%------------------------------------------------------------------------------ % 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 : n008.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 08:41:00 AM UTC 2026 % Result : Theorem 0.44s 0.69s % Output : Proof 0.44s % 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 % 0.17/0.34 % Computer : n008.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 12:32:33 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.69 % SZS status Theorem % 0.44/0.69 % SZS output start Proof % 0.44/0.69 ( % 0.44/0.69 (declare-sort $$unsorted 0) % 0.44/0.69 (declare-const tptp.times_times_nat (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.plus_plus_nat (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.zprime (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.zero_zero_nat $$unsorted) % 0.44/0.69 (declare-const tptp.power_power_nat (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.ord_less_eq_nat (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.one_one_nat $$unsorted) % 0.44/0.69 (declare-const tptp.twoSqu526106917sum2sq (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.ord_less_eq_int (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.power_power_int (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.zero_zero_int $$unsorted) % 0.44/0.69 (declare-const tptp.pls $$unsorted) % 0.44/0.69 (declare-const tptp.t $$unsorted) % 0.44/0.69 (declare-const tptp.bit1 (-> $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.one_one_int $$unsorted) % 0.44/0.69 (declare-const tptp.m $$unsorted) % 0.44/0.69 (declare-const tptp.s $$unsorted) % 0.44/0.69 (declare-const tptp.ord_less_nat (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.ord_less_int (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.bit0 (-> $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.number_number_of_int (-> $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.times_times_int (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.plus_plus_int (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.number_number_of_nat (-> $$unsorted $$unsorted)) % 0.44/0.69 (define @t1 () (tptp.bit1 tptp.pls)) % 0.44/0.69 (define @t2 () (tptp.bit0 @t1)) % 0.44/0.69 (define @t3 () (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 @t2)) tptp.m) tptp.one_one_int)) % 0.44/0.69 (define @t4 () (tptp.times_times_int @t3 tptp.zero_zero_int)) % 0.44/0.69 (define @t5 () (tptp.times_times_int @t3 tptp.t)) % 0.44/0.69 (define @t6 () (tptp.ord_less_int @t5 @t4)) % 0.44/0.69 (define @t7 () (tptp.number_number_of_nat @t2)) % 0.44/0.69 (define @t8 () (tptp.power_power_int tptp.s @t7)) % 0.44/0.69 (define @t9 () (tptp.plus_plus_int @t8 tptp.one_one_int)) % 0.44/0.69 (define @t10 () (= @t9 tptp.zero_zero_int)) % 0.44/0.69 (define @t11 () (@var "Y" $$unsorted)) % 0.44/0.69 (define @t12 () (@var "X" $$unsorted)) % 0.44/0.69 (define @t13 () (@list @t12 @t11)) % 0.44/0.69 (define @t14 () (@var "Y_1" $$unsorted)) % 0.44/0.69 (define @t15 () (= @t14 tptp.zero_zero_int)) % 0.44/0.69 (define @t16 () (@var "X_1" $$unsorted)) % 0.44/0.69 (define @t17 () (= @t16 tptp.zero_zero_int)) % 0.44/0.69 (define @t18 () (tptp.plus_plus_int (tptp.power_power_int @t16 @t7) (tptp.power_power_int @t14 @t7))) % 0.44/0.69 (define @t19 () (@list @t16 @t14)) % 0.44/0.69 (define @t20 () (and @t17 @t15)) % 0.44/0.69 (define @t21 () (= (= @t18 tptp.zero_zero_int) @t20)) % 0.44/0.69 (define @t22 () (forall @t19 @t21)) % 0.44/0.69 (define @t23 () (@var "A_2" $$unsorted)) % 0.44/0.69 (define @t24 () (@var "A_1" $$unsorted)) % 0.44/0.69 (define @t25 () (= @t24 tptp.zero_zero_int)) % 