%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV182+1 : TPTP v9.2.1. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n023.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 09:00:40 AM UTC 2026 % Result : Theorem 0.44s 0.65s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV182+1 : TPTP v9.2.1. Bugfixed v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n023.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 19:59:43 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.65 % SZS status Theorem % 0.44/0.65 % SZS output start Proof % 0.44/0.65 ( % 0.44/0.65 (declare-sort $$unsorted 0) % 0.44/0.65 (declare-const tptp.tptp_float_0_001 $$unsorted) % 0.44/0.65 (declare-const tptp.n135299 $$unsorted) % 0.44/0.65 (declare-const tptp.q_init $$unsorted) % 0.44/0.65 (declare-const tptp.mu_init $$unsorted) % 0.44/0.65 (declare-const tptp.sigma_init $$unsorted) % 0.44/0.65 (declare-const tptp.rho_init $$unsorted) % 0.44/0.65 (declare-const tptp.def $$unsorted) % 0.44/0.65 (declare-const tptp.use $$unsorted) % 0.44/0.65 (declare-const tptp.true Bool) % 0.44/0.65 (declare-const tptp.tptp_update2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.center_init $$unsorted) % 0.44/0.65 (declare-const tptp.a_select3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.uniform_int_rnd (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.loopcounter $$unsorted) % 0.44/0.65 (declare-const tptp.n3 $$unsorted) % 0.44/0.65 (declare-const tptp.tptp_const_array1 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.pred (-> $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.tptp_minus_1 $$unsorted) % 0.44/0.65 (declare-const tptp.n0 $$unsorted) % 0.44/0.65 (declare-const tptp.tptp_msub (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.n1 $$unsorted) % 0.44/0.65 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.n5 $$unsorted) % 0.44/0.65 (declare-const tptp.pv76 $$unsorted) % 0.44/0.65 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.tptp_update3 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.minus (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.init $$unsorted) % 0.44/0.65 (declare-const tptp.tptp_const_array2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.trans (-> $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.a_select2 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.inv (-> $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.dim (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.plus (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.tptp_madd (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.sum (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.tptp_mmul (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.tptp_float_0_0 $$unsorted) % 0.44/0.65 (declare-const tptp.n4 $$unsorted) % 0.44/0.65 (declare-const tptp.n2 $$unsorted) % 0.44/0.65 (define @t1 () (@var "Y" $$unsorted)) % 0.44/0.65 (define @t2 () (@var "X" $$unsorted)) % 0.44/0.65 (define @t3 () (= @t2 @t1)) % 0.44/0.65 (define @t4 () (tptp.gt @t1 @t2)) % 0.44/0.65 (define @t5 () (tptp.gt @t2 @t1)) % 0.44/0.65 (define @t6 () (@list @t2 @t1)) % 0.44/0.65 (define @t7 () (@var "Z" $$unsorted)) % 0.44/0.65 (define @t8 () (@list @t2 @t1 @t7)) % 0.44/0.65 (define @t9 () (@list @t2)) % 0.44/0.65 (define @t10 () (tptp.leq @t2 @t1)) % 0.44/0.65 (define @t11 () (tptp.succ @t2)) % 0.44/0.65 (define @t12 () (tptp.succ @t1)) % 0.44/0.65 (define @t13 () (@var "C" $$unsorted)) % 0.44/0.65 (define @t14 () (tptp.uniform_int_rnd @t13 @t2)) % 0.44/0.65 (define @t15 () (tptp.leq tptp.n0 @t2)) % 0.44/0.65 (define @t16 () (@list @t2 @t13)) % 0.44/0.65 (define @t17 () (@var "Val" $$unsorted)) % 0.44/0.65 (define @t18 () (@var "I" $$unsorted)) % 0.44/0.65 (define @t19 () (@var "U" $$unsorted)) % 0.44/0.65 (define @t20 () (@var "L" $$unsorted)) % 0.44/0.65 (define @t21 () (tptp.leq @t18 @t19)) % 0.44/0.65 (define @t22 () (@var "J" $$unsorted)) % 0.44/0.65 (define @t23 () (@var "U2" $$unsorted)) % 0.44/0.65 (define @t24 () (@var "L2" $$unsorted)) % 0.44/0.65 (define @t25 () (@var "U1" $$unsorted)) % 0.44/0.65 (define @t26 () (@var "L1" $$unsorted)) % 0.44/0.65 (define @t27 () (@var "A" $$unsorted)) % 0.44/0.65 (define @t28 () (tptp.trans @t27)) % 0.44/0.65 (define @t29 () (@var "N" $$unsorted)) % 0.44/0.65 (define @t30 () (tptp.leq @t22 @t29)) % 0.44/0.65 (define @t31 () (tptp.leq tptp.n0 @t22)) % 0.44/0.65 (define @t32 () (tptp.leq @t18 @t29)) % 0.44/0.65 (define @t33 () (tptp.leq tptp.n0 @t18)) % 0.44/0.65 (define @t34 () (and @t33 @t32 @t31 @t30)) % 0.44/0.65 (define @t35 () (@list @t18 @t22)) % 0.44/0.65 (define @t36 () (forall @t35 (=> @t34 (= (tptp.a_select3 @t27 @t18 @t22) (tptp.a_select3 @t27 @t22 @t18))))) % 0.44/0.65 (define @t37 () (@list @t27 @t29)) % 0.44/0.65 (define @t38 () (tptp.inv @t27)) % 0.44/0.65 (define @t39 () (@var "VAL" $$unsorted)) % 0.44/0.65 (define @t40 () (@var "K" $$unsorted)) % 0.44/0.65 (define @t41 () (tptp.tptp_update3 @t27 @t40 @t40 @t39)) % 0.44/0.65 (define @t42 () (@var "B" $$unsorted)) % 0.44/0.65 (define @t43 () (tptp.tptp_madd @t27 @t42)) % 0.44/0.65 (define @t44 () (= (tptp.a_select3 @t42 @t18 @t22) (tptp.a_select3 @t42 @t22 @t18))) % 0.44/0.65 (define @t45 () (forall @t35 (=> @t34 @t44))) % 0.44/0.65 (define @t46 () (and @t36 @t45)) % 0.44/0.65 (define @t47 () (@list @t27 @t42 @t29)) % 0.44/0.65 (define @t48 () (tptp.tptp_msub @t27 @t42)) % 0.44/0.65 (define @t49 () (tptp.tptp_mmul @t27 (tptp.tptp_mmul @t42 @t28))) % 0.44/0.65 (define @t50 () (forall @t35 (=> @t34 (= (tptp.a_select3 @t49 @t18 @t22) (tptp.a_select3 @t49 @t22 @t18))))) % 0.44/0.65 (define @t51 () (@var "M" $$unsorted)) % 0.44/0.65 (define @t52 () (and @t33 (tptp.leq @t18 @t51) @t31 (tptp.leq @t22 @t51))) % 0.44/0.65 (define @t53 () (@var "E" $$unsorted)) % 0.44/0.65 (define @t54 () (@var "F" $$unsorted)) % 0.44/0.65 (define @t55 () (@var "D" $$unsorted)) % 0.44/0.65 (define @t56 () (tptp.tptp_madd @t27 (tptp.tptp_mmul @t42 (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul @t13 (tptp.tptp_mmul @t55 (tptp.trans @t13))) (tptp.tptp_mmul @t53 (tptp.tptp_mmul @t54 (tptp.trans @t53)))) (tptp.trans @t42))))) % 0.44/0.65 (define @t57 () (@var "Body" $$unsorted)) % 0.44/0.65 (define @t58 () (tptp.sum tptp.n0 tptp.tptp_minus_1 @t57)) % 0.44/0.65 (define @t59 () (@list @t57)) % 0.44/0.65 (define @t60 () (tptp.succ @t11)) % 0.44/0.65 (define @t61 () (tptp.succ @t60)) % 0.44/0.65 (define @t62 () (tptp.succ @t61)) % 0.44/0.65 (define @t63 () (tptp.succ @t62)) % 0.44/0.65 (define @t64 () (tptp.pred @t2)) % 0.44/0.65 (define @t65 () (tptp.leq @t11 @t1)) % 0.44/0.65 (define @t66 () (forall @t6 (=> @t65 @t4))) % 0.44/0.65 (define @t67 () (@var "V" $$unsorted)) % 0.44/0.65 (define @t68 () (tptp.tptp_update3 @t2 @t19 @t67 @t39)) % 0.44/0.65 (define @t69 () (@var "VAL2" $$unsorted)) % 0.44/0.65 (define @t70 () (not (= @t18 @t19))) % 0.44/0.65 (define @t71 () (@var "J0" $$unsorted)) % 0.44/0.65 (define @t72 () (@var "I0" $$unsorted)) % 0.44/0.65 (define @t73 () (tptp.leq @t72 @t19)) % 0.44/0.65 (define @t74 () (tptp.leq tptp.n0 @t72)) % 0.44/0.65 (define @t75 () (tptp.tptp_update2 @t2 @t19 @t39)) % 0.44/0.65 (define @t76 () (@var "G" $$unsorted)) % 0.44/0.65 (define @t77 () (tptp.a_select2 tptp.rho_init @t76)) % 0.44/0.65 (define @t78 () (tptp.leq @t76 tptp.n4)) % 0.44/0.65 (define @t79 () (tptp.leq tptp.n0 @t76)) % 0.44/0.65 (define @t80 () (and @t79 @t78)) % 0.44/0.65 (define @t81 () (=> @t80 (= @t77 tptp.init))) % 0.44/0.65 (define @t82 () (@list @t76)) % 0.44/0.65 (define @t83 () (forall @t82 @t81)) % 0.44/0.65 (define @t84 () (tptp.a_select2 tptp.sigma_init @t54)) % 0.44/0.65 (define @t85 () (tptp.leq @t54 tptp.n4)) % 0.44/0.65 (define @t86 () (tptp.leq tptp.n0 @t54)) % 0.44/0.65 (define @t87 () (and @t86 @t85)) % 0.44/0.65 (define @t88 () (=> @t87 (= @t84 tptp.init))) % 0.44/0.65 (define @t89 () (@list @t54)) % 0.44/0.65 (define @t90 () (forall @t89 @t88)) % 0.44/0.65 (define @t91 () (tptp.gt tptp.loopcounter tptp.n0)) % 0.44/0.65 (define @t92 () (=> @t91 @t90)) % 0.44/0.65 (define @t93 () (tptp.a_select2 tptp.rho_init @t53)) % 0.44/0.65 (define @t94 () (tptp.leq @t53 tptp.n4)) % 0.44/0.65 (define @t95 () (tptp.leq tptp.n0 @t53)) % 0.44/0.65 (define @t96 () (and @t95 @t94)) % 0.44/0.65 (define @t97 () (=> @t96 (= @t93 tptp.init))) % 0.44/0.65 (define @t98 () (@list @t53)) % 0.44/0.65 (define @t99 () (forall @t98 @t97)) % 0.44/0.65 (define @t100 () (=> @t91 @t99)) % 0.44/0.65 (define @t101 () (tptp.a_select2 tptp.mu_init @t55)) % 0.44/0.65 (define @t102 () (tptp.leq @t55 tptp.n4)) % 0.44/0.65 (define @t103 () (tptp.leq tptp.n0 @t55)) % 0.44/0.65 (define @t104 () (and @t103 @t102)) % 0.44/0.65 (define @t105 () (=> @t104 (= @t101 tptp.init))) % 0.44/0.65 (define @t106 () (@list @t55)) % 0.44/0.65 (define @t107 () (forall @t106 @t105)) % 0.44/0.65 (define @t108 () (=> @t91 @t107)) % 0.44/0.65 (define @t109 () (tptp.a_select3 tptp.center_init @t13 tptp.n0)) % 0.44/0.65 (define @t110 () (tptp.leq @t13 tptp.n4)) % 0.44/0.65 (define @t111 () (tptp.leq tptp.n0 @t13)) % 0.44/0.65 (define @t112 () (and @t111 @t110)) % 0.44/0.65 (define @t113 () (=> @t112 (= @t109 tptp.init))) % 0.44/0.65 (define @t114 () (@list @t13)) % 0.44/0.65 (define @t115 () (forall @t114 @t113)) % 0.44/0.65 (define @t116 () (tptp.a_select3 tptp.q_init @t27 @t42)) % 0.44/0.65 (define @t117 () (tptp.leq @t42 tptp.n4)) % 0.44/0.65 (define @t118 () (tptp.leq tptp.n0 @t42)) % 0.44/0.65 (define @t119 () (and @t118 @t117)) % 0.44/0.65 (define @t120 () (=> @t119 (= @t116 tptp.init))) % 0.44/0.65 (define @t121 () (@list @t42)) % 0.44/0.65 (define @t122 () (forall @t121 @t120)) % 0.44/0.65 (define @t123 () (tptp.leq @t27 tptp.n135299)) % 0.44/0.65 (define @t124 () (tptp.leq tptp.n0 @t27)) % 0.44/0.65 (define @t125 () (and @t124 @t123)) % 0.44/0.65 (define @t126 () (=> @t125 @t122)) % 0.44/0.65 (define @t127 () (@list @t27)) % 0.44/0.65 (define @t128 () (forall @t127 @t126)) % 0.44/0.65 (define @t129 () (tptp.leq tptp.n1 tptp.loopcounter)) % 0.44/0.65 (define @t130 () (tptp.leq tptp.tptp_float_0_001 tptp.pv76)) % 0.44/0.65 (define @t131 () (and @t130 @t129 @t128 @t115 @t108 @t100 @t92)) % 0.44/0.65 (define @t132 () (=> @t131 @t83)) % 0.44/0.65 (define @t133 () (not @t132)) % 0.44/0.65 (define @t134 () (= @t2 tptp.n4)) % 0.44/0.65 (define @t135 () (= @t2 tptp.n3)) % 0.44/0.65 (define @t136 () (= @t2 tptp.n2)) % 0.44/0.65 (define @t137 () (= @t2 tptp.n1)) % 0.44/0.65 (define @t138 () (= @t2 tptp.n0)) % 0.44/0.65 (define @t139 () (tptp.succ tptp.n0)) % 0.44/0.65 (define @t140 () (tptp.succ @t139)) % 0.44/0.65 (define @t141 () (tptp.succ @t140)) % 0.44/0.65 (define @t142 () (tptp.succ @t141)) % 0.44/0.65 (define @t143 () (= tptp.init @t77)) % 0.44/0.65 (define @t144 () (not @t78)) % 0.44/0.65 (define @t145 () (not @t79)) % 0.44/0.65 (define @t146 () (or @t145 @t144 @t143)) % 0.44/0.65 (define @t147 () (= tptp.init @t84)) % 0.44/0.65 (define @t148 () (not @t85)) % 0.44/0.65 (define @t149 () (not @t86)) % 0.44/0.65 (define @t150 () (= tptp.init @t93)) % 0.44/0.65 (define @t151 () (not @t94)) % 0.44/0.65 (define @t152 () (not @t95)) % 0.44/0.65 (define @t153 () (or @t152 @t151 @t150)) % 0.44/0.65 (define @t154 () (= tptp.init @t101)) % 0.44/0.65 (define @t155 () (not @t102)) % 0.44/0.65 (define @t156 () (not @t103)) % 0.44/0.65 (define @t157 () (= tptp.init @t109)) % 0.44/0.65 (define @t158 () (not @t110)) % 0.44/0.65 (define @t159 () (not @t111)) % 0.44/0.65 (define @t160 () (@var "BOUND_VARIABLE_8424" $$unsorted)) % 0.44/0.65 (define @t161 () (= tptp.init (tptp.a_select3 tptp.q_init @t27 @t160))) % 0.44/0.65 (define @t162 () (not (tptp.leq @t160 tptp.n4))) % 0.44/0.65 (define @t163 () (not (tptp.leq tptp.n0 @t160))) % 0.44/0.65 (define @t164 () (not @t123)) % 0.44/0.65 (define @t165 () (not @t124)) % 0.44/0.65 (define @t166 () (or @t163 @t162 @t161)) % 0.44/0.65 (define @t167 () (or @t165 @t164 @t166)) % 0.44/0.65 (define @t168 () (forall (@list @t27 @t160) @t167)) % 0.44/0.65 (define @t169 () (@list @t160)) % 0.44/0.65 (define @t170 () (forall @t169 @t167)) % 0.44/0.65 (define @t171 () (forall @t169 @t166)) % 0.44/0.65 (define @t172 () (or @t165 @t164 @t171)) % 0.44/0.65 (define @t173 () (= tptp.init @t116)) % 0.44/0.65 (define @t174 () (not @t117)) % 0.44/0.65 (define @t175 () (not @t118)) % 0.44/0.65 (define @t176 () (or @t175 @t174 @t173)) % 0.44/0.65 (define @t177 () (forall @t121 @t176)) % 0.44/0.65 (define @t178 () (or @t165 @t164 @t177)) % 0.44/0.65 (define @t179 () (forall @t98 @t153)) % 0.44/0.65 (define @t180 () (not @t179)) % 0.44/0.65 (define @t181 () (forall @t82 @t146)) % 0.44/0.65 (define @t182 () (@list true)) % 0.44/0.65 (define @t183 () (not @t91)) % 0.44/0.65 (define @t184 () (not (tptp.leq @t139 tptp.loopcounter))) % 0.44/0.65 (define @t185 () (or @t184 @t91)) % 0.44/0.65 (assume @p1 (forall @t6 (or @t5 @t4 @t3))) % 0.44/0.65 (assume @p2 (forall @t8 (=> (and @t5 (tptp.gt @t1 @t7)) (tptp.gt @t2 @t7)))) % 0.44/0.65 (assume @p3 (forall @t9 (not (tptp.gt @t2 @t2)))) % 0.44/0.65 (assume @p4 (forall @t9 (tptp.leq @t2 @t2))) % 0.44/0.65 (assume @p5 (forall @t8 (=> (and @t10 (tptp.leq @t1 @t7)) (tptp.leq @t2 @t7)))) % 0.44/0.65 (assume @p6 (forall @t6 (= (tptp.lt @t2 @t1) @t4))) % 0.44/0.65 (assume @p7 (forall @t6 (= (tptp.geq @t2 @t1) (tptp.leq @t1 @t2)))) % 0.44/0.65 (assume @p8 (forall @t6 (=> @t4 @t10))) % 0.44/0.65 (assume @p9 (forall @t6 (=> (and @t10 (not @t3)) @t4))) % 0.44/0.65 (assume @p10 (forall @t6 (= (tptp.leq @t2 (tptp.pred @t1)) @t4))) % 0.44/0.65 (assume @p11 (forall @t9 (tptp.gt @t11 @t2))) % 0.44/0.65 (assume @p12 (forall @t6 (=> @t10 (tptp.leq @t2 @t12)))) % 0.44/0.65 (assume @p13 (forall @t6 (= @t10 (tptp.gt @t12 @t2)))) % 0.44/0.65 (assume @p14 (forall @t16 (=> @t15 (tptp.leq @t14 @t2)))) % 0.44/0.65 (assume @p15 (forall @t16 (=> @t15 (tptp.leq tptp.n0 @t14)))) % 0.44/0.65 (assume @p16 (forall (@list @t18 @t20 @t19 @t17) (=> (and (tptp.leq @t20 @t18) @t21) (= (tptp.a_select2 (tptp.tptp_const_array1 (tptp.dim @t20 @t19) @t17) @t18) @t17)))) % 0.44/0.65 (assume @p17 (forall (@list @t18 @t26 @t25 @t22 @t24 @t23 @t17) (=> (and (tptp.leq @t26 @t18) (tptp.leq @t18 @t25) (tptp.leq @t24 @t22) (tptp.leq @t22 @t23)) (= (tptp.a_select3 (tptp.tptp_const_array2 (tptp.dim @t26 @t25) (tptp.dim @t24 @t23) @t17) @t18 @t22) @t17)))) % 0.44/0.65 (assume @p18 (forall @t37 (=> @t36 (forall @t35 (=> @t34 (= (tptp.a_select3 @t28 @t18 @t22) (tptp.a_select3 @t28 @t22 @t18))))))) % 0.44/0.65 (assume @p19 (forall @t37 (=> @t36 (forall @t35 (=> @t34 (= (tptp.a_select3 @t38 @t18 @t22) (tptp.a_select3 @t38 @t22 @t18))))))) % 0.44/0.65 (assume @p20 (forall @t37 (=> @t36 (forall (@list @t18 @t22 @t40 @t39) (=> (and @t33 @t32 @t31 @t30 (tptp.leq tptp.n0 @t40) (tptp.leq @t40 @t29)) (= (tptp.a_select3 @t41 @t18 @t22) (tptp.a_select3 @t41 @t22 @t18))))))) % 0.44/0.65 (assume @p21 (forall @t47 (=> @t46 (forall @t35 (=> @t34 (= (tptp.a_select3 @t43 @t18 @t22) (tptp.a_select3 @t43 @t22 @t18))))))) % 0.44/0.65 (assume @p22 (forall @t47 (=> @t46 (forall @t35 (=> @t34 (= (tptp.a_select3 @t48 @t18 @t22) (tptp.a_select3 @t48 @t22 @t18))))))) % 0.44/0.65 (assume @p23 (forall @t47 (=> @t45 @t50))) % 0.44/0.65 (assume @p24 (forall (@list @t27 @t42 @t29 @t51) (=> (forall @t35 (=> @t52 @t44)) @t50))) % 0.44/0.65 (assume @p25 (forall (@list @t27 @t42 @t13 @t55 @t53 @t54 @t29 @t51) (=> (and (forall @t35 (=> @t52 (= (tptp.a_select3 @t55 @t18 @t22) (tptp.a_select3 @t55 @t22 @t18)))) @t36 (forall @t35 (=> @t34 (= (tptp.a_select3 @t54 @t18 @t22) (tptp.a_select3 @t54 @t22 @t18))))) (forall @t35 (=> @t34 (= (tptp.a_select3 @t56 @t18 @t22) (tptp.a_select3 @t56 @t22 @t18))))))) % 0.44/0.65 (assume @p26 (forall @t59 (= @t58 tptp.n0))) % 0.44/0.65 (assume @p27 (forall @t59 (= tptp.tptp_float_0_0 @t58))) % 0.44/0.65 (assume @p28 (= (tptp.succ tptp.tptp_minus_1) tptp.n0)) % 0.44/0.65 (assume @p29 (forall @t9 (= (tptp.plus @t2 tptp.n1) @t11))) % 0.44/0.65 (assume @p30 (forall @t9 (= (tptp.plus tptp.n1 @t2) @t11))) % 0.44/0.65 (assume @p31 (forall @t9 (= (tptp.plus @t2 tptp.n2) @t60))) % 0.44/0.65 (assume @p32 (forall @t9 (= (tptp.plus tptp.n2 @t2) @t60))) % 0.44/0.65 (assume @p33 (forall @t9 (= (tptp.plus @t2 tptp.n3) @t61))) % 0.44/0.65 (assume @p34 (forall @t9 (= (tptp.plus tptp.n3 @t2) @t61))) % 0.44/0.65 (assume @p35 (forall @t9 (= (tptp.plus @t2 tptp.n4) @t62))) % 0.44/0.65 (assume @p36 (forall @t9 (= (tptp.plus tptp.n4 @t2) @t62))) % 0.44/0.65 (assume @p37 (forall @t9 (= (tptp.plus @t2 tptp.n5) @t63))) % 0.44/0.65 (assume @p38 (forall @t9 (= (tptp.plus tptp.n5 @t2) @t63))) % 0.44/0.65 (assume @p39 (forall @t9 (= (tptp.minus @t2 tptp.n1) @t64))) % 0.44/0.65 (assume @p40 (forall @t9 (= (tptp.pred @t11) @t2))) % 0.44/0.65 (assume @p41 (forall @t9 (= (tptp.succ @t64) @t2))) % 0.44/0.65 (assume @p42 (forall @t6 (= (tptp.leq @t11 @t12) @t10))) % 0.44/0.65 (assume @p43 @t66) % 0.44/0.65 (assume @p44 (forall @t6 (=> (tptp.leq (tptp.minus @t2 @t1) @t2) (tptp.leq tptp.n0 @t1)))) % 0.44/0.65 (assume @p45 (forall (@list @t2 @t19 @t67 @t39) (= (tptp.a_select3 @t68 @t19 @t67) @t39))) % 0.44/0.65 (assume @p46 (forall (@list @t18 @t22 @t19 @t67 @t2 @t39 @t69) (=> (and @t70 (= @t22 @t67) (= (tptp.a_select3 @t2 @t19 @t67) @t39)) (= (tptp.a_select3 (tptp.tptp_update3 @t2 @t18 @t22 @t69) @t19 @t67) @t39)))) % 0.44/0.65 (assume @p47 (forall (@list @t18 @t22 @t19 @t67 @t2 @t39) (=> (and (forall (@list @t72 @t71) (=> (and @t74 (tptp.leq tptp.n0 @t71) @t73 (tptp.leq @t71 @t67)) (= (tptp.a_select3 @t2 @t72 @t71) @t39))) @t33 @t21 @t31 (tptp.leq @t22 @t67)) (= (tptp.a_select3 @t68 @t18 @t22) @t39)))) % 0.44/0.65 (assume @p48 (forall (@list @t2 @t19 @t39) (= (tptp.a_select2 @t75 @t19) @t39))) % 0.44/0.65 (assume @p49 (forall (@list @t18 @t19 @t2 @t39 @t69) (=> (and @t70 (= (tptp.a_select2 @t2 @t19) @t39)) (= (tptp.a_select2 (tptp.tptp_update2 @t2 @t18 @t69) @t19) @t39)))) % 0.44/0.65 (assume @p50 (forall (@list @t18 @t19 @t2 @t39) (=> (and (forall (@list @t72) (=> (and @t74 @t73) (= (tptp.a_select2 @t2 @t72) @t39))) @t33 @t21) (= (tptp.a_select2 @t75 @t18) @t39)))) % 0.44/0.65 (assume @p51 tptp.true) % 0.44/0.65 (assume @p52 (not (= tptp.def tptp.use))) % 0.44/0.65 (assume @p53 @t133) % 0.44/0.65 (assume @p54 (tptp.gt tptp.n5 tptp.n4)) % 0.44/0.65 (assume @p55 (tptp.gt tptp.n135299 tptp.n4)) % 0.44/0.65 (assume @p56 (tptp.gt tptp.n135299 tptp.n5)) % 0.44/0.65 (assume @p57 (tptp.gt tptp.n4 tptp.tptp_minus_1)) % 0.44/0.65 (assume @p58 (tptp.gt tptp.n5 tptp.tptp_minus_1)) % 0.44/0.65 (assume @p59 (tptp.gt tptp.n135299 tptp.tptp_minus_1)) % 0.44/0.65 (assume @p60 (tptp.gt tptp.n0 tptp.tptp_minus_1)) % 0.44/0.65 (assume @p61 (tptp.gt tptp.n1 tptp.tptp_minus_1)) % 0.44/0.65 (assume @p62 (tptp.gt tptp.n2 tptp.tptp_minus_1)) % 0.44/0.65 (assume @p63 (tptp.gt tptp.n3 tptp.tptp_minus_1)) % 0.44/0.65 (assume @p64 (tptp.gt tptp.n4 tptp.n0)) % 0.44/0.65 (assume @p65 (tptp.gt tptp.n5 tptp.n0)) % 0.44/0.65 (assume @p66 (tptp.gt tptp.n135299 tptp.n0)) % 0.44/0.65 (assume @p67 (tptp.gt tptp.n1 tptp.n0)) % 0.44/0.65 (assume @p68 (tptp.gt tptp.n2 tptp.n0)) % 0.44/0.65 (assume @p69 (tptp.gt tptp.n3 tptp.n0)) % 0.44/0.65 (assume @p70 (tptp.gt tptp.n4 tptp.n1)) % 0.44/0.65 (assume @p71 (tptp.gt tptp.n5 tptp.n1)) % 0.44/0.65 (assume @p72 (tptp.gt tptp.n135299 