%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV184+1 : TPTP v9.2.1. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n003.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 0.36s 0.62s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV184+1 : TPTP v9.2.1. Bugfixed v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n003.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 19:58:29 EDT 2026 % 0.18/0.34 % CPUTime : % 0.28/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.62 % SZS status Theorem % 0.36/0.62 % SZS output start Proof % 0.36/0.62 ( % 0.36/0.62 (declare-sort $$unsorted 0) % 0.36/0.62 (declare-const tptp.rho_init $$unsorted) % 0.36/0.62 (declare-const tptp.rhoold_init $$unsorted) % 0.36/0.62 (declare-const tptp.loopcounter $$unsorted) % 0.36/0.62 (declare-const tptp.sigmaold_init $$unsorted) % 0.36/0.62 (declare-const tptp.init $$unsorted) % 0.36/0.62 (declare-const tptp.def $$unsorted) % 0.36/0.62 (declare-const tptp.use $$unsorted) % 0.36/0.62 (declare-const tptp.true Bool) % 0.36/0.62 (declare-const tptp.tptp_update2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.muold_init $$unsorted) % 0.36/0.62 (declare-const tptp.a_select3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.uniform_int_rnd (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.q_init $$unsorted) % 0.36/0.62 (declare-const tptp.n3 $$unsorted) % 0.36/0.62 (declare-const tptp.tptp_const_array1 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.pred (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.tptp_minus_1 $$unsorted) % 0.36/0.62 (declare-const tptp.n0 $$unsorted) % 0.36/0.62 (declare-const tptp.tptp_msub (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.n1 $$unsorted) % 0.36/0.62 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.n5 $$unsorted) % 0.36/0.62 (declare-const tptp.n135299 $$unsorted) % 0.36/0.62 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.tptp_update3 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.minus (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.center_init $$unsorted) % 0.36/0.62 (declare-const tptp.tptp_const_array2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.trans (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.a_select2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.inv (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.dim (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.plus (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.tptp_madd (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.sum (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.tptp_mmul (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.tptp_float_0_0 $$unsorted) % 0.36/0.62 (declare-const tptp.n4 $$unsorted) % 0.36/0.62 (declare-const tptp.n2 $$unsorted) % 0.36/0.62 (define @t1 () (@var "Y" $$unsorted)) % 0.36/0.62 (define @t2 () (@var "X" $$unsorted)) % 0.36/0.62 (define @t3 () (= @t2 @t1)) % 0.36/0.62 (define @t4 () (tptp.gt @t1 @t2)) % 0.36/0.62 (define @t5 () (tptp.gt @t2 @t1)) % 0.36/0.62 (define @t6 () (@list @t2 @t1)) % 0.36/0.62 (define @t7 () (@var "Z" $$unsorted)) % 0.36/0.62 (define @t8 () (@list @t2 @t1 @t7)) % 0.36/0.62 (define @t9 () (@list @t2)) % 0.36/0.62 (define @t10 () (tptp.leq @t2 @t1)) % 0.36/0.62 (define @t11 () (tptp.succ @t2)) % 0.36/0.62 (define @t12 () (tptp.succ @t1)) % 0.36/0.62 (define @t13 () (@var "C" $$unsorted)) % 0.36/0.62 (define @t14 () (tptp.uniform_int_rnd @t13 @t2)) % 0.36/0.62 (define @t15 () (tptp.leq tptp.n0 @t2)) % 0.36/0.62 (define @t16 () (@list @t2 @t13)) % 0.36/0.62 (define @t17 () (@var "Val" $$unsorted)) % 0.36/0.62 (define @t18 () (@var "I" $$unsorted)) % 0.36/0.62 (define @t19 () (@var "U" $$unsorted)) % 0.36/0.62 (define @t20 () (@var "L" $$unsorted)) % 0.36/0.62 (define @t21 () (tptp.leq @t18 @t19)) % 0.36/0.62 (define @t22 () (@var "J" $$unsorted)) % 0.36/0.62 (define @t23 () (@var "U2" $$unsorted)) % 0.36/0.62 (define @t24 () (@var "L2" $$unsorted)) % 0.36/0.62 (define @t25 () (@var "U1" $$unsorted)) % 0.36/0.62 (define @t26 () (@var "L1" $$unsorted)) % 0.36/0.62 (define @t27 () (@var "A" $$unsorted)) % 0.36/0.62 (define @t28 () (tptp.trans @t27)) % 0.36/0.62 (define @t29 () (@var "N" $$unsorted)) % 0.36/0.62 (define @t30 () (tptp.leq @t22 @t29)) % 0.36/0.62 (define @t31 () (tptp.leq tptp.n0 @t22)) % 0.36/0.62 (define @t32 () (tptp.leq @t18 @t29)) % 0.36/0.62 (define @t33 () (tptp.leq tptp.n0 @t18)) % 0.36/0.62 (define @t34 () (and @t33 @t32 @t31 @t30)) % 0.36/0.62 (define @t35 () (@list @t18 @t22)) % 0.36/0.62 (define @t36 () (forall @t35 (=> @t34 (= (tptp.a_select3 @t27 @t18 @t22) (tptp.a_select3 @t27 @t22 @t18))))) % 0.36/0.62 (define @t37 () (@list @t27 @t29)) % 0.36/0.62 (define @t38 () (tptp.inv @t27)) % 0.36/0.62 (define @t39 () (@var "VAL" $$unsorted)) % 0.36/0.62 (define @t40 () (@var "K" $$unsorted)) % 0.36/0.62 (define @t41 () (tptp.tptp_update3 @t27 @t40 @t40 @t39)) % 0.36/0.62 (define @t42 () (@var "B" $$unsorted)) % 0.36/0.62 (define @t43 () (tptp.tptp_madd @t27 @t42)) % 0.36/0.62 (define @t44 () (= (tptp.a_select3 @t42 @t18 @t22) (tptp.a_select3 @t42 @t22 @t18))) % 0.36/0.62 (define @t45 () (forall @t35 (=> @t34 @t44))) % 0.36/0.62 (define @t46 () (and @t36 @t45)) % 0.36/0.62 (define @t47 () (@list @t27 @t42 @t29)) % 0.36/0.62 (define @t48 () (tptp.tptp_msub @t27 @t42)) % 0.36/0.62 (define @t49 () (tptp.tptp_mmul @t27 (tptp.tptp_mmul @t42 @t28))) % 0.36/0.62 (define @t50 () (forall @t35 (=> @t34 (= (tptp.a_select3 @t49 @t18 @t22) (tptp.a_select3 @t49 @t22 @t18))))) % 0.36/0.62 (define @t51 () (@var "M" $$unsorted)) % 0.36/0.62 (define @t52 () (and @t33 (tptp.leq @t18 @t51) @t31 (tptp.leq @t22 @t51))) % 0.36/0.62 (define @t53 () (@var "E" $$unsorted)) % 0.36/0.62 (define @t54 () (@var "F" $$unsorted)) % 0.36/0.62 (define @t55 () (@var "D" $$unsorted)) % 0.36/0.62 (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))))) % 0.36/0.62 (define @t57 () (@var "Body" $$unsorted)) % 0.36/0.62 (define @t58 () (tptp.sum tptp.n0 tptp.tptp_minus_1 @t57)) % 0.36/0.62 (define @t59 () (@list @t57)) % 0.36/0.62 (define @t60 () (tptp.succ @t11)) % 0.36