%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM926+5 : 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 : n024.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 08:41:07 AM UTC 2026 % Result : Theorem 0.15s 0.41s % Output : Proof 0.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : NUM926+5 : TPTP v9.2.1. Released v5.3.0. % 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 07:35:00 EDT 2026 % 0.07/0.25 % CPUTime : % 0.15/0.34 %----Proving TF0_NAR, FOF, or CNF % 0.15/0.41 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.15/0.41 % SZS status Theorem % 0.15/0.41 % SZS output start Proof % 0.15/0.41 ( % 0.15/0.41 (declare-sort $$unsorted 0) % 0.15/0.41 (declare-const tptp.ring_char_0 (-> $$unsorted Bool)) % 0.15/0.41 (declare-const tptp.t $$unsorted) % 0.15/0.41 (declare-const tptp.twoSqu33214720sum2sq (-> $$unsorted Bool)) % 0.15/0.41 (declare-const tptp.number_semiring (-> $$unsorted Bool)) % 0.15/0.41 (declare-const tptp.power_power (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.15/0.41 (declare-const tptp.ord_less_eq (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.15/0.41 (declare-const tptp.linorder (-> $$unsorted Bool)) % 0.15/0.41 (declare-const tptp.ord_less (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.15/0.41 (declare-const tptp.linordered_idom (-> $$unsorted Bool)) % 0.15/0.41 (declare-const tptp.m $$unsorted) % 0.15/0.41 (declare-const tptp.number (-> $$unsorted Bool)) % 0.15/0.41 (declare-const tptp.number_number_of (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.41 (declare-const tptp.number_ring (-> $$unsorted Bool)) % 0.15/0.41 (declare-const tptp.one_one (-> $$unsorted $$unsorted)) % 0.15/0.41 (declare-const tptp.bit1 (-> $$unsorted $$unsorted)) % 0.15/0.41 (declare-const tptp.nat $$unsorted) % 0.15/0.41 (declare-const tptp.ti (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.41 (declare-const tptp.s $$unsorted) % 0.15/0.41 (declare-const tptp.zprime (-> $$unsorted Bool)) % 0.15/0.41 (declare-const tptp.plus_plus (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.15/0.41 (declare-const tptp.comm_semiring_1 (-> $$unsorted Bool)) % 0.15/0.41 (declare-const tptp.times_times (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.15/0.41 (declare-const tptp.pls $$unsorted) % 0.15/0.41 (declare-const tptp.undefined (-> $$unsorted $$unsorted)) % 0.15/0.41 (declare-const tptp.monoid_mult (-> $$unsorted Bool)) % 0.15/0.41 (declare-const tptp.semiring_1 (-> $$unsorted Bool)) % 0.15/0.41 (declare-const tptp.bit0 (-> $$unsorted $$unsorted)) % 0.15/0.41 (declare-const tptp.int $$unsorted) % 0.15/0.41 (define @t1 () (@var "X_a" $$unsorted)) % 0.15/0.41 (define @t2 () (tptp.one_one @t1)) % 0.15/0.41 (define @t3 () (tptp.semiring_1 @t1)) % 0.15/0.41 (define @t4 () (@list @t1)) % 0.15/0.41 (define @t5 () (@var "B_2" $$unsorted)) % 0.15/0.41 (define @t6 () (@var "B_1" $$unsorted)) % 0.15/0.41 (define @t7 () (tptp.plus_plus @t1 @t6 @t5)) % 0.15/0.41 (define @t8 () (tptp.ti @t1 @t6)) % 0.15/0.41 (define @t9 () (tptp.comm_semiring_1 @t1)) % 0.15/0.41 (define @t10 () (@list @t6 @t5 @t1)) % 0.15/0.41 (define @t11 () (tptp.ti @t1 @t5)) % 0.15/0.41 (define @t12 () (tptp.times_times @t1 @t6 @t5)) % 0.15/0.41 (define @t13 () (tptp.monoid_mult @t1)) % 0.15/0.41 (define @t14 () (tptp.undefined @t1)) % 0.15/0.41 (define @t15 () (tptp.ti tptp.int @t6)) % 0.15/0.41 (define @t16 () (@list @t6)) % 0.15/0.41 (define @t17 () (tptp.bit0 @t6)) % 0.15/0.41 (define @t18 () (tptp.bit1 @t6)) % 0.15/0.41 (define @t19 () (tptp.number_number_of @t1 @t6)) % 0.15/0.41 (define @t20 () (tptp.number @t1)) % 0.15/0.41 (define @t21 () (@list @t6 @t1)) % 0.15/0.41 (define @t22 () (tptp.ord_less @t1 @t6 @t5)) % 0.15/0.41 (define @t23 () (and @t20 (tptp.linorder @t1))) % 0.15/0.41 (define @t24 () (tptp.ord_less_eq @t1 @t6 @t5)) % 0.15/0.41 (define @t25 () (tptp.power_power @t1 @t6 @t5)) % 0.15/0.41 (define @t26 () (tptp.one_one tptp.int)) % 0.15/0.41 (define @t27 () (tptp.ord_less_eq tptp.int @t26 tptp.t)) % 0.15/0.41 (define @t28 () (tptp.bit1 tptp.pls)) % 0.15/0.41 (define @t29 () (tptp.bit0 @t28)) % 0.15/0.41 (define @t30 () (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 @t29)) tptp.m) @t26)) % 0.15/0.41 (define @t31 () (tptp.number_number_of tptp.nat @t29)) % 0.15/0.41 (define @t32 () (@var "Y" $$unsorted)) % 0.15/0.41 (define @t33 () (@var "X" $$unsorted)) % 0.15/0.41 (define @t34 () (= (tptp.plus_plus tptp.int (tptp.power_power tptp.int @t33 @t31) (tptp.power_power tptp.int @t32 @t31)) @t30)) % 0.15/0.41 (define @t35 () (@list @t33 @t32)) % 0.15/0.41 (define @t36 () (exists @t35 @t34)) % 0.15/0.41 (define @t37 () (= tptp.t @t26)) % 0.15/0.41 (define @t38 () (=> @t37 @t36)) % 0.15/0.41 (define @t39 () (tptp.ord_less tptp.int @t26 tptp.t)) % 0.15/0.41 (define @t40 () (=> @t39 @t36)) % 0.15/0.41 (define @t41 () (tptp.times_times tptp.int @t30 tptp.t)) % 0.15/0.41 (define @t42 () (tptp.plus_plus tptp.int (tptp.power_power tptp.int tptp.s @t31) @t26)) % 0.15/0.41 (define @t43 () (@var "B" $$unsorted)) % 0.15/0.41 (define @t44 () (tptp.power_power tptp.int @t43 @t31)) % 0.15/0.41 (define @t45 () (@var "A_1" $$unsorted)) % 0.15/0.41 (define @t46 () (tptp.number_number_of tptp.int @t29)) % 0.15/0.41 (define @t47 () (tptp.power_power tptp.int @t45 @t31)) % 0.15/0.41 (define @t48 () (tptp.plus_plus tptp.int @t45 @t43)) % 0.15/0.41 (define @t49 () (@list @t45 @t43)) % 0.15/0.41 (define @t50 () (tptp.bit1 @t28)) % 0.15/0.41 (define @t51 () (tptp.number_number_of tptp.nat @t50)) % 0.15/0.41 (define @t52 () (tptp.number_number_of tptp.int @t50)) % 0.15/0.41 (define @t53 () (tptp.power_power tptp.int @t45 @t51)) % 0.15/0.41 (define @t54 () (@var "Y_1" $$unsorted)) % 0.15/0.41 (define @t55 () (@var "X_1" $$unsorted)) % 0.15/0.41 (define @t56 () (tptp.number_number_of @t1 @t29)) % 0.15/0.41 (define @t57 () (tptp.power_power @t1 @t55 @t31)) % 0.15/0.41 (define @t58 () (@list @t55 @t54)) % 0.15/0.41 (define @t59 () (@var "W" $$unsorted)) % 0.15/0.41 (define @t60 () (@var "X_b" $$unsorted)) % 0.15/0.41 (define @t61 () (tptp.number_number_of @t60 @t59)) % 0.15/0.41 (define @t62 () (@list @t59)) % 0.15/0.41 (define @t63 () (@list @t45)) % 0.15/0.41 (define @t64 () (@list @t55)) % 0.15/0.41 (define @t65 () (@var "N" $$unsorted)) % 0.15/0.41 (define @t66 () (tptp.power_power @t1 @t55 @t65)) % 0.15/0.41 (define @t67 () (tptp.number_ring @t1)) % 0.15/0.41 (define @t68 () (@var "V" $$unsorted)) % 0.15/0.41 (define @t69 () (@var "T_1" $$unsorted)) % 0.15/0.41 (define @t70 () (@var "Z" $$unsorted)) % 0.15/0.41 (define @t71 () (tptp.ord_less_eq tptp.int @t59 @t70)) % 0.15/0.41 (define @t72 () (tptp.ord_less_eq tptp.int @t70 @t59)) % 0.15/0.41 (define @t73 () (@list @t70 @t59)) % 0.15/0.41 (define @t74 () (@var "W_1" $$unsorted)) % 0.15/0.41 (define @t75 () (@var "Z_1" $$unsorted)) % 0.15/0.41 (define @t76 () (forall (@list @t75 @t74) (= (tptp.ord_less tptp.int @t75 @t74) (and (tptp.ord_less_eq tptp.int @t75 @t74) (not (= @t75 @t74)))))) % 0.15/0.41 (define @t77 () (@var "K_1" $$unsorted)) % 0.15/0.41 (define @t78 () (@var "I" $$unsorted)) % 0.15/0.41 (define @t79 () (@var "J" $$unsorted)) % 0.15/0.41 (define @t80 () (tptp.ord_less_eq tptp.int @t78 @t79)) % 0.15/0.41 (define @t81 () (@list @t77 @t78 @t79)) % 0.15/0.41 (define @t82 () (@var "Q" $$unsorted)) % 0.15/0.41 (define @t83 () (@var "P" $$unsorted)) % 0.15/0.41 (define @t84 () (tptp.power_power @t1 @t55 @t83)) % 0.15/0.41 (define @t85 () (@list @t55 @t83 @t82)) % 0.15/0.41 (define @t86 () (tptp.one_one tptp.nat)) % 0.15/0.41 (define @t87 () (tptp.power_power tptp.int @t55 @t54)) % 0.15/0.41 (define @t88 () (@list @t55 @t54 @t70)) % 0.15/0.41 (define @t89 () (@var "V_2" $$unsorted)) % 0.15/0.41 (define @t90 () (tptp.number_number_of @t1 @t89)) % 0.15/0.41 (define @t91 () (tptp.number_number_of @t1 @t74)) % 0.15/0.41 (define @t92 () (@var "Y_2" $$unsorted)) % 0.15/0.41 (define @t93 () (@var "X_2" $$unsorted)) % 0.15/0.41 (define @t94 () (tptp.number_number_of @t1 @t92)) % 0.15/0.41 (define @t95 () (tptp.number_number_of @t1 @t93)) % 0.15/0.41 (define @t96 () (@list @t93 @t92)) % 0.15/0.41 (define @t97 () (and @t67 (tptp.linordered_idom @t1))) % 0.15/0.41 (define @t98 () (tptp.plus_plus tptp.int @t59 @t70)) % 0.15/0.41 (define @t99 () (@var "Z_2" $$unsorted)) % 0.15/0.41 (define @t100 () (@var "W_2" $$unsorted)) % 0.15/0.41 (define @t101 () (tptp.plus_plus tptp.nat @t70 @t70)) % 0.15/0.41 (define @t102 () (@list @t70)) % 0.15/0.41 (define @t103 () (@var "K2" $$unsorted)) % 0.15/0.41 (define @t104 () (@var "K1" $$unsorted)) % 0.15/0.41 (define @t105 () (tptp.ord_less tptp.int @t104 @t103)) % 0.15/0.41 (define @t106 () (tptp.bit1 @t103)) % 0.15/0.41 (define @t107 () (tptp.bit1 @t104)) % 0.15/0.41 (define @t108 () (@list @t104 @t103)) % 0.15/0.41 (define @t109 () (@var "L" $$unsorted)) % 0.15/0.41 (define @t110 () (@var "K" $$unsorted)) % 0.15/0.41 (define @t111 () (tptp.ord_less tptp.int @t110 @t109)) % 0.15/0.41 (define @t112 () (tptp.bit1 @t109)) % 0.15/0.41 (define @t113 () (tptp.bit1 @t110)) % 0.15/0.41 (define @t114 () (@list @t110 @t109)) % 0.15/0.41 (define @t115 () (tptp.ord_less_eq tptp.int @t104 @t103)) % 0.15/0.41 (define @t116 () (tptp.ord_less_eq tptp.int @t110 @t109)) % 0.15/0.41 (define @t117 () (tptp.bit0 @t103)) % 0.15/0.41 (define @t118 () (tptp.bit0 @t104)) % 0.15/0.41 (define @t119 () (tptp.bit0 @t109)) % 0.15/0.41 (define @t120 () (tptp.bit0 @t110)) % 0.15/0.41 (define @t121 () (tptp.number_number_of tptp.int @t109)) % 0.15/0.41 (define @t122 () (tptp.number_number_of tptp.int @t110)) % 0.15/0.41 (define @t123 () (@var "V_1" $$unsorted)) % 0.15/0.41 (define @t124 () (tptp.number_number_of tptp.nat @t123)) % 0.15/0.41 (define @t125 () (tptp.number_number_of tptp.nat @t68)) % 0.15/0.41 (define @t126 () (tptp.plus_plus tptp.nat @t125 @t124)) % 0.15/0.41 (define @t127 () (tptp.ord_less tptp.int @t123 tptp.pls)) % 0.15/0.41 (define @t128 () (tptp.ord_less tptp.int @t68 tptp.pls)) % 0.15/0.41 (define @t129 () (tptp.number_number_of tptp.nat @t28)) % 0.15/0.41 (define @t130 () (tptp.ord_less tptp.int @t110 tptp.pls)) % 0.15/0.41 (define @t131 () (@list @t110)) % 0.15/0.41 (define @t132 () (tptp.ord_less_eq tptp.int tptp.pls @t110)) % 0.15/0.41 (define @t133 () (@list @t74 @t75)) % 0.15/0.41 (define @t134 () (@var "Ry" $$unsorted)) % 0.15/0.41 (define @t135 () (@var "Ly" $$unsorted)) % 0.15/0.41 (define @t136 () (@var "Rx" $$unsorted)) % 0.15/0.41 (define @t137 () (@var "Lx" $$unsorted)) % 0.15/0.41 (define @t138 () (tptp.times_times @t1 @t137 @t136)) % 0.15/0.41 (define @t139 () (tptp.times_times @t1 @t136 @t134)) % 0.15/0.41 (define @t140 () (tptp.times_times @t1 @t137 @t135)) % 0.15/0.41 (define @t141 () (tptp.times_times @t1 @t140 @t139)) % 0.15/0.41 (define @t142 () (@list @t137 @t135 @t136 @t134)) % 0.15/0.41 (define @t143 () (tptp.times_times @t1 @t140 @t136)) % 0.15/0.41 (define @t144 () (@list @t137 @t135 @t136)) % 0.15/0.41 (define @t145 () (tptp.times_times @t1 @t137 @t139)) % 0.15/0.41 (define @t146 () (@list @t137 @t136 @t134)) % 0.15/0.41 (define @t147 () (@var "D" $$unsorted)) % 0.15/0.41 (define @t148 () (@var "C" $$unsorted)) % 0.15/0.41 (define @t149 () (tptp.plus_plus @t1 @t45 @t148)) % 0.15/0.41 (define @t150 () (tptp.plus_plus @t1 @t148 @t147)) % 0.15/0.41 (define @t151 () (tptp.plus_plus @t1 @t45 @t43)) % 0.15/0.41 (define @t152 () (tptp.plus_plus @t1 @t151 @t148)) % 0.15/0.41 (define @t153 () (@list @t45 @t43 @t148)) % 0.15/0.41 (define @t154 () (tptp.plus_plus @t1 @t45 @t150)) % 0.15/0.41 (define @t155 () (@list @t45 @t148 @t147)) % 0.15/0.41 (define @t156 () (tptp.ti @t1 @t93)) % 0.15/0.41 (define @t157 () (= @t110 @t109)) % 0.15/0.41 (define @t158 () (@var "Z3" $$unsorted)) % 0.15/0.41 (define @t159 () (@var "Z2" $$unsorted)) % 0.15/0.41 (define @t160 () (@var "Z1" $$unsorted)) % 0.15/0.41 (define @t161 () (@list @t160 @t159 @t158)) % 0.15/0.41 (define @t162 () (@var "A" $$unsorted)) % 0.15/0.41 (define @t163 () (@var "T" $$unsorted)) % 0.15/0.41 (define @t164 () (tptp.ti @t163 @t162)) % 0.15/0.41 (define @t165 () (not @t36)) % 0.15/0.41 (define @t166 () (forall @t35 (not @t34))) % 0.15/0.41 (define @t167 () (not @t166)) % 0.15/0.41 (define @t168 () (not @t39)) % 0.15/0.41 (define @t169 () (@list false)) % 0.15/0.41 (define @t170 () (@list @t166)) % 0.15/0.41 (define @t171 () (not @t37)) % 0.15/0.41 (define @t172 () (not @t27)) % 0.15/0.41 (define @t173 () (and @t27 @t171)) % 0.15/0.41 (define @t174 () (not (= @t26 tptp.t))) % 0.15/0.41 (define @t175 () (and @t27 @t174)) % 0.15/0.41 (define @t176 () (= @t39 @t175)) % 0.15/0.41 (define @t177 () (= @t39 @t173)) % 0.15/0.41 (assume @p1 (forall @t4 (=> @t3 (= (tptp.ti @t1 @t2) @t2)))) % 0.15/0.41 (assume @p2 (forall @t10 (=> @t9 (= (tptp.plus_plus @t1 @t8 @t5) @t7)))) % 0.15/0.41 (assume @p3 (forall @t10 (=> @t9 (= (tptp.plus_plus @t1 @t6 @t11) @t7)))) % 0.15/0.41 (assume @p4 (forall @t10 (=> @t9 (= (tptp.ti @t1 @t7) @t7)))) % 0.15/0.41 (assume @p5 (forall @t10 (=> @t13 (= (tptp.times_times @t1 @t8 @t5) @t12)))) % 0.15/0.41 (assume @p6 (forall @t10 (=> @t13 (= (tptp.times_times @t1 @t6 @t11) @t12)))) % 0.15/0.41 (assume @p7 (forall @t10 (=> @t13 (= (tptp.ti @t1 @t12) @t12)))) % 0.15/0.41 (assume @p8 (forall @t4 (= (tptp.ti @t1 @t14) @t14))) % 0.15/0.41 (assume @p9 (forall @t16 (= (tptp.zprime @t15) (tptp.zprime @t6)))) % 0.15/0.41 (assume @p10 (forall @t16 (= (tptp.bit0 @t15) @t17))) % 0.15/0.41 (assume @p11 (forall @t16 (= (tptp.ti tptp.int @t17) @t17))) % 0.15/0.41 (assume @p12 (forall @t16 (= (tptp.bit1 @t15) @t18))) % 0.15/0.41 (assume @p13 (forall @t16 (= (tptp.ti tptp.int @t18) @t18))) % 0.15/0.41 (assume @p14 (= (tptp.ti tptp.int tptp.pls) tptp.pls)) % 0.15/0.41 (assume @p15 (forall @t21 (=> @t20 (= (tptp.number_number_of @t1 @t15) @t19)))) % 0.15/0.41 (assume @p16 (forall @t21 (=> @t20 (= (tptp.ti @t1 @t19) @t19)))) % 0.15/0.41 (assume @p17 (forall @t10 (=> @t23 (= (tptp.ord_less @t1 @t8 @t5) @t22)))) % 0.15/0.41 (assume @p18 (forall @t10 (=> @t23 (= (tptp.ord_less @t1 @t6 @t11) @t22)))) % 0.15/0.41 (assume @p19 (forall @t10 (=> @t23 (= (tptp.ord_less_eq @t1 @t8 @t5) @t24)))) % 0.15/0.41 (assume @p20 (forall @t10 (=> @t23 (= (tptp.ord_less_eq @t1 @t6 @t11) @t24)))) % 0.15/0.41 (assume @p21 (forall @t10 (=> @t13 (= (tptp.power_power @t1 @t8 @t5) @t25)))) % 0.15/0.41 (assume @p22 (forall @t10 (=> @t13 (= (tptp.power_power @t1 @t6 (tptp.ti tptp.nat @t5)) @t25)))) % 0.15/0.41 (assume @p23 (forall @t10 (=> @t13 (= (tptp.ti @t1 @t25) @t25)))) % 0.15/0.41 (assume @p24 (forall @t16 (= (tptp.twoSqu33214720sum2sq @t15) (tptp.twoSqu33214720sum2sq @t6)))) % 0.15/0.41 (assume @p25 (= (tptp.ti tptp.int tptp.m) tptp.m)) % 0.15/0.41 (assume @p26 (= (tptp.ti tptp.int tptp.s) tptp.s)) % 0.15/0.41 (assume @p27 (= (tptp.ti tptp.int tptp.t) tptp.t)) % 0.15/0.41 (assume @p28 @t27) % 0.15/0.41 (assume @p29 @t38) % 0.15/0.41 (assume @p30 @t40) % 0.15/0.41 (assume @p31 (tptp.ord_less tptp.int tptp.t @t30)) % 0.15/0.41 (assume @p32 (tptp.zprime @t30)) % 0.15/0.41 (assume @p33 (= @t42 @t41)) % 0.15/0.41 (assume @p34 (tptp.twoSqu33214720sum2sq @t41)) % 0.15/0.41 (assume @p35 (forall @t49 (= (tptp.power_power tptp.int @t48 @t31) (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int @t47 (tptp.times_times