%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM924^1 : 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 : n004.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 08:41:01 AM UTC 2026 % Result : Theorem 0.45s 0.68s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM924^1 : 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 % 0.16/0.33 % Computer : n004.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Tue Jun 2 12:32:37 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.51 %----Proving TH0 % 0.45/0.68 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.45/0.68 % SZS status Theorem % 0.45/0.68 % SZS output start Proof % 0.45/0.68 ( % 0.45/0.68 (declare-sort tptp.nat 0) % 0.45/0.68 (declare-sort tptp.int 0) % 0.45/0.68 (declare-const tptp.ord_less_eq_nat (-> tptp.nat tptp.nat Bool)) % 0.45/0.68 (declare-const tptp.ord_less_nat (-> tptp.nat tptp.nat Bool)) % 0.45/0.68 (declare-const tptp.times_times_nat (-> tptp.nat tptp.nat tptp.nat)) % 0.45/0.68 (declare-const tptp.plus_plus_nat (-> tptp.nat tptp.nat tptp.nat)) % 0.45/0.68 (declare-const tptp.twoSqu1013291560sum2sq (-> tptp.int Bool)) % 0.45/0.68 (declare-const tptp.zprime (-> tptp.int Bool)) % 0.45/0.68 (declare-const tptp.zero_zero_nat tptp.nat) % 0.45/0.68 (declare-const tptp.power_power_nat (-> tptp.nat tptp.nat tptp.nat)) % 0.45/0.68 (declare-const tptp.ord_less_eq_int (-> tptp.int tptp.int Bool)) % 0.45/0.68 (declare-const tptp.power_power_int (-> tptp.int tptp.nat tptp.int)) % 0.45/0.68 (declare-const tptp.zero_zero_int tptp.int) % 0.45/0.68 (declare-const tptp.t tptp.int) % 0.45/0.68 (declare-const tptp.number_number_of_nat (-> tptp.int tptp.nat)) % 0.45/0.68 (declare-const tptp.ord_less_int (-> tptp.int tptp.int Bool)) % 0.45/0.68 (declare-const tptp.bit0 (-> tptp.int tptp.int)) % 0.45/0.68 (declare-const tptp.one_one_int tptp.int) % 0.45/0.68 (declare-const tptp.m tptp.int) % 0.45/0.68 (declare-const tptp.number_number_of_int (-> tptp.int tptp.int)) % 0.45/0.68 (declare-const tptp.plus_plus_int (-> tptp.int tptp.int tptp.int)) % 0.45/0.68 (declare-const tptp.pls tptp.int) % 0.45/0.68 (declare-const tptp.bit1 (-> tptp.int tptp.int)) % 0.45/0.68 (declare-const tptp.times_times_int (-> tptp.int tptp.int tptp.int)) % 0.45/0.68 (declare-const tptp.one_one_nat tptp.nat) % 0.45/0.68 (declare-const tptp.s tptp.int) % 0.45/0.68 (define @t1 () (_ tptp.ord_less_int tptp.t)) % 0.45/0.68 (define @t2 () (_ tptp.bit1 tptp.pls)) % 0.45/0.68 (define @t3 () (_ tptp.bit0 @t2)) % 0.45/0.68 (define @t4 () (_ tptp.bit0 @t3)) % 0.45/0.68 (define @t5 () (_ tptp.number_number_of_int @t4)) % 0.45/0.68 (define @t6 () (_ (_ tptp.times_times_int @t5) tptp.m)) % 0.45/0.68 (define @t7 () (_ (_ tptp.plus_plus_int @t6) tptp.one_one_int)) % 0.45/0.68 (define @t8 () (_ tptp.times_times_int @t7)) % 0.45/0.68 (define @t9 () (_ @t8 tptp.t)) % 0.45/0.68 (define @t10 () (_ tptp.ord_less_int @t9)) % 0.45/0.68 (define @t11 () (_ tptp.number_number_of_nat @t3)) % 0.45/0.68 (define @t12 () (_ tptp.power_power_int tptp.s)) % 0.45/0.68 (define @t13 () (_ @t12 @t11)) % 0.45/0.68 (define @t14 () (_ (_ tptp.plus_plus_int @t13) tptp.one_one_int)) % 0.45/0.68 (define @t15 () (_ tptp.ord_less_eq_int tptp.one_one_int)) % 0.45/0.68 (define @t16 () (_ tptp.ord_less_int tptp.zero_zero_int)) % 0.45/0.68 (define @t17 () (@var "Y" tptp.int)) % 0.45/0.68 (define @t18 () (@var "X" tptp.int)) % 0.45/0.68 (define @t19 () (_ tptp.power_power_int @t18)) % 0.45/0.68 (define @t20 () (@list @t18 @t17)) % 0.45/0.68 (define @t21 () (@var "Y_9" tptp.int)) % 0.45/0.68 (define @t22 () (@var "X_10" tptp.int)) % 0.45/0.68 (define @t23 () (@var "Y_8" tptp.int)) % 0.45/0.68 (define @t24 () (@var "X_9" tptp.int)) % 0.45/0.68 (define @t25 () (@var "A_3" tptp.int)) % 0.45/0.68 (define @t26 () (@var "A_2" tptp.int)) % 0.45/0.68 (define @t27 () (@var "A_1" tptp.int)) % 0.45/0.68 (define @t28 () (@var "W_7" tptp.int)) % 0.45/0.68 (define @t29 () (_ tptp.plus_plus_int tptp.one_one_int)) % 0.45/0.68 (define @t30 () (@var "V_12" tptp.int)) % 0.45/0.68 (define @t31 () (@var "T" tptp.int)) % 0.45/0.68 (define @t32 () (@var "W" tptp.int)) % 0.45/0.68 (define @t33 () (_ tptp.ord_less_eq_int @t32)) % 0.45/0.68 (define @t34 () (@list @t32)) % 0.45/0.68 (define @t35 () (@var "K" tptp.int)) % 0.45/0.68 (define @t36 () (_ tptp.number_number_of_int @t35)) % 0.45/0.68 (define @t37 () (@list @t35)) % 0.45/0.68 (define @t38 () (forall @t37 (= @t36 @t35))) % 0.45/0.68 (define @t39 () (@var "Z" tptp.int)) % 0.45/0.68 (define @t40 () (_ tptp.times_times_int @t32)) % 0.45/0.68 (define @t41 () (_ @t40 @t39)) % 0.45/0.68 (define @t42 () (_ tptp.times_times_int @t39)) % 0.45/0.68 (define @t43 () (_ @t42 @t32)) % 0.45/0.68 (define @t44 () (= @t43 @t41)) % 0.45/0.68 (define @t45 () (@list @t39 @t32)) % 0.45/0.68 (define @t46 () (forall @t45 @t44)) % 0.45/0.68 (define @t47 () (_ @t33 @t39)) % 0.45/0.68 (define @t48 () (_ (_ tptp.ord_less_eq_int @t39) @t32)) % 0.45/0.68 (define @t49 () (@var "V_2" tptp.int)) % 0.45/0.68 (define @t50 () (_ tptp.number_number_of_int @t32)) % 0.45/0.68 (define @t51 () (_ tptp.number_number_of_int @t49)) % 0.45/0.68 (define @t52 () (@list @t49 @t32)) % 0.45/0.68 (define @t53 () (@var "L" tptp.int)) % 0.45/0.68 (define @t54 () (_ tptp.ord_less_eq_int @t35)) % 0.45/0.68 (define @t55 () (_ @t54 @t53)) % 0.45/0.68 (define @t56 () (_ tptp.number_number_of_int @t53)) % 0.45/0.68 (define @t57 () (@list @t35 @t53)) % 0.45/0.68 (define @t58 () (@var "Y_7" tptp.int)) % 0.45/0.68 (define @t59 () (@var "X_8" tptp.int)) % 0.45/0.68 (define @t60 () (@var "Z3" tptp.int)) % 0.45/0.68 (define @t61 () (@var "Z2" tptp.int)) % 0.45/0.68 (define @t62 () (_ tptp.times_times_int @t61)) % 0.45/0.68 (define @t63 () (@var "Z1" tptp.int)) % 0.45/0.68 (define @t64 () (_ tptp.times_times_int @t63)) % 0.45/0.68 (define @t65 () (@list @t63 @t61 @t60)) % 0.45/0.68 (define @t66 () (@var "I" tptp.int)) % 0.45/0.68 (define @t67 () (_ tptp.ord_less_eq_int @t66)) % 0.45/0.68 (define @t68 () (@var "J" tptp.int)) % 0.45/0.68 (define @t69 () (_ @t67 @t68)) % 0.45/0.68 (define @t70 () (@list @t35 @t66 @t68)) % 0.45/0.68 (define @t71 () (= @t39 @t32)) % 0.45/0.68 (define @t72 () (@var "Z" tptp.nat)) % 0.45/0.68 (define @t73 () (@var "Y" tptp.nat)) % 0.45/0.68 (define @t74 () (@var "K2" tptp.int)) % 0.45/0.68 (define @t75 () (@var "K1" tptp.int)) % 0.45/0.68 (define @t76 () (_ (_ tptp.ord_less_eq_int @t75) @t74)) % 0.45/0.68 (define @t77 () (_ tptp.bit1 @t74)) % 0.45/0.68 (define @t78 () (_ tptp.ord_less_eq_int (_ tptp.bit1 @t75))) % 0.45/0.68 (define @t79 () (@list @t75 @t74)) % 0.45/0.68 (define @t80 () (_ tptp.bit1 @t53)) % 0.45/0.68 (define @t81 () (_ tptp.bit1 @t35)) % 0.45/0.68 (define @t82 () (_ tptp.ord_less_eq_int @t81)) % 0.45/0.68 (define @t83 () (_ tptp.ord_less_eq_int tptp.pls)) % 0.45/0.68 (define @t84 () (_ tptp.bit0 @t74)) % 0.45/0.68 (define @t85 () (_ tptp.bit0 @t75)) % 0.45/0.68 (define @t86 () (_ tptp.ord_less_eq_int @t85)) % 0.45/0.68 (define @t87 () (_ tptp.bit0 @t53)) % 0.45/0.68 (define @t88 () (_ tptp.bit0 @t35)) % 0.45/0.68 (define @t89 () (_ tptp.ord_less_eq_int @t88)) % 0.45/0.68 (define @t90 () (_ tptp.plus_plus_int @t35)) % 0.45/0.68 (define @t91 () (_ (_ tptp.ord_less_eq_int @t49) tptp.pls)) % 0.45/0.68 (define @t92 () (_ tptp.number_number_of_nat @t49)) % 0.45/0.68 (define @t93 () (@list @t49)) % 0.45/0.68 (define @t94 () (@var "V_11" tptp.int)) % 0.45/0.68 (define @t95 () (@var "V_10" tptp.int)) % 0.45/0.68 (define @t96 () (_ (_ tptp.times_times_int @t95) @t94)) % 0.45/0.68 (define @t97 () (_ @t83 @t94)) % 0.45/0.68 (define @t98 () (_ @t83 @t95)) % 0.45/0.68 (define @t99 () (@list @t94 @t95)) % 0.45/0.68 (define @t100 () (@var "Z_2" tptp.int)) % 0.45/0.68 (define @t101 () (@var "W_6" tptp.int)) % 0.45/0.68 (define @t102 () (@var "V_9" tptp.int)) % 0.45/0.68 (define @t103 () (@var "W_5" tptp.int)) % 0.45/0.68 (define @t104 () (@var "V_8" tptp.int)) % 0.45/0.68 (define @t105 () (@var "W_4" tptp.int)) % 0.45/0.68 (define @t106 () (@var "V_7" tptp.int)) % 0.45/0.68 (define @t107 () (@var "Y_6" tptp.int)) % 0.45/0.68 (define @t108 () (@var "X_7" tptp.int)) % 0.45/0.68 (define @t109 () (@var "Y_5" tptp.int)) % 0.45/0.68 (define @t110 () (@var "X_6" tptp.int)) % 0.45/0.68 (define @t111 () (_ tptp.ord_less_eq_int tptp.zero_zero_int)) % 0.45/0.68 (define @t112 () (@var "X_5" tptp.int)) % 0.45/0.68 (define @t113 () (@var "Y_4" tptp.int)) % 0.45/0.68 (define @t114 () (_ tptp.ord_less_int tptp.pls)) % 0.45/0.68 (define @t115 () (@var "V_6" tptp.int)) % 0.45/0.68 (define @t116 () (_ tptp.number_number_of_int @t115)) % 0.45/0.68 (define @t117 () (@var "W_3" tptp.int)) % 0.45/0.68 (define @t118 () (_ tptp.number_number_of_int @t117)) % 0.45/0.68 (define @t119 () (@list @t115 @t117)) % 0.45/0.68 (define @t120 () (_ tptp.number_number_of_nat @t115)) % 0.45/0.68 (define @t121 () (_ tptp.number_number_of_nat @t117)) % 0.45/0.68 (define @t122 () (_ @t83 @t35)) % 0.45/0.68 (define @t123 () (_ tptp.plus_plus_int @t32)) % 0.45/0.68 (define @t124 () (_ @t123 @t39)) % 0.45/0.68 (define @t125 () (@var "Z_1" tptp.int)) % 0.45/0.68 (define @t126 () (@var "W_2" tptp.int)) % 0.45/0.68 (define @t127 () (_ tptp.number_number_of_nat tptp.pls)) % 0.45/0.68 (define @t128 () (@var "X_4" tptp.int)) % 0.45/0.68 (define @t129 () (@var "Y_3" tptp.int)) % 0.45/0.68 (define @t130 () (_ (_ tptp.times_times_int tptp.pls) @t32)) % 0.45/0.68 (define @t131 () (forall @t34 (= @t130 tptp.pls))) % 0.45/0.68 (define @t132 () (_ tptp.ord_less_int @t35)) % 0.45/0.68 (define @t133 () (_ @t132 @t53)) % 0.45/0.68 (define @t134 () (@list @t39)) % 0.45/0.68 (define @t135 () (_ tptp.plus_plus_int @t49)) % 0.45/0.68 (define @t136 () (_ tptp.plus_plus_int @t63)) % 0.45/0.68 (define @t137 () (_ @t136 @t61)) % 0.45/0.68 (define @t138 () (@var "V_3" tptp.int)) % 0.45/0.68 (define @t139 () (_ tptp.ord_less_int @t49)) % 0.45/0.68 (define @t140 () (_ @t139 @t138)) % 0.45/0.68 (define @t141 () (_ tptp.number_number_of_nat @t138)) % 0.45/0.68 (define @t142 () (_ tptp.number_number_of_nat @t2)) % 0.45/0.68 (define @t143 () (_ @t123 tptp.one_one_int)) % 0.45/0.68 (define @t144 () (_ (_ tptp.ord_less_eq_int @t143) @t39)) % 0.45/0.68 (define @t145 () (_ tptp.ord_less_int @t32)) % 0.45/0.68 (define @t146 () (_ @t145 @t39)) % 0.45/0.68 (define @t147 () (@list @t32 @t39)) % 0.45/0.68 (define @t148 () (forall @t147 (=> @t146 @t144))) % 0.45/0.68 (define @t149 () (forall @t147 (= @t144 @t146))) % 0.45/0.68 (define @t150 () (_ tptp.plus_plus_int @t39)) % 0.45/0.68 (define @t151 () (@var "V_5" tptp.int)) % 0.45/0.68 (define @t152 () (@var "V_4" tptp.int)) % 0.45/0.68 (define @t153 () (_ (_ tptp.plus_plus_int @t152) @t151)) % 0.45/0.68 (define @t154 () (_ @t83 @t151)) % 0.45/0.68 (define @t155 () (_ @t83 @t152)) % 0.45/0.68 (define @t156 () (@list @t151 @t152)) % 0.45/0.68 (define @t157 () (_ (_ tptp.plus_plus_nat @t92) @t141)) % 0.45/0.68 (define @t158 () (_ (_ tptp.ord_less_int @t138) tptp.pls)) % 0.45/0.68 (define @t159 () (_ @t139 tptp.pls)) % 0.45/0.68 (define @t160 () (@var "Y_2" tptp.int)) % 0.45/0.68 (define @t161 () (@var "X_3" tptp.int)) % 0.45/0.68 (define @t162 () (@var "W_1" tptp.int)) % 0.45/0.68 (define @t163 () (_ tptp.number_number_of_nat @t162)) % 0.45/0.68 (define @t164 () (@var "X_2" tptp.nat)) % 0.45/0.68 (define @t165 () (_ tptp.number_number_of_int @t162)) % 0.45/0.68 (define @t166 () (@var "X_2" tptp.int)) % 0.45/0.68 (define @t167 () (= @t35 @t53)) % 0.45/0.68 (define @t168 () (@var "Y_1" tptp.int)) % 0.45/0.68 (define @t169 () (@var "X_1" tptp.int)) % 0.45/0.68 (define @t170 () (@var "V_1" tptp.int)) % 0.45/0.68 (define @t171 () (_ tptp.number_number_of_int @t170)) % 0.45/0.68 (define @t172 () (@var "B_1" tptp.int)) % 0.45/0.68 (define @t173 () (@var "A" tptp.int)) % 0.45/0.68 (define @t174 () (_ tptp.number_number_of_nat @t170)) % 0.45/0.68 (define @t175 () (@var "B_1" tptp.nat)) % 0.45/0.68 (define @t176 () (@var "A" tptp.nat)) % 0.45/0.68 (define @t177 () (@var "C" tptp.int)) % 0.45/0.68 (define @t178 () (@var "V" tptp.int)) % 0.45/0.68 (define @t179 () (_ tptp.times_times_int (_ tptp.number_number_of_int @t178))) % 0.45/0.68 (define @t180 () (@var "B" tptp.int)) % 0.45/0.68 (define @t181 () (@var "C" tptp.nat)) % 0.45/0.69 (define @t182 () (_ tptp.times_times_nat (_ tptp.number_number_of_nat @t178))) % 0.45/0.69 (define @t183 () (@var "B" tptp.nat)) % 0.45/0.69 (define @t184 () (_ tptp.plus_plus_int @t18)) % 0.45/0.69 (define @t185 () (_ tptp.plus_plus_int @t17)) % 0.45/0.69 (define @t186 () (_ tptp.number_number_of_int tptp.pls)) % 0.45/0.69 (define @t187 () (_ tptp.ord_less_int @t14)) % 0.45/0.69 (define @t188 () (not (_ @t187 tptp.zero_zero_int))) % 0.45/0.69 (define @t189 () (tptp.plus_plus_int @t32 tptp.one_one_int)) % 0.45/0.69 (define @t190 () (tptp.ord_less_eq_int @t189 @t39)) % 0.45/0.69 (define @t191 () (tptp.ord_less_int @t32 @t39)) % 0.45/0.69 (define @t192 () (= @t146 @t144)) % 0.45/0.69 (define @t193 () (tptp.number_number_of_int tptp.pls)) % 0.45/0.69 (define @t194 () (tptp.bit1 tptp.pls)) % 0.45/0.69 (define @t195 () (tptp.bit0 @t194)) % 0.45/0.69 (define @t196 () (tptp.number_number_of_nat @t195)) % 0.45/0.69 (define @t197 () (tptp.power_power_int tptp.s @t196)) % 0.45/0.69 (define @t198 () (tptp.plus_plus_int @t197 tptp.one_one_int)) % 0.45/0.69 (define @t199 () (tptp.ord_less_int @t198 @t193)) % 0.45/0.69 (define @t200 () (_ @t187 @t186)) % 0.45/0.69 (define @t201 () (tptp.ord_less_eq_int (tptp.plus_plus_int @t198 tptp.one_one_int) @t193)) % 0.45/0.69 (define @t202 () (= @t199 @t201)) % 0.45/0.69 (define @t203 () (not @t201)) % 0.45/0.69 (define @t204 () (tptp.number_number_of_int @t35)) % 0.45/0.69 (define @t205 () (= @t35 @t36)) % 0.45/0.69 (define @t206 () (tptp.times_times_int tptp.pls @t32)) % 0.45/0.69 (define @t207 () (= tptp.pls @t130)) % 0.45/0.69 (define @t208 () (tptp.bit0 @t195)) % 0.45/0.69 (define @t209 () (tptp.number_number_of_int @t208)) % 0.45/0.69 (define @t210 () (tptp.times_times_int @t209 tptp.m)) % 0.45/0.69 (define @t211 () (tptp.plus_plus_int @t210 tptp.one_one_int)) % 0.45/0.69 (define @t212 () (tptp.times_times_int @t32 @t39)) % 0.45/0.69 (define @t213 () (tptp.times_times_int @t39 @t32)) % 0.45/0.69 (define @t214 () (tptp.times_times_int @t211 tptp.t)) % 0.45/0.69 (define @t215 () (_ tptp.times_times_int @t211)) % 0.45/0.69 (define @t216 () (tptp.plus_plus_int @t214 tptp.one_one_int)) % 0.45/0.69 (define @t217 () (tptp.times_times_int @t211 @t193)) % 0.45/0.69 (define @t218 () (tptp.ord_less_eq_int @t216 @t217)) % 0.45/0.69 (define @t219 () (not @t146)) % 0.45/0.69 (define @t220 () (or @t219 @t144)) % 0.45/0.69 (define @t221 () (_ @t8 @t186)) % 0.45/0.69 (define @t222 () (tptp.ord_less_int @t214 @t217)) % 0.45/0.69 (define @t223 () (not @t222)) % 0.45/0.69 (define @t224 () (or @t223 @t218)) % 0.45/0.69 (assume @p1 (_ @t1 tptp.zero_zero_int)) % 0.45/0.69 (assume @p2 (_ @t1 tptp.one_one_int)) % 0.45/0.69 (assume @p3 (_ @t10 (_ @t8 tptp.zero_zero_int))) % 0.45/0.69 (assume @p4 (= @t14 @t9)) % 0.45/0.69 (assume @p5 (=> (= tptp.t tptp.zero_zero_int) (= @t14 tptp.zero_zero_int))) % 0.45/0.69 (assume @p6 (not (_ @t15 tptp.t))) % 0.45/0.69 (assume @p7 (_ @t16 @t7)) % 0.45/0.69 (assume @p8 (forall @t20 (not (_ (_ tptp.ord_less_int (_ (_ tptp.plus_plus_int (_ @t19 @t11)) (_ (_ tptp.power_power_int @t17) @t11))) tptp.zero_zero_int)))) % 0.45/0.69 (assume @p9 (forall (@list @t22 @t21) (= (_ @t16 (_ (_ tptp.plus_plus_int (_ (_ tptp.power_power_int @t22) @t11)) (_ (_ tptp.power_power_int @t21) @t11))) (or (not (= @t22 tptp.zero_zero_int)) (not (= @t21 tptp.zero_zero_int)))))) % 0.45/0.69 (assume @p10 (forall (@list @t24 @t23) (= (= (_ (_ tptp.plus_plus_int (_ (_ tptp.power_power_int @t24) @t11)) (_ (_ tptp.power_power_int @t23) @t11)) tptp.zero_zero_int) (and (= @t24 tptp.zero_zero_int) (= @t23 tptp.zero_zero_int))))) % 0.45/0.69 (assume @p11 (forall (@list @t25) (not (_ (_ tptp.ord_less_int (_ (_ tptp.power_power_int @t25) @t11)) tptp.zero_zero_int)))) % 0.45/0.69 (assume @p12 (forall (@list @t26) (= (_ @t16 (_ (_ tptp.power_power_int @t26) @t11)) (not (= @t26 tptp.zero_zero_int))))) % 0.45/0.69 (assume @p13 (= (_ (_ tptp.power_power_nat tptp.one_one_nat) @t11) tptp.one_one_nat)) % 0.45/0.69 (assume @p14 (= (_ (_ tptp.power_power_int tptp.one_one_int) @t11) tptp.one_one_int)) % 0.45/0.69 (assume @p15 (= (_ (_ tptp.power_power_nat tptp.zero_zero_nat) @t11) tptp.zero_zero_nat)) % 0.45/0.69 (assume @p16 (= (_ (_ tptp.power_power_int tptp.zero_zero_int) @t11) tptp.zero_zero_int)) % 0.45/0.69 (assume @p17 (forall (@list @t27) (= (= (_ (_ tptp.power_power_int @t27) @t11) tptp.zero_zero_int) (= @t27 tptp.zero_zero_int)))) % 0.45/0.69 (assume @p18 (forall (@list @t28) (= (_ @t29 (_ tptp.number_number_of_int @t28)) (_ tptp.number_number_of_int (_ (_ tptp.plus_plus_int @t2) @t28))))) % 0.45/0.69 (assume @p19 (forall (@list @t30) (= (_ (_ tptp.plus_plus_int (_ tptp.number_number_of_int @t30)) tptp.one_one_int) (_ tptp.number_number_of_int (_ (_ tptp.plus_plus_int @t30) @t2))))) % 0.45/0.69 (assume @p20 (_ @t1 @t7)) % 0.45/0.69 (assume @p21 (not (forall (@list @t31) (not (= @t14 (_ @t8 @t31)))))) % 0.45/0.69 (assume @p22 (_ tptp.zprime @t7)) % 0.45/0.69 (assume @p23 (_ tptp.twoSqu1013291560sum2sq @t9)) % 0.45/0.69 (assume @p24 (forall @t34 (_ @t33 @t32))) % 0.45/0.69 (assume @p25 @t38) % 0.45/0.69 (assume @p26 @t46) % 0.45/0.69 (assume @p27 (forall @t45 (or @t48 @t47))) % 0.45/0.69 (assume @p28 (forall @t52 (= (_ (_ tptp.times_times_int @t51) @t50) (_ tptp.number_number_of_int (_ (_ tptp.times_times_int @t49) @t32))))) % 0.45/0.69 (assume @p29 (forall @t57 (= (_ (_ tptp.ord_less_eq_int @t36) @t56) @t55))) % 0.45/0.69 (assume @p30 (forall (@list @t59 @t58) (= (_ (_ tptp.ord_less_eq_int (_ tptp.number_number_of_int @t59)) (_ tptp.number_number_of_int @t58)) (_ (_ tptp.ord_less_eq_int @t59) @t58)))) % 0.45/0.69 (assume @p31 (forall @t65 (= (_ (_ tptp.times_times_int (_ @t64 @t61)) @t60) (_ @t64 (_ @t62 @t60))))) % 0.45/0.69 (assume @p32 (forall @t70 (=> @t69 (=> (_ (_ tptp.ord_less_eq_int @t68) @t35) (_ @t67 @t35))))) % 0.45/0.69 (assume @p33 (forall @t45 (=> @t48 (=> @t47 @t71)))) % 0.45/0.69 (assume @p34 (forall (@list @t18 @t73 @t72) (= (_ @t19 (_ (_ tptp.plus_plus_nat @t73) @t72)) (_ (_ tptp.times_times_int (_ @t19 @t73)) (_ @t19 @t72))))) % 0.45/0.69 (assume @p35 (forall @t79 (= (_ @t78 @t77) @t76))) % 0.45/0.69 (assume @p36 (forall @t57 (= (_ @t82 @t80) @t55))) % 0.45/0.69 (assume @p37 (_ @t83 tptp.pls)) % 0.45/0.69 (assume @p38 (forall @t79 (= (_ @t86 @t84) @t76))) % 0.45/0.69 (assume @p39 (forall @t57 (= (_ @t89 @t87) @t55))) % 0.45/0.69 (assume @p40 (forall @t45 (= (_ (_ tptp.ord_less_int @t39) @t32) (and @t48 (not @t71))))) % 0.45/0.69 (assume @p41 (forall @t70 (=> @t69 (_ (_ tptp.ord_less_eq_int (_ @t90 @t66)) (_ @t90 @t68))))) % 0.45/0.69 (assume @p42 (forall @t93 (= (= @t92 tptp.zero_zero_nat) @t91))) % 0.45/0.69 (assume @p43 (forall @t93 (= (= tptp.zero_zero_nat @t92) @t91))) % 0.45/0.69 (assume @p44 (forall @t99 (=> @t98 (=> @t97 (= (_ (_ tptp.times_times_nat (_ tptp.number_number_of_nat @t95)) (_ tptp.number_number_of_nat @t94)) (_ tptp.number_number_of_nat @t96)))))) % 0.45/0.69 (assume @p45 (forall @t99 (=> @t98 (=> @t97 (= (_ (_ tptp.times_times_int (_ tptp.number_number_of_int @t95)) (_ tptp.number_number_of_int @t94)) (_ tptp.number_number_of_int @t96)))))) % 