tptp.n1)) % 0.44/0.65 (assume @p73 (tptp.gt tptp.n2 tptp.n1)) % 0.44/0.65 (assume @p74 (tptp.gt tptp.n3 tptp.n1)) % 0.44/0.65 (assume @p75 (tptp.gt tptp.n4 tptp.n2)) % 0.44/0.65 (assume @p76 (tptp.gt tptp.n5 tptp.n2)) % 0.44/0.65 (assume @p77 (tptp.gt tptp.n135299 tptp.n2)) % 0.44/0.65 (assume @p78 (tptp.gt tptp.n3 tptp.n2)) % 0.44/0.65 (assume @p79 (tptp.gt tptp.n4 tptp.n3)) % 0.44/0.65 (assume @p80 (tptp.gt tptp.n5 tptp.n3)) % 0.44/0.65 (assume @p81 (tptp.gt tptp.n135299 tptp.n3)) % 0.44/0.65 (assume @p82 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n4)) (or @t138 @t137 @t136 @t135 @t134)))) % 0.44/0.65 (assume @p83 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n5)) (or @t138 @t137 @t136 @t135 @t134 (= @t2 tptp.n5))))) % 0.44/0.65 (assume @p84 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n0)) @t138))) % 0.44/0.65 (assume @p85 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n1)) (or @t138 @t137)))) % 0.44/0.65 (assume @p86 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n2)) (or @t138 @t137 @t136)))) % 0.44/0.65 (assume @p87 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n3)) (or @t138 @t137 @t136 @t135)))) % 0.44/0.65 (assume @p88 (= @t142 tptp.n4)) % 0.44/0.65 (assume @p89 (= (tptp.succ @t142) tptp.n5)) % 0.44/0.65 (assume @p90 (= @t139 tptp.n1)) % 0.44/0.65 (assume @p91 (= @t140 tptp.n2)) % 0.44/0.65 (assume @p92 (= @t141 tptp.n3)) % 0.44/0.65 (assume @p93 true) % 0.44/0.65 (step @p94 :rule evaluate :args ((= true false))) % 0.44/0.65 (step @p95 :rule bool-impl-elim :args (@t65 @t4)) % 0.44/0.65 (step @p96 :rule cong :premises (@p95) :args (@t66)) % 0.44/0.65 (step @p97 :rule eq_resolve :premises (@p43 @p96)) % 0.44/0.65 (step @p98 :rule instantiate :premises (@p97) :args ((@list tptp.n0 tptp.loopcounter))) % 0.44/0.65 (step @p99 :rule aci_norm :args ((= (or (or @t145 @t144) @t143) @t146))) % 0.44/0.65 (step @p100 :rule refl :args (@t143)) % 0.44/0.65 (step @p101 :rule bool-and-de-morgan :args (@t79 @t78 true)) % 0.44/0.65 (step @p102 :rule nary_cong :premises (@p101 @p100) :args ((or (not @t80) @t143))) % 0.44/0.65 (step @p103 :rule trans :premises (@p102 @p99)) % 0.44/0.65 (step @p104 :rule bool-impl-elim :args (@t80 @t143)) % 0.44/0.65 (step @p105 :rule trans :premises (@p104 @p103)) % 0.44/0.65 (step @p106 :rule cong :premises (@p105) :args ((forall @t82 (=> @t80 @t143)))) % 0.44/0.65 (step @p107 :rule eq-symm :args (@t77 tptp.init)) % 0.44/0.65 (step @p108 :rule refl :args (@t80)) % 0.44/0.65 (step @p109 :rule cong :premises (@p108 @p107) :args (@t81)) % 0.44/0.65 (step @p110 :rule cong :premises (@p109) :args (@t83)) % 0.44/0.65 (step @p111 :rule trans :premises (@p110 @p106)) % 0.44/0.65 (step @p112 :rule aci_norm :args ((= (or (or @t149 @t148) @t147) (or @t149 @t148 @t147)))) % 0.44/0.65 (step @p113 :rule refl :args (@t147)) % 0.44/0.65 (step @p114 :rule bool-and-de-morgan :args (@t86 @t85 true)) % 0.44/0.65 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((or (not @t87) @t147))) % 0.44/0.65 (step @p116 :rule trans :premises (@p115 @p112)) % 0.44/0.65 (step @p117 :rule bool-impl-elim :args (@t87 @t147)) % 0.44/0.65 (step @p118 :rule trans :premises (@p117 @p116)) % 0.44/0.65 (step @p119 :rule cong :premises (@p118) :args ((forall @t89 (=> @t87 @t147)))) % 0.44/0.65 (step @p120 :rule eq-symm :args (@t84 tptp.init)) % 0.44/0.65 (step @p121 :rule refl :args (@t87)) % 0.44/0.65 (step @p122 :rule cong :premises (@p121 @p120) :args (@t88)) % 0.44/0.65 (step @p123 :rule cong :premises (@p122) :args (@t90)) % 0.44/0.65 (step @p124 :rule trans :premises (@p123 @p119)) % 0.44/0.65 (step @p125 :rule refl :args (@t91)) % 0.44/0.65 (step @p126 :rule cong :premises (@p125 @p124) :args (@t92)) % 0.44/0.65 (step @p127 :rule aci_norm :args ((= (or (or @t152 @t151) @t150) @t153))) % 0.44/0.65 (step @p128 :rule refl :args (@t150)) % 