tptp.int (tptp.times_times tptp.int @t46 @t45) @t43)) @t44)))) % 0.15/0.41 (assume @p36 (forall @t49 (= (tptp.power_power tptp.int @t48 @t51) (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int @t53 (tptp.times_times tptp.int (tptp.times_times tptp.int @t52 @t47) @t43)) (tptp.times_times tptp.int (tptp.times_times tptp.int @t52 @t45) @t44)) (tptp.power_power tptp.int @t43 @t51))))) % 0.15/0.41 (assume @p37 (forall @t4 (=> (tptp.number_semiring @t1) (forall @t58 (= (tptp.power_power @t1 (tptp.plus_plus @t1 @t55 @t54) @t31) (tptp.plus_plus @t1 (tptp.plus_plus @t1 @t57 (tptp.power_power @t1 @t54 @t31)) (tptp.times_times @t1 (tptp.times_times @t1 @t56 @t55) @t54))))))) % 0.15/0.41 (assume @p38 (forall (@list @t60) (=> (and (tptp.monoid_mult @t60) (tptp.number @t60)) (forall @t62 (= (tptp.power_power @t60 @t61 @t31) (tptp.times_times @t60 @t61 @t61)))))) % 0.15/0.41 (assume @p39 (forall @t63 (= (tptp.times_times tptp.int @t45 @t47) @t53))) % 0.15/0.41 (assume @p40 (forall @t4 (=> @t3 (= (tptp.power_power @t1 @t2 @t31) @t2)))) % 0.15/0.41 (assume @p41 (forall @t4 (=> @t9 (forall @t64 (= (tptp.times_times @t1 @t55 @t55) @t57))))) % 0.15/0.41 (assume @p42 (forall @t4 (=> @t13 (forall @t63 (= (tptp.power_power @t1 @t45 @t31) (tptp.times_times @t1 @t45 @t45)))))) % 0.15/0.41 (assume @p43 (forall @t4 (=> @t9 (forall (@list @t55 @t65) (= (tptp.power_power @t1 @t55 (tptp.times_times tptp.nat @t31 @t65)) (tptp.times_times @t1 @t66 @t66)))))) % 0.15/0.41 (assume @p44 (forall @t4 (=> @t67 (forall @t62 (= (tptp.plus_plus @t1 @t2 (tptp.number_number_of @t1 @t59)) (tptp.number_number_of @t1 (tptp.plus_plus tptp.int @t28 @t59))))))) % 0.15/0.41 (assume @p45 (forall @t4 (=> @t67 (forall (@list @t68) (= (tptp.plus_plus @t1 (tptp.number_number_of @t1 @t68) @t2) (tptp.number_number_of @t1 (tptp.plus_plus tptp.int @t68 @t28))))))) % 0.15/0.41 (assume @p46 (forall @t4 (=> @t67 (= (tptp.plus_plus @t1 @t2 @t2) @t56)))) % 0.15/0.41 (assume @p47 (not (forall (@list @t69) (not (= @t42 (tptp.times_times tptp.int @t30 @t69)))))) % 0.15/0.41 (assume @p48 (forall @t62 (tptp.ord_less_eq tptp.int @t59 @t59))) % 0.15/0.41 (assume @p49 (forall @t73 (or @t72 @t71))) % 0.15/0.41 (assume @p50 @t76) % 0.15/0.41 (assume @p51 (forall @t58 (or (tptp.ord_less tptp.int @t55 @t54) (= @t55 @t54) (tptp.ord_less tptp.int @t54 @t55)))) % 0.15/0.41 (assume @p52 (forall @t81 (=> @t80 (=> (tptp.ord_less_eq tptp.int @t79 @t77) (tptp.ord_less_eq tptp.int @t78 @t77))))) % 0.15/0.41 (assume @p53 (forall @t73 (=> @t72 (=> @t71 (= @t70 @t59))))) % 0.15/0.41 (assume @p54 (forall @t4 (=> @t9 (forall @t85 (= (tptp.power_power @t1 @t84 @t82) (tptp.power_power @t1 @t55 (tptp.times_times tptp.nat @t83 @t82))))))) % 0.15/0.41 (assume @p55 (forall @t4 (=> @t9 (forall @t64 (= (tptp.power_power @t1 @t55 @t86) (tptp.ti @t1 @t55)))))) % 0.15/0.41 (assume @p56 (forall @t88 (= (tptp.power_power tptp.int @t87 @t70) (tptp.power_power tptp.int @t55 (tptp.times_times tptp.nat @t54 @t70))))) % 0.15/0.41 (assume @p57 (forall @t4 (=> @t23 (forall (@list @t89 @t74) (= (tptp.ord_less_eq @t1 @t90 @t91) (not (tptp.ord_less @t1 @t91 @t90))))))) % 0.15/0.41 (assume @p58 (forall @t4 (=> @t97 (forall @t96 (= (tptp.ord_less @t1 @t95 @t94) (tptp.ord_less tptp.int @t93 @t92)))))) % 0.15/0.41 (assume @p59 (forall @t4 (=> @t97 (forall @t96 (= (tptp.ord_less_eq @t1 @t95 @t94) (tptp.ord_less_eq tptp.int @t93 @t92)))))) % 0.15/0.41 (assume @p60 (forall (@list @t99 @t70 @t100 @t59) (=> (tptp.ord_less tptp.int @t100 @t59) (=> (tptp.ord_less_eq tptp.int @t99 @t70) (tptp.ord_less tptp.int (tptp.plus_plus tptp.int @t100 @t99) @t98))))) % 0.15/0.41 (assume @p61 (forall @t4 (=> @t9 (forall @t85 (= (tptp.times_times @t1 @t84 (tptp.power_power @t1 @t55 @t82)) (tptp.power_power @t1 @t55 (tptp.plus_plus tptp.nat @t83 @t82))))))) % 