0.45/0.69 (assume @p46 (forall (@list @t102 @t101 @t100) (= (_ (_ tptp.times_times_int (_ tptp.number_number_of_int @t102)) (_ (_ tptp.times_times_int (_ tptp.number_number_of_int @t101)) @t100)) (_ (_ tptp.times_times_int (_ tptp.number_number_of_int (_ (_ tptp.times_times_int @t102) @t101))) @t100)))) % 0.45/0.69 (assume @p47 (forall (@list @t104 @t103) (= (_ (_ tptp.times_times_int (_ tptp.number_number_of_int @t104)) (_ tptp.number_number_of_int @t103)) (_ tptp.number_number_of_int (_ (_ tptp.times_times_int @t104) @t103))))) % 0.45/0.69 (assume @p48 (forall (@list @t106 @t105) (= (_ tptp.number_number_of_int (_ (_ tptp.times_times_int @t106) @t105)) (_ (_ tptp.times_times_int (_ tptp.number_number_of_int @t106)) (_ tptp.number_number_of_int @t105))))) % 0.45/0.69 (assume @p49 (forall (@list @t108 @t107) (= (_ (_ tptp.ord_less_eq_int (_ (_ tptp.plus_plus_int (_ (_ tptp.times_times_int @t108) @t108)) (_ (_ tptp.times_times_int @t107) @t107))) tptp.zero_zero_int) (and (= @t108 tptp.zero_zero_int) (= @t107 tptp.zero_zero_int))))) % 0.45/0.69 (assume @p50 (forall (@list @t110 @t109) (_ @t111 (_ (_ tptp.plus_plus_int (_ (_ tptp.times_times_int @t110) @t110)) (_ (_ tptp.times_times_int @t109) @t109))))) % 0.45/0.69 (assume @p51 (forall (@list @t112) (= (_ (_ tptp.ord_less_eq_int (_ tptp.number_number_of_int @t112)) tptp.zero_zero_int) (_ (_ tptp.ord_less_eq_int @t112) tptp.pls)))) % 0.45/0.69 (assume @p52 (forall (@list @t113) (= (_ @t111 (_ tptp.number_number_of_int @t113)) (_ @t83 @t113)))) % 0.45/0.69 (assume @p53 (forall @t93 (= (_ (_ tptp.ord_less_nat tptp.zero_zero_nat) @t92) (_ @t114 @t49)))) % 0.45/0.69 (assume @p54 (forall @t119 (= (_ (_ tptp.ord_less_eq_int @t116) @t118) (not (_ (_ tptp.ord_less_int @t118) @t116))))) % 0.45/0.69 (assume @p55 (forall @t119 (= (_ (_ tptp.ord_less_eq_nat @t120) @t121) (not (_ (_ tptp.ord_less_nat @t121) @t120))))) % 0.45/0.69 (assume @p56 (forall @t37 (= (_ @t83 @t81) @t122))) % 0.45/0.69 (assume @p57 (forall @t79 (= (_ @t86 @t77) @t76))) % 0.45/0.69 (assume @p58 (forall @t57 (= (_ @t89 @t80) @t55))) % 0.45/0.69 (assume @p59 (forall @t37 (= (_ @t89 tptp.pls) (_ @t54 tptp.pls)))) % 0.45/0.69 (assume @p60 (forall @t37 (= (_ @t83 @t88) @t122))) % 0.45/0.69 (assume @p61 (forall (@list @t125 @t39 @t126 @t32) (=> (_ (_ tptp.ord_less_int @t126) @t32) (=> (_ (_ tptp.ord_less_eq_int @t125) @t39) (_ (_ tptp.ord_less_int (_ (_ tptp.plus_plus_int @t126) @t125)) @t124))))) % 0.45/0.69 (assume @p62 (= @t127 tptp.zero_zero_nat)) % 0.45/0.69 (assume @p63 (= tptp.zero_zero_nat @t127)) % 0.45/0.69 (assume @p64 (forall (@list @t128) (= (_ (_ tptp.ord_less_eq_int (_ tptp.number_number_of_int @t128)) tptp.one_one_int) (_ (_ tptp.ord_less_eq_int @t128) @t2)))) % 0.45/0.69 (assume @p65 (forall (@list @t129) (= (_ @t15 (_ tptp.number_number_of_int @t129)) (_ (_ tptp.ord_less_eq_int @t2) @t129)))) % 0.45/0.69 (assume @p66 (= (_ (_ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) @t11)) % 0.45/0.69 (assume @p67 @t131) % 0.45/0.69 (assume @p68 (forall @t57 (= (_ (_ tptp.times_times_int @t88) @t53) (_ tptp.bit0 (_ (_ tptp.times_times_int @t35) @t53))))) % 0.45/0.69 (assume @p69 (forall @t57 (= (_ (_ tptp.ord_less_int @t36) @t56) @t133))) % 0.45/0.69 (assume @p70 (forall @t134 (= (_ @t42 tptp.one_one_int) @t39))) % 0.45/0.69 (assume @p71 (forall @t134 (= (_ (_ tptp.times_times_int tptp.one_one_int) @t39) @t39))) % 0.45/0.69 (assume @p72 (forall @t52 (= (_ (_ tptp.plus_plus_int @t51) @t50) (_ tptp.number_number_of_int (_ @t135 @t32))))) % 0.45/0.69 (assume @p73 (forall (@list @t63 @t61 @t32) (= (_ (_ tptp.times_times_int @t137) @t32) (_ (_ tptp.plus_plus_int (_ @t64 @t32)) (_ @t62 @t32))))) % 0.45/0.69 (assume @p74 (forall (@list @t32 @t63 @t61) (= (_ @t40 @t137) (_ (_ tptp.plus_plus_int (_ @t40 @t63)) (_ @t40 @t61))))) % 0.45/0.69 (assume @p75 (forall @t37 (= (_ @t82 tptp.pls) (_ @t132 tptp.pls)))) % 0.45/0.69 (assume @p76 (forall @t37 (= (_ @t114 @t81) @t122))) % 0.45/0.69 (assume @p77 (forall @t79 (= (_ @t78 @t84) (_ (_ tptp.ord_less_int @t75) @t74)))) % 0.45/0.69 (assume @p78 (forall @t57 (= (_ @t82 @t87) @t133))) % 0.45/0.69 (assume @p79 (forall @t79 (= (_ (_ tptp.ord_less_int @t85) @t77) @t76))) % 0.45/0.69 (assume @p80 (forall @t57 (= (_ (_ tptp.ord_less_int @t88) @t80) @t55))) % 0.45/0.69 (assume @p81 (forall (@list @t49 @t138) (= (_ (_ tptp.ord_less_nat @t92) @t141) (and (=> @t140 (_ @t114 @t138)) @t140)))) % 0.45/0.69 (assume @p82 (forall @t134 (= (_ @t15 @t39) (_ @t16 @t39)))) % 0.45/0.69 (assume @p83 (= @t142 tptp.one_one_nat)) % 0.45/0.69 (assume @p84 (= tptp.one_one_nat @t142)) % 0.45/0.69 (assume @p85 @t148) % 0.45/0.69 (assume @p86 @t149) % 0.45/0.69 (assume @p87 (forall @t147 (= (_ @t145 (_ @t150 tptp.one_one_int)) @t47))) % 0.45/0.69 (assume @p88 (forall @t156 (=> @t155 (=> @t154 (= (_ (_ tptp.plus_plus_int (_ tptp.number_number_of_int @t152)) (_ tptp.number_number_of_int @t151)) (_ tptp.number_number_of_int @t153)))))) % 0.45/0.69 (assume @p89 (forall @t156 (=> @t155 (=> @t154 (= (_ (_ tptp.plus_plus_nat (_ tptp.number_number_of_nat @t152)) (_ tptp.number_number_of_nat @t151)) (_ tptp.number_number_of_nat @t153)))))) % 0.45/0.69 (assume @p90 (forall (@list @t138 @t49) (and (=> @t159 (= @t157 @t141)) (=> (not @t159) (and (=> @t158 (= @t157 @t92)) (=> (not @t158) (= @t157 (_ tptp.number_number_of_nat (_ @t135 @t138))))))))) % 0.45/0.69 (assume @p91 (forall @t134 (=> (_ @t111 @t39) (_ @t16 (_ @t29 @t39))))) % 0.45/0.69 (assume @p92 (forall (@list @t161 @t160) (= (= (_ tptp.number_number_of_int @t161) (_ tptp.number_number_of_int @t160)) (= @t161 @t160)))) % 0.45/0.69 (assume @p93 (forall (@list @t162 @t164) (= (= @t163 @t164) (= @t164 @t163)))) % 0.45/0.69 (assume @p94 (forall (@list @t162 @t166) (= (= @t165 @t166) (= @t166 @t165)))) % 0.45/0.69 (assume @p95 (forall @t57 (= (= @t81 @t80) @t167))) % 0.45/0.69 (assume @p96 (forall @t57 (= (= @t88 @t87) @t167))) % 0.45/0.69 (assume @p97 (forall @t20 (or (_ (_ tptp.ord_less_int @t18) @t17) (= @t18 @t17) (_ (_ tptp.ord_less_int @t17) @t18)))) % 0.45/0.69 (assume @p98 (forall (@list @t169 @t168) (= (= (_ (_ tptp.plus_plus_int (_ (_ tptp.times_times_int @t169) @t169)) (_ (_ tptp.times_times_int @t168) @t168)) tptp.zero_zero_int) (and (= @t169 tptp.zero_zero_int) (= @t168 tptp.zero_zero_int))))) % 0.45/0.69 (assume @p99 (forall (@list @t173 @t172 @t170) (= (_ (_ tptp.times_times_int (_ (_ tptp.plus_plus_int @t173) @t172)) @t171) (_ (_ tptp.plus_plus_int (_ (_ tptp.times_times_int @t173) @t171)) (_ (_ tptp.times_times_int @t172) @t171))))) % 0.45/0.69 (assume @p100 (forall (@list @t176 @t175 @t170) (= (_ (_ tptp.times_times_nat (_ (_ tptp.plus_plus_nat @t176) @t175)) @t174) (_ (_ tptp.plus_plus_nat (_ (_ tptp.times_times_nat @t176) @t174)) (_ (_ tptp.times_times_nat @t175) @t174))))) % 0.45/0.69 (assume @p101 (forall (@list @t178 @t180 @t177) (= (_ @t179 (_ (_ tptp.plus_plus_int @t180) @t177)) (_ (_ tptp.plus_plus_int (_ @t179 @t180)) (_ @t179 @t177))))) % 0.45/0.69 (assume @p102 (forall (@list @t178 @t183 @t181) (= (_ @t182 (_ (_ tptp.plus_plus_nat @t183) @t181)) (_ (_ tptp.plus_plus_nat (_ @t182 @t183)) (_ @t182 @t181))))) % 0.45/0.69 (assume @p103 (forall @t65 (= (_ (_ tptp.plus_plus_int @t137) @t60) (_ @t136 (_ (_ tptp.plus_plus_int @t61) @t60))))) % 0.45/0.69 (assume @p104 (forall (@list @t18 @t17 @t39) (= (_ @t184 (_ @t185 @t39)) (_ @t185 (_ @t184 @t39))))) % 0.45/0.69 (assume @p105 (forall @t45 (= (_ @t150 @t32) @t124))) % 0.45/0.69 (assume @p106 (= tptp.zero_zero_int @t186)) % 0.45/0.69 (assume @p107 @t188) % 0.45/0.69 (assume @p108 true) % 0.45/0.69 (step @p109 :rule evaluate :args ((= true false))) % 0.45/0.69 (step @p110 :rule refl :args ((tptp.ord_less_eq_int @t143 @t39))) % 0.45/0.69 (step @p111 :rule