%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM925+5 : TPTP v9.2.1. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:41:05 AM UTC 2026 % Result : Theorem 0.45s 0.65s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM925+5 : TPTP v9.2.1. Released v5.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n021.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 12:35:20 EDT 2026 % 0.15/0.34 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.45/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.45/0.65 % SZS status Theorem % 0.45/0.65 % SZS output start Proof % 0.45/0.65 ( % 0.45/0.65 (declare-sort $$unsorted 0) % 0.45/0.65 (declare-const tptp.ring_11004092258visors (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.semiring_1 (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.t $$unsorted) % 0.45/0.65 (declare-const tptp.n $$unsorted) % 0.45/0.65 (declare-const tptp.linordered_idom (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.ring_char_0 (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.ord_less (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.number (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.number_number_of (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.pls $$unsorted) % 0.45/0.65 (declare-const tptp.power_power (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.bit1 (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.int $$unsorted) % 0.45/0.65 (declare-const tptp.zero_zero (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.number_ring (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.semiring_0 (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.power (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.no_zero_divisors (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.plus_plus (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.nat $$unsorted) % 0.45/0.65 (declare-const tptp.linord219039673up_add (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.one_one (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.number_semiring (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.zero_neq_one (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.semiring_1_of_nat (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.mult_zero (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.undefined (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.ti (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.bit0 (-> $$unsorted $$unsorted)) % 0.45/0.65 (define @t1 () (@var "X_a" $$unsorted)) % 0.45/0.65 (define @t2 () (tptp.one_one @t1)) % 0.45/0.65 (define @t3 () (tptp.power @t1)) % 0.45/0.65 (define @t4 () (and @t3 (tptp.semiring_0 @t1))) % 0.45/0.65 (define @t5 () (@list @t1)) % 0.45/0.65 (define @t6 () (@var "B_2" $$unsorted)) % 0.45/0.65 (define @t7 () (@var "B_1" $$unsorted)) % 0.45/0.65 (define @t8 () (tptp.plus_plus @t1 @t7 @t6)) % 0.45/0.65 (define @t9 () (tptp.ti @t1 @t7)) % 0.45/0.65 (define @t10 () (= (tptp.plus_plus @t1 @t9 @t6) @t8)) % 0.45/0.65 (define @t11 () (tptp.linord219039673up_add @t1)) % 0.45/0.65 (define @t12 () (@list @t7 @t6 @t1)) % 0.45/0.65 (define @t13 () (tptp.ti @t1 @t6)) % 0.45/0.65 (define @t14 () (= (tptp.plus_plus @t1 @t7 @t13) @t8)) % 0.45/0.65 (define @t15 () (tptp.ti @t1 @t8)) % 0.45/0.65 (define @t16 () (= @t15 @t8)) % 0.45/0.65 (define @t17 () (=> @t11 @t16)) % 0.45/0.65 (define @t18 () (forall @t12 @t17)) % 0.45/0.65 (define @t19 () (tptp.number_semiring @t1)) % 0.45/0.65 (define @t20 () (tptp.zero_zero @t1)) % 0.45/0.65 (define @t21 () (= (tptp.ti @t1 @t20) @t20)) % 0.45/0.65 (define @t22 () (and @t3 (tptp.mult_zero @t1) (tptp.no_zero_divisors @t1) (tptp.zero_neq_one @t1))) % 0.45/0.65 (define @t23 () (tptp.undefined @t1)) % 0.45/0.65 (define @t24 () (tptp.bit0 @t7)) % 0.45/0.65 (define @t25 () (tptp.ti tptp.int @t7)) % 0.45/0.65 (define @t26 () (@list @t7)) % 0.45/0.65 (define @t27 () (tptp.bit1 @t7)) % 0.45/0.65 (define @t28 () (tptp.number_number_of @t1 @t7)) % 0.45/0.65 (define @t29 () (tptp.number @t1)) % 0.45/0.65 (define @t30 () (@list @t7 @t1)) % 0.45/0.65 (define @t31 () (tptp.semiring_1_of_nat @t1 @t7)) % 0.45/0.65 (define @t32 () (tptp.ti tptp.nat @t7)) % 0.45/0.65 (define @t33 () (tptp.ord_less @t1 @t7 @t6)) % 0.45/0.65 (define @t34 () (tptp.linordered_idom @t1)) % 0.45/0.65 (define @t35 () (tptp.ord_less tptp.nat @t7 @t6)) % 0.45/0.65 (define @t36 () (@list @t7 @t6)) % 0.45/0.65 (define @t37 () (tptp.ti tptp.nat @t6)) % 0.45/0.65 (define @t38 () (tptp.power_power @t1 @t7 @t6)) % 0.45/0.65 (define @t39 () (= (tptp.power_power @t1 @t9 @t6) @t38)) % 0.45/0.65 (define @t40 () (= (tptp.power_power @t1 @t7 @t37) @t38)) % 0.45/0.65 (define @t41 () (= (tptp.ti @t1 @t38) @t38)) % 0.45/0.65 (define @t42 () (tptp.semiring_1_of_nat tptp.int tptp.n)) % 0.45/0.65 (define @t43 () (tptp.one_one tptp.int)) % 0.45/0.65 (define @t44 () (tptp.plus_plus tptp.int @t43 @t42)) % 0.45/0.65 (define @t45 () (tptp.zero_zero tptp.int)) % 0.45/0.65 (define @t46 () (tptp.ord_less tptp.int @t45 @t44)) % 0.45/0.65 (define @t47 () (@var "Ya" $$unsorted)) % 0.45/0.65 (define @t48 () (= (tptp.ti @t1 @t47) @t20)) % 0.45/0.65 (define @t49 () (@var "Xa" $$unsorted)) % 0.45/0.65 (define @t50 () (tptp.ti @t1 @t49)) % 0.45/0.65 (define @t51 () (= @t50 @t20)) % 0.45/0.65 (define @t52 () (tptp.bit1 tptp.pls)) % 0.45/0.65 (define @t53 () (tptp.bit0 @t52)) % 0.45/0.65 (define @t54 () (tptp.number_number_of tptp.nat @t53)) % 0.45/0.65 (define @t55 () (tptp.plus_plus @t1 (tptp.power_power @t1 @t49 @t54) (tptp.power_power @t1 @t47 @t54))) % 0.45/0.65 (define @t56 () (@list @t49 @t47)) % 0.45/0.65 (define @t57 () (tptp.semiring_1 @t1)) % 0.45/0.65 (define @t58 () (@var "A_2" $$unsorted)) % 0.45/0.65 (define @t59 () (tptp.ti @t1 @t58)) % 0.45/0.65 (define @t60 () (= @t59 @t20)) % 0.45/0.65 (define @t61 () (tptp.power_power @t1 @t58 @t54)) % 0.45/0.65 (define @t62 () (= (= @t61 @t20) @t60)) % 0.45/0.65 (define @t63 () (@list @t58)) % 0.45/0.65 (define @t64 () (forall @t63 @t62)) % 0.45/0.65 (define @t65 () (tptp.ring_11004092258visors @t1)) % 0.45/0.65 (define @t66 () (=> @t65 @t64)) % 0.45/0.65 (define @t67 () (forall @t5 @t66)) % 0.45/0.65 (define @t68 () (@var "W" $$unsorted)) % 0.45/0.65 (define @t69 () (tptp.number_number_of @t1 @t68)) % 0.45/0.65 (define @t70 () (@list @t68)) % 0.45/0.65 (define @t71 () (tptp.number_ring @t1)) % 0.45/0.65 (define @t72 () (@var "V" $$unsorted)) % 0.45/0.65 (define @t73 () (tptp.number_number_of @t1 @t72)) % 0.45/0.65 (define @t74 () (= (tptp.plus_plus @t1 @t2 @t2) (tptp.number_number_of @t1 @t53))) % 0.45/0.65 (define @t75 () (@var "X" $$unsorted)) % 0.45/0.65 (define @t76 () (tptp.number_number_of tptp.nat @t68)) % 0.45/0.65 (define @t77 () (tptp.power_power @t1 @t20 @t76)) % 0.45/0.65 (define @t78 () (tptp.zero_zero tptp.nat)) % 0.45/0.65 (define @t79 () (= @t76 @t78)) % 0.45/0.65 (define @t80 () (tptp.number_number_of @t1 @t52)) % 0.45/0.65 (define @t81 () (@var "Y" $$unsorted)) % 0.45/0.65 (define @t82 () (@var "L_1" $$unsorted)) % 0.45/0.65 (define @t83 () (@var "K_1" $$unsorted)) % 0.45/0.65 (define @t84 () (tptp.ord_less tptp.int @t83 @t82)) % 0.45/0.65 (define @t85 () (@list @t83 @t82)) % 0.45/0.65 (define @t86 () (tptp.plus_plus tptp.int @t72 @t68)) % 0.45/0.65 (define @t87 () (@list @t72 @t68)) % 0.45/0.65 (define @t88 () (tptp.number_number_of @t1 @t47)) % 0.45/0.65 (define @t89 () (tptp.number_number_of @t1 @t49)) % 0.45/0.65 (define @t90 () (and @t71 @t34)) % 0.45/0.65 (define @t91 () (@var "N" $$unsorted)) % 0.45/0.65 (define @t92 () (@var "M" $$unsorted)) % 0.45/0.65 (define @t93 () (tptp.semiring_1_of_nat tptp.int (tptp.power_power tptp.nat @t92 @t91))) % 0.45/0.65 (define @t94 () (tptp.semiring_1_of_nat tptp.int @t92)) % 0.45/0.65 (define @t95 () (tptp.power_power tptp.int @t94 @t91)) % 0.45/0.65 (define @t96 () (@list @t92 @t91)) % 0.45/0.65 (define @t97 () (@var "Z" $$unsorted)) % 0.45/0.65 (define @t98 () (tptp.semiring_1_of_nat tptp.int (tptp.plus_plus tptp.nat @t92 @t91))) % 0.45/0.65 (define @t99 () (tptp.semiring_1_of_nat tptp.int @t91)) % 0.45/0.65 (define @t100 () (tptp.one_one tptp.nat)) % 0.45/0.65 (define @t101 () (tptp.number_number_of tptp.nat tptp.pls)) % 0.45/0.65 (define @t102 () (@var "Na" $$unsorted)) % 0.45/0.65 (define @t103 () (tptp.semiring_1_of_nat tptp.int @t102)) % 0.45/0.65 (define @t104 () (@var "K2" $$unsorted)) % 0.45/0.65 (define @t105 () (@var "K1" $$unsorted)) % 0.45/0.65 (define @t106 () (tptp.ord_less tptp.int @t105 @t104)) % 0.45/0.65 (define @t107 () (tptp.bit1 @t105)) % 0.45/0.65 (define @t108 () (@list @t105 @t104)) % 0.45/0.65 (define @t109 () (tptp.bit1 @t82)) % 0.45/0.65 (define @t110 () (tptp.bit1 @t83)) % 0.45/0.65 (define @t111 () (tptp.bit0 @t104)) % 0.45/0.65 (define @t112 () (tptp.bit0 @t82)) % 0.45/0.65 (define @t113 () (tptp.bit0 @t83)) % 0.45/0.65 (define @t114 () (@var "K" $$unsorted)) % 0.45/0.65 (define @t115 () (@var "J" $$unsorted)) % 0.45/0.65 (define @t116 () (@var "I" $$unsorted)) % 0.45/0.65 (define @t117 () (@var "V_1" $$unsorted)) % 0.45/0.65 (define @t118 () (tptp.number_number_of tptp.nat @t117)) % 0.45/0.65 (define @t119 () (tptp.number_number_of tptp.nat @t72)) % 0.45/0.65 (define @t120 () (tptp.plus_plus tptp.nat @t119 @t118)) % 0.45/0.65 (define @t121 () (tptp.ord_less tptp.int @t117 tptp.pls)) % 0.45/0.65 (define @t122 () (tptp.ord_less tptp.int @t72 tptp.pls)) % 0.45/0.65 (define @t123 () (tptp.number_number_of tptp.nat @t52)) % 0.45/0.65 (define @t124 () (@var "Wa" $$unsorted)) % 0.45/0.65 (define @t125 () (tptp.number_number_of @t1 @t124)) % 0.45/0.65 (define @t126 () (= @t83 @t82)) % 0.45/0.65 (define @t127 () (tptp.plus_plus @t1 @t58 @t58)) % 0.45/0.65 (define @t128 () (@var "Z3" $$unsorted)) % 0.45/0.65 (define @t129 () (@var "Z2" $$unsorted)) % 0.45/0.65 (define @t130 () (@var "Z1" $$unsorted)) % 0.45/0.65 (define @t131 () (@var "Ma" $$unsorted)) % 0.45/0.65 (define @t132 () (@list @t49)) % 0.45/0.65 (define @t133 () (@list @t47)) % 0.45/0.65 (define @t134 () (tptp.ord_less tptp.int @t83 tptp.pls)) % 0.45/0.65 (define @t135 () (@list @t83)) % 0.45/0.65 (define @t136 () (tptp.ord_less tptp.int @t124 @t45)) % 0.45/0.65 (define @t137 () (@list @t124)) % 0.45/0.65 (define @t138 () (@var "Z_1" $$unsorted)) % 0.45/0.65 (define @t139 () (@list @t114)) % 0.45/0.65 (define @t140 () (tptp.bit1 @t114)) % 0.45/0.65 (define @t141 () (@var "L" $$unsorted)) % 0.45/0.65 (define @t142 () (tptp.bit1 @t141)) % 0.45/0.65 (define @t143 () (tptp.bit0 @t141)) % 0.45/0.65 (define @t144 () (@list @t114 @t141)) % 0.45/0.65 (define @t145 () (tptp.bit0 @t114)) % 0.45/0.65 (define @t146 () (tptp.plus_plus tptp.int @t114 @t141)) % 0.45/0.65 (define @t147 () (@list @t97)) % 0.45/0.65 (define @t148 () (tptp.number_number_of @t1 tptp.pls)) % 0.45/0.65 (define @t149 () (= @t148 @t20)) % 0.45/0.65 (define @t150 () (@var "A_1" $$unsorted)) % 0.45/0.65 (define @t151 () (tptp.ti @t1 @t150)) % 0.45/0.65 (define @t152 () (@list @t150)) % 0.45/0.65 (define @t153 () (tptp.number_number_of tptp.nat @t124)) % 0.45/0.65 (define @t154 () (tptp.number_number_of @t1 @t86)) % 0.45/0.65 (define @t155 () (tptp.plus_plus @t1 @t73 @t69)) % 0.45/0.65 (define @t156 () (tptp.bit1 @t146)) % 0.45/0.65 (define @t157 () (tptp.linord219039673up_add