0.44/0.69 (define @t26 () (tptp.power_power_int @t24 @t7)) % 0.44/0.69 (define @t27 () (@list @t24)) % 0.44/0.69 (define @t28 () (tptp.power_power_int tptp.one_one_int @t7)) % 0.44/0.69 (define @t29 () (@var "W_6" $$unsorted)) % 0.44/0.69 (define @t30 () (@var "V_13" $$unsorted)) % 0.44/0.69 (define @t31 () (@var "T" $$unsorted)) % 0.44/0.69 (define @t32 () (@var "W" $$unsorted)) % 0.44/0.69 (define @t33 () (@list @t32)) % 0.44/0.69 (define @t34 () (@var "K_1" $$unsorted)) % 0.44/0.69 (define @t35 () (tptp.number_number_of_int @t34)) % 0.44/0.69 (define @t36 () (forall (@list @t34) (= @t35 @t34))) % 0.44/0.69 (define @t37 () (@var "Z" $$unsorted)) % 0.44/0.69 (define @t38 () (@list @t37 @t32)) % 0.44/0.69 (define @t39 () (tptp.ord_less_eq_int @t32 @t37)) % 0.44/0.69 (define @t40 () (tptp.ord_less_eq_int @t37 @t32)) % 0.44/0.69 (define @t41 () (@var "V_2" $$unsorted)) % 0.44/0.69 (define @t42 () (tptp.number_number_of_int @t32)) % 0.44/0.69 (define @t43 () (tptp.number_number_of_int @t41)) % 0.44/0.69 (define @t44 () (@list @t41 @t32)) % 0.44/0.69 (define @t45 () (@var "L" $$unsorted)) % 0.44/0.69 (define @t46 () (@var "K" $$unsorted)) % 0.44/0.69 (define @t47 () (tptp.ord_less_eq_int @t46 @t45)) % 0.44/0.69 (define @t48 () (tptp.number_number_of_int @t45)) % 0.44/0.69 (define @t49 () (tptp.number_number_of_int @t46)) % 0.44/0.69 (define @t50 () (@list @t46 @t45)) % 0.44/0.69 (define @t51 () (tptp.number_number_of_int @t14)) % 0.44/0.69 (define @t52 () (tptp.number_number_of_int @t16)) % 0.44/0.69 (define @t53 () (@var "Z3" $$unsorted)) % 0.44/0.69 (define @t54 () (@var "Z2" $$unsorted)) % 0.44/0.69 (define @t55 () (@var "Z1" $$unsorted)) % 0.44/0.69 (define @t56 () (@list @t55 @t54 @t53)) % 0.44/0.69 (define @t57 () (@var "I" $$unsorted)) % 0.44/0.69 (define @t58 () (@var "J" $$unsorted)) % 0.44/0.69 (define @t59 () (tptp.ord_less_eq_int @t57 @t58)) % 0.44/0.69 (define @t60 () (@list @t34 @t57 @t58)) % 0.44/0.69 (define @t61 () (@list @t12 @t11 @t37)) % 0.44/0.69 (define @t62 () (@var "K2" $$unsorted)) % 0.44/0.69 (define @t63 () (@var "K1" $$unsorted)) % 0.44/0.69 (define @t64 () (tptp.ord_less_eq_int @t63 @t62)) % 0.44/0.69 (define @t65 () (tptp.bit1 @t62)) % 0.44/0.69 (define @t66 () (tptp.bit1 @t63)) % 0.44/0.69 (define @t67 () (@list @t63 @t62)) % 0.44/0.69 (define @t68 () (tptp.bit1 @t45)) % 0.44/0.69 (define @t69 () (tptp.bit1 @t46)) % 0.44/0.69 (define @t70 () (tptp.ord_less_eq_int tptp.pls tptp.pls)) % 0.44/0.69 (define @t71 () (tptp.bit0 @t62)) % 0.44/0.69 (define @t72 () (tptp.bit0 @t63)) % 0.44/0.69 (define @t73 () (tptp.bit0 @t45)) % 0.44/0.69 (define @t74 () (tptp.bit0 @t46)) % 0.44/0.69 (define @t75 () (@var "W_1" $$unsorted)) % 0.44/0.69 (define @t76 () (@var "Z_1" $$unsorted)) % 0.44/0.69 (define @t77 () (forall (@list @t76 @t75) (= (tptp.ord_less_int @t76 @t75) (and (tptp.ord_less_eq_int @t76 @t75) (not (= @t76 @t75)))))) % 0.44/0.69 (define @t78 () (@var "V_7" $$unsorted)) % 0.44/0.69 (define @t79 () (tptp.ord_less_eq_int @t78 tptp.pls)) % 0.44/0.69 (define @t80 () (tptp.number_number_of_nat @t78)) % 0.44/0.69 (define @t81 () (@list @t78)) % 0.44/0.69 (define @t82 () (@var "V_12" $$unsorted)) % 0.44/0.69 (define @t83 () (@var "V_11" $$unsorted)) % 0.44/0.69 (define @t84 () (tptp.times_times_int @t83 @t82)) % 0.44/0.69 (define @t85 () (tptp.ord_less_eq_int tptp.pls @t82)) % 0.44/0.69 (define @t86 () (tptp.ord_less_eq_int tptp.pls @t83)) % 0.44/0.69 (define @t87 () (@list @t82 @t83)) % 0.44/0.69 (define @t88 () (@var "Z_3" $$unsorted)) % 0.44/0.69 (define @t89 () (@var "W_5" $$unsorted)) % 0.44/0.69 (define @t90 () (@var "V_10" $$unsorted)) % 