refl :args (@t39)) % 0.45/0.69 (step @p112 :rule refl :args (@t189)) % 0.45/0.69 (step @p113 :rule cong :premises (@p112 @p111) :args (@t190)) % 0.45/0.69 (step @p114 :rule trans :premises (@p113 @p110)) % 0.45/0.69 (step @p115 :rule refl :args (tptp.ord_less_eq_int)) % 0.45/0.69 (step @p116 :rule ho_cong :premises (@p115 @p112)) % 0.45/0.69 (step @p117 :rule ho_cong :premises (@p116 @p111)) % 0.45/0.69 (step @p118 :rule cong :premises (@p117 @p114) :args ((= (_ (_ tptp.ord_less_eq_int @t189) @t39) @t190))) % 0.45/0.69 (step @p119 :rule symm :premises (@p118)) % 0.45/0.69 (step @p120 :rule refl :args (@t144)) % 0.45/0.69 (step @p121 :rule eq_resolve :premises (@p120 @p119)) % 0.45/0.69 (step @p122 :rule refl :args (@t143)) % 0.45/0.69 (step @p123 :rule cong :premises (@p122 @p112) :args ((= @t143 @t189))) % 0.45/0.69 (step @p124 :rule symm :premises (@p123)) % 0.45/0.69 (step @p125 :rule eq_resolve :premises (@p122 @p124)) % 0.45/0.69 (step @p126 :rule ho_cong :premises (@p115 @p125)) % 0.45/0.69 (step @p127 :rule ho_cong :premises (@p126 @p111)) % 0.45/0.69 (step @p128 :rule trans :premises (@p127 @p121)) % 0.45/0.69 (step @p129 :rule refl :args (@t191)) % 0.45/0.69 (step @p130 :rule refl :args (@t146)) % 0.45/0.69 (step @p131 :rule cong :premises (@p130 @p129) :args ((= @t146 @t191))) % 0.45/0.69 (step @p132 :rule symm :premises (@p131)) % 0.45/0.69 (step @p133 :rule eq_resolve :premises (@p130 @p132)) % 0.45/0.69 (step @p134 :rule cong :premises (@p133 @p128) :args (@t192)) % 0.45/0.69 (step @p135 :rule cong :premises (@p134) :args ((forall @t147 @t192))) % 0.45/0.69 (step @p136 :rule eq-symm :args (@t144 @t146)) % 0.45/0.69 (step @p137 :rule cong :premises (@p136) :args (@t149)) % 0.45/0.69 (step @p138 :rule trans :premises (@p137 @p135)) % 0.45/0.69 (step @p139 :rule eq_resolve :premises (@p86 @p138)) % 0.45/0.69 (step @p140 :rule instantiate :premises (@p139) :args ((@list @t198 @t193))) % 0.45/0.69 (step @p141 :rule refl :args ((tptp.ord_less_int @t14 @t186))) % 0.45/0.69 (step @p142 :rule refl :args (@t193)) % 0.45/0.69 (step @p143 :rule refl :args ((tptp.plus_plus_int @t13 tptp.one_one_int))) % 0.45/0.69 (step @p144 :rule refl :args (tptp.one_one_int)) % 0.45/0.69 (step @p145 :rule refl :args ((tptp.power_power_int tptp.s @t11))) % 0.45/0.69 (step @p146 :rule refl :args ((tptp.number_number_of_nat @t3))) % 0.45/0.69 (step @p147 :rule refl :args ((tptp.bit0 @t2))) % 0.45/0.69 (step @p148 :rule refl :args (@t194)) % 0.45/0.69 (step @p149 :rule cong :premises (@p148) :args (@t195)) % 0.45/0.69 (step @p150 :rule trans :premises (@p149 @p147)) % 0.45/0.69 (step @p151 :rule cong :premises (@p150) :args (@t196)) % 0.45/0.69 (step @p152 :rule trans :premises (@p151 @p146)) % 0.45/0.69 (step @p153 :rule refl 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(step @p305 :rule ho_cong :premises (@p291 @p284)) % 0.45/0.69 (step @p306 :rule ho_cong :premises (@p305 @p278)) % 0.45/0.69 (step @p307 :rule cong :premises (@p306 @p286) :args ((= (_ (_ tptp.times_times_int @t209) tptp.m) @t210))) % 0.45/0.69 (step @p308 :rule symm :premises (@p307)) % 0.45/0.69 (step @p309 :rule refl :args (@t6)) % 0.45/0.69 (step @p310 :rule eq_resolve :premises (@p309 @p308)) % 0.45/0.69 (step @p311 :rule refl :args (tptp.m)) % 0.45/0.69 (step @p312 :rule refl :args (tptp.number_number_of_int)) % 0.45/0.69 (step @p313 :rule ho_cong :premises (@p312 @p282)) % 0.45/0.69 (step @p314 :rule cong :premises (@p313 @p284) :args ((= (_ tptp.number_number_of_int @t208) @t209))) % 0.45/0.69 (step @p315 :rule symm :premises (@p314)) % 0.45/0.69 (step @p316 :rule refl :args (@t5)) % 0.45/0.69 (step @p317 :rule eq_resolve :premises (@p316 @p315)) % 0.45/0.69 (step @p318 :rule ho_cong :premises (@p191 @p150)) % 0.45/0.69 (step @p319 :rule cong :premises (@p318 @p282) :args ((= 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