0.15/0.41 (assume @p62 (forall @t88 (= (tptp.power_power tptp.int @t55 (tptp.plus_plus tptp.nat @t54 @t70)) (tptp.times_times tptp.int @t87 (tptp.power_power tptp.int @t55 @t70))))) % 0.15/0.41 (assume @p63 (forall @t102 (= (tptp.times_times tptp.nat @t31 @t70) @t101))) % 0.15/0.41 (assume @p64 (forall @t102 (= (tptp.times_times tptp.nat @t70 @t31) @t101))) % 0.15/0.41 (assume @p65 (= (tptp.plus_plus tptp.nat @t86 @t86) @t31)) % 0.15/0.41 (assume @p66 (forall @t108 (= (tptp.ord_less tptp.int @t107 @t106) @t105))) % 0.15/0.41 (assume @p67 (forall @t114 (= (tptp.ord_less tptp.int @t113 @t112) @t111))) % 0.15/0.41 (assume @p68 (forall @t108 (= (tptp.ord_less_eq tptp.int @t107 @t106) @t115))) % 0.15/0.41 (assume @p69 (forall @t114 (= (tptp.ord_less_eq tptp.int @t113 @t112) @t116))) % 0.15/0.41 (assume @p70 (not (tptp.ord_less tptp.int tptp.pls tptp.pls))) % 0.15/0.41 (assume @p71 (forall @t108 (= (tptp.ord_less tptp.int @t118 @t117) @t105))) % 0.15/0.41 (assume @p72 (forall @t114 (= (tptp.ord_less tptp.int @t120 @t119) @t111))) % 0.15/0.41 (assume @p73 (tptp.ord_less_eq tptp.int tptp.pls tptp.pls)) % 0.15/0.41 (assume @p74 (forall @t108 (= (tptp.ord_less_eq tptp.int @t118 @t117) @t115))) % 0.15/0.41 (assume @p75 (forall @t114 (= (tptp.ord_less_eq tptp.int @t120 @t119) @t116))) % 0.15/0.41 (assume @p76 (forall @t114 (= (tptp.ord_less tptp.int @t122 @t121) @t111))) % 0.15/0.41 (assume @p77 (forall @t114 (= (tptp.ord_less_eq tptp.int @t122 @t121) @t116))) % 0.15/0.41 (assume @p78 (forall @t81 (=> (tptp.ord_less tptp.int @t78 @t79) (tptp.ord_less tptp.int (tptp.plus_plus tptp.int @t78 @t77) (tptp.plus_plus tptp.int @t79 @t77))))) % 0.15/0.41 (assume @p79 (forall @t81 (=> @t80 (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int @t77 @t78) (tptp.plus_plus tptp.int @t77 @t79))))) % 0.15/0.41 (assume @p80 (forall (@list @t123 @t68) (and (=> @t128 (= @t126 @t124)) (=> (not @t128) (and (=> @t127 (= @t126 @t125)) (=> (not @t127) (= @t126 (tptp.number_number_of tptp.nat (tptp.plus_plus tptp.int @t68 @t123))))))))) % 0.15/0.41 (assume @p81 (= @t129 @t86)) % 0.15/0.41 (assume @p82 (= @t86 @t129)) % 0.15/0.41 (assume @p83 (forall @t131 (= (tptp.ord_less_eq tptp.int @t113 tptp.pls) @t130))) % 0.15/0.41 (assume @p84 (forall @t131 (= (tptp.ord_less tptp.int tptp.pls @t113) @t132))) % 0.15/0.41 (assume @p85 (forall @t108 (= (tptp.ord_less_eq tptp.int @t107 @t117) @t105))) % 0.15/0.41 (assume @p86 (forall @t114 (= (tptp.ord_less_eq tptp.int @t113 @t119) @t111))) % 0.15/0.41 (assume @p87 (forall @t108 (= (tptp.ord_less tptp.int @t118 @t106) @t115))) % 0.15/0.41 (assume @p88 (forall @t114 (= (tptp.ord_less tptp.int @t120 @t112) @t116))) % 0.15/0.41 (assume @p89 (forall (@list @t59 @t70) (=> (tptp.ord_less tptp.int @t59 @t70) (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int @t59 @t26) @t70)))) % 0.15/0.41 (assume @p90 (forall @t133 (= (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int @t74 @t26) @t75) (tptp.ord_less tptp.int @t74 @t75)))) % 0.15/0.41 (assume @p91 (forall @t133 (= (tptp.ord_less tptp.int @t74 (tptp.plus_plus tptp.int @t75 @t26)) (tptp.ord_less_eq tptp.int @t74 @t75)))) % 0.15/0.41 (assume @p92 (tptp.zprime @t46)) % 0.15/0.41 (assume @p93 (forall (@list @t54 @t55) (=> (tptp.twoSqu33214720sum2sq @t55) (=> (tptp.twoSqu33214720sum2sq @t54) (tptp.twoSqu33214720sum2sq (tptp.times_times tptp.int @t55 @t54)))))) % 0.15/0.41 (assume @p94 (forall @t4 (=> @t9 (forall @t142 (= @t141 (tptp.times_times @t1 @t138 (tptp.times_times @t1 @t135 @t134))))))) % 0.15/0.41 (assume @p95 (forall @t4 (=> @t9 (forall @t142 (= @t141 (tptp.times_times @t1 @t136 (tptp.times_times @t1 @t140 @t134))))))) % 0.15/0.41 (assume @p96 (forall @t4 (=> @t9 (forall @t142 (= @t141 (tptp.times_times @t1 @t137 (tptp.times_times @t1 @t135 @t139))))))) % 0.15/0.41 (assume @p97 (forall @t4 (=> @t9 (forall @t144 (= @t143 (tptp.times_times @t1 @t138 @t135)))))) % 0.15/0.41 (assume @p98 (forall @t4 (=> @t9 (forall @t144 (= @t143 (tptp.times_times @t1 @t137 (tptp.times_times @t1 @t135 @t136))))))) % 0.15/0.41 (assume @p99 (forall @t4 (=> @t9 (forall @t146 (= @t145 (tptp.times_times @t1 @t138 @t134)))))) % 0.15/0.41 (assume @p100 (forall @t4 (=> @t9 (forall @t146 (= @t145 (tptp.times_times @t1 @t136 (tptp.times_times @t1 @t137 @t134))))))) % 0.15/0.41 (assume @p101 (forall @t4 (=> @t9 (forall @t49 (= (tptp.times_times @t1 @t45 @t43) (tptp.times_times @t1 @t43 @t45)))))) % 0.15/0.41 (assume @p102 (forall @t4 (=> @t9 (forall (@list @t45 @t43 @t148 @t147) (= (tptp.plus_plus @t1 @t151 @t150) (tptp.plus_plus @t1 @t149 (tptp.plus_plus @t1 @t43 @t147))))))) % 0.15/0.41 (assume @p103 (forall @t4 (=> @t9 (forall @t153 (= @t152 (tptp.plus_plus @t1 @t149 @t43)))))) % 0.15/0.41 (assume @p104 (forall @t4 (=> @t9 (forall @t153 (= @t152 (tptp.plus_plus @t1 @t45 (tptp.plus_plus @t1 @t43 @t148))))))) % 0.15/0.41 (assume @p105 (forall @t4 (=> @t9 (forall @t155 (= @t154 (tptp.plus_plus @t1 @t149 @t147)))))) % 0.15/0.41 (assume @p106 (forall @t4 (=> @t9 (forall @t155 (= @t154 (tptp.plus_plus @t1 @t148 (tptp.plus_plus @t1 @t45 @t147))))))) % 0.15/0.41 (assume @p107 (forall @t4 (=> @t9 (forall (@list @t45 @t148) (= @t149 (tptp.plus_plus @t1 @t148 @t45)))))) % 0.15/0.41 (assume @p108 (forall @t4 (=> (and @t67 (tptp.ring_char_0 @t1)) (forall @t96 (= (= @t95 @t94) (= @t93 @t92)))))) % 0.15/0.41 (assume @p109 (forall @t4 (=> @t20 (forall (@list @t74 @t93) (= (= @t91 @t156) (= @t156 @t91)))))) % 0.15/0.41 (assume @p110 (forall @t114 (= (= @t113 @t112) @t157))) % 0.15/0.41 (assume @p111 (forall @t114 (= (= @t120 @t119) @t157))) % 0.15/0.41 (assume @p112 (forall @t161 (= (tptp.times_times tptp.int (tptp.times_times tptp.int @t160 @t159) @t158) (tptp.times_times tptp.int @t160 (tptp.times_times tptp.int @t159 @t158))))) % 0.15/0.41 (assume @p113 (forall @t73 (= (tptp.times_times tptp.int @t70 @t59) (tptp.times_times tptp.int @t59 @t70)))) % 0.15/0.41 (assume @p114 (forall (@list @t77) (= (tptp.number_number_of tptp.int @t77) @t77))) % 0.15/0.41 (assume @p115 (forall @t161 (= (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int @t160 @t159) @t158) (tptp.plus_plus tptp.int @t160 (tptp.plus_plus tptp.int @t159 @t158))))) % 0.15/0.41 (assume @p116 (forall @t88 (= (tptp.plus_plus tptp.int @t55 (tptp.plus_plus tptp.int @t54 @t70)) (tptp.plus_plus tptp.int @t54 (tptp.plus_plus tptp.int @t55 @t70))))) % 0.15/0.41 (assume @p117 (forall @t73 (= (tptp.plus_plus tptp.int @t70 @t59) @t98))) % 0.15/0.41 (assume @p118 (forall @t131 (= (tptp.ord_less tptp.int @t113 tptp.pls) @t130))) % 0.15/0.41 (assume @p119 (forall @t108 (= (tptp.ord_less tptp.int @t107 @t117) @t105))) % 0.15/0.41 (assume @p120 (forall @t114 (= (tptp.ord_less tptp.int @t113 @t119) @t111))) % 0.15/0.41 (assume @p121 (forall @t131 (= (tptp.ord_less tptp.int @t120 tptp.pls) @t130))) % 0.15/0.41 (assume @p122 (forall @t131 (= (tptp.ord_less tptp.int tptp.pls @t120) (tptp.ord_less tptp.int tptp.pls @t110)))) % 0.15/0.41 (assume @p123 (forall @t131 (= (tptp.ord_less_eq tptp.int tptp.pls @t113) @t132))) % 0.15/0.41 (assume @p124 (forall @t108 (= (tptp.ord_less_eq tptp.int @t118 @t106) @t115))) % 0.15/0.41 (assume @p125 (forall @t114 (= (tptp.ord_less_eq tptp.int @t120 @t112) @t116))) % 0.15/0.41 (assume @p126 (tptp.linordered_idom tptp.int)) % 0.15/0.41 (assume @p127 (tptp.comm_semiring_1 tptp.int)) % 0.15/0.41 (assume @p128 (tptp.number_semiring tptp.int)) % 0.15/0.41 (assume @p129 (tptp.linorder tptp.int)) % 0.15/0.41 (assume @p130 (tptp.monoid_mult tptp.int)) % 0.15/0.41 (assume @p131 (tptp.semiring_1 tptp.int)) % 0.15/0.41 (assume @p132 (tptp.ring_char_0 tptp.int)) % 0.15/0.41 (assume @p133 (tptp.number_ring tptp.int)) % 0.15/0.41 (assume @p134 (tptp.number tptp.int)) % 0.15/0.41 (assume @p135 (tptp.comm_semiring_1 tptp.nat)) % 0.15/0.41 (assume @p136 (tptp.number_semiring tptp.nat)) % 0.15/0.41 (assume @p137 (tptp.linorder tptp.nat)) % 0.15/0.41 (assume @p138 (tptp.monoid_mult tptp.nat)) % 0.15/0.41 (assume @p139 (tptp.semiring_1 tptp.nat)) % 0.15/0.41 (assume @p140 (tptp.number tptp.nat)) % 0.15/0.41 (assume @p141 (forall (@list @t163 @t162) (= (tptp.ti @t163 @t164) @t164))) % 0.15/0.41 (assume @p142 @t165) % 0.15/0.41 (assume @p143 true) % 0.15/0.41 (step @p144 :rule bool-double-not-elim :args (@t166)) % 0.15/0.41 (step @p145 :rule exists-elim :args ((= @t36 @t167))) % 0.15/0.41 (step @p146 :rule cong :premises (@p145) :args (@t165)) % 0.15/0.41 (step @p147 :rule trans :premises (@p146 @p144)) % 0.15/0.41 (step @p148 :rule eq_resolve :premises (@p142 @p147)) % 0.15/0.41 (step @p149 :rule refl :args (@t39)) % 0.15/0.41 (step @p150 :rule cong :premises (@p149 @p145) :args (@t40)) % 0.15/0.41 (step @p151 :rule eq_resolve :premises (@p30 @p150)) % 0.15/0.41 (step @p152 :rule implies_elim :premises (@p151)) % 0.15/0.41 (step @p153 :rule reordering :premises (@p152) :args ((or @t167 @t168))) % 0.15/0.41 (step @p154 :rule chain_m_resolution :premises (@p153 @p148) :args (@t168 @t169 @t170)) % 0.15/0.41 (step @p155 :rule refl :args (@t37)) % 0.15/0.41 (step @p156 :rule cong :premises (@p155 @p145) :args (@t38)) % 0.15/0.41 (step @p157 :rule eq_resolve :premises (@p29 @p156)) % 0.15/0.41 (step @p158 :rule implies_elim :premises (@p157)) % 0.15/0.41 (step @p159 :rule reordering :premises (@p158) :args ((or @t167 @t171))) % 0.15/0.41 (step @p160 :rule chain_m_resolution :premises (@p159 @p148) :args (@t171 @t169 @t170)) % 0.15/0.41 (step @p161 :rule bool-double-not-elim :args (@t37)) % 0.15/0.41 (step @p162 :rule refl :args (@t172)) % 0.15/0.41 (step @p163 :rule refl :args (@t173)) % 0.15/0.41 (step @p164 :rule nary_cong :premises (@p163 @p162 @p161) :args ((or @t173 @t172 (not @t171)))) % 0.15/0.41 (step @p165 :rule cnf_and_neg :args (@t173)) % 0.15/0.41 (step @p166 :rule eq_resolve :premises (@p165 @p164)) % 0.15/0.41 (step @p167 :rule reordering :premises (@p166) :args ((or @t37 @t172 @t173))) % 0.15/0.41 (step @p168 :rule chain_m_resolution :premises (@p167 @p160 @p28) :args (@t173 (@list true false) (@list @t37 @t27))) % 0.15/0.41 (step @p169 :rule eq-symm :args (@t26 tptp.t)) % 0.15/0.41 (step @p170 :rule cong :premises (@p169) :args (@t174)) % 0.15/0.41 (step @p171 :rule refl :args (@t27)) % 0.15/0.41 (step @p172 :rule nary_cong :premises (@p171 @p170) :args (@t175)) % 0.15/0.41 (step @p173 :rule cong :premises (@p149 @p172) :args (@t176)) % 0.15/0.41 (step @p174 :rule refl :args (@t76)) % 0.15/0.41 (step @p175 :rule cong :premises (@p174 @p173) :args ((=> @t76 @t176))) % 0.15/0.41 (assume-push @p186 @t76) % 0.15/0.41 (step @p177 :rule instantiate :premises (@p50) :args ((@list @t26 tptp.t))) % 0.15/0.41 (step-pop @p187 :rule scope :premises (@p177)) % 0.15/0.41 (step @p178 :rule process_scope :premises (@p187) :args (@t176)) % 0.15/0.42 (step @p180 :rule eq_resolve :premises (@p178 @p175)) % 0.15/0.42 (step @p181 :rule implies_elim :premises (@p180)) % 0.15/0.42 (step @p182 :rule chain_m_resolution :premises (@p181 @p50) :args (@t177 @t169 (@list @t76))) % 0.15/0.42 (step @p183 :rule cnf_equiv_pos2 :args (@t177)) % 0.15/0.42 (step @p184 :rule reordering :premises (@p183) :args ((or @t39 (not @t173) (not @t177)))) % 0.15/0.42 (step @p185 false :rule chain_m_resolution :premises (@p184 @p182 @p168 @p154) :args (false (@list false false true) (@list @t177 @t173 @t39))) % 0.15/0.42 ) % 0.15/0.42 % SZS output end Proof % 0.15/0.42 % cvc5 exiting %------------------------------------------------------------------------------