%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM926+1 : TPTP v9.2.1. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n019.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 0.37s 0.63s % Output : Proof 0.37s % 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/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n019.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 12:33:49 EDT 2026 % 0.15/0.34 % CPUTime : % 0.27/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.63 % SZS status Theorem % 0.37/0.63 % SZS output start Proof % 0.37/0.63 ( % 0.37/0.63 (declare-sort $$unsorted 0) % 0.37/0.63 (declare-const tptp.ord_less_eq_nat (-> $$unsorted $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.ord_less_nat (-> $$unsorted $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.one_one_nat $$unsorted) % 0.37/0.63 (declare-const tptp.plus_plus_nat (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.power_power_nat (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.times_times_nat (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.twoSqu526106917sum2sq (-> $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.bit1 (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.one_one_int $$unsorted) % 0.37/0.63 (declare-const tptp.zprime (-> $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.ord_less_eq_int (-> $$unsorted $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.number_number_of_nat (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.m $$unsorted) % 0.37/0.63 (declare-const tptp.t $$unsorted) % 0.37/0.63 (declare-const tptp.bit0 (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.pls $$unsorted) % 0.37/0.63 (declare-const tptp.ord_less_int (-> $$unsorted $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.s $$unsorted) % 0.37/0.63 (declare-const tptp.number_number_of_int (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.times_times_int (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.plus_plus_int (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.power_power_int (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (define @t1 () (tptp.ord_less_eq_int tptp.one_one_int tptp.t)) % 0.37/0.63 (define @t2 () (tptp.bit1 tptp.pls)) % 0.37/0.63 (define @t3 () (tptp.bit0 @t2)) % 0.37/0.63 (define @t4 () (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 @t3)) tptp.m) tptp.one_one_int)) % 0.37/0.63 (define @t5 () (tptp.number_number_of_nat @t3)) % 0.37/0.63 (define @t6 () (@var "Y" $$unsorted)) % 0.37/0.63 (define @t7 () (@var "X" $$unsorted)) % 0.37/0.63 (define @t8 () (= (tptp.plus_plus_int (tptp.power_power_int @t7 @t5) (tptp.power_power_int @t6 @t5)) @t4)) % 0.37/0.63 (define @t9 () (@list @t7 @t6)) % 0.37/0.63 (define @t10 () (exists @t9 @t8)) % 0.37/0.63 (define @t11 () (=> (= tptp.t tptp.one_one_int) @t10)) % 0.37/0.63 (define @t12 () (tptp.ord_less_int tptp.one_one_int tptp.t)) % 0.37/0.63 (define @t13 () (=> @t12 @t10)) % 0.37/0.63 (define @t14 () (tptp.times_times_int @t4 tptp.t)) % 0.37/0.63 (define @t15 () (tptp.plus_plus_int (tptp.power_power_int tptp.s @t5) tptp.one_one_int)) % 0.37/0.63 (define @t16 () (@var "B_4" $$unsorted)) % 0.37/0.63 (define @t17 () (tptp.power_power_int @t16 @t5)) % 0.37/0.63 (define @t18 () (@var "A_8" $$unsorted)) % 0.37/0.63 (define @t19 () (tptp.number_number_of_int @t3)) % 0.37/0.63 (define @t20 () (tptp.power_power_int @t18 @t5)) % 0.37/0.63 (define @t21 () (tptp.plus_plus_int @t18 @t16)) % 0.37/0.63 (define @t22 () (@list @t18 @t16)) % 0.37/0.63 (define @t23 () (tptp.bit1 @t2)) % 0.37/0.63 (define @t24 () (tptp.number_number_of_nat @t23)) % 0.37/0.63 (define @t25 () (tptp.number_number_of_int @t23)) % 0.37/0.63 (define @t26 () (tptp.power_power_int @t18 @t24)) % 0.37/0.63 (define @t27 () (@var "Y_2" $$unsorted)) % 0.37/0.63 (define @t28 () (@var "X_2" $$unsorted)) % 0.37/0.63 (define @t29 () (@list @t28 @t27)) % 0.37/0.63 (define @t30 () (@var "W_4" $$unsorted)) % 0.37/0.63 (define @t31 () (tptp.number_number_of_int @t30)) % 0.37/0.63 (define @t32 () (@list @t30)) % 0.37/0.63 (define @t33 () (tptp.number_number_of_nat @t30)) % 0.37/0.63 (define @t34 () (@var "X_7" $$unsorted)) % 0.37/0.63 (define @t35 () (@list @t34)) % 0.37/0.63 (define @t36 () (@var "A_7" $$unsorted)) % 0.37/0.63 (define @t37 () (@list @t36)) % 0.37/0.63 (define @t38 () (@var "N" $$unsorted)) % 0.37/0.63 (define @t39 () (@var "X_6" $$unsorted)) % 0.37/0.63 (define @t40 () (tptp.power_power_int @t39 @t38)) % 0.37/0.63 (define @t41 () (tptp.times_times_nat @t5 @t38)) % 0.37/0.63 (define @t42 () (@list @t39 @t38)) % 0.37/0.63 (define @t43 () (tptp.power_power_nat @t39 @t38)) % 0.37/0.63 (define @t44 () (@var "W_3" $$unsorted)) % 0.37/0.63 (define @t45 () (@var "V_3" $$unsorted)) % 0.37/0.63 (define @t46 () (@var "T" $$unsorted)) % 0.37/0.63 (define @t47 () (@var "W" $$unsorted)) % 0.37/0.63 (define @t48 () (@var "Z" $$unsorted)) % 0.37/0.63 (define @t49 () (tptp.ord_less_eq_int @t47 @t48)) % 0.37/0.63 (define @t50 () (tptp.ord_less_eq_int @t48 @t47)) % 0.37/0.63 (define @t51 () (@list @t48 @t47)) % 0.37/0.63 (define @t52 () (@var "W_1" $$unsorted)) % 0.37/0.63 (define @t53 () (@var "Z_1" $$unsorted)) % 0.37/0.63 (define @t54 () (@var "X_1" $$unsorted)) % 0.37/0.63 (define @t55 () (@var "Y_1" $$unsorted)) % 0.37/0.63 (define @t56 () (@var "K_1" $$unsorted)) % 0.37/0.63 (define @t57 () (@var "I" $$unsorted)) % 0.37/0.63 (define @t58 () (@var "J" $$unsorted)) % 0.37/0.63 (define @t59 () (tptp.ord_less_eq_int @t57 @t58)) % 0.37/0.63 (define @t60 () (@list @t56 @t57 @t58)) % 0.37/0.63 (define @t61 () (@var "Q_1" $$unsorted)) % 0.37/0.63 (define @t62 () (@var "P_1" $$unsorted)) % 0.37/0.63 (define @t63 () (tptp.times_times_nat @t62 @t61)) % 0.37/0.63 (define @t64 () (@var "X_5" $$unsorted)) % 0.37/0.63 (define @t65 () (@list @t64 @t62 @t61)) % 0.37/0.63 (define @t66 () (@var "X_4" $$unsorted)) % 0.37/0.63 (define @t67 () (@list @t66)) % 0.37/0.63 (define @t68 () (tptp.power_power_int @t54 @t55)) % 0.37/0.63 (define @t69 () (@list @t54 @t55 @t48)) % 0.37/0.63 (define @t70 () (@var "V_2" $$unsorted)) % 0.37/0.63 (define @t71 () (tptp.number_number_of_nat @t70)) % 0.37/0.63 (define @t72 () (tptp.number_number_of_nat @t52)) % 0.37/0.63 (define @t73 () (@list @t70 @t52)) % 0.37/0.63 (define @t74 () (tptp.number_number_of_int @t70)) % 0.37/0.63 (define @t75 () (tptp.number_number_of_int @t52)) % 0.37/0.63 (define @t76 () (tptp.number_number_of_int @t27)) % 0.37/0.63 (define @t77 () (tptp.number_number_of_int @t28)) % 0.37/0.63 (define @t78 () (tptp.plus_plus_int @t47 @t48)) % 0.37/0.63 (define @t79 () (@var "Z_2" $$unsorted)) % 0.37/0.63 (define @t80 () (@var "W_2" $$unsorted)) % 0.37/0.63 (define @t81 () (@var "Q" $$unsorted)) % 0.37/0.63 (define @t82 () (@var "P" $$unsorted)) % 0.37/0.63 (define @t83 () (tptp.plus_plus_nat @t82 @t81)) % 0.37/0.63 (define @t84 () (@var "X_3" $$unsorted)) % 0.37/0.63 (define @t85 () (@list @t84 @t82 @t81)) % 0.37/0.63 (define @t86 () (tptp.plus_plus_nat @t48 @t48)) % 0.37/0.63 (define @t87 () (@list @t48)) % 0.37/0.63 (define @t88 () (@var "K2" $$unsorted)) % 0.37/0.63 (define @t89 () (@var "K1" $$unsorted)) % 0.37/0.63 (define @t90 () (tptp.ord_less_int @t89 @t88)) % 0.37/0.63 (define @t91 () (tptp.bit1 @t88)) % 0.37/0.63 (define @t92 () (tptp.bit1 @t89)) % 0.37/0.63 (define @t93 () (@list @t89 @t88)) % 0.37/0.63 (define @t94 () (@var "L" $$unsorted)) % 0.37/0.63 (define @t95 () (@var "K" $$unsorted)) % 0.37/0.63 (define @t96 () (tptp.ord_less_int @t95 @t94)) % 0.37/0.63 (define @t97 () (tptp.bit1 @t94)) % 0.37/0.63 (define @t98 () (tptp.bit1 @t95)) % 0.37/0.63 (define @t99 () (@list @t95 @t94)) % 0.37/0.63 (define @t100 () (tptp.ord_less_eq_int @t89 @t88)) % 0.37/0.63 (define @t101 () (tptp.ord_less_eq_int @t95 @t94)) % 0.37/0.63 (define @t102 () (tptp.bit0 @t88)) % 0.37/0.63 (define @t103 () (tptp.bit0 @t89)) % 0.37/0.63 (define @t104 () (tptp.bit0 @t94)) % 0.37/0.63 (define @t105 () (tptp.bit0 @t95)) % 0.37/0.63 (define @t106 () (tptp.number_number_of_int @t94)) % 0.37/0.63 (define @t107 () (tptp.number_number_of_int @t95)) % 0.37/0.63 (define @t108 () (@var "V_1" $$unsorted)) % 0.37/0.63 (define @t109 () (@var "V" $$unsorted)) % 0.37/0.63 (define @t110 () (tptp.number_number_of_nat @t108)) % 0.37/0.63 (define @t111 () (tptp.number_number_of_nat @t109)) % 0.37/0.63 (define @t112 () (tptp.plus_plus_nat @t111 @t110)) % 0.37/0.63 (define @t113 () (tptp.ord_less_int @t108 tptp.pls)) % 0.37/0.63 (define @t114 () (tptp.ord_less_int @t109 tptp.pls)) % 0.37/0.63 (define @t115 () (tptp.number_number_of_nat @t2)) % 0.37/0.63 (define @t116 () (tptp.ord_less_int @t95 tptp.pls)) % 0.37/0.63 (define @t117 () (@list @t95)) % 0.37/0.63 (define @t118 () (tptp.ord_less_eq_int tptp.pls @t95)) % 0.37/0.63 (define @t119 () (@list @t52 @t53)) % 0.37/0.63 (define @t120 () (@var "Ry_4" $$unsorted)) % 0.37/0.63 (define @t121 () (@var "Ly_4" $$unsorted)) % 0.37/0.63 (define @t122 () (@var "Rx_6" $$unsorted)) % 0.37/0.63 (define @t123 () (@var "Lx_6" $$unsorted)) % 0.37/0.63 (define @t124 () (@list @t123 @t121 @t122 @t120)) % 0.37/0.63 (define @t125 () (@var "Ry_3" $$unsorted)) % 0.37/0.63 (define @t126 () (@var "Ly_3" $$unsorted)) % 0.37/0.63 (define @t127 () (@var "Lx_5" $$unsorted)) % 0.37/0.63 (define @t128 () (tptp.times_times_int @t127 @t126)) % 0.37/0.63 (define @t129 () (@var "Rx_5" $$unsorted)) % 0.37/0.63 (define @t130 () (@list @t127 @t126 @t129 @t125)) % 0.37/0.63 (define @t131 () (tptp.times_times_nat @t127 @t126)) % 0.37/0.63 (define @t132 () (@var "Ry_2" $$unsorted)) % 0.37/0.63 (define @t133 () (@var "Rx_4" $$unsorted)) % 0.37/0.63 (define @t134 () (tptp.times_times_int @t133 @t132)) % 0.37/0.63 (define @t135 () (@var "Ly_2" $$unsorted)) % 0.37/0.63 (define @t136 () (@var "Lx_4" $$unsorted)) % 0.37/0.63 (define @t137 () (@list @t136 @t135 @t133 @t132)) % 0.37/0.63 (define @t138 () (tptp.times_times_nat @t133 @t132)) % 0.37/0.63 (define @t139 () (@var "Ly_1" $$unsorted)) % 0.37/0.63 (define @t140 () (@var "Rx_3" $$unsorted)) % 0.37/0.63 (define @t141 () (@var "Lx_3" $$unsorted)) % 0.37/0.63 (define @t142 () (@list @t141 @t139 @t140)) % 0.37/0.63 (define @t143 () (@var "Rx_2" $$unsorted)) % 0.37/0.63 (define @t144 () (@var "Ly" $$unsorted)) % 0.37/0.63 (define @t145 () (@var "Lx_2" $$unsorted)) % 0.37/0.63 (define @t146 () (@list @t145 @t144 @t143)) % 0.37/0.63 (define @t147 () (@var "Ry_1" $$unsorted)) % 0.37/0.63 (define @t148 () (@var "Rx_1" $$unsorted)) % 0.37/0.63 (define @t149 () (@var "Lx_1" $$unsorted)) % 0.37/0.63 (define @t150 () (@list @t149 @t148 @t147)) % 0.37/0.63 (define @t151 () (@var "Ry" $$unsorted)) % 0.37/0.63 (define @t152 () (@var "Lx" $$unsorted)) % 0.37/0.63 (define @t153 () (@var "Rx" $$unsorted)) % 0.37/0.63 (define @t154 () (@list @t152 @t153 @t151)) % 0.37/0.63 (define @t155 () (@var "A_6" $$unsorted)) % 0.37/0.63 (define @t156 () (@var "B_3" $$unsorted)) % 0.37/0.63 (define @t157 () (@list @t155 @t156)) % 0.37/0.63 (define @t158 () (@var "D_2" $$unsorted)) % 0.37/0.63 (define @t159 () (@var "B_2" $$unsorted)) % 0.37/0.63 (define @t160 () (@var "C_5" $$unsorted)) % 0.37/0.63 (define @t161 () (@var "A_5" $$unsorted)) % 0.37/0.63 (define @t162 () (@list @t161 @t159 @t160 @t158)) % 0.37/0.63 (define @t163 () (@var "B_1" $$unsorted)) % 0.37/0.63 (define @t164 () (@var "C_4" $$unsorted)) % 0.37/0.63 (define @t165 () (@var "A_4" $$unsorted)) % 0.37/0.63 (define @t166 () (@list @t165 @t163 @t164)) % 0.37/0.63 (define @t167 () (@var "C_3" $$unsorted)) % 0.37/0.63 (define @t168 () (@var "B" $$unsorted)) % 0.37/0.63 (define @t169 () (@var "A_3" $$unsorted)) % 0.37/0.63 (define @t170 () (@list @t169 @t168 @t167)) % 0.37/0.63 (define @t171 () (@var "D_1" $$unsorted)) % 0.37/0.63 (define @t172 () (@var "C_2" $$unsorted)) % 0.37/0.63 (define @t173 () (@var "A_2" $$unsorted)) % 0.37/0.63 (define @t174 () (@list @t173 @t172 @t171)) % 0.37/0.63 (define @t175 () (@var "D" $$unsorted)) % 0.37/0.63 (define @t176 () (@var "A_1" $$unsorted)) % 0.37/0.63 (define @t177 () (@var "C_1" $$unsorted)) % 0.37/0.63 (define @t178 () (@list @t176 @t177 @t175)) % 0.37/0.63 (define @t179 () (@var "A" $$unsorted)) % 0.37/0.63 (define @t180 () (@var "C" $$unsorted)) % 0.37/0.63 (define @t181 () (@list @t179 @t180)) % 0.37/0.63 (define @t182 () (@list @t52 @t28)) % 0.37/0.63 (define @t183 () (= @t95 @t94)) % 0.37/0.63 (define @t184 () (@var "Z3" $$unsorted)) % 0.37/0.63 (define @t185 () (@var "Z2" $$unsorted)) % 0.37/0.63 (define @t186 () (@var "Z1" $$unsorted)) % 0.37/0.63 (define @t187 () (@list @t186 @t185 @t184)) % 0.37/0.63 (define @t188 () (not @t10)) % 0.37/0.63 (define @t189 () (forall @t9 (not @t8))) % 0.37/0.63 (define @t190 () (not @t189)) % 0.37/0.63 (define @t191 () (not @t12)) % 0.37/0.63 (define @t192 () (@list false)) % 0.37/0.63 (define @t193 () (@list @t189)) % 0.37/0.63 (define @t194 () (= tptp.one_one_int tptp.t)) % 0.37/0.63 (define @t195 () (not @t194)) % 0.37/0.63 (define @t196 () (not @t1)) % 0.37/0.63 (define @t197 () (and @t1 @t195)) % 0.37/0.63 (define @t198 () (= @t12 @t197)) % 0.37/0.63 (assume @p1 @t1) % 0.37/0.63 (assume @p2 @t11) % 0.37/0.63 (assume @p3 @t13) % 0.37/0.63 (assume @p4 (tptp.ord_less_int tptp.t @t4)) % 0.37/0.63 (assume @p5 (tptp.zprime @t4)) % 0.37/0.63 (assume @p6 (= @t15 @t14)) % 0.37/0.63 (assume @p7 (tptp.twoSqu526106917sum2sq @t14)) % 0.37/0.63 (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)))) % 0.37/0.63 (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))))) % 0.37/0.63 (assume @p10 (forall @t29 (= (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))))) % 0.37/0.63 (assume @p11 (forall @t29 (= (tptp.power_power_int (tptp.plus_plus_int @t28 @t27) @t5) (tptp.plus_plus_int (tptp.plus_plus_int (tptp.power_power_int @t28 @t5) (tptp.power_power_int @t27 @t5)) (tptp.times_times_int (tptp.times_times_int @t19 @t28) @t27))))) % 0.37/0.63 (assume @p12 (forall @t32 (= (tptp.power_power_int @t31 @t5) (tptp.times_times_int @t31 @t31)))) % 0.37/0.63 (assume @p13 (forall @t32 (= (tptp.power_power_nat @t33 @t5) (tptp.times_times_nat @t33 @t33)))) % 0.37/0.63 (assume @p14 (forall (@list @t18) (= (tptp.times_times_int @t18 @t20) @t26))) % 0.37/0.63 (assume @p15 (= (tptp.power_power_nat tptp.one_one_nat @t5) tptp.one_one_nat)) % 0.37/0.63 (assume @p16 (= (tptp.power_power_int tptp.one_one_int @t5) tptp.one_one_int)) % 0.37/0.63 (assume @p17 (forall @t35 (= (tptp.times_times_int @t34 @t34) (tptp.power_power_int @t34 @t5)))) % 0.37/0.63 (assume @p18 (forall @t35 (= (tptp.times_times_nat @t34 @t34) (tptp.power_power_nat @t34 @t5)))) % 0.37/0.63 (assume @p19 (forall @t37 (= (tptp.power_power_int @t36 @t5) (tptp.times_times_int @t36 @t36)))) % 0.37/0.63 (assume @p20 (forall @t37 (= (tptp.power_power_nat @t36 @t5) (tptp.times_times_nat @t36 @t36)))) % 0.37/0.63 (assume @p21 (forall @t42 (= (tptp.power_power_int @t39 @t41) (tptp.times_times_int @t40 @t40)))) % 0.37/0.63 (assume @p22 (forall @t42 (= (tptp.power_power_nat @t39 @t41) (tptp.times_times_nat @t43 @t43)))) % 