tptp.int)) % 0.45/0.65 (define @t158 () (tptp.ring_11004092258visors tptp.int)) % 0.45/0.65 (define @t159 () (@var "A" $$unsorted)) % 0.45/0.65 (define @t160 () (@var "T" $$unsorted)) % 0.45/0.65 (define @t161 () (tptp.ti @t160 @t159)) % 0.45/0.65 (define @t162 () (tptp.power_power tptp.int @t44 @t54)) % 0.45/0.65 (define @t163 () (= @t162 @t45)) % 0.45/0.65 (define @t164 () (@var "BOUND_VARIABLE_8325" $$unsorted)) % 0.45/0.65 (define @t165 () (= (= @t20 (tptp.power_power @t1 @t164 @t54)) (= @t20 (tptp.ti @t1 @t164)))) % 0.45/0.65 (define @t166 () (not @t65)) % 0.45/0.65 (define @t167 () (or @t166 @t165)) % 0.45/0.65 (define @t168 () (@list @t164)) % 0.45/0.65 (define @t169 () (forall @t168 @t167)) % 0.45/0.65 (define @t170 () (forall @t168 @t165)) % 0.45/0.65 (define @t171 () (or @t166 @t170)) % 0.45/0.65 (define @t172 () (forall @t63 (= (= @t20 @t61) (= @t20 @t59)))) % 0.45/0.65 (define @t173 () (tptp.ti tptp.int @t44)) % 0.45/0.65 (define @t174 () (= @t45 @t173)) % 0.45/0.65 (define @t175 () (= @t45 @t162)) % 0.45/0.65 (define @t176 () (= @t175 @t174)) % 0.45/0.65 (define @t177 () (not @t158)) % 0.45/0.65 (define @t178 () (or @t177 @t176)) % 0.45/0.65 (define @t179 () (@list false false)) % 0.45/0.65 (define @t180 () (= @t8 @t15)) % 0.45/0.65 (define @t181 () (= @t44 @t173)) % 0.45/0.65 (define @t182 () (not @t157)) % 0.45/0.65 (define @t183 () (or @t182 @t181)) % 0.45/0.65 (assume @p1 (forall @t5 (=> @t4 (= (tptp.ti @t1 @t2) @t2)))) % 0.45/0.65 (assume @p2 (forall @t12 (=> @t11 @t10))) % 0.45/0.65 (assume @p3 (forall @t12 (=> @t11 @t14))) % 0.45/0.65 (assume @p4 @t18) % 0.45/0.65 (assume @p5 (forall @t12 (=> @t19 @t10))) % 0.45/0.65 (assume @p6 (forall @t12 (=> @t19 @t14))) % 0.45/0.65 (assume @p7 (forall @t12 (=> @t19 @t16))) % 0.45/0.65 (assume @p8 (forall @t5 (=> @t22 @t21))) % 0.45/0.65 (assume @p9 (forall @t5 (=> @t11 @t21))) % 0.45/0.65 (assume @p10 (forall @t5 (=> @t4 @t21))) % 0.45/0.65 (assume @p11 (forall @t5 (= (tptp.ti @t1 @t23) @t23))) % 0.45/0.65 (assume @p12 (forall @t26 (= (tptp.bit0 @t25) @t24))) % 0.45/0.65 (assume @p13 (forall @t26 (= (tptp.ti tptp.int @t24) @t24))) % 0.45/0.65 (assume @p14 (forall @t26 (= (tptp.bit1 @t25) @t27))) % 0.45/0.65 (assume @p15 (forall @t26 (= (tptp.ti tptp.int @t27) @t27))) % 0.45/0.65 (assume @p16 (= (tptp.ti tptp.int tptp.pls) tptp.pls)) % 0.45/0.65 (assume @p17 (forall @t30 (=> @t29 (= (tptp.number_number_of @t1 @t25) @t28)))) % 0.45/0.65 (assume @p18 (forall @t30 (=> @t29 (= (tptp.ti @t1 @t28) @t28)))) % 0.45/0.65 (assume @p19 (forall @t30 (=> @t19 (= (tptp.semiring_1_of_nat @t1 @t32) @t31)))) % 0.45/0.65 (assume @p20 (forall @t30 (=> @t19 (= (tptp.ti @t1 @t31) @t31)))) % 0.45/0.65 (assume @p21 (forall @t12 (=> @t34 (= (tptp.ord_less @t1 @t9 @t6) @t33)))) % 0.45/0.65 (assume @p22 (forall @t12 (=> @t34 (= (tptp.ord_less @t1 @t7 @t13) @t33)))) % 0.45/0.65 (assume @p23 (forall @t36 (= (tptp.ord_less tptp.nat @t32 @t6) @t35))) % 0.45/0.65 (assume @p24 (forall @t36 (= (tptp.ord_less tptp.nat @t7 @t37) @t35))) % 0.45/0.65 (assume @p25 (forall @t12 (=> @t22 @t39))) % 0.45/0.65 (assume @p26 (forall @t12 (=> @t22 @t40))) % 0.45/0.65 (assume @p27 (forall @t12 (=> @t22 @t41))) % 0.45/0.65 (assume @p28 (forall @t12 (=> @t4 @t39))) % 0.45/0.65 (assume @p29 (forall @t12 (=> @t4 @t40))) % 0.45/0.65 (assume @p30 (forall @t12 (=> @t4 @t41))) % 0.45/0.65 (assume @p31 (= (tptp.ti tptp.nat tptp.n) tptp.n)) % 0.45/0.65 (assume @p32 (= (tptp.ti tptp.int tptp.t) tptp.t)) % 0.45/0.65 (assume @p33 @t46) % 0.45/0.65 (assume @p34 (tptp.ord_less tptp.int @t43 tptp.t)) % 0.45/0.65 (assume @p35 (forall @t5 (=> @t34 (forall @t56 (= (= @t55 @t20) (and @t51 @t48)))))) % 0.45/0.65 (assume @p36 (forall @t5 (=> @t57 (= (tptp.power_power @t1 @t2 @t54) @t2)))) % 0.45/0.65 (assume @p37 (forall @t5 (=> @t57 (= (tptp.power_power @t1 @t20 @t54) @t20)))) % 0.45/0.65 (assume @p38 @t67) % 0.45/0.65 (assume @p39 (forall @t5 (=> @t71 (forall @t70 (= (tptp.plus_plus @t1 @t2 @t69) (tptp.number_number_of @t1 (tptp.plus_plus tptp.int @t52 @t68))))))) % 0.45/0.65 (assume @p40 (forall @t5 (=> @t71 (forall (@list @t72) (= (tptp.plus_plus @t1 @t73 @t2) (tptp.number_number_of @t1 (tptp.plus_plus tptp.int @t72 @t52))))))) % 0.45/0.65 (assume @p41 (forall @t5 (=> @t71 @t74))) % 0.45/0.65 (assume @p42 (forall @t5 (=> @t19 @t74))) % 0.45/0.65 (assume @p43 (forall (@list @t75) (= (tptp.power_power tptp.int (tptp.power_power tptp.int @t75 @t54) @t54) (tptp.power_power tptp.int @t75 (tptp.number_number_of tptp.nat (tptp.bit0 @t53)))))) % 0.45/0.65 (assume @p44 (forall @t5 (=> @t4 (forall @t70 (and (=> @t79 (= @t77 @t2)) (=> (not @t79) (= @t77 @t20))))))) % 0.45/0.65 (assume @p45 (forall @t5 (=> @t71 (= @t2 @t80)))) % 0.45/0.65 (assume @p46 (forall @t5 (=> @t71 (= @t80 @t2)))) % 0.45/0.65 (assume @p47 (tptp.ord_less tptp.nat @t78 tptp.n)) % 0.45/0.65 (assume @p48 (forall (@list @t75 @t81) (or (tptp.ord_less tptp.int @t75 @t81) (= @t75 @t81) (tptp.ord_less tptp.int @t81 @t75)))) % 0.45/0.65 (assume @p49 (forall @t85 (= (tptp.ord_less tptp.int (tptp.number_number_of tptp.int @t83) (tptp.number_number_of tptp.int @t82)) @t84))) % 0.45/0.65 (assume @p50 (forall @t87 (= (tptp.plus_plus tptp.int (tptp.number_number_of tptp.int @t72) (tptp.number_number_of tptp.int @t68)) (tptp.number_number_of tptp.int @t86)))) % 0.45/0.65 (assume @p51 (forall @t5 (=> @t90 (forall @t56 (= (tptp.ord_less @t1 @t89 @t88) (tptp.ord_less tptp.int @t49 @t47)))))) % 0.45/0.65 (assume @p52 (= @t45 (tptp.number_number_of tptp.int tptp.pls))) % 0.45/0.65 (assume @p53 (forall @t96 (= @t95 @t93))) % 0.45/0.65 (assume @p54 (forall @t96 (= @t93 @t95))) % 0.45/0.65 (assume @p55 (forall (@list @t92 @t91 @t97) (= (tptp.plus_plus tptp.int @t94 (tptp.plus_plus tptp.int @t99 @t97)) (tptp.plus_plus tptp.int @t98 @t97)))) % 0.45/0.65 (assume @p56 (forall @t96 (= (tptp.plus_plus tptp.int @t94 @t99) @t98))) % 0.45/0.65 (assume @p57 (= (tptp.semiring_1_of_nat tptp.int @t100) @t43)) % 0.45/0.65 (assume @p58 (= @t101 @t78)) % 0.45/0.65 (assume @p59 (= @t78 @t101)) % 0.45/0.65 (assume @p60 (forall (@list @t102) (= (= @t103 @t45) (= @t102 @t78)))) % 0.45/0.65 (assume @p61 (= (tptp.semiring_1_of_nat tptp.int @t78) @t45)) % 0.45/0.65 (assume @p62 (= (tptp.plus_plus tptp.nat @t100 @t100) @t54)) % 0.45/0.65 (assume @p63 (forall @t108 (= (tptp.ord_less tptp.int @t107 (tptp.bit1 @t104)) @t106))) % 0.45/0.65 (assume @p64 (forall @t85 (= (tptp.ord_less tptp.int @t110 @t109) @t84))) % 0.45/0.65 (assume @p65 (not (tptp.ord_less tptp.int tptp.pls tptp.pls))) % 0.45/0.65 (assume @p66 (forall @t108 (= (tptp.ord_less tptp.int (tptp.bit0 @t105) @t111) @t106))) % 0.45/0.65 (assume @p67 (forall @t85 (= (tptp.ord_less tptp.int @t113 @t112) @t84))) % 0.45/0.65 (assume @p68 (forall (@list @t114 @t116 @t115) (=> (tptp.ord_less tptp.int @t116 @t115) (tptp.ord_less tptp.int (tptp.plus_plus tptp.int @t116 @t114) (tptp.plus_plus tptp.int @t115 @t114))))) % 0.45/0.65 (assume @p69 (forall (@list @t117 @t72) (and (=> @t122 (= @t120 @t118)) (=> (not @t122) (and (=> @t121 (= @t120 @t119)) (=> (not @t121) (= @t120 (tptp.number_number_of tptp.nat (tptp.plus_plus tptp.int @t72 @t117))))))))) % 0.45/0.65 (assume @p70 (= @t43 (tptp.number_number_of tptp.int @t52))) % 0.45/0.65 (assume @p71 (= @t123 @t100)) % 0.45/0.65 (assume @p72 (= @t100 @t123)) % 0.45/0.65 (assume @p73 (forall @t5 (=> (and @t71 (tptp.ring_char_0 @t1)) (forall @t56 (= (= @t89 @t88) (= @t49 @t47)))))) % 0.45/0.65 (assume @p74 (forall @t5 (=> @t29 (forall (@list @t124 @t49) (= (= @t125 @t50) (= @t50 @t125)))))) % 0.45/0.65 (assume @p75 (forall @t85 (= (= @t110 @t109) @t126))) % 0.45/0.65 (assume @p76 (forall @t85 (= (= @t113 @t112) @t126))) % 0.45/0.65 (assume @p77 (forall @t5 (=> @t34 (forall @t63 (= (tptp.ord_less @t1 @t127 @t20) (tptp.ord_less @t1 @t58 @t20)))))) % 0.45/0.65 (assume @p78 (forall (@list @t130 @t129 @t128) (= (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int @t130 @t129) @t128) (tptp.plus_plus tptp.int @t130 (tptp.plus_plus tptp.int @t129 @t128))))) % 0.45/0.65 (assume @p79 (forall (@list @t75 @t81 @t97) (= (tptp.plus_plus tptp.int @t75 (tptp.plus_plus tptp.int @t81 @t97)) (tptp.plus_plus tptp.int @t81 (tptp.plus_plus tptp.int @t75 @t97))))) % 0.45/0.65 (assume @p80 (forall (@list @t97 @t68) (= (tptp.plus_plus tptp.int @t97 @t68) (tptp.plus_plus tptp.int @t68 @t97)))) % 0.45/0.65 (assume @p81 (forall (@list @t131 @t102) (= (= (tptp.semiring_1_of_nat tptp.int @t131) @t103) (= @t131 @t102)))) % 0.45/0.65 (assume @p82 (forall @t5 (=> @t90 (forall @t132 (= (tptp.ord_less @t1 @t89 @t20) (tptp.ord_less tptp.int @t49 tptp.pls)))))) % 0.45/0.65 (assume @p83 (forall @t5 (=> @t90 (forall @t133 (= (tptp.ord_less @t1 @t20 @t88) (tptp.ord_less tptp.int tptp.pls @t47)))))) % 0.45/0.65 (assume @p84 (forall @t135 (= (tptp.ord_less tptp.int @t110 tptp.pls) @t134))) % 0.45/0.65 (assume @p85 (forall @t108 (= (tptp.ord_less tptp.int @t107 @t111) @t106))) % 0.45/0.65 (assume @p86 (forall @t85 (= (tptp.ord_less tptp.int @t110 @t112) @t84))) % 0.45/0.65 (assume @p87 (forall @t135 (= (tptp.ord_less tptp.int @t113 tptp.pls) @t134))) % 0.45/0.65 (assume @p88 (forall @t135 (= (tptp.ord_less tptp.int tptp.pls @t113) (tptp.ord_less tptp.int tptp.pls @t83)))) % 0.45/0.65 (assume @p89 (forall @t137 (= (tptp.ord_less tptp.int (tptp.bit1 @t124) @t45) @t136))) % 0.45/0.65 (assume @p90 (not (tptp.ord_less tptp.int tptp.pls @t45))) % 0.45/0.65 (assume @p91 (forall @t137 (= (tptp.ord_less tptp.int (tptp.bit0 @t124) @t45) @t136))) % 0.45/0.65 (assume @p92 (tptp.ord_less tptp.int @t45 @t43)) % 0.45/0.65 (assume @p93 (forall (@list @t124 @t138) (= (tptp.ord_less tptp.int @t124 (tptp.plus_plus tptp.int @t138 @t43)) (or (tptp.ord_less tptp.int @t124 @t138) (= @t124 @t138))))) % 0.45/0.65 (assume @p94 (forall @t139 (not (tptp.ord_less tptp.int (tptp.semiring_1_of_nat tptp.int @t114) @t45)))) % 0.45/0.65 (assume @p95 (forall @t5 (=> @t90 (forall @t132 (= (tptp.ord_less @t1 @t89 @t2) (tptp.ord_less tptp.int @t49 @t52)))))) % 0.45/0.65 (assume @p96 (forall @t5 (=> @t90 (forall @t133 (= (tptp.ord_less @t1 @t2 @t88) (tptp.ord_less tptp.int @t52 @t47)))))) % 0.45/0.65 (assume @p97 (forall (@list @t138) (= (tptp.ord_less tptp.int (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int @t43 @t138) @t138) @t45) (tptp.ord_less tptp.int @t138 @t45)))) % 0.45/0.65 (assume @p98 (forall @t5 (=> @t11 (forall @t63 (= (= @t127 @t20) @t60))))) % 0.45/0.65 (assume @p99 (forall @t139 (not (= @t140 tptp.pls)))) % 0.45/0.65 (assume @p100 (forall (@list @t141) (not (= tptp.pls @t142)))) % 0.45/0.65 (assume @p101 (forall @t144 (not (= @t140 @t143)))) % 0.45/0.65 (assume @p102 (forall @t144 (not (= @t145 @t142)))) % 0.45/0.65 (assume @p103 (forall @t135 (= (= @t113 tptp.pls) (= @t83 tptp.pls)))) % 0.45/0.65 (assume @p104 (forall (@list @t82) (= (= tptp.pls @t112) (= tptp.pls @t82)))) % 0.45/0.65 (assume @p105 (= (tptp.bit0 tptp.pls) tptp.pls)) % 0.45/0.65 (assume @p106 (= tptp.pls @t45)) % 0.45/0.65 (assume @p107 (not (= @t45 @t43))) % 0.45/0.65 (assume @p108 (forall @t139 (= (tptp.plus_plus tptp.int @t114 tptp.pls) @t114))) % 0.45/0.65 (assume @p109 (forall @t139 (= (tptp.plus_plus tptp.int tptp.pls @t114) @t114))) % 0.45/0.65 (assume @p110 (forall @t144 (= (tptp.plus_plus