0.44/0.65 (step @p129 :rule bool-and-de-morgan :args (@t95 @t94 true)) % 0.44/0.65 (step @p130 :rule nary_cong :premises (@p129 @p128) :args ((or (not @t96) @t150))) % 0.44/0.65 (step @p131 :rule trans :premises (@p130 @p127)) % 0.44/0.65 (step @p132 :rule bool-impl-elim :args (@t96 @t150)) % 0.44/0.65 (step @p133 :rule trans :premises (@p132 @p131)) % 0.44/0.65 (step @p134 :rule cong :premises (@p133) :args ((forall @t98 (=> @t96 @t150)))) % 0.44/0.65 (step @p135 :rule eq-symm :args (@t93 tptp.init)) % 0.44/0.65 (step @p136 :rule refl :args (@t96)) % 0.44/0.65 (step @p137 :rule cong :premises (@p136 @p135) :args (@t97)) % 0.44/0.65 (step @p138 :rule cong :premises (@p137) :args (@t99)) % 0.44/0.65 (step @p139 :rule trans :premises (@p138 @p134)) % 0.44/0.65 (step @p140 :rule cong :premises (@p125 @p139) :args (@t100)) % 0.44/0.65 (step @p141 :rule aci_norm :args ((= (or (or @t156 @t155) @t154) (or @t156 @t155 @t154)))) % 0.44/0.65 (step @p142 :rule refl :args (@t154)) % 0.44/0.65 (step @p143 :rule bool-and-de-morgan :args (@t103 @t102 true)) % 0.44/0.65 (step @p144 :rule nary_cong :premises (@p143 @p142) :args ((or (not @t104) @t154))) % 0.44/0.65 (step @p145 :rule trans :premises (@p144 @p141)) % 0.44/0.65 (step @p146 :rule bool-impl-elim :args (@t104 @t154)) % 0.44/0.65 (step @p147 :rule trans :premises (@p146 @p145)) % 0.44/0.65 (step @p148 :rule cong :premises (@p147) :args ((forall @t106 (=> @t104 @t154)))) % 0.44/0.65 (step @p149 :rule eq-symm :args (@t101 tptp.init)) % 0.44/0.65 (step @p150 :rule refl :args (@t104)) % 0.44/0.65 (step @p151 :rule cong :premises (@p150 @p149) :args (@t105)) % 0.44/0.65 (step @p152 :rule cong :premises (@p151) :args (@t107)) % 0.44/0.65 (step @p153 :rule trans :premises (@p152 @p148)) % 0.44/0.65 (step @p154 :rule cong :premises (@p125 @p153) :args (@t108)) % 0.44/0.65 (step @p155 :rule aci_norm :args ((= (or (or @t159 @t158) @t157) (or @t159 @t158 @t157)))) % 0.44/0.65 (step @p156 :rule refl :args (@t157)) % 0.44/0.65 (step @p157 :rule bool-and-de-morgan :args (@t111 @t110 true)) % 0.44/0.65 (step @p158 :rule nary_cong :premises (@p157 @p156) :args ((or (not @t112) @t157))) % 0.44/0.65 (step @p159 :rule trans :premises (@p158 @p155)) % 0.44/0.65 (step @p160 :rule bool-impl-elim :args (@t112 @t157)) % 0.44/0.65 (step @p161 :rule trans :premises (@p160 @p159)) % 0.44/0.65 (step @p162 :rule cong :premises (@p161) :args ((forall @t114 (=> @t112 @t157)))) % 0.44/0.65 (step @p163 :rule eq-symm :args (@t109 tptp.init)) % 0.44/0.65 (step @p164 :rule refl :args (@t112)) % 0.44/0.65 (step @p165 :rule cong :premises (@p164 @p163) :args (@t113)) % 0.44/0.65 (step @p166 :rule cong :premises (@p165) :args (@t115)) % 0.44/0.65 (step @p167 :rule trans :premises (@p166 @p162)) % 0.44/0.65 (step @p168 :rule aci_norm :args ((= @t167 (or @t165 @t164 @t163 @t162 @t161)))) % 0.44/0.65 (step @p169 :rule cong :premises (@p168) :args (@t168)) % 0.44/0.65 (step @p170 :rule quant-merge-prenex :args ((= (forall @t127 @t170) @t168))) % 0.44/0.65 (step @p171 :rule alpha_equiv :args (@t171 (@list @t160) (@list @t42))) % 0.44/0.65 (step @p172 :rule refl :args (@t164)) % 0.44/0.65 (step @p173 :rule refl :args (@t165)) % 0.44/0.65 (step @p174 :rule nary_cong :premises (@p173 @p172 @p171) :args (@t172)) % 0.44/0.65 (step @p175 :rule quant-miniscope-or :args ((= @t170 @t172))) % 0.44/0.65 (step @p176 :rule trans :premises (@p175 @p174)) % 0.44/0.65 (step @p177 :rule symm :premises (@p176)) % 0.44/0.65 (step @p178 :rule cong :premises (@p177) :args ((forall @t127 @t178))) % 0.44/0.65 (step @p179 :rule trans :premises (@p178 @p170)) % 0.44/0.65 (step @p180 :rule trans :premises (@p179 @p169)) % 0.44/0.65 (step @p181 :rule aci_norm :args ((= (or (or @t165 @t164) @t177) @t178))) % 0.44/0.65 (step @p182 :rule refl :args (@t177)) % 0.44/0.65 (step @p183 :rule bool-and-de-morgan :args (@t124 @t123 true)) % 0.44/0.65 (step @p184 :rule nary_cong :premises (@p183 @p182) :args ((or (not @t125) @t177))) % 0.44/0.65 (step @p185 :rule trans :premises (@p184 @p181)) % 0.44/0.65 (step @p186 :rule bool-impl-elim :args (@t125 @t177)) % 0.44/0.65 (step @p187 :rule trans :premises (@p186 @p185)) % 0.44/0.65 (step @p188 :rule cong :premises (@p187) :args ((forall @t127 (=> @t125 @t177)))) % 0.44/0.65 (step @p189 :rule trans :premises (@p188 @p180)) % 0.44/0.65 (step @p190 :rule aci_norm :args ((= (or (or @t175 @t174) @t173) @t176))) % 0.44/0.65 (step @p191 :rule refl :args (@t173)) % 0.44/0.65 (step @p192 :rule bool-and-de-morgan :args (@t118 @t117 true)) % 0.44/0.65 (step @p193 :rule nary_cong :premises (@p192 @p191) :args ((or (not @t119) @t173))) % 0.44/0.65 (step @p194 :rule trans :premises (@p193 @p190)) % 0.44/0.65 (step @p195 :rule bool-impl-elim :args (@t119 @t173)) % 0.44/0.65 (step @p196 :rule trans :premises (@p195 @p194)) % 0.44/0.65 (step @p197 :rule cong :premises (@p196) :args ((forall @t121 (=> @t119 @t173)))) % 0.44/0.65 (step @p198 :rule eq-symm :args (@t116 tptp.init)) % 0.44/0.65 (step @p199 :rule refl :args (@t119)) % 0.44/0.65 (step @p200 :rule cong :premises (@p199 @p198) :args (@t120)) % 0.44/0.65 (step @p201 :rule cong :premises (@p200) :args (@t122)) % 0.44/0.65 (step @p202 :rule trans :premises (@p201 @p197)) % 0.44/0.65 (step @p203 :rule refl :args (@t125)) % 0.44/0.65 (step @p204 :rule cong :premises (@p203 @p202) :args (@t126)) % 0.44/0.65 (step @p205 :rule cong :premises (@p204) :args (@t128)) % 0.44/0.65 (step @p206 :rule trans :premises (@p205 @p189)) % 0.44/0.65 (step @p207 :rule refl :args (@t129)) % 0.44/0.65 (step @p208 :rule refl :args (@t130)) % 0.44/0.65 (step @p209 :rule nary_cong :premises (@p208 @p207 @p206 @p167 @p154 @p140 @p126) :args (@t131)) % 0.44/0.65 (step @p210 :rule cong :premises (@p209 @p111) :args (@t132)) % 0.44/0.65 (step @p211 :rule cong :premises (@p210) :args (@t133)) % 0.44/0.65 (step @p212 :rule eq_resolve :premises (@p53 @p211)) % 0.44/0.65 (step @p213 :rule not_implies_elim2 :premises (@p212)) % 0.44/0.65 (step @p214 :rule alpha_equiv :args (@t179 (@list @t53) (@list @t76))) % 0.44/0.65 (step @p215 :rule equiv_elim1 :premises (@p214)) % 0.44/0.65 (step @p216 :rule reordering :premises (@p215) :args ((or @t181 @t180))) % 0.44/0.65 (step @p217 :rule chain_m_resolution :premises (@p216 @p213) :args (@t180 @t182 (@list @t181))) % 0.44/0.65 (step @p218 :rule not_implies_elim1 :premises (@p212)) % 0.44/0.65 (step @p219 :rule and_elim :premises (@p218) :args (5)) % 0.44/0.65 (step @p220 :rule implies_elim :premises (@p219)) % 0.44/0.65 (step @p221 :rule reordering :premises (@p220) :args ((or @t179 @t183))) % 0.44/0.65 (step @p222 :rule chain_m_resolution :premises (@p221 @p217) :args (@t183 @t182 (@list @t179))) % 0.44/0.65 (step @p223 :rule cnf_or_pos :args (@t185)) % 0.44/0.65 (step @p224 :rule reordering :premises (@p223) :args ((or @t91 @t184 (not @t185)))) % 0.44/0.65 (step @p225 :rule chain_m_resolution :premises (@p224 @p222 @p98) :args (@t184 (@list true false) (@list @t91 @t185))) % 0.44/0.65 (step @p226 :rule false_intro :premises (@p225)) % 0.44/0.65 (step @p227 :rule refl :args (tptp.loopcounter)) % 0.44/0.65 (step @p228 :rule symm :premises (@p90)) % 0.44/0.65 (step @p229 :rule cong :premises (@p228 @p227) :args (@t129)) % 0.44/0.65 (step @p230 :rule and_elim :premises (@p218) :args (1)) % 0.44/0.65 (step @p231 :rule true_intro :premises (@p230)) % 0.44/0.65 (step @p232 :rule symm :premises (@p231)) % 0.44/0.65 (step @p233 :rule trans :premises (@p232 @p229 @p226)) % 0.44/0.65 (step @p234 false :rule eq_resolve :premises (@p233 @p94)) % 0.44/0.65 ) % 0.44/0.65 % SZS output end Proof % 0.44/0.65 % cvc5 exiting %------------------------------------------------------------------------------