0.37/0.63 (assume @p23 (forall (@list @t44) (= (tptp.plus_plus_int tptp.one_one_int (tptp.number_number_of_int @t44)) (tptp.number_number_of_int (tptp.plus_plus_int @t2 @t44))))) % 0.37/0.63 (assume @p24 (forall (@list @t45) (= (tptp.plus_plus_int (tptp.number_number_of_int @t45) tptp.one_one_int) (tptp.number_number_of_int (tptp.plus_plus_int @t45 @t2))))) % 0.37/0.63 (assume @p25 (= (tptp.plus_plus_int tptp.one_one_int tptp.one_one_int) @t19)) % 0.37/0.63 (assume @p26 (not (forall (@list @t46) (not (= @t15 (tptp.times_times_int @t4 @t46)))))) % 0.37/0.63 (assume @p27 (forall (@list @t47) (tptp.ord_less_eq_int @t47 @t47))) % 0.37/0.63 (assume @p28 (forall @t51 (or @t50 @t49))) % 0.37/0.63 (assume @p29 (forall (@list @t53 @t52) (= (tptp.ord_less_int @t53 @t52) (and (tptp.ord_less_eq_int @t53 @t52) (not (= @t53 @t52)))))) % 0.37/0.63 (assume @p30 (forall (@list @t54 @t55) (or (tptp.ord_less_int @t54 @t55) (= @t54 @t55) (tptp.ord_less_int @t55 @t54)))) % 0.37/0.63 (assume @p31 (forall @t60 (=> @t59 (=> (tptp.ord_less_eq_int @t58 @t56) (tptp.ord_less_eq_int @t57 @t56))))) % 0.37/0.63 (assume @p32 (forall @t51 (=> @t50 (=> @t49 (= @t48 @t47))))) % 0.37/0.63 (assume @p33 (forall @t65 (= (tptp.power_power_int (tptp.power_power_int @t64 @t62) @t61) (tptp.power_power_int @t64 @t63)))) % 0.37/0.63 (assume @p34 (forall @t65 (= (tptp.power_power_nat (tptp.power_power_nat @t64 @t62) @t61) (tptp.power_power_nat @t64 @t63)))) % 0.37/0.63 (assume @p35 (forall @t67 (= (tptp.power_power_int @t66 tptp.one_one_nat) @t66))) % 0.37/0.63 (assume @p36 (forall @t67 (= (tptp.power_power_nat @t66 tptp.one_one_nat) @t66))) % 0.37/0.63 (assume @p37 (forall @t69 (= (tptp.power_power_int @t68 @t48) (tptp.power_power_int @t54 (tptp.times_times_nat @t55 @t48))))) % 0.37/0.63 (assume @p38 (forall @t73 (= (tptp.ord_less_eq_nat @t71 @t72) (not (tptp.ord_less_nat @t72 @t71))))) % 0.37/0.63 (assume @p39 (forall @t73 (= (tptp.ord_less_eq_int @t74 @t75) (not (tptp.ord_less_int @t75 @t74))))) % 0.37/0.63 (assume @p40 (forall @t29 (= (tptp.ord_less_int @t77 @t76) (tptp.ord_less_int @t28 @t27)))) % 0.37/0.63 (assume @p41 (forall @t29 (= (tptp.ord_less_eq_int @t77 @t76) (tptp.ord_less_eq_int @t28 @t27)))) % 0.37/0.63 (assume @p42 (forall (@list @t79 @t48 @t80 @t47) (=> (tptp.ord_less_int @t80 @t47) (=> (tptp.ord_less_eq_int @t79 @t48) (tptp.ord_less_int (tptp.plus_plus_int @t80 @t79) @t78))))) % 0.37/0.63 (assume @p43 (forall @t85 (= (tptp.times_times_int (tptp.power_power_int @t84 @t82) (tptp.power_power_int @t84 @t81)) (tptp.power_power_int @t84 @t83)))) % 0.37/0.63 (assume @p44 (forall @t85 (= (tptp.times_times_nat (tptp.power_power_nat @t84 @t82) (tptp.power_power_nat @t84 @t81)) (tptp.power_power_nat @t84 @t83)))) % 0.37/0.63 (assume @p45 (forall @t69 (= (tptp.power_power_int @t54 (tptp.plus_plus_nat @t55 @t48)) (tptp.times_times_int @t68 (tptp.power_power_int @t54 @t48))))) % 0.37/0.63 (assume @p46 (forall @t87 (= (tptp.times_times_nat @t5 @t48) @t86))) % 0.37/0.63 (assume @p47 (forall @t87 (= (tptp.times_times_nat @t48 @t5) @t86))) % 0.37/0.63 (assume @p48 (= (tptp.plus_plus_nat tptp.one_one_nat tptp.one_one_nat) @t5)) % 0.37/0.63 (assume @p49 (forall @t93 (= (tptp.ord_less_int @t92 @t91) @t90))) % 0.37/0.63 (assume @p50 (forall @t99 (= (tptp.ord_less_int @t98 @t97) @t96))) % 0.37/0.63 (assume @p51 (forall @t93 (= (tptp.ord_less_eq_int @t92 @t91) @t100))) % 0.37/0.63 (assume @p52 (forall @t99 (= (tptp.ord_less_eq_int @t98 @t97) @t101))) % 0.37/0.63 (assume @p53 (not (tptp.ord_less_int tptp.pls tptp.pls))) % 0.37/0.63 (assume @p54 (forall @t93 (= (tptp.ord_less_int @t103 @t102) @t90))) % 0.37/0.63 (assume @p55 (forall @t99 (= (tptp.ord_less_int @t105 @t104) @t96))) % 0.37/0.63 (assume @p56 (tptp.ord_less_eq_int tptp.pls