 @t184) (= (tptp.plus_plus_nat (tptp.plus_plus_nat @t187 @t185) (tptp.plus_plus_nat @t186 @t184)) (tptp.plus_plus_nat (tptp.plus_plus_nat @t187 @t186) (tptp.plus_plus_nat @t185 @t184))))) % 0.38/0.64 (assume @p95 (forall (@list @t190 @t188 @t189) (= (tptp.plus_plus_int (tptp.plus_plus_int @t190 @t188) @t189) (tptp.plus_plus_int (tptp.plus_plus_int @t190 @t189) @t188)))) % 0.38/0.64 (assume @p96 (forall (@list @t193 @t191 @t192) (= (tptp.plus_plus_nat (tptp.plus_plus_nat @t193 @t191) @t192) (tptp.plus_plus_nat (tptp.plus_plus_nat @t193 @t192) @t191)))) % 0.38/0.64 (assume @p97 (forall (@list @t196 @t195 @t194) (= (tptp.plus_plus_int (tptp.plus_plus_int @t196 @t195) @t194) (tptp.plus_plus_int @t196 (tptp.plus_plus_int @t195 @t194))))) % 0.38/0.64 (assume @p98 (forall (@list @t199 @t198 @t197) (= (tptp.plus_plus_nat (tptp.plus_plus_nat @t199 @t198) @t197) (tptp.plus_plus_nat @t199 (tptp.plus_plus_nat @t198 @t197))))) % 0.38/0.64 (assume @p99 (forall (@list @t202 @t201 @t200) (= (tptp.plus_plus_int @t202 (tptp.plus_plus_int @t201 @t200)) (tptp.plus_plus_int (tptp.plus_plus_int @t202 @t201) @t200)))) % 0.38/0.64 (assume @p100 (forall (@list @t205 @t204 @t203) (= (tptp.plus_plus_nat @t205 (tptp.plus_plus_nat @t204 @t203)) (tptp.plus_plus_nat (tptp.plus_plus_nat @t205 @t204) @t203)))) % 0.38/0.64 (assume @p101 (forall (@list @t207 @t208 @t206) (= (tptp.plus_plus_int @t207 (tptp.plus_plus_int @t208 @t206)) (tptp.plus_plus_int @t208 (tptp.plus_plus_int @t207 @t206))))) % 0.38/0.64 (assume @p102 (forall (@list @t210 @t211 @t209) (= (tptp.plus_plus_nat @t210 (tptp.plus_plus_nat @t211 @t209)) (tptp.plus_plus_nat @t211 (tptp.plus_plus_nat @t210 @t209))))) % 0.38/0.64 (assume @p103 (forall (@list @t212 @t213) (= (tptp.plus_plus_int @t212 @t213) (tptp.plus_plus_int @t213 @t212)))) % 0.38/0.64 (assume @p104 (forall (@list @t214 @t215) (= (tptp.plus_plus_nat @t214 @t215) (tptp.plus_plus_nat @t215 @t214)))) % 0.38/0.64 (assume @p105 (forall @t31 (= (= @t81 @t80) (= @t30 @t29)))) % 0.38/0.64 (assume @p106 (forall (@list @t54 @t28) (= (= @t76 @t28) (= @t28 @t76)))) % 0.38/0.64 (assume @p107 (forall (@list @t54 @t30) (= (= @t79 @t30) (= @t30 @t79)))) % 0.38/0.64 (assume @p108 (forall @t103 (= (= @t102 @t101) @t216))) % 0.38/0.64 (assume @p109 (forall @t103 (= (= @t109 @t108) @t216))) % 0.38/0.64 (assume @p110 (forall @t220 (= (tptp.times_times_int (tptp.times_times_int @t219 @t218) @t217) (tptp.times_times_int @t219 (tptp.times_times_int @t218 @t217))))) % 0.38/0.64 (assume @p111 (forall @t53 (= (tptp.times_times_int @t50 @t49) (tptp.times_times_int @t49 @t50)))) % 0.38/0.64 (assume @p112 (forall (@list @t58) (= (tptp.number_number_of_int @t58) @t58))) % 0.38/0.64 (assume @p113 (forall @t220 (= (tptp.plus_plus_int (tptp.plus_plus_int @t219 @t218) @t217) (tptp.plus_plus_int @t219 (tptp.plus_plus_int @t218 @t217))))) % 0.38/0.64 (assume @p114 (forall (@list @t56 @t57 @t50) (= (tptp.plus_plus_int @t56 (tptp.plus_plus_int @t57 @t50)) (tptp.plus_plus_int @t57 (tptp.plus_plus_int @t56 @t50))))) % 0.38/0.64 (assume @p115 (forall @t53 (= (tptp.plus_plus_int @t50 @t49) @t82))) % 0.38/0.64 (assume @p116 (forall @t121 (= (tptp.ord_less_int @t102 tptp.pls) @t120))) % 0.38/0.64 (assume @p117 (forall @t97 (= (tptp.ord_less_int @t96 @t106) @t94))) % 0.38/0.64 (assume @p118 (forall @t103 (= (tptp.ord_less_int @t102 @t108) @t100))) % 0.38/0.64 (assume @p119 (forall @t121 (= (tptp.ord_less_int @t109 tptp.pls) @t120))) % 0.38/0.64 (assume @p120 (forall @t121 (= (tptp.ord_less_int tptp.pls @t109) (tptp.ord_less_int tptp.pls @t99)))) % 0.38/0.64 (assume @p121 (forall @t121 (= (tptp.ord_less_eq_int tptp.pls @t102) @t122))) % 0.38/0.64 (assume @p122 (forall @t97 (= (tptp.ord_less_eq_int @t107 @t95) @t104))) % 0.38/0.64 (assume @p123 (forall @t103 (= (tptp.ord_less_eq_int @t109 @t101) @t105))) % 0.38/0.64 (assume @p124 @t221) % 0.38/0.64 (assume @p125 true) % 0.38/0.64 (step @p126 :rule bool-double-not-elim :args (@t222)) % 0.38/0.64 (step @p127 :rule exists-elim :args ((= @t10 @t223))) % 0.38/0.64 (step @p128 :rule cong :premises (@p127) :args (@t221)) % 0.38/0.64 (step @p129 :rule trans :premises (@p128 @p126)) % 0.38/0.64 (step @p130 :rule eq_resolve :premises (@p124 @p129)) % 0.38/0.64 (step @p131 :rule refl :args (@t12)) % 0.38/0.64 (step @p132 :rule cong :premises (@p131 @p127) :args (@t13)) % 0.38/0.64 (step @p133 :rule eq_resolve :premises (@p3 @p132)) % 0.38/0.64 (step @p134 :rule implies_elim :premises (@p133)) % 0.38/0.64 (step @p135 :rule reordering :premises (@p134) :args ((or @t223 @t224))) % 0.38/0.64 (step @p136 :rule chain_m_resolution :premises (@p135 @p130) :args (@t224 @t225 @t226)) % 0.38/0.64 (step @p137 :rule eq-symm :args (tptp.t tptp.one_one_int)) % 0.38/0.64 (step @p138 :rule cong :premises (@p137 @p127) :args (@t11)) % 0.38/0.64 (step @p139 :rule eq_resolve :premises (@p2 @p138)) % 0.38/0.64 (step @p140 :rule implies_elim :premises (@p139)) % 0.38/0.64 (step @p141 :rule reordering :premises (@p140) :args ((or @t223 @t228))) % 0.38/0.64 (step @p142 :rule chain_m_resolution :premises (@p141 @p130) :args (@t228 @t225 @t226)) % 0.38/0.64 (step @p143 :rule bool-double-not-elim :args (@t227)) % 0.38/0.64 (step @p144 :rule refl :args (@t229)) % 0.38/0.64 (step @p145 :rule refl :args (@t230)) % 0.38/0.64 (step @p146 :rule nary_cong :premises (@p145 @p144 @p143) :args ((or @t230 @t229 (not @t228)))) % 0.38/0.64 (step @p147 :rule cnf_and_neg :args (@t230)) % 0.38/0.64 (step @p148 :rule eq_resolve :premises (@p147 @p146)) % 0.38/0.64 (step @p149 :rule reordering :premises (@p148) :args ((or @t227 @t229 @t230))) % 0.38/0.64 (step @p150 :rule chain_m_resolution :premises (@p149 @p142 @p1) :args (@t230 (@list true false) (@list @t227 @t1))) % 0.38/0.64 (step @p151 :rule instantiate :premises (@p29) :args ((@list tptp.one_one_int tptp.t))) % 0.38/0.64 (step @p152 :rule cnf_equiv_pos2 :args (@t231)) % 0.38/0.64 (step @p153 :rule reordering :premises (@p152) :args ((or @t12 (not @t230) (not @t231)))) % 0.38/0.64 (step @p154 false :rule chain_m_resolution :premises (@p153 @p151 @p150 @p136) :args (false (@list false false true) (@list @t231 @t230 @t12))) % 0.38/0.64 ) % 0.38/0.64 % SZS output end Proof % 0.38/0.64 % cvc5 exiting %------------------------------------------------------------------------------