0.44/0.69 (define @t91 () (@var "W_4" $$unsorted)) % 0.44/0.69 (define @t92 () (@var "V_9" $$unsorted)) % 0.44/0.69 (define @t93 () (@var "W_3" $$unsorted)) % 0.44/0.69 (define @t94 () (@var "V_8" $$unsorted)) % 0.44/0.69 (define @t95 () (tptp.plus_plus_int (tptp.times_times_int @t16 @t16) (tptp.times_times_int @t14 @t14))) % 0.44/0.69 (define @t96 () (@var "Y_2" $$unsorted)) % 0.44/0.69 (define @t97 () (@var "X_2" $$unsorted)) % 0.44/0.69 (define @t98 () (@list @t16)) % 0.44/0.69 (define @t99 () (@list @t14)) % 0.44/0.69 (define @t100 () (tptp.number_number_of_int @t78)) % 0.44/0.69 (define @t101 () (tptp.number_number_of_int @t75)) % 0.44/0.69 (define @t102 () (@list @t78 @t75)) % 0.44/0.69 (define @t103 () (tptp.number_number_of_nat @t75)) % 0.44/0.69 (define @t104 () (tptp.ord_less_eq_int tptp.pls @t46)) % 0.44/0.69 (define @t105 () (@list @t46)) % 0.44/0.69 (define @t106 () (tptp.plus_plus_int @t32 @t37)) % 0.44/0.69 (define @t107 () (@var "Z_2" $$unsorted)) % 0.44/0.69 (define @t108 () (@var "W_2" $$unsorted)) % 0.44/0.69 (define @t109 () (tptp.number_number_of_nat tptp.pls)) % 0.44/0.69 (define @t110 () (forall @t99 (= (tptp.ord_less_eq_int tptp.one_one_int @t51) (tptp.ord_less_eq_int @t1 @t14)))) % 0.44/0.69 (define @t111 () (tptp.plus_plus_nat tptp.one_one_nat tptp.one_one_nat)) % 0.44/0.69 (define @t112 () (tptp.times_times_int tptp.pls @t32)) % 0.44/0.69 (define @t113 () (forall @t33 (= @t112 tptp.pls))) % 0.44/0.69 (define @t114 () (@var "L_1" $$unsorted)) % 0.44/0.69 (define @t115 () (tptp.ord_less_int @t46 @t45)) % 0.44/0.69 (define @t116 () (@list @t37)) % 0.44/0.69 (define @t117 () (tptp.plus_plus_int @t55 @t54)) % 0.44/0.69 (define @t118 () (forall @t105 (= (tptp.ord_less_eq_int @t69 tptp.pls) (tptp.ord_less_int @t46 tptp.pls)))) % 0.44/0.69 (define @t119 () (@var "V_6" $$unsorted)) % 0.44/0.69 (define @t120 () (tptp.ord_less_int @t78 @t119)) % 0.44/0.69 (define @t121 () (tptp.number_number_of_nat @t1)) % 0.44/0.69 (define @t122 () (@list @t75 @t76)) % 0.44/0.69 (define @t123 () (@var "V_5" $$unsorted)) % 0.44/0.69 (define @t124 () (@var "V_4" $$unsorted)) % 0.44/0.69 (define @t125 () (tptp.plus_plus_int @t124 @t123)) % 0.44/0.69 (define @t126 () (tptp.ord_less_eq_int tptp.pls @t123)) % 0.44/0.69 (define @t127 () (tptp.ord_less_eq_int tptp.pls @t124)) % 0.44/0.69 (define @t128 () (@list @t123 @t124)) % 0.44/0.69 (define @t129 () (@var "V_3" $$unsorted)) % 0.44/0.69 (define @t130 () (tptp.number_number_of_nat @t129)) % 0.44/0.69 (define @t131 () (tptp.number_number_of_nat @t41)) % 0.44/0.69 (define @t132 () (tptp.plus_plus_nat @t131 @t130)) % 0.44/0.69 (define @t133 () (tptp.ord_less_int @t129 tptp.pls)) % 0.44/0.69 (define @t134 () (tptp.ord_less_int @t41 tptp.pls)) % 0.44/0.69 (define @t135 () (@list @t75 @t16)) % 0.44/0.69 (define @t136 () (= @t46 @t45)) % 0.44/0.69 (define @t137 () (@var "V_1" $$unsorted)) % 0.44/0.69 (define @t138 () (tptp.number_number_of_int @t137)) % 0.44/0.69 (define @t139 () (@var "B_1" $$unsorted)) % 0.44/0.69 (define @t140 () (@var "A" $$unsorted)) % 0.44/0.69 (define @t141 () (@list @t140 @t139 @t137)) % 0.44/0.69 (define @t142 () (tptp.number_number_of_nat @t137)) % 0.44/0.69 (define @t143 () (@var "C" $$unsorted)) % 0.44/0.69 (define @t144 () (@var "V" $$unsorted)) % 0.44/0.69 (define @t145 () (tptp.number_number_of_int @t144)) % 0.44/0.69 (define @t146 () (@var "B" $$unsorted)) % 0.44/0.69 (define @t147 () (@list @t144 @t146 @t143)) % 0.44/0.69 (define @t148 () (tptp.number_number_of_nat @t144)) % 0.44/0.69 (define @t149 () (tptp.number_number_of_int tptp.pls)) % 0.44/0.69 (define @t150 () (= tptp.zero_zero_int @t149)) % 