tptp.pls)) % 0.37/0.63 (assume @p57 (forall @t93 (= (tptp.ord_less_eq_int @t103 @t102) @t100))) % 0.37/0.63 (assume @p58 (forall @t99 (= (tptp.ord_less_eq_int @t105 @t104) @t101))) % 0.37/0.63 (assume @p59 (forall @t99 (= (tptp.ord_less_int @t107 @t106) @t96))) % 0.37/0.63 (assume @p60 (forall @t99 (= (tptp.ord_less_eq_int @t107 @t106) @t101))) % 0.37/0.63 (assume @p61 (forall @t60 (=> (tptp.ord_less_int @t57 @t58) (tptp.ord_less_int (tptp.plus_plus_int @t57 @t56) (tptp.plus_plus_int @t58 @t56))))) % 0.37/0.63 (assume @p62 (forall @t60 (=> @t59 (tptp.ord_less_eq_int (tptp.plus_plus_int @t56 @t57) (tptp.plus_plus_int @t56 @t58))))) % 0.37/0.63 (assume @p63 (forall (@list @t108 @t109) (and (=> @t114 (= @t112 @t110)) (=> (not @t114) (and (=> @t113 (= @t112 @t111)) (=> (not @t113) (= @t112 (tptp.number_number_of_nat (tptp.plus_plus_int @t109 @t108))))))))) % 0.37/0.63 (assume @p64 (= @t115 tptp.one_one_nat)) % 0.37/0.63 (assume @p65 (= tptp.one_one_nat @t115)) % 0.37/0.63 (assume @p66 (forall @t117 (= (tptp.ord_less_eq_int @t98 tptp.pls) @t116))) % 0.37/0.63 (assume @p67 (forall @t117 (= (tptp.ord_less_int tptp.pls @t98) @t118))) % 0.37/0.63 (assume @p68 (forall @t93 (= (tptp.ord_less_eq_int @t92 @t102) @t90))) % 0.37/0.63 (assume @p69 (forall @t99 (= (tptp.ord_less_eq_int @t98 @t104) @t96))) % 0.37/0.63 (assume @p70 (forall @t93 (= (tptp.ord_less_int @t103 @t91) @t100))) % 0.37/0.63 (assume @p71 (forall @t99 (= (tptp.ord_less_int @t105 @t97) @t101))) % 0.37/0.63 (assume @p72 (forall (@list @t47 @t48) (=> (tptp.ord_less_int @t47 @t48) (tptp.ord_less_eq_int (tptp.plus_plus_int @t47 tptp.one_one_int) @t48)))) % 0.37/0.63 (assume @p73 (forall @t119 (= (tptp.ord_less_eq_int (tptp.plus_plus_int @t52 tptp.one_one_int) @t53) (tptp.ord_less_int @t52 @t53)))) % 0.37/0.63 (assume @p74 (forall @t119 (= (tptp.ord_less_int @t52 (tptp.plus_plus_int @t53 tptp.one_one_int)) (tptp.ord_less_eq_int @t52 @t53)))) % 0.37/0.63 (assume @p75 (tptp.zprime @t19)) % 0.37/0.63 (assume @p76 (forall (@list @t55 @t54) (=> (tptp.twoSqu526106917sum2sq @t54) (=> (tptp.twoSqu526106917sum2sq @t55) (tptp.twoSqu526106917sum2sq (tptp.times_times_int @t54 @t55)))))) % 0.37/0.63 (assume @p77 (forall @t124 (= (tptp.times_times_int (tptp.times_times_int @t123 @t121) (tptp.times_times_int @t122 @t120)) (tptp.times_times_int (tptp.times_times_int @t123 @t122) (tptp.times_times_int @t121 @t120))))) % 0.37/0.63 (assume @p78 (forall @t124 (= (tptp.times_times_nat (tptp.times_times_nat @t123 @t121) (tptp.times_times_nat @t122 @t120)) (tptp.times_times_nat (tptp.times_times_nat @t123 @t122) (tptp.times_times_nat @t121 @t120))))) % 0.37/0.63 (assume @p79 (forall @t130 (= (tptp.times_times_int @t128 (tptp.times_times_int @t129 @t125)) (tptp.times_times_int @t129 (tptp.times_times_int @t128 @t125))))) % 0.37/0.63 (assume @p80 (forall @t130 (= (tptp.times_times_nat @t131 (tptp.times_times_nat @t129 @t125)) (tptp.times_times_nat @t129 (tptp.times_times_nat @t131 @t125))))) % 0.37/0.63 (assume @p81 (forall @t137 (= (tptp.times_times_int (tptp.times_times_int @t136 @t135) @t134) (tptp.times_times_int @t136 (tptp.times_times_int @t135 @t134))))) % 0.37/0.63 (assume @p82 (forall @t137 (= (tptp.times_times_nat (tptp.times_times_nat @t136 @t135) @t138) (tptp.times_times_nat @t136 (tptp.times_times_nat @t135 @t138))))) % 0.37/0.63 (assume @p83 (forall @t142 (= (tptp.times_times_int (tptp.times_times_int @t141 @t139) @t140) (tptp.times_times_int (tptp.times_times_int @t141 @t140) @t139)))) % 0.37/0.63 (assume @p84 (forall @t142 (= (tptp.times_times_nat (tptp.times_times_nat @t141 @t139) @t140) (tptp.times_times_nat (tptp.times_times_nat @t141 @t140) @t139)))) % 0.37/0.63 (assume @p85 (forall @t146 (= (tptp.times_times_int (tptp.times_times_int @t145 @t144) @t143) (tptp.times_times_int @t145 (tptp.times_times_int @t144 @t143))))) % 0.37/0.63 (assume @p86 (forall @t146 (= (tptp.times_times_nat (tptp.times_times_nat @t145 @t144) @t143) (tptp.times_times_nat @t145 (tptp.times_times_nat @t144 @t143))))) % 0.37/0.63 (assume @p87 (forall @t150 (= (tptp.times_times_int @t149 (tptp.times_times_int @t148 @t147)) (tptp.times_times_int (tptp.times_times_int @t149 @t148) @t147)))) % 0.37/0.63 (assume @p88 (forall @t150 (= (tptp.times_times_nat @t149 (tptp.times_times_nat @t148 @t147)) (tptp.times_times_nat (tptp.times_times_nat @t149 @t148) @t147)))) % 0.37/0.63 (assume @p89 (forall @t154 (= (tptp.times_times_int @t152 (tptp.times_times_int @t153 @t151)) (tptp.times_times_int @t153 (tptp.times_times_int @t152 @t151))))) % 0.37/0.63 (assume @p90 (forall @t154 (= (tptp.times_times_nat @t152 (tptp.times_times_nat @t153 @t151)) (tptp.times_times_nat @t153 (tptp.times_times_nat @t152 @t151))))) % 0.37/0.63 (assume @p91 (forall @t157 (= (tptp.times_times_int @t155 @t156) (tptp.times_times_int @t156 @t155)))) % 0.37/0.63 (assume @p92 (forall @t157 (= (tptp.times_times_nat @t155 @t156) (tptp.times_times_nat @t156 @t155)))) % 0.37/0.63 (assume @p93 (forall @t162 (= (tptp.plus_plus_int (tptp.plus_plus_int @t161 @t159) (tptp.plus_plus_int @t160 @t158)) (tptp.plus_plus_int (tptp.plus_plus_int @t161 @t160) (tptp.plus_plus_int @t159 @t158))))) % 0.37/0.63 (assume @p94 (forall @t162 (= (tptp.plus_plus_nat (tptp.plus_plus_nat @t161 @t159) (tptp.plus_plus_nat @t160 @t158)) (tptp.plus_plus_nat (tptp.plus_plus_nat @t161 @t160) (tptp.plus_plus_nat @t159 @t158))))) % 0.37/0.63 (assume @p95 (forall @t166 (= (tptp.plus_plus_int (tptp.plus_plus_int @t165 @t163) @t164) (tptp.plus_plus_int (tptp.plus_plus_int @t165 @t164) @t163)))) % 0.37/0.63 (assume @p96 (forall @t166 (= (tptp.plus_plus_nat (tptp.plus_plus_nat @t165 @t163) @t164) (tptp.plus_plus_nat (tptp.plus_plus_nat @t165 @t164) @t163)))) % 0.37/0.63 (assume @p97 (forall @t170 (= (tptp.plus_plus_int (tptp.plus_plus_int @t169 @t168) @t167) (tptp.plus_plus_int @t169 (tptp.plus_plus_int @t168 @t167))))) % 0.37/0.63 (assume @p98 (forall @t170 (= (tptp.plus_plus_nat (tptp.plus_plus_nat @t169 @t168) @t167) (tptp.plus_plus_nat @t169 (tptp.plus_plus_nat @t168 @t167))))) % 0.37/0.63 (assume @p99 (forall @t174 (= (tptp.plus_plus_int @t173 (tptp.plus_plus_int @t172 @t171)) (tptp.plus_plus_int (tptp.plus_plus_int @t173 @t172) @t171)))) % 0.37/0.63 (assume @p100 (forall @t174 (= (tptp.plus_plus_nat @t173 (tptp.plus_plus_nat @t172 @t171)) (tptp.plus_plus_nat (tptp.plus_plus_nat @t173 @t172) @t171)))) % 0.37/0.63 (assume @p101 (forall @t178 (= (tptp.plus_plus_int @t176 (tptp.plus_plus_int @t177 @t175)) (tptp.plus_plus_int @t177 (tptp.plus_plus_int @t176 @t175))))) % 0.37/0.63 (assume @p102 (forall @t178 (= (tptp.plus_plus_nat @t176 (tptp.plus_plus_nat @t177 @t175)) (tptp.plus_plus_nat @t177 (tptp.plus_plus_nat @t176 @t175))))) % 0.37/0.63 (assume @p103 (forall @t181 (= (tptp.plus_plus_int @t179 @t180) (tptp.plus_plus_int @t180 @t179)))) % 0.37/0.63 (assume @p104 (forall @t181 (= (tptp.plus_plus_nat @t179 @t180) (tptp.plus_plus_nat @t180 @t179)))) % 0.37/0.63 (assume @p105 (forall @t29 (= (= @t77 @t76) (= @t28 @t27)))) % 0.37/0.63 (assume @p106 (forall @t182 (= (= @t72 @t28) (= @t28 @t72)))) % 0.37/0.63 (assume @p107 (forall @t182 (= (= @t75 @t28) (= @t28 @t75)))) % 0.37/0.63 (assume @p108 (forall @t99 (= (= @t98 @t97) @t183))) % 0.37/0.63 (assume @p109 (forall @t99 (= (= @t105 @t104) @t183))) % 0.37/0.63 (assume @p110 (forall @t187 (= (tptp.times_times_int (tptp.times_times_int @t186 @t185) @t184) (tptp.times_times_int @t186 (tptp.times_times_int @t185 @t184))))) % 0.37/0.63 (assume @p111 (forall @t51 (= (tptp.times_times_int @t48 @t47) (tptp.times_times_int @t47 @t48)))) % 0.37/0.63 (assume @p112 (forall (@list @t56) (= (tptp.number_number_of_int @t56) @t56))) % 0.37/0.63 (assume @p113 (forall @t187 (= (tptp.plus_plus_int (tptp.plus_plus_int @t186 @t185) @t184) (tptp.plus_plus_int @t186 (tptp.plus_plus_int @t185 @t184))))) % 0.37/0.63 (assume @p114 (forall @t69 (= (tptp.plus_plus_int @t54 (tptp.plus_plus_int @t55 @t48)) (tptp.plus_plus_int @t55 (tptp.plus_plus_int @t54 @t48))))) % 0.37/0.63 (assume @p115 (forall @t51 (= (tptp.plus_plus_int @t48 @t47) @t78))) % 0.37/0.63 (assume @p116 (forall @t117 (= (tptp.ord_less_int @t98 tptp.pls) @t116))) % 0.37/0.63 (assume @p117 (forall @t93 (= (tptp.ord_less_int @t92 @t102) @t90))) % 0.37/0.63 (assume @p118 (forall @t99 (= (tptp.ord_less_int @t98 @t104) @t96))) % 0.37/0.63 (assume @p119 (forall @t117 (= (tptp.ord_less_int @t105 tptp.pls) @t116))) % 0.37/0.63 (assume @p120 (forall @t117 (= (tptp.ord_less_int tptp.pls @t105) (tptp.ord_less_int tptp.pls @t95)))) % 0.37/0.63 (assume @p121 (forall @t117 (= (tptp.ord_less_eq_int tptp.pls @t98) @t118))) % 0.37/0.63 (assume @p122 (forall @t93 (= (tptp.ord_less_eq_int @t103 @t91) @t100))) % 0.37/0.63 (assume @p123 (forall @t99 (= (tptp.ord_less_eq_int @t105 @t97) @t101))) % 0.37/0.63 (assume @p124 @t188) % 0.37/0.63 (assume @p125 true) % 0.37/0.63 (step @p126 :rule bool-double-not-elim :args (@t189)) % 0.37/0.63 (step @p127 :rule exists-elim :args ((= @t10 @t190))) % 0.37/0.63 (step @p128 :rule cong :premises (@p127) :args (@t188)) % 0.37/0.63 (step @p129 :rule trans :premises (@p128 @p126)) % 0.37/0.63 (step @p130 :rule eq_resolve :premises (@p124 @p129)) % 0.37/0.63 (step @p131 :rule refl :args (@t12)) % 0.37/0.63 (step @p132 :rule cong :premises (@p131 @p127) :args (@t13)) % 0.37/0.63 (step @p133 :rule eq_resolve :premises (@p3 @p132)) % 0.37/0.63 (step @p134 :rule implies_elim :premises (@p133)) % 0.37/0.63 (step @p135 :rule reordering :premises (@p134) :args ((or @t190 @t191))) % 0.37/0.63 (step @p136 :rule chain_m_resolution :premises (@p135 @p130) :args (@t191 @t192 @t193)) % 0.37/0.63 (step @p137 :rule eq-symm :args (tptp.t tptp.one_one_int)) % 0.37/0.63 (step @p138 :rule cong :premises (@p137 @p127) :args (@t11)) % 0.37/0.63 (step @p139 :rule eq_resolve :premises (@p2 @p138)) % 0.37/0.63 (step @p140 :rule implies_elim :premises (@p139)) % 0.37/0.63 (step @p141 :rule reordering :premises (@p140) :args ((or @t190 @t195))) % 0.37/0.63 (step @p142 :rule chain_m_resolution :premises (@p141 @p130) :args (@t195 @t192 @t193)) % 0.37/0.64 (step @p143 :rule bool-double-not-elim :args (@t194)) % 0.37/0.64 (step @p144 :rule refl :args (@t196)) % 0.37/0.64 (step @p145 :rule refl :args (@t197)) % 0.37/0.64 (step @p146 :rule nary_cong :premises (@p145 @p144 @p143) :args ((or @t197 @t196 (not @t195)))) % 0.37/0.64 (step @p147 :rule cnf_and_neg :args (@t197)) % 0.37/0.64 (step @p148 :rule eq_resolve :premises (@p147 @p146)) % 0.37/0.64 (step @p149 :rule reordering :premises (@p148) :args ((or @t194 @t196 @t197))) % 0.37/0.64 (step @p150 :rule chain_m_resolution :premises (@p149 @p142 @p1) :args (@t197 (@list true false) (@list @t194 @t1))) % 0.37/0.64 (step @p151 :rule instantiate :premises (@p29) :args ((@list tptp.one_one_int tptp.t))) % 0.37/0.64 (step @p152 :rule cnf_equiv_pos2 :args (@t198)) % 0.37/0.64 (step @p153 :rule reordering :premises (@p152) :args ((or @t12 (not @t197) (not @t198)))) % 0.37/0.64 (step @p154 false :rule chain_m_resolution :premises (@p153 @p151 @p150 @p136) :args (false (@list false false true) (@list @t198 @t197 @t12))) % 0.37/0.64 ) % 0.37/0.64 % SZS output end Proof % 0.37/0.64 % cvc5 exiting %------------------------------------------------------------------------------