%------------------------------------------------------------------------------ % 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 : 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 08:41:01 AM UTC 2026 % Result : Theorem 0.37s 0.69s % Output : Proof 0.37s % 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. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n019.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 12:32:49 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.69 % SZS status Theorem % 0.37/0.69 % SZS output start Proof % 0.37/0.69 ( % 0.37/0.69 (declare-sort tptp.nat 0) % 0.37/0.69 (declare-sort tptp.int 0) % 0.37/0.69 (declare-const tptp.ord_less_eq_nat (-> tptp.nat tptp.nat Bool)) % 0.37/0.69 (declare-const tptp.ord_less_nat (-> tptp.nat tptp.nat Bool)) % 0.37/0.69 (declare-const tptp.times_times_nat (-> tptp.nat tptp.nat tptp.nat)) % 0.37/0.69 (declare-const tptp.plus_plus_nat (-> tptp.nat tptp.nat tptp.nat)) % 0.37/0.69 (declare-const tptp.twoSqu1431725154sum2sq (-> tptp.int Bool)) % 0.37/0.69 (declare-const tptp.zprime (-> tptp.int Bool)) % 0.37/0.69 (declare-const tptp.zero_zero_nat tptp.nat) % 0.37/0.69 (declare-const tptp.power_power_nat (-> tptp.nat tptp.nat tptp.nat)) % 0.37/0.69 (declare-const tptp.ord_less_eq_int (-> tptp.int tptp.int Bool)) % 0.37/0.69 (declare-const tptp.power_power_int (-> tptp.int tptp.nat tptp.int)) % 0.37/0.69 (declare-const tptp.zero_zero_int tptp.int) % 0.37/0.69 (declare-const tptp.t tptp.int) % 0.37/0.69 (declare-const tptp.number_number_of_nat (-> tptp.int tptp.nat)) % 0.37/0.69 (declare-const tptp.ord_less_int (-> tptp.int tptp.int Bool)) % 0.37/0.69 (declare-const tptp.bit0 (-> tptp.int tptp.int)) % 0.37/0.69 (declare-const tptp.one_one_int tptp.int) % 0.37/0.69 (declare-const tptp.m tptp.int) % 0.37/0.69 (declare-const tptp.number_number_of_int (-> tptp.int tptp.int)) % 0.37/0.69 (declare-const tptp.plus_plus_int (-> tptp.int tptp.int tptp.int)) % 0.37/0.69 (declare-const tptp.pls tptp.int) % 0.37/0.69 (declare-const tptp.bit1 (-> tptp.int tptp.int)) % 0.37/0.69 (declare-const tptp.times_times_int (-> tptp.int tptp.int tptp.int)) % 0.37/0.69 (declare-const tptp.one_one_nat tptp.nat) % 0.37/0.69 (declare-const tptp.s tptp.int) % 0.37/0.69 (define @t1 () (tptp.bit1 tptp.pls)) % 0.37/0.69 (define @t2 () (tptp.bit0 @t1)) % 0.37/0.69 (define @t3 () (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 @t2)) tptp.m) tptp.one_one_int)) % 0.37/0.69 (define @t4 () (tptp.times_times_int @t3 tptp.zero_zero_int)) % 0.37/0.69 (define @t5 () (tptp.times_times_int @t3 tptp.t)) % 0.37/0.69 (define @t6 () (tptp.ord_less_int @t5 @t4)) % 0.37/0.69 (define @t7 () (tptp.number_number_of_nat @t2)) % 0.37/0.69 (define @t8 () (tptp.power_power_int tptp.s @t7)) % 0.37/0.69 (define @t9 () (tptp.plus_plus_int @t8 tptp.one_one_int)) % 0.37/0.69 (define @t10 () (= @t9 tptp.zero_zero_int)) % 0.37/0.69 (define @t11 () (@var "Y" tptp.int)) % 0.37/0.69 (define @t12 () (@var "X" tptp.int)) % 0.37/0.69 (define @t13 () (@list @t12 @t11)) % 0.37/0.69 (define @t14 () (@var "Y_1" tptp.int)) % 0.37/0.69 (define @t15 () (= @t14 tptp.zero_zero_int)) % 0.37/0.69 (define @t16 () (@var "X_1" tptp.int)) % 0.37/0.69 (define @t17 () (= @t16 tptp.zero_zero_int)) % 0.37/0.69 (define @t18 () (tptp.plus_plus_int (tptp.power_power_int @t16 @t7) (tptp.power_power_int @t14 @t7))) % 0.37/0.69 (define @t19 () (@list @t16 @t14)) % 0.37/0.69 (define @t20 () (and @t17 @t15)) % 0.37/0.69 (define @t21 () (= (= @t18 tptp.zero_zero_int) @t20)) % 0.37/0.69 (define @t22 () (forall @t19 @t21)) % 0.37/0.69 (define @t23 () (@var "A_2" tptp.int)) % 0.37/0.69 (define @t24 () (@var "A_1" tptp.int)) % 0.37/0.69 (define @t25 () (= @t24 tptp.zero_zero_int)) % 0.37/0.69 (define @t26 () (tptp.power_power_int @t24 @t7)) % 0.37/0.69 (define @t27 () (@list @t24)) % 0.37/0.69 (define @t28 () (tptp.power_power_int tptp.one_one_int @t7)) % 0.37/0.69 (define @t29 () (@var "W_6" tptp.int)) % 0.37/0.69 (define @t30 () (@var "V_13" tptp.int)) % 0.37/0.69 (define @t31 () (@var "T" tptp.int)) % 0.37/0.69 (define @t32 () (@var "W" tptp.int)) % 0.37/0.69 (define @t33 () (@list @t32)) % 0.37/0.69 (define @t34 () (@var "K_1" tptp.int)) % 0.37/0.69 (define @t35 () (tptp.number_number_of_int @t34)) % 0.37/0.69 (define @t36 () (forall (@list @t34) (= @t35 @t34))) % 0.37/0.69 (define @t37 () (@var "Z" tptp.int)) % 0.37/0.69 (define @t38 () (@list @t37 @t32)) % 0.37/0.69 (define @t39 () (tptp.ord_less_eq_int @t32 @t37)) % 0.37/0.69 (define @t40 () (tptp.ord_less_eq_int @t37 @t32)) % 0.37/0.69 (define @t41 () (@var "V_2" tptp.int)) % 0.37/0.69 (define @t42 () (tptp.number_number_of_int @t32)) % 0.37/0.69 (define @t43 () (tptp.number_number_of_int @t41)) % 0.37/0.69 (define @t44 () (@list @t41 @t32)) % 0.37/0.69 (define @t45 () (@var "L" tptp.int)) % 0.37/0.69 (define @t46 () (@var "K" tptp.int)) % 0.37/0.69 (define @t47 () (tptp.ord_less_eq_int @t46 @t45)) % 0.37/0.69 (define @t48 () (tptp.number_number_of_int @t45)) % 0.37/0.69 (define @t49 () (tptp.number_number_of_int @t46)) % 0.37/0.69 (define @t50 () (@list @t46 @t45)) % 0.37/0.69 (define @t51 () (tptp.number_number_of_int @t14)) % 0.37/0.69 (define @t52 () (tptp.number_number_of_int @t16)) % 0.37/0.69 (define @t53 () (@var "Z3" tptp.int)) % 0.37/0.69 (define @t54 () (@var "Z2" tptp.int)) % 0.37/0.69 (define @t55 () (@var "Z1" tptp.int)) % 0.37/0.69 (define @t56 () (@list @t55 @t54 @t53)) % 0.37/0.69 (define @t57 () (@var "I" tptp.int)) % 0.37/0.69 (define @t58 () (@var "J" tptp.int)) % 0.37/0.69 (define @t59 () (tptp.ord_less_eq_int @t57 @t58)) % 0.37/0.69 (define @t60 () (@list @t34 @t57 @t58)) % 0.37/0.69 (define @t61 () (@var "Z" tptp.nat)) % 0.37/0.69 (define @t62 () (@var "Y" tptp.nat)) % 0.37/0.69 (define @t63 () (@var "K2" tptp.int)) % 0.37/0.69 (define @t64 () (@var "K1" tptp.int)) % 0.37/0.69 (define @t65 () (tptp.ord_less_eq_int @t64 @t63)) % 0.37/0.69 (define @t66 () (tptp.bit1 @t63)) % 0.37/0.69 (define @t67 () (tptp.bit1 @t64)) % 0.37/0.69 (define @t68 () (@list @t64 @t63)) % 0.37/0.69 (define @t69 () (tptp.bit1 @t45)) % 0.37/0.69 (define @t70 () (tptp.bit1 @t46)) % 0.37/0.69 (define @t71 () (tptp.ord_less_eq_int tptp.pls tptp.pls)) % 0.37/0.69 (define @t72 () (tptp.bit0 @t63)) % 0.37/0.69 (define @t73 () (tptp.bit0 @t64)) % 0.37/0.69 (define @t74 () (tptp.bit0 @t45)) % 0.37/0.69 (define @t75 () (tptp.bit0 @t46)) % 0.37/0.69 (define @t76 () (@var "W_1" tptp.int)) % 0.37/0.69 (define @t77 () (@var "Z_1" tptp.int)) % 0.37/0.69 (define @t78 () (forall (@list @t77 @t76) (= (tptp.ord_less_int @t77 @t76) (and (tptp.ord_less_eq_int @t77 @t76) (not (= @t77 @t76)))))) % 0.37/0.69 (define @t79 () (@var "V_7" tptp.int)) % 0.37/0.69 (define @t80 () (tptp.ord_less_eq_int @t79 tptp.pls)) % 0.37/0.69 (define @t81 () (tptp.number_number_of_nat @t79)) % 0.37/0.69 (define @t82 () (@list @t79)) % 0.37/0.69 (define @t83 () (@var "V_12" tptp.int)) % 0.37/0.69 (define @t84 () (@var "V_11" tptp.int)) % 0.37/0.69 (define @t85 () (tptp.times_times_int @t84 @t83)) % 0.37/0.69 (define @t86 () (tptp.ord_less_eq_int tptp.pls @t83)) % 0.37/0.69 (define @t87 () (tptp.ord_less_eq_int tptp.pls @t84)) % 0.37/0.69 (define @t88 () (@list @t83 @t84)) % 0.37/0.69 (define @t89 () (@var "Z_3" tptp.int)) % 0.37/0.69 (define @t90 () (@var "W_5" tptp.int)) % 0.37/0.69 (define @t91 () (@var "V_10" tptp.int)) % 0.37/0.69 (define @t92 () (@var "W_4" tptp.int)) % 0.37/0.69 (define @t93 () (@var "V_9" tptp.int)) % 0.37/0.69 (define @t94 () (@var "W_3" tptp.int)) % 0.37/0.69 (define @t95 () (@var "V_8" tptp.int)) % 0.37/0.69 (define @t96 () (tptp.plus_plus_int (tptp.times_times_int @t16 @t16) (tptp.times_times_int @t14 @t14))) % 0.37/0.69 (define @t97 () (@var "Y_2" tptp.int)) % 0.37/0.69 (define @t98 () (@var "X_2" tptp.int)) % 0.37/0.69 (define @t99 () (@list @t16)) % 0.37/0.69 (define @t100 () (@list @t14)) % 0.37/0.69 (define @t101 () (tptp.number_number_of_int @t79)) % 0.37/0.69 (define @t102 () (tptp.number_number_of_int @t76)) % 0.37/0.69 (define @t103 () (@list @t79 @t76)) % 0.37/0.69 (define @t104 () (tptp.number_number_of_nat @t76)) % 0.37/0.69 (define @t105 () (tptp.ord_less_eq_int tptp.pls @t46)) % 0.37/0.69 (define @t106 () (@list @t46)) % 0.37/0.69 (define @t107 () (tptp.plus_plus_int @t32 @t37)) % 0.37/0.69 (define @t108 () (@var "Z_2" tptp.int)) % 0.37/0.69 (define @t109 () (@var "W_2" tptp.int)) % 0.37/0.69 (define @t110 () (tptp.number_number_of_nat tptp.pls)) % 0.37/0.69 (define @t111 () (forall @t100 (= (tptp.ord_less_eq_int tptp.one_one_int @t51) (tptp.ord_less_eq_int @t1 @t14)))) % 0.37/0.69 (define @t112 () (tptp.plus_plus_nat tptp.one_one_nat tptp.one_one_nat)) % 0.37/0.69 (define @t113 () (tptp.times_times_int tptp.pls @t32)) % 0.37/0.69 (define @t114 () (forall @t33 (= @t113 tptp.pls))) % 0.37/0.69 (define @t115 () (@var "L_1" tptp.int)) % 0.37/0.69 (define @t116 () (tptp.ord_less_int @t46 @t45)) % 0.37/0.69 (define @t117 () (@list @t37)) % 0.37/0.69 (define @t118 () (tptp.plus_plus_int @t55 @t54)) % 0.37/0.69 (define @t119 () (forall @t106 (= (tptp.ord_less_eq_int @t70 tptp.pls) (tptp.ord_less_int @t46 tptp.pls)))) % 0.37/0.69 (define @t120 () (@var "V_6" tptp.int)) % 0.37/0.69 (define @t121 () (tptp.ord_less_int @t79 @t120)) % 0.37/0.69 (define @t122 () (tptp.number_number_of_nat @t1)) % 0.37/0.69 (define @t123 () (@list @t76 @t77)) % 0.37/0.69 (define @t124 () (@var "V_5" tptp.int)) % 0.37/0.69 (define @t125 () (@var "V_4" tptp.int)) % 0.37/0.69 (define @t126 () (tptp.plus_plus_int @t125 @t124)) % 0.37/0.69 (define @t127 () (tptp.ord_less_eq_int tptp.pls @t124)) % 0.37/0.69 (define @t128 () (tptp.ord_less_eq_int tptp.pls @t125)) % 0.37/0.69 (define @t129 () (@list @t124 @t125)) % 0.37/0.69 (define @t130 () (@var "V_3" tptp.int)) % 0.37/0.69 (define @t131 () (tptp.number_number_of_nat @t130)) % 0.37/0.69 (define @t132 () (tptp.number_number_of_nat @t41)) % 0.37/0.69 (define @t133 () (tptp.plus_plus_nat @t132 @t131)) % 0.37/0.69 (define @t134 () (tptp.ord_less_int @t130 tptp.pls)) % 0.37/0.69 (define @t135 () (tptp.ord_less_int @t41 tptp.pls)) % 0.37/0.69 (define @t136 () (@var "X_1" tptp.nat)) % 0.37/0.69 (define @t137 () (= @t46 @t45)) % 0.37/0.69 (define @t138 () (@var "V_1" tptp.int)) % 0.37/0.69 (define @t139 () (tptp.number_number_of_int @t138)) % 0.37/0.69 (define @t140 () (@var "B_1" tptp.int)) % 0.37/0.69 (define @t141 () (@var "A" tptp.int)) % 0.37/0.69 (define @t142 () (tptp.number_number_of_nat @t138)) % 0.37/0.69 (define @t143 () (@var "B_1" tptp.nat)) % 0.37/0.69 (define @t144 () (@var "A" tptp.nat)) % 0.37/0.69 (define @t145 () (@var "C" tptp.int)) % 0.37/0.69 (define @t146 () (@var "V" tptp.int)) % 0.37/0.69 (define @t147 () (tptp.number_number_of_int @t146)) % 0.37/0.69 (define @t148 () (@var "B" tptp.int)) % 0.37/0.69 (define @t149 () (@var "C" tptp.nat)) % 0.37/0.69 (define @t150 () (tptp.number_number_of_nat @t146)) % 0.37/0.69 (define @t151 () (@var "B" tptp.nat)) % 0.37/0.69 (define @t152 () (tptp.number_number_of_int tptp.pls)) % 0.37/0.69 (define @t153 () (= tptp.zero_zero_int @t152)) % 0.37/0.69 (define @t154 () (tptp.ord_less_int @t9 tptp.zero_zero_int)) % 0.37/0.69 (define @t155 () (@list tptp.pls)) % 0.37/0.69 (define @t156 () (tptp.ord_less_eq_int @t5 @t4)) % 0.37/0.69 (define @t157 () (and @t156 (not (= @t5 @t4)))) % 0.37/0.69 (define @t158 () (= @t6 @t157)) % 0.37/0.69 (define @t159 () (@list false)) % 0.37/0.69 (define @t160 () (not @t10)) % 0.37/0.69 (define @t161 () (tptp.ord_less_eq_int @t9 tptp.zero_zero_int)) % 0.37/0.69 (define @t162 () (and @t161 @t160)) % 0.37/0.69 (define @t163 () (= @t154 @t162)) % 0.37/0.69 (define @t164 () (= tptp.zero_zero_int @t9)) % 0.37/0.69 (define @t165 () (not @t164)) % 0.37/0.69 (define @t166 () (and @t161 @t165)) % 0.37/0.69 (define @t167 () (= @t154 @t166)) % 0.37/0.69 (define @t168 () (@list @t78)) % 0.37/0.69 (define @t169 () (not @t166)) % 0.37/0.69 (define @t170 () (@list true false)) % 0.37/0.69 (define @t171 () (= tptp.zero_zero_int tptp.s)) % 0.37/0.69 (define @t172 () (and @t171 (= tptp.zero_zero_int tptp.one_one_int))) % 0.37/0.69 (define @t173 () (tptp.plus_plus_int @t8 @t28)) % 0.37/0.69 (define @t174 () (= tptp.zero_zero_int @t173)) % 0.37/0.69 (define @t175 () (= @t174 @t172)) % 0.37/0.69 (define @t176 () (forall @t19 (= (= tptp.zero_zero_int @t18) (and (= tptp.zero_zero_int @t16) (= tptp.zero_zero_int @t14))))) % 0.37/0.69 (define @t177 () (= tptp.one_one_int tptp.zero_zero_int)) % 0.37/0.69 (define @t178 () (and @t171 @t177)) % 0.37/0.69 (define @t179 () (= @t174 @t178)) % 0.37/0.69 (define @t180 () (tptp.ord_less_eq_int tptp.one_one_int @t152)) % 0.37/0.69 (define @t181 () (tptp.ord_less_eq_int @t1 tptp.pls)) % 0.37/0.69 (define @t182 () (= @t180 @t181)) % 0.37/0.69 (define @t183 () (= @t181 @t180)) % 0.37/0.69 (define @t184 () (tptp.ord_less_int tptp.pls tptp.pls)) % 0.37/0.69 (define @t185 () (= @t181 @t184)) % 0.37/0.69 (define @t186 () (= @t184 @t181)) % 0.37/0.69 (define @t187 () (not (= tptp.pls tptp.pls))) % 0.37/0.69 (define @t188 () (and @t71 @t187)) % 0.37/0.69 (define @t189 () (= @t184 @t188)) % 0.37/0.69 (define @t190 () (not @t181)) % 0.37/0.69 (define @t191 () (not @t180)) % 0.37/0.69 (define @t192 () (= tptp.pls @t152)) % 0.37/0.69 (define @t193 () (not @t192)) % 0.37/0.69 (define @t194 () (not @t177)) % 0.37/0.69 (define @t195 () (not @t153)) % 0.37/0.69 (define @t196 () (not @t71)) % 0.37/0.69 (define @t197 () (= false true)) % 0.37/0.69 (define @t198 () (and @t71 @t192 @t153 @t177 @t191)) % 0.37/0.69 (define @t199 () (not @t178)) % 0.37/0.69 (define @t200 () (not @t174)) % 0.37/0.69 (define @t201 () (= tptp.one_one_int @t28)) % 0.37/0.69 (define @t202 () (not @t201)) % 0.37/0.69 (define @t203 () (and @t201 @t200)) % 0.37/0.69 (define @t204 () (not @t161)) % 0.37/0.69 (define @t205 () (tptp.times_times_int tptp.pls @t3)) % 0.37/0.69 (define @t206 () (= tptp.pls @t205)) % 0.37/0.69 (define @t207 () (not @t206)) % 0.37/0.69 (define @t208 () (not @t156)) % 0.37/0.69 (define @t209 () (tptp.power_power_int tptp.one_one_int tptp.one_one_nat)) % 0.37/0.69 (define @t210 () (tptp.times_times_int @t209 @t209)) % 0.37/0.69 (define @t211 () (tptp.power_power_int tptp.one_one_int @t112)) % 0.37/0.69 (define @t212 () (= @t211 @t210)) % 0.37/0.69 (define @t213 () (not @t212)) % 0.37/0.69 (define @t214 () (tptp.power_power_int tptp.s tptp.one_one_nat)) % 0.37/0.69 (define @t215 () (tptp.times_times_int @t214 @t214)) % 0.37/0.69 (define @t216 () (tptp.power_power_int tptp.s @t112)) % 0.37/0.69 (define @t217 () (= @t216 @t215)) % 0.37/0.69 (define @t218 () (not @t217)) % 0.37/0.69 (define @t219 () (= @t4 (tptp.times_times_int tptp.zero_zero_int @t3))) % 0.37/0.69 (define @t220 () (not @t219)) % 0.37/0.69 (define @t221 () (= @t7 @t112)) % 0.37/0.69 (define @t222 () (not @t221)) % 0.37/0.69 (define @t223 () (= @t5 @t9)) % 0.37/0.69 (define @t224 () (not @t223)) % 0.37/0.69 (define @t225 () (tptp.plus_plus_int @t215 @t210)) % 0.37/0.69 (define @t226 () (and @t156 @t223 @t201 @t221 @t217 @t212 @t219 @t153 @t192 @t206 @t204)) % 0.37/0.69 (assume @p1 (tptp.ord_less_int tptp.t tptp.zero_zero_int)) % 0.37/0.69 (assume @p2 (tptp.ord_less_int tptp.t tptp.one_one_int)) % 0.37/0.69 (assume @p3 @t6) % 0.37/0.69 (assume @p4 (= @t9 @t5)) % 0.37/0.69 (assume @p5 (=> (= tptp.t tptp.zero_zero_int) @t10)) % 0.37/0.69 (assume @p6 (not (tptp.ord_less_eq_int tptp.one_one_int tptp.t))) % 0.37/0.69 (assume @p7 (tptp.ord_less_int tptp.zero_zero_int @t3)) % 0.37/0.69 (assume @p8 (forall @t13 (not (tptp.ord_less_int (tptp.plus_plus_int (tptp.power_power_int @t12 @t7) (tptp.power_power_int @t11 @t7)) tptp.zero_zero_int)))) % 0.37/0.69 (assume @p9 (forall @t19 (= (tptp.ord_less_int tptp.zero_zero_int @t18) (or (not @t17) (not @t15))))) % 0.37/0.69 (assume @p10 @t22) % 0.37/0.69 (assume @p11 (forall (@list @t23) (not (tptp.ord_less_int (tptp.power_power_int @t23 @t7) tptp.zero_zero_int)))) % 0.37/0.69 (assume @p12 (forall @t27 (= (tptp.ord_less_int tptp.zero_zero_int @t26) (not @t25)))) % 0.37/0.69 (assume @p13 (= (tptp.power_power_nat tptp.one_one_nat @t7) tptp.one_one_nat)) % 0.37/0.69 (assume @p14 (= @t28 tptp.one_one_int)) % 0.37/0.69 (assume @p15 (= (tptp.power_power_nat tptp.zero_zero_nat @t7) tptp.zero_zero_nat)) % 0.37/0.69 (assume @p16 (= (tptp.power_power_int tptp.zero_zero_int @t7) tptp.zero_zero_int)) % 0.37/0.69 (assume @p17 (forall @t27 (= (= @t26 tptp.zero_zero_int) @t25))) % 0.37/0.69 (assume @p18 (forall (@list @t29) (= (tptp.plus_plus_int tptp.one_one_int (tptp.number_number_of_int @t29)) (tptp.number_number_of_int (tptp.plus_plus_int @t1 @t29))))) % 0.37/0.69 (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 @t1))))) % 0.37/0.69 (assume @p20 (tptp.ord_less_int tptp.t @t3)) % 0.37/0.69 (assume @p21 (not (forall (@list @t31) (not (= @t9 (tptp.times_times_int @t3 @t31)))))) % 0.37/0.69 (assume @p22 (tptp.zprime @t3)) % 0.37/0.69 (assume @p23 (tptp.twoSqu1431725154sum2sq @t5)) % 0.37/0.69 (assume @p24 (forall @t33 (tptp.ord_less_eq_int @t32 @t32))) % 0.37/0.69 (assume @p25 @t36) % 0.37/0.69 (assume @p26 (forall @t38 (= (tptp.times_times_int @t37 @t32) (tptp.times_times_int @t32 @t37)))) % 0.37/0.69 (assume @p27 (forall @t38 (or @t40 @t39))) % 0.37/0.69 (assume @p28 (forall @t44 (= (tptp.times_times_int @t43 @t42) (tptp.number_number_of_int (tptp.times_times_int @t41 @t32))))) % 0.37/0.69 (assume @p29 (forall @t50 (= (tptp.ord_less_eq_int @t49 @t48) @t47))) % 0.37/0.69 (assume @p30 (forall @t19 (= (tptp.ord_less_eq_int @t52 @t51) (tptp.ord_less_eq_int @t16 @t14)))) % 0.37/0.69 (assume @p31 (forall @t56 (= (tptp.times_times_int (tptp.times_times_int @t55 @t54) @t53) (tptp.times_times_int @t55 (tptp.times_times_int @t54 @t53))))) % 0.37/0.69 (assume @p32 (forall @t60 (=> @t59 (=> (tptp.ord_less_eq_int @t58 @t34) (tptp.ord_less_eq_int @t57 @t34))))) % 0.37/0.69 (assume @p33 (forall @t38 (=> @t40 (=> @t39 (= @t37 @t32))))) % 0.37/0.69 (assume @p34 (forall (@list @t12 @t62 @t61) (= (tptp.power_power_int @t12 (tptp.plus_plus_nat @t62 @t61)) (tptp.times_times_int (tptp.power_power_int @t12 @t62) (tptp.power_power_int @t12 @t61))))) % 0.37/0.69 (assume @p35 (forall @t68 (= (tptp.ord_less_eq_int @t67 @t66) @t65))) % 0.37/0.69 (assume @p36 (forall @t50 (= (tptp.ord_less_eq_int @t70 @t69) @t47))) % 0.37/0.69 (assume @p37 @t71) % 0.37/0.69 (assume @p38 (forall @t68 (= (tptp.ord_less_eq_int @t73 @t72) @t65))) % 0.37/0.69 (assume @p39 (forall @t50 (= (tptp.ord_less_eq_int @t75 @t74) @t47))) % 0.37/0.69 (assume @p40 @t78) % 0.37/0.69 (assume @p41 (forall @t60 (=> @t59 (tptp.ord_less_eq_int (tptp.plus_plus_int @t34 @t57) (tptp.plus_plus_int @t34 @t58))))) % 0.37/0.69 (assume @p42 (forall @t82 (= (= @t81 tptp.zero_zero_nat) @t80))) % 0.37/0.69 (assume @p43 (forall @t82 (= (= tptp.zero_zero_nat @t81) @t80))) % 0.37/0.69 (assume @p44 (forall @t88 (=> @t87 (=> @t86 (= (tptp.times_times_nat (tptp.number_number_of_nat @t84) (tptp.number_number_of_nat @t83)) (tptp.number_number_of_nat @t85)))))) % 0.37/0.69 (assume @p45 (forall @t88 (=> @t87 (=> @t86 (= (tptp.times_times_int (tptp.number_number_of_int @t84) (tptp.number_number_of_int @t83)) (tptp.number_number_of_int @t85)))))) % 0.37/0.69 (assume @p46 (forall (@list @t91 @t90 @t89) (= (tptp.times_times_int (tptp.number_number_of_int @t91) (tptp.times_times_int (tptp.number_number_of_int @t90) @t89)) (tptp.times_times_int (tptp.number_number_of_int (tptp.times_times_int @t91 @t90)) @t89)))) % 0.37/0.69 (assume @p47 (forall (@list @t93 @t92) (= (tptp.times_times_int (tptp.number_number_of_int @t93) (tptp.number_number_of_int @t92)) (tptp.number_number_of_int (tptp.times_times_int @t93 @t92))))) % 0.37/0.69 (assume @p48 (forall (@list @t95 @t94) (= (tptp.number_number_of_int (tptp.times_times_int @t95 @t94)) (tptp.times_times_int (tptp.number_number_of_int @t95) (tptp.number_number_of_int @t94))))) % 0.37/0.69 (assume @p49 (forall @t19 (= (tptp.ord_less_eq_int @t96 tptp.zero_zero_int) @t20))) % 0.37/0.69 (assume @p50 (forall (@list @t98 @t97) (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.plus_plus_int (tptp.times_times_int @t98 @t98) (tptp.times_times_int @t97 @t97))))) % 0.37/0.69 (assume @p51 (forall @t99 (= (tptp.ord_less_eq_int @t52 tptp.zero_zero_int) (tptp.ord_less_eq_int @t16 tptp.pls)))) % 0.37/0.69 (assume @p52 (forall @t100 (= (tptp.ord_less_eq_int tptp.zero_zero_int @t51) (tptp.ord_less_eq_int tptp.pls @t14)))) % 0.37/0.69 (assume @p53 (forall @t82 (= (tptp.ord_less_nat tptp.zero_zero_nat @t81) (tptp.ord_less_int tptp.pls @t79)))) % 0.37/0.69 (assume @p54 (forall @t103 (= (tptp.ord_less_eq_int @t101 @t102) (not (tptp.ord_less_int @t102 @t101))))) % 0.37/0.69 (assume @p55 (forall @t103 (= (tptp.ord_less_eq_nat @t81 @t104) (not (tptp.ord_less_nat @t104 @t81))))) % 0.37/0.69 (assume @p56 (forall @t106 (= (tptp.ord_less_eq_int tptp.pls @t70) @t105))) % 0.37/0.69 (assume @p57 (forall @t68 (= (tptp.ord_less_eq_int @t73 @t66) @t65))) % 0.37/0.69 (assume @p58 (forall @t50 (= (tptp.ord_less_eq_int @t75 @t69) @t47))) % 0.37/0.69 (assume @p59 (forall @t106 (= (tptp.ord_less_eq_int @t75 tptp.pls) (tptp.ord_less_eq_int @t46 tptp.pls)))) % 0.37/0.69 (assume @p60 (forall @t106 (= (tptp.ord_less_eq_int tptp.pls @t75) @t105))) % 0.37/0.69 (assume @p61 (forall (@list @t108 @t37 @t109 @t32) (=> (tptp.ord_less_int @t109 @t32) (=> (tptp.ord_less_eq_int @t108 @t37) (tptp.ord_less_int (tptp.plus_plus_int @t109 @t108) @t107))))) % 0.37/0.69 (assume @p62 (= @t110 tptp.zero_zero_nat)) % 0.37/0.69 (assume @p63 (= tptp.zero_zero_nat @t110)) % 0.37/0.69 (assume @p64 (forall @t99 (= (tptp.ord_less_eq_int @t52 tptp.one_one_int) (tptp.ord_less_eq_int @t16 @t1)))) % 0.37/0.69 (assume @p65 @t111) % 0.37/0.69 (assume @p66 (= @t112 @t7)) % 0.37/0.69 (assume @p67 @t114) % 0.37/0.69 (assume @p68 (forall (@list @t34 @t115) (= (tptp.times_times_int (tptp.bit0 @t34) @t115) (tptp.bit0 (tptp.times_times_int @t34 @t115))))) % 0.37/0.69 (assume @p69 (forall @t50 (= (tptp.ord_less_int @t49 @t48) @t116))) % 0.37/0.69 (assume @p70 (forall @t117 (= (tptp.times_times_int @t37 tptp.one_one_int) @t37))) % 0.37/0.69 (assume @p71 (forall @t117 (= (tptp.times_times_int tptp.one_one_int @t37) @t37))) % 0.37/0.69 (assume @p72 (forall @t44 (= (tptp.plus_plus_int @t43 @t42) (tptp.number_number_of_int (tptp.plus_plus_int @t41 @t32))))) % 0.37/0.69 (assume @p73 (forall (@list @t55 @t54 @t32) (= (tptp.times_times_int @t118 @t32) (tptp.plus_plus_int (tptp.times_times_int @t55 @t32) (tptp.times_times_int @t54 @t32))))) % 0.37/0.69 (assume @p74 (forall (@list @t32 @t55 @t54) (= (tptp.times_times_int @t32 @t118) (tptp.plus_plus_int (tptp.times_times_int @t32 @t55) (tptp.times_times_int @t32 @t54))))) % 0.37/0.69 (assume @p75 @t119) % 0.37/0.69 (assume @p76 (forall @t106 (= (tptp.ord_less_int tptp.pls @t70) @t105))) % 0.37/0.69 (assume @p77 (forall @t68 (= (tptp.ord_less_eq_int @t67 @t72) (tptp.ord_less_int @t64 @t63)))) % 0.37/0.69 (assume @p78 (forall @t50 (= (tptp.ord_less_eq_int @t70 @t74) @t116))) % 0.37/0.69 (assume @p79 (forall @t68 (= (tptp.ord_less_int @t73 @t66) @t65))) % 0.37/0.69 (assume @p80 (forall @t50 (= (tptp.ord_less_int @t75 @t69) @t47))) % 0.37/0.69 (assume @p81 (forall (@list @t79 @t120) (= (tptp.ord_less_nat @t81 (tptp.number_number_of_nat @t120)) (and (=> @t121 (tptp.ord_less_int tptp.pls @t120)) @t121)))) % 0.37/0.69 (assume @p82 (forall (@list @t77) (= (tptp.ord_less_eq_int tptp.one_one_int @t77) (tptp.ord_less_int tptp.zero_zero_int @t77)))) % 0.37/0.69 (assume @p83 (= @t122 tptp.one_one_nat)) % 0.37/0.69 (assume @p84 (= tptp.one_one_nat @t122)) % 0.37/0.69 (assume @p85 (forall (@list @t32 @t37) (=> (tptp.ord_less_int @t32 @t37) (tptp.ord_less_eq_int (tptp.plus_plus_int @t32 tptp.one_one_int) @t37)))) % 0.37/0.69 (assume @p86 (forall @t123 (= (tptp.ord_less_eq_int (tptp.plus_plus_int @t76 tptp.one_one_int) @t77) (tptp.ord_less_int @t76 @t77)))) % 0.37/0.69 (assume @p87 (forall @t123 (= (tptp.ord_less_int @t76 (tptp.plus_plus_int @t77 tptp.one_one_int)) (tptp.ord_less_eq_int @t76 @t77)))) % 0.37/0.69 (assume @p88 (forall @t129 (=> @t128 (=> @t127 (= (tptp.plus_plus_int (tptp.number_number_of_int @t125) (tptp.number_number_of_int @t124)) (tptp.number_number_of_int @t126)))))) % 0.37/0.69 (assume @p89 (forall @t129 (=> @t128 (=> @t127 (= (tptp.plus_plus_nat (tptp.number_number_of_nat @t125) (tptp.number_number_of_nat @t124)) (tptp.number_number_of_nat @t126)))))) % 0.37/0.69 (assume @p90 (forall (@list @t130 @t41) (and (=> @t135 (= @t133 @t131)) (=> (not @t135) (and (=> @t134 (= @t133 @t132)) (=> (not @t134) (= @t133 (tptp.number_number_of_nat (tptp.plus_plus_int @t41 @t130))))))))) % 0.37/0.69 (assume @p91 (forall @t117 (=> (tptp.ord_less_eq_int tptp.zero_zero_int @t37) (tptp.ord_less_int tptp.zero_zero_int (tptp.plus_plus_int tptp.one_one_int @t37))))) % 0.37/0.69 (assume @p92 (forall @t19 (= (= @t52 @t51) (= @t16 @t14)))) % 0.37/0.69 (assume @p93 (forall (@list @t76 @t136) (= (= @t104 @t136) (= @t136 @t104)))) % 0.37/0.69 (assume @p94 (forall (@list @t76 @t16) (= (= @t102 @t16) (= @t16 @t102)))) % 0.37/0.69 (assume @p95 (forall @t50 (= (= @t70 @t69) @t137))) % 0.37/0.69 (assume @p96 (forall @t50 (= (= @t75 @t74) @t137))) % 0.37/0.69 (assume @p97 (forall @t13 (or (tptp.ord_less_int @t12 @t11) (= @t12 @t11) (tptp.ord_less_int @t11 @t12)))) % 0.37/0.69 (assume @p98 (forall @t19 (= (= @t96 tptp.zero_zero_int) @t20))) % 0.37/0.69 (assume @p99 (forall (@list @t141 @t140 @t138) (= (tptp.times_times_int (tptp.plus_plus_int @t141 @t140) @t139) (tptp.plus_plus_int (tptp.times_times_int @t141 @t139) (tptp.times_times_int @t140 @t139))))) % 0.37/0.69 (assume @p100 (forall (@list @t144 @t143 @t138) (= (tptp.times_times_nat (tptp.plus_plus_nat @t144 @t143) @t142) (tptp.plus_plus_nat (tptp.times_times_nat @t144 @t142) (tptp.times_times_nat @t143 @t142))))) % 0.37/0.69 (assume @p101 (forall (@list @t146 @t148 @t145) (= (tptp.times_times_int @t147 (tptp.plus_plus_int @t148 @t145)) (tptp.plus_plus_int (tptp.times_times_int @t147 @t148) (tptp.times_times_int @t147 @t145))))) % 0.37/0.69 (assume @p102 (forall (@list @t146 @t151 @t149) (= (tptp.times_times_nat @t150 (tptp.plus_plus_nat @t151 @t149)) (tptp.plus_plus_nat (tptp.times_times_nat @t150 @t151) (tptp.times_times_nat @t150 @t149))))) % 0.37/0.69 (assume @p103 (forall @t56 (= (tptp.plus_plus_int @t118 @t53) (tptp.plus_plus_int @t55 (tptp.plus_plus_int @t54 @t53))))) % 0.37/0.69 (assume @p104 (forall (@list @t12 @t11 @t37) (= (tptp.plus_plus_int @t12 (tptp.plus_plus_int @t11 @t37)) (tptp.plus_plus_int @t11 (tptp.plus_plus_int @t12 @t37))))) % 0.37/0.69 (assume @p105 (forall @t38 (= (tptp.plus_plus_int @t37 @t32) @t107))) % 0.37/0.69 (assume @p106 @t153) % 0.37/0.69 (assume @p107 (not @t154)) % 0.37/0.69 (assume @p108 true) % 0.37/0.69 (step @p109 :rule symm :premises (@p4)) % 0.37/0.69 (step @p110 :rule symm :premises (@p14)) % 0.37/0.69 (step @p111 :rule symm :premises (@p66)) % 0.37/0.69 (step @p112 :rule eq-symm :args (@t35 @t34)) % 0.37/0.69 (step @p113 :rule cong :premises (@p112) :args (@t36)) % 0.37/0.69 (step @p114 :rule eq_resolve :premises (@p25 @p113)) % 0.37/0.69 (step @p115 :rule instantiate :premises (@p114) :args (@t155)) % 0.37/0.69 (step @p116 :rule instantiate :premises (@p26) :args ((@list @t3 tptp.zero_zero_int))) % 0.37/0.69 (step @p117 :rule instantiate :premises (@p34) :args ((@list tptp.s tptp.one_one_nat tptp.one_one_nat))) % 0.37/0.69 (step @p118 :rule instantiate :premises (@p34) :args ((@list tptp.one_one_int tptp.one_one_nat tptp.one_one_nat))) % 0.37/0.69 (step @p119 :rule instantiate :premises (@p40) :args ((@list @t5 @t4))) % 0.37/0.69 (step @p120 :rule cnf_equiv_pos1 :args (@t158)) % 0.37/0.69 (step @p121 :rule reordering :premises (@p120) :args ((or (not @t6) @t157 (not @t158)))) % 0.37/0.69 (step @p122 :rule chain_m_resolution :premises (@p121 @p3 @p119) :args (@t157 (@list false false) (@list @t6 @t158))) % 0.37/0.69 (step @p123 :rule cnf_and_pos :args (@t157 0)) % 0.37/0.69 (step @p124 :rule reordering :premises (@p123) :args ((or @t156 (not @t157)))) % 0.37/0.69 (step @p125 :rule chain_m_resolution :premises (@p124 @p122) :args (@t156 @t159 (@list @t157))) % 0.37/0.69 (step @p126 :rule eq-symm :args (@t9 tptp.zero_zero_int)) % 0.37/0.69 (step @p127 :rule cong :premises (@p126) :args (@t160)) % 0.37/0.69 (step @p128 :rule refl :args (@t161)) % 0.37/0.69 (step @p129 :rule nary_cong :premises (@p128 @p127) :args (@t162)) % 0.37/0.69 (step @p130 :rule refl :args (@t154)) % 0.37/0.69 (step @p131 :rule cong :premises (@p130 @p129) :args (@t163)) % 0.37/0.69 (step @p132 :rule refl :args (@t78)) % 0.37/0.69 (step @p133 :rule cong :premises (@p132 @p131) :args ((=> 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0.37/0.69 (step @p340 :rule trans :premises (@p339 @p338)) % 0.37/0.69 (step @p341 :rule cong :premises (@p340 @p336) :args (@t225)) % 0.37/0.69 (step @p342 :rule trans :premises (@p341 @p332 @p4)) % 0.37/0.69 (step @p343 :rule cong :premises (@p342 @p331) :args ((tptp.ord_less_eq_int @t225 tptp.zero_zero_int))) % 0.37/0.69 (step @p276 :rule refl :args (tptp.zero_zero_int)) % 0.37/0.69 (step @p344 :rule symm :premises (@p342)) % 0.37/0.69 (step @p345 :rule trans :premises (@p4 @p344)) % 0.37/0.69 (step @p346 :rule cong :premises (@p345 @p276) :args (@t161)) % 0.37/0.69 (step @p347 :rule false_intro :premises (@p441)) % 0.37/0.69 (step @p348 :rule symm :premises (@p347)) % 0.37/0.69 (step @p349 :rule trans :premises (@p348 @p346 @p343 @p326)) % 0.37/0.69 (step @p350 false :rule eq_resolve :premises (@p349 @p222)) % 0.37/0.69 (step-pop @p442 :rule scope :premises (@p350)) % 0.37/0.69 (step-pop @p443 :rule scope :premises (@p442)) % 0.37/0.69 (step-pop @p444 :rule scope :premises (@p443)) % 0.37/0.69 (step-pop @p445 :rule scope :premises (@p444)) % 0.37/0.69 (step-pop @p446 :rule scope :premises (@p445)) % 0.37/0.69 (step-pop @p447 :rule scope :premises (@p446)) % 0.37/0.69 (step-pop @p448 :rule scope :premises (@p447)) % 0.37/0.69 (step-pop @p449 :rule scope :premises (@p448)) % 0.37/0.69 (step-pop @p450 :rule scope :premises (@p449)) % 0.37/0.69 (step-pop @p451 :rule scope :premises (@p450)) % 0.37/0.69 (step-pop @p452 :rule scope :premises (@p451)) % 0.37/0.69 (step @p351 :rule process_scope :premises (@p452) :args (false)) % 0.37/0.69 (assume-push @p453 @t153) % 0.37/0.69 (assume-push @p454 @t223) % 0.37/0.69 (assume-push @p455 @t201) % 0.37/0.69 (assume-push @p456 @t221) % 0.37/0.69 (assume-push @p457 @t192) % 0.37/0.69 (assume-push @p458 @t219) % 0.37/0.69 (assume-push @p459 @t217) % 0.37/0.69 (assume-push @p460 @t212) % 0.37/0.69 (assume-push @p461 @t156) % 0.37/0.69 (assume-push @p462 @t204) % 0.37/0.69 (assume-push @p463 @t206) % 0.37/0.69 (step @p374 :rule and_intro :premises (@p125 @p109 @p110 @p111 @p117 @p118 @p116 @p106 @p115 @p305 @p462)) % 0.37/0.69 (step-pop @p464 :rule scope :premises (@p374)) % 0.37/0.69 (step-pop @p465 :rule scope :premises (@p464)) % 0.37/0.69 (step-pop @p466 :rule scope :premises (@p465)) % 0.37/0.69 (step-pop @p467 :rule scope :premises (@p466)) % 0.37/0.69 (step-pop @p468 :rule scope :premises (@p467)) % 0.37/0.69 (step-pop @p469 :rule scope :premises (@p468)) % 0.37/0.69 (step-pop @p470 :rule scope :premises (@p469)) % 0.37/0.69 (step-pop @p471 :rule scope :premises (@p470)) % 0.37/0.69 (step-pop @p472 :rule scope :premises (@p471)) % 0.37/0.69 (step-pop @p473 :rule scope :premises (@p472)) % 0.37/0.69 (step-pop @p474 :rule scope :premises (@p473)) % 0.37/0.69 (step @p375 :rule process_scope :premises (@p474) :args (@t226)) % 0.37/0.69 (step @p387 :rule implies_elim :premises (@p375)) % 0.37/0.69 (step @p388 :rule resolution :premises (@p387 @p351) :args (true @t226)) % 0.37/0.69 (step @p389 :rule not_and :premises (@p388)) % 0.37/0.69 (step @p390 :rule eq_resolve :premises (@p389 @p314)) % 0.37/0.69 (step @p391 :rule reordering :premises (@p390) :args ((or @t224 @t202 @t222 @t195 @t161 @t193 @t220 @t218 @t213 @t208 @t207))) % 0.37/0.69 (step @p392 false :rule chain_m_resolution :premises (@p391 @p305 @p301 @p125 @p118 @p117 @p116 @p115 @p106 @p111 @p110 @p109) :args (false (@list false true false false false false false false false false false) (@list @t206 @t161 @t156 @t212 @t217 @t219 @t192 @t153 @t221 @t201 @t223))) % 0.37/0.69 ) % 0.37/0.69 % SZS output end Proof % 0.37/0.69 % cvc5 exiting %------------------------------------------------------------------------------