tptp.int @t145 @t143) (tptp.bit0 @t146)))) % 0.45/0.65 (assume @p111 (forall @t139 (= @t145 (tptp.plus_plus tptp.int @t114 @t114)))) % 0.45/0.65 (assume @p112 (forall @t147 (= (tptp.plus_plus tptp.int @t97 @t45) @t97))) % 0.45/0.65 (assume @p113 (forall @t147 (= (tptp.plus_plus tptp.int @t45 @t97) @t97))) % 0.45/0.65 (assume @p114 (forall @t5 (=> @t19 @t149))) % 0.45/0.65 (assume @p115 (forall @t5 (=> @t71 @t149))) % 0.45/0.65 (assume @p116 (forall @t5 (=> @t71 (= @t20 @t148)))) % 0.45/0.65 (assume @p117 (forall @t5 (=> @t71 (forall @t152 (= (tptp.plus_plus @t1 @t148 @t150) @t151))))) % 0.45/0.65 (assume @p118 (forall @t5 (=> @t71 (forall @t152 (= (tptp.plus_plus @t1 @t150 @t148) @t151))))) % 0.45/0.65 (assume @p119 (forall @t5 (=> @t22 (forall (@list @t58 @t124) (= (= (tptp.power_power @t1 @t58 @t153) @t20) (and @t60 (not (= @t153 @t78)))))))) % 0.45/0.65 (assume @p120 (forall @t5 (=> @t71 (forall (@list @t72 @t68 @t97) (= (tptp.plus_plus @t1 @t73 (tptp.plus_plus @t1 @t69 @t97)) (tptp.plus_plus @t1 @t154 @t97)))))) % 0.45/0.65 (assume @p121 (forall @t5 (=> @t71 (forall @t87 (= @t155 @t154))))) % 0.45/0.65 (assume @p122 (forall @t5 (=> @t71 (forall @t87 (= @t154 @t155))))) % 0.45/0.65 (assume @p123 (forall @t144 (= (tptp.plus_plus tptp.int @t140 @t143) @t156))) % 0.45/0.65 (assume @p124 (forall @t144 (= (tptp.plus_plus tptp.int @t145 @t142) @t156))) % 0.45/0.65 (assume @p125 (forall @t139 (= @t140 (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int @t43 @t114) @t114)))) % 0.45/0.65 (assume @p126 (forall @t147 (not (= (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int @t43 @t97) @t97) @t45)))) % 0.45/0.65 (assume @p127 (forall @t5 (=> @t19 (forall (@list @t91) (= (tptp.number_number_of @t1 @t99) (tptp.semiring_1_of_nat @t1 @t91)))))) % 0.45/0.65 (assume @p128 (forall @t5 (=> @t34 (forall @t63 (= (tptp.ord_less @t1 @t20 @t61) (not @t60)))))) % 0.45/0.65 (assume @p129 (forall @t5 (=> @t34 (forall @t152 (not (tptp.ord_less @t1 (tptp.power_power @t1 @t150 @t54) @t20)))))) % 0.45/0.65 (assume @p130 (forall @t5 (=> @t34 (forall @t56 (= (tptp.ord_less @t1 @t20 @t55) (or (not @t51) (not @t48))))))) % 0.45/0.65 (assume @p131 @t157) % 0.45/0.65 (assume @p132 @t158) % 0.45/0.65 (assume @p133 (tptp.no_zero_divisors tptp.int)) % 0.45/0.65 (assume @p134 (tptp.linordered_idom tptp.int)) % 0.45/0.65 (assume @p135 (tptp.number_semiring tptp.int)) % 0.45/0.65 (assume @p136 (tptp.zero_neq_one tptp.int)) % 0.45/0.65 (assume @p137 (tptp.semiring_1 tptp.int)) % 0.45/0.65 (assume @p138 (tptp.semiring_0 tptp.int)) % 0.45/0.65 (assume @p139 (tptp.mult_zero tptp.int)) % 0.45/0.66 (assume @p140 (tptp.ring_char_0 tptp.int)) % 0.45/0.66 (assume @p141 (tptp.number_ring tptp.int)) % 0.45/0.66 (assume @p142 (tptp.power tptp.int)) % 0.45/0.66 (assume @p143 (tptp.number tptp.int)) % 0.45/0.66 (assume @p144 (tptp.no_zero_divisors tptp.nat)) % 0.45/0.66 (assume @p145 (tptp.number_semiring tptp.nat)) % 0.45/0.66 (assume @p146 (tptp.zero_neq_one tptp.nat)) % 0.45/0.66 (assume @p147 (tptp.semiring_1 tptp.nat)) % 0.45/0.66 (assume @p148 (tptp.semiring_0 tptp.nat)) % 0.45/0.66 (assume @p149 (tptp.mult_zero tptp.nat)) % 0.45/0.66 (assume @p150 (tptp.power tptp.nat)) % 0.45/0.66 (assume @p151 (tptp.number tptp.nat)) % 0.45/0.66 (assume @p152 (forall (@list @t160 @t159) (= (tptp.ti @t160 @t161) @t161))) % 0.45/0.66 (assume @p153 (not (not @t163))) % 0.45/0.66 (assume @p154 true) % 0.45/0.66 (step @p155 :rule evaluate :args ((= true false))) % 0.45/0.66 (step @p156 :rule false_intro :premises (@p90)) % 0.45/0.66 (step @p157 :rule quant-merge-prenex :args ((= (forall @t5 @t169) (forall (@list @t1 @t164) @t167)))) % 0.45/0.66 (step @p158 :rule alpha_equiv :args (@t170 (@list @t164) (@list @t58))) % 0.45/0.66 (step @p159 :rule refl :args (@t166)) % 0.45/0.66 (step @p160 :rule nary_cong :premises (@p159 @p158) :args (@t171)) % 0.45/0.66 (step @p161 :rule quant-miniscope-or :args ((= @t169 @t171))) % 0.45/0.66 (step @p162 :rule trans :premises (@p161 @p160)) % 0.45/0.66 (step @p163 :rule symm :premises (@p162)) % 0.45/0.66 (step @p164 :rule cong :premises (@p163) :args ((forall @t5 (or @t166 @t172)))) % 0.45/0.66 (step @p165 :rule trans :premises (@p164 @p157)) % 0.45/0.66 (step @p166 :rule bool-impl-elim :args (@t65 @t172)) % 0.45/0.66 (step @p167 :rule cong :premises (@p166) :args ((forall @t5 (=> @t65 @t172)))) % 0.45/0.66 (step @p168 :rule trans :premises (@p167 @p165)) % 0.45/0.66 (step @p169 :rule eq-symm :args (@t59 @t20)) % 0.45/0.66 (step @p170 :rule eq-symm :args (@t61 @t20)) % 0.45/0.66 (step @p171 :rule cong :premises (@p170 @p169) :args (@t62)) % 0.45/0.66 (step @p172 :rule cong :premises (@p171) :args (@t64)) % 0.45/0.66 (step @p173 :rule refl :args (@t65)) % 0.45/0.66 (step @p174 :rule cong :premises (@p173 @p172) :args (@t66)) % 0.45/0.66 (step @p175 :rule cong :premises (@p174) :args (@t67)) % 0.45/0.66 (step @p176 :rule trans :premises (@p175 @p168)) % 0.45/0.66 (step @p177 :rule eq_resolve :premises (@p38 @p176)) % 0.45/0.66 (step @p178 :rule instantiate :premises (@p177) :args ((@list tptp.int @t44))) % 0.45/0.66 (step @p179 :rule cnf_or_pos :args (@t178)) % 0.45/0.66 (step @p180 :rule reordering :premises (@p179) :args ((or @t177 @t176 (not @t178)))) % 0.45/0.66 (step @p181 :rule chain_m_resolution :premises (@p180 @p132 @p178) :args (@t176 @t179 (@list @t158 @t178))) % 0.45/0.66 (step @p182 :rule eq-symm :args (@t162 @t45)) % 0.45/0.66 (step @p183 :rule bool-double-not-elim :args (@t163)) % 0.45/0.66 (step @p184 :rule trans :premises (@p183 @p182)) % 0.45/0.66 (step @p185 :rule eq_resolve :premises (@p153 @p184)) % 0.45/0.66 (step @p186 :rule cnf_equiv_pos1 :args (@t176)) % 0.45/0.66 (step @p187 :rule reordering :premises (@p186) :args ((or (not @t175) @t174 (not @t176)))) % 0.45/0.66 (step @p188 :rule chain_m_resolution :premises (@p187 @p185 @p181) :args (@t174 @t179 (@list @t175 @t176))) % 0.45/0.66 (step @p189 :rule symm :premises (@p188)) % 0.45/0.66 (step @p190 :rule bool-impl-elim :args (@t11 @t180)) % 0.45/0.66 (step @p191 :rule cong :premises (@p190) :args ((forall @t12 (=> @t11 @t180)))) % 0.45/0.66 (step @p192 :rule eq-symm :args (@t15 @t8)) % 0.45/0.66 (step @p193 :rule refl :args (@t11)) % 0.45/0.66 (step @p194 :rule cong :premises (@p193 @p192) :args (@t17)) % 0.45/0.66 (step @p195 :rule cong :premises (@p194) :args (@t18)) % 0.45/0.66 (step @p196 :rule trans :premises (@p195 @p191)) % 0.45/0.66 (step @p197 :rule eq_resolve :premises (@p4 @p196)) % 0.45/0.66 (step @p198 :rule instantiate :premises (@p197) :args ((@list @t43 @t42 tptp.int))) % 0.45/0.66 (step @p199 :rule cnf_or_pos :args (@t183)) % 0.45/0.66 (step @p200 :rule reordering :premises (@p199) :args ((or @t182 @t181 (not @t183)))) % 0.45/0.66 (step @p201 :rule chain_m_resolution :premises (@p200 @p131 @p198) :args (@t181 @t179 (@list @t157 @t183))) % 0.45/0.66 (step @p202 :rule trans :premises (@p201 @p189)) % 0.45/0.66 (step @p203 :rule symm :premises (@p106)) % 0.45/0.66 (step @p204 :rule refl :args (tptp.int)) % 0.45/0.66 (step @p205 :rule cong :premises (@p204 @p203 @p202) :args (@t46)) % 0.45/0.66 (step @p206 :rule true_intro :premises (@p33)) % 0.45/0.66 (step @p207 :rule symm :premises (@p206)) % 0.45/0.66 (step @p208 :rule trans :premises (@p207 @p205 @p156)) % 0.45/0.66 (step @p209 false :rule eq_resolve :premises (@p208 @p155)) % 0.45/0.66 ) % 0.45/0.66 % SZS output end Proof % 0.45/0.66 % cvc5 exiting %------------------------------------------------------------------------------