0.44/0.69 (define @t151 () (tptp.ord_less_int @t9 tptp.zero_zero_int)) % 0.44/0.69 (define @t152 () (@list tptp.pls)) % 0.44/0.69 (define @t153 () (tptp.ord_less_eq_int @t5 @t4)) % 0.44/0.69 (define @t154 () (and @t153 (not (= @t5 @t4)))) % 0.44/0.69 (define @t155 () (= @t6 @t154)) % 0.44/0.69 (define @t156 () (@list false)) % 0.44/0.69 (define @t157 () (not @t10)) % 0.44/0.69 (define @t158 () (tptp.ord_less_eq_int @t9 tptp.zero_zero_int)) % 0.44/0.69 (define @t159 () (and @t158 @t157)) % 0.44/0.69 (define @t160 () (= @t151 @t159)) % 0.44/0.69 (define @t161 () (= tptp.zero_zero_int @t9)) % 0.44/0.69 (define @t162 () (not @t161)) % 0.44/0.69 (define @t163 () (and @t158 @t162)) % 0.44/0.69 (define @t164 () (= @t151 @t163)) % 0.44/0.69 (define @t165 () (@list @t77)) % 0.44/0.69 (define @t166 () (not @t163)) % 0.44/0.69 (define @t167 () (@list true false)) % 0.44/0.69 (define @t168 () (tptp.ord_less_eq_int tptp.one_one_int @t149)) % 0.44/0.69 (define @t169 () (tptp.ord_less_eq_int @t1 tptp.pls)) % 0.44/0.69 (define @t170 () (= @t168 @t169)) % 0.44/0.69 (define @t171 () (= @t169 @t168)) % 0.44/0.69 (define @t172 () (tptp.ord_less_int tptp.pls tptp.pls)) % 0.44/0.69 (define @t173 () (= @t169 @t172)) % 0.44/0.69 (define @t174 () (= @t172 @t169)) % 0.44/0.69 (define @t175 () (not (= tptp.pls tptp.pls))) % 0.44/0.69 (define @t176 () (and @t70 @t175)) % 0.44/0.69 (define @t177 () (= @t172 @t176)) % 0.44/0.69 (define @t178 () (not @t169)) % 0.44/0.69 (define @t179 () (not @t168)) % 0.44/0.69 (define @t180 () (= tptp.pls @t149)) % 0.44/0.69 (define @t181 () (not @t180)) % 0.44/0.69 (define @t182 () (= tptp.zero_zero_int tptp.one_one_int)) % 0.44/0.69 (define @t183 () (not @t182)) % 0.44/0.69 (define @t184 () (not @t150)) % 0.44/0.69 (define @t185 () (not @t70)) % 0.44/0.69 (define @t186 () (= false true)) % 0.44/0.69 (define @t187 () (and @t70 @t180 @t150 @t182 @t179)) % 0.44/0.69 (define @t188 () (and (= tptp.zero_zero_int tptp.s) @t182)) % 0.44/0.69 (define @t189 () (not @t188)) % 0.44/0.69 (define @t190 () (tptp.plus_plus_int @t8 @t28)) % 0.44/0.69 (define @t191 () (= tptp.zero_zero_int @t190)) % 0.44/0.69 (define @t192 () (= @t191 @t188)) % 0.44/0.69 (define @t193 () (not @t191)) % 0.44/0.69 (define @t194 () (= tptp.one_one_int @t28)) % 0.44/0.69 (define @t195 () (not @t194)) % 0.44/0.69 (define @t196 () (and @t194 @t193)) % 0.44/0.69 (define @t197 () (not @t158)) % 0.44/0.69 (define @t198 () (tptp.times_times_int tptp.pls @t3)) % 0.44/0.69 (define @t199 () (= tptp.pls @t198)) % 0.44/0.69 (define @t200 () (not @t199)) % 0.44/0.69 (define @t201 () (not @t153)) % 0.44/0.69 (define @t202 () (tptp.power_power_int tptp.one_one_int tptp.one_one_nat)) % 0.44/0.69 (define @t203 () (tptp.times_times_int @t202 @t202)) % 0.44/0.69 (define @t204 () (tptp.power_power_int tptp.one_one_int @t111)) % 0.44/0.69 (define @t205 () (= @t204 @t203)) % 0.44/0.69 (define @t206 () (not @t205)) % 0.44/0.69 (define @t207 () (tptp.power_power_int tptp.s tptp.one_one_nat)) % 0.44/0.69 (define @t208 () (tptp.times_times_int @t207 @t207)) % 0.44/0.69 (define @t209 () (tptp.power_power_int tptp.s @t111)) % 0.44/0.69 (define @t210 () (= @t209 @t208)) % 0.44/0.69 (define @t211 () (not @t210)) % 0.44/0.69 (define @t212 () (= @t4 (tptp.times_times_int tptp.zero_zero_int @t3))) % 0.44/0.69 (define @t213 () (not @t212)) % 0.44/0.69 (define @t214 () (= @t7 @t111)) % 0.44/0.69 (define @t215 () (not @t214)) % 0.44/0.69 (define @t216 () (= @t5 @t9)) % 0.44/0.69 (define @t217 () (not @t216)) % 0.44/0.69 (define @t218 () (tptp.plus_plus_int @t208 @t203)) % 0.44/0.69 (define @t219 () (and @t153 @t216 @t194 @t214 @t210 @t205 @t212 @t150 @t180 @t199 @t197)) % 0.44/0.69 (assume @p1 (tptp.ord_less_int tptp.t tptp.zero_zero_int)) % 0.44/0.69 (assume @p2 (tptp.ord_less_int tptp.t tptp.one_one_int)) % 0.44/0.69 (assume @p3 @t6) % 0.44/0.69 (assume @p4 (= @t9 @t5)) % 0.44/0.69 (assume @p5 (=> (= tptp.t tptp.zero_zero_int) @t10)) % 0.44/0.69 (assume @p6 (not (tptp.ord_less_eq_int tptp.one_one_int tptp.t))) % 0.44/0.69 (assume @p7 (tptp.ord_less_int tptp.zero_zero_int @t3)) % 0.44/0.69 (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)))) % 0.44/0.69 (assume @p9 (forall @t19 (= (tptp.ord_less_int tptp.zero_zero_int @t18) (or (not @t17) (not @t15))))) % 0.44/0.69 (assume @p10 @t22) % 0.44/0.69 (assume @p11 (forall (@list @t23) (not (tptp.ord_less_int (tptp.power_power_int @t23 @t7) tptp.zero_zero_int)))) % 0.44/0.69 (assume @p12 (forall @t27 (= (tptp.ord_less_int tptp.zero_zero_int @t26) (not @t25)))) % 0.44/0.69 (assume @p13 (= (tptp.power_power_nat tptp.one_one_nat @t7) tptp.one_one_nat)) % 0.44/0.69 (assume @p14 (= @t28 tptp.one_one_int)) % 0.44/0.69 (assume @p15 (= (tptp.power_power_nat tptp.zero_zero_nat @t7) tptp.zero_zero_nat)) % 0.44/0.69 (assume @p16 (= (tptp.power_power_int tptp.zero_zero_int @t7) tptp.zero_zero_int)) % 0.44/0.69 (assume @p17 (forall @t27 (= (= @t26 tptp.zero_zero_int) @t25))) % 0.44/0.69 (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))))) % 0.44/0.69 (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))))) % 0.44/0.69 (assume @p20 (tptp.ord_less_int tptp.t @t3)) % 0.44/0.69 (assume @p21 (not (forall (@list @t31) (not (= @t9 (tptp.times_times_int @t3 @t31)))))) % 0.44/0.69 (assume @p22 (tptp.zprime @t3)) % 0.44/0.69 (assume @p23 (tptp.twoSqu526106917sum2sq @t5)) % 0.44/0.69 (assume @p24 (forall @t33 (tptp.ord_less_eq_int @t32 @t32))) % 0.44/0.69 (assume @p25 @t36) % 0.44/0.69 (assume @p26 (forall @t38 (= (tptp.times_times_int @t37 @t32) (tptp.times_times_int @t32 @t37)))) % 0.44/0.69 (assume @p27 (forall @t38 (or @t40 @t39))) % 0.44/0.69 (assume @p28 (forall @t44 (= (tptp.times_times_int @t43 @t42) (tptp.number_number_of_int (tptp.times_times_int @t41 @t32))))) % 0.44/0.69 (assume @p29 (forall @t50 (= (tptp.ord_less_eq_int @t49 @t48) @t47))) % 0.44/0.69 (assume @p30 (forall @t19 (= (tptp.ord_less_eq_int @t52 @t51) (tptp.ord_less_eq_int @t16 @t14)))) % 0.44/0.69 (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))))) % 0.44/0.69 (assume @p32 (forall @t60 (=> @t59 (=> (tptp.ord_less_eq_int @t58 @t34) (tptp.ord_less_eq_int @t57 @t34))))) % 0.44/0.69 (assume @p33 (forall @t38 (=> @t40 (=> @t39 (= @t37 @t32))))) % 0.44/0.69 (assume @p34 (forall @t61 (= (tptp.power_power_int @t12 (tptp.plus_plus_nat @t11 @t37)) (tptp.times_times_int (tptp.power_power_int @t12 @t11) (tptp.power_power_int @t12 @t37))))) % 0.44/0.69 (assume @p35 (forall @t67 (= (tptp.ord_less_eq_int @t66 @t65) @t64))) % 0.44/0.69 (assume @p36 (forall @t50 (= (tptp.ord_less_eq_int @t69 @t68) @t47))) % 0.44/0.69 (assume @p37 @t70) % 0.44/0.69 (assume @p38 (forall @t67 (= (tptp.ord_less_eq_int @t72 @t71) @t64))) % 0.44/0.69 (assume @p39 (forall @t50 (= (tptp.ord_less_eq_int @t74 @t73) @t47))) % 0.44/0.69 (assume @p40 @t77) % 0.44/0.69 (assume @p41 (forall @t60 (=> @t59 (tptp.ord_less_eq_int (tptp.plus_plus_int @t34 @t57) (tptp.plus_plus_int @t34 @t58))))) % 0.44/0.69 (assume @p42 (forall @t81 (= (= @t80 tptp.zero_zero_nat) @t79))) % 0.44/0.69 (assume @p43 (forall @t81 (= (= tptp.zero_zero_nat @t80) @t79))) % 0.44/0.69 (assume @p44 (forall @t87 (=> @t86 (=> @t85 (= (tptp.times_times_nat (tptp.number_number_of_nat @t83) (tptp.number_number_of_nat @t82)) (tptp.number_number_of_nat @t84)))))) % 0.44/0.69 (assume @p45 (forall @t87 (=> @t86 (=> @t85 (= (tptp.times_times_int (tptp.number_number_of_int @t83) (tptp.number_number_of_int @t82)) (tptp.number_number_of_int @t84)))))) % 0.44/0.69 (assume @p46 (forall (@list @t90 @t89 @t88) (= (tptp.times_times_int (tptp.number_number_of_int @t90) (tptp.times_times_int (tptp.number_number_of_int @t89) @t88)) (tptp.times_times_int (tptp.number_number_of_int (tptp.times_times_int @t90 @t89)) @t88)))) % 0.44/0.69 (assume @p47 (forall (@list @t92 @t91) (= (tptp.times_times_int (tptp.number_number_of_int @t92) (tptp.number_number_of_int @t91)) (tptp.number_number_of_int (tptp.times_times_int @t92 @t91))))) % 0.44/0.69 (assume @p48 (forall (@list @t94 @t93) (= (tptp.number_number_of_int (tptp.times_times_int @t94 @t93)) (tptp.times_times_int (tptp.number_number_of_int @t94) (tptp.number_number_of_int @t93))))) % 0.44/0.69 (assume @p49 (forall @t19 (= (tptp.ord_less_eq_int @t95 tptp.zero_zero_int) @t20))) % 0.44/0.69 (assume @p50 (forall (@list @t97 @t96) (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.plus_plus_int (tptp.times_times_int @t97 @t97) (tptp.times_times_int @t96 @t96))))) % 0.44/0.69 (assume @p51 (forall @t98 (= (tptp.ord_less_eq_int @t52 tptp.zero_zero_int) (tptp.ord_less_eq_int @t16 tptp.pls)))) % 0.44/0.69 (assume @p52 (forall @t99 (= (tptp.ord_less_eq_int tptp.zero_zero_int @t51) (tptp.ord_less_eq_int tptp.pls @t14)))) % 0.44/0.69 (assume @p53 (forall @t81 (= (tptp.ord_less_nat tptp.zero_zero_nat @t80) (tptp.ord_less_int tptp.pls @t78)))) % 0.44/0.69 (assume @p54 (forall @t102 (= (tptp.ord_less_eq_int @t100 @t101) (not (tptp.ord_less_int @t101 @t100))))) % 0.44/0.69 (assume @p55 (forall @t102 (= (tptp.ord_less_eq_nat @t80 @t103) (not (tptp.ord_less_nat @t103 @t80))))) % 0.44/0.69 (assume @p56 (forall @t105 (= (tptp.ord_less_eq_int tptp.pls @t69) @t104))) % 0.44/0.69 (assume @p57 (forall @t67 (= (tptp.ord_less_eq_int @t72 @t65) @t64))) % 0.44/0.69 (assume @p58 (forall @t50 (= (tptp.ord_less_eq_int @t74 @t68) @t47))) % 0.44/0.69 (assume @p59 (forall @t105 (= (tptp.ord_less_eq_int @t74 tptp.pls) (tptp.ord_less_eq_int @t46 tptp.pls)))) % 0.44/0.69 (assume @p60 (forall @t105 (= (tptp.ord_less_eq_int tptp.pls @t74) @t104))) % 0.44/0.69 (assume @p61 (forall (@list @t107 @t37 @t108 @t32) (=> (tptp.ord_less_int @t108 @t32) (=> (tptp.ord_less_eq_int @t107 @t37) (tptp.ord_less_int (tptp.plus_plus_int @t108 @t107) @t106))))) % 0.44/0.69 (assume @p62 (= @t109 tptp.zero_zero_nat)) % 0.44/0.69 (assume @p63 (= tptp.zero_zero_nat @t109)) % 0.44/0.69 (assume @p64 (forall @t98 (= (tptp.ord_less_eq_int @t52 tptp.one_one_int) (tptp.ord_less_eq_int @t16 @t1)))) % 0.44/0.69 (assume @p65 @t110) % 0.44/0.69 (assume @p66 (= @t111 @t7)) % 0.44/0.69 (assume @p67 @t113) % 0.44/0.69 (assume @p68 (forall (@list @t34 @t114) (= (tptp.times_times_int (tptp.bit0 @t34) @t114) (tptp.bit0 (tptp.times_times_int @t34 @t114))))) % 0.44/0.69 (assume @p69 (forall @t50 (= (tptp.ord_less_int @t49 @t48) @t115))) % 0.44/0.69 (assume @p70 (forall @t116 (= (tptp.times_times_int @t37 tptp.one_one_int) @t37))) % 0.44/0.69 (assume @p71 (forall @t116 (= (tptp.times_times_int tptp.one_one_int @t37) @t37))) % 0.44/0.69 (assume @p72 (forall @t44 (= (tptp.plus_plus_int @t43 @t42) (tptp.number_number_of_int (tptp.plus_plus_int @t41 @t32))))) % 0.44/0.69 (assume @p73 (forall (@list @t55 @t54 @t32) (= (tptp.times_times_int @t117 @t32) (tptp.plus_plus_int (tptp.times_times_int @t55 @t32) (tptp.times_times_int @t54 @t32))))) % 0.44/0.69 (assume @p74 (forall (@list @t32 @t55 @t54) (= (tptp.times_times_int @t32 @t117) (tptp.plus_plus_int (tptp.times_times_int @t32 @t55) (tptp.times_times_int @t32 @t54))))) % 0.44/0.69 (assume @p75 @t118) % 0.44/0.69 (assume @p76 (forall @t105 (= (tptp.ord_less_int tptp.pls @t69) @t104))) % 0.44/0.69 (assume @p77 (forall @t67 (= (tptp.ord_less_eq_int @t66 @t71) (tptp.ord_less_int @t63 @t62)))) % 0.44/0.69 (assume @p78 (forall @t50 (= (tptp.ord_less_eq_int @t69 @t73) @t115))) % 0.44/0.69 (assume @p79 (forall @t67 (= (tptp.ord_less_int @t72 @t65) @t64))) % 0.44/0.69 (assume @p80 (forall @t50 (= (tptp.ord_less_int @t74 @t68) @t47))) % 0.44/0.69 (assume @p81 (forall (@list @t78 @t119) (= (tptp.ord_less_nat @t80 (tptp.number_number_of_nat @t119)) (and (=> @t120 (tptp.ord_less_int tptp.pls @t119)) @t120)))) % 0.44/0.69 (assume @p82 (forall (@list @t76) (= (tptp.ord_less_eq_int tptp.one_one_int @t76) (tptp.ord_less_int tptp.zero_zero_int @t76)))) % 0.44/0.69 (assume @p83 (= @t121 tptp.one_one_nat)) % 0.44/0.69 (assume @p84 (= tptp.one_one_nat @t121)) % 0.44/0.69 (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)))) % 0.44/0.69 (assume @p86 (forall @t122 (= (tptp.ord_less_eq_int (tptp.plus_plus_int @t75 tptp.one_one_int) @t76) (tptp.ord_less_int @t75 @t76)))) % 0.44/0.69 (assume @p87 (forall @t122 (= (tptp.ord_less_int @t75 (tptp.plus_plus_int @t76 tptp.one_one_int)) (tptp.ord_less_eq_int @t75 @t76)))) % 0.44/0.69 (assume @p88 (forall @t128 (=> @t127 (=> @t126 (= (tptp.plus_plus_int (tptp.number_number_of_int @t124) (tptp.number_number_of_int @t123)) (tptp.number_number_of_int @t125)))))) % 0.44/0.69 (assume @p89 (forall @t128 (=> @t127 (=> @t126 (= (tptp.plus_plus_nat (tptp.number_number_of_nat @t124) (tptp.number_number_of_nat @t123)) (tptp.number_number_of_nat @t125)))))) % 0.44/0.69 (assume @p90 (forall (@list @t129 @t41) (and (=> @t134 (= @t132 @t130)) (=> (not @t134) (and (=> @t133 (= @t132 @t131)) (=> (not @t133) (= @t132 (tptp.number_number_of_nat (tptp.plus_plus_int @t41 @t129))))))))) % 0.44/0.69 (assume @p91 (forall @t116 (=> (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))))) % 0.44/0.69 (assume @p92 (forall @t19 (= (= @t52 @t51) (= @t16 @t14)))) % 0.44/0.69 (assume @p93 (forall @t135 (= (= @t103 @t16) (= @t16 @t103)))) % 0.44/0.69 (assume @p94 (forall @t135 (= (= @t101 @t16) (= @t16 @t101)))) % 0.44/0.69 (assume @p95 (forall @t50 (= (= @t69 @t68) @t136))) % 0.44/0.69 (assume @p96 (forall @t50 (= (= @t74 @t73) @t136))) % 0.44/0.69 (assume @p97 (forall @t13 (or (tptp.ord_less_int @t12 @t11) (= @t12 @t11) (tptp.ord_less_int @t11 @t12)))) % 0.44/0.69 (assume @p98 (forall @t19 (= (= @t95 tptp.zero_zero_int) @t20))) % 0.44/0.69 (assume @p99 (forall @t141 (= (tptp.times_times_int (tptp.plus_plus_int @t140 @t139) @t138) (tptp.plus_plus_int (tptp.times_times_int @t140 @t138) (tptp.times_times_int @t139 @t138))))) % 0.44/0.69 (assume @p100 (forall @t141 (= (tptp.times_times_nat (tptp.plus_plus_nat @t140 @t139) @t142) (tptp.plus_plus_nat (tptp.times_times_nat @t140 @t142) (tptp.times_times_nat @t139 @t142))))) % 0.44/0.69 (assume @p101 (forall @t147 (= (tptp.times_times_int @t145 (tptp.plus_plus_int @t146 @t143)) (tptp.plus_plus_int (tptp.times_times_int @t145 @t146) (tptp.times_times_int @t145 @t143))))) % 0.44/0.69 (assume @p102 (forall @t147 (= (tptp.times_times_nat @t148 (tptp.plus_plus_nat @t146 @t143)) (tptp.plus_plus_nat (tptp.times_times_nat @t148 @t146) (tptp.times_times_nat @t148 @t143))))) % 0.44/0.69 (assume @p103 (forall @t56 (= (tptp.plus_plus_int @t117 @t53) (tptp.plus_plus_int @t55 (tptp.plus_plus_int @t54 @t53))))) % 0.44/0.69 (assume @p104 (forall @t61 (= (tptp.plus_plus_int @t12 (tptp.plus_plus_int @t11 @t37)) (tptp.plus_plus_int @t11 (tptp.plus_plus_int @t12 @t37))))) % 0.44/0.69 (assume @p105 (forall @t38 (= (tptp.plus_plus_int @t37 @t32) @t106))) % 0.44/0.69 (assume @p106 @t150) % 0.44/0.69 (assume @p107 (not @t151)) % 0.44/0.69 (assume @p108 true) % 0.44/0.69 (step @p109 :rule symm :premises (@p4)) % 0.44/0.69 (step @p110 :rule symm :premises (@p14)) % 0.44/0.69 (step @p111 :rule symm :premises (@p66)) % 0.44/0.69 (step @p112 :rule eq-symm :args (@t35 @t34)) % 0.44/0.69 (step @p113 :rule cong :premises (@p112) :args (@t36)) % 0.44/0.69 (step @p114 :rule eq_resolve :premises (@p25 @p113)) % 0.44/0.69 (step @p115 :rule instantiate :premises (@p114) :args (@t152)) % 0.44/0.69 (step @p116 :rule instantiate :premises (@p26) :args ((@list @t3 tptp.zero_zero_int))) % 0.44/0.69 (step @p117 :rule instantiate :premises (@p34) :args ((@list tptp.s tptp.one_one_nat tptp.one_one_nat))) % 0.44/0.69 (step @p118 :rule instantiate :premises (@p34) :args ((@list tptp.one_one_int tptp.one_one_nat tptp.one_one_nat))) % 0.44/0.69 (step @p119 :rule instantiate :premises (@p40) :args ((@list @t5 @t4))) % 0.44/0.69 (step @p120 :rule cnf_equiv_pos1 :args (@t155)) % 0.44/0.69 (step @p121 :rule reordering :premises (@p120) :args ((or (not @t6) @t154 (not @t155)))) % 0.44/0.69 (step @p122 :rule chain_m_resolution :premises (@p121 @p3 @p119) :args (@t154 (@list false false) (@list @t6 @t155))) % 0.44/0.69 (step @p123 :rule cnf_and_pos :args (@t154 0)) % 0.44/0.69 (step @p124 :rule reordering :premises (@p123) :args ((or @t153 (not @t154)))) % 0.44/0.69 (step @p125 :rule chain_m_resolution :premises (@p124 @p122) :args (@t153 @t156 (@list @t154))) % 0.44/0.69 (step @p126 :rule eq-symm :args (@t9 tptp.zero_zero_int)) % 0.44/0.69 (step @p127 :rule cong :premises (@p126) :args (@t157)) % 0.44/0.69 (step @p128 :rule refl :args (@t158)) % 0.44/0.69 (step @p129 :rule nary_cong :premises (@p128 @p127) :args (@t159)) % 0.44/0.69 (step @p130 :rule refl :args (@t151)) % 0.44/0.69 (step @p131 :rule cong :premises (@p130 @p129) :args (@t160)) % 0.44/0.69 (step @p132 :rule refl :args (@t77)) % 0.44/0.69 (step @p133 :rule cong :premises (@p132 @p131) :args ((=> @t77 @t160))) % 0.44/0.69 (assume-push @p381 @t77) % 0.44/0.69 (step @p135 :rule instantiate :premises (@p40) :args ((@list @t9 tptp.zero_zero_int))) % 0.44/0.69 (step-pop @p382 :rule scope :premises (@p135)) % 0.44/0.69 (step @p136 :rule process_scope :premises (@p382) :args (@t160)) % 0.44/0.69 (step @p138 :rule eq_resolve :premises (@p136 @p133)) % 0.44/0.69 (step @p139 :rule implies_elim :premises (@p138)) % 0.44/0.69 (step @p140 :rule chain_m_resolution :premises (@p139 @p40) :args (@t164 @t156 @t165)) % 0.44/0.69 (step @p141 :rule cnf_equiv_pos2 :args (@t164)) % 0.44/0.69 (step @p142 :rule reordering :premises (@p141) :args ((or @t151 @t166 (not @t164)))) % 0.44/0.69 (step @p143 :rule chain_m_resolution :premises (@p142 @p107 @p140) :args (@t166 @t167 (@list @t151 @t164))) % 0.44/0.69 (step @p144 :rule eq-symm :args (@t14 tptp.zero_zero_int)) % 0.44/0.69 (step @p145 :rule eq-symm :args (@t16 tptp.zero_zero_int)) % 0.44/0.69 (step @p146 :rule nary_cong :premises (@p145 @p144) :args (@t20)) % 0.44/0.69 (step @p147 :rule eq-symm :args (@t18 tptp.zero_zero_int)) % 0.44/0.69 (step @p148 :rule cong :premises (@p147 @p146) :args (@t21)) % 0.44/0.69 (step @p149 :rule cong :premises (@p148) :args (@t22)) % 0.44/0.69 (step @p150 :rule eq_resolve :premises (@p10 @p149)) % 0.44/0.69 (step @p151 :rule instantiate :premises (@p150) :args ((@list tptp.s tptp.one_one_int))) % 0.44/0.69 (step @p152 :rule eq-symm :args (@t168 @t169)) % 0.44/0.69 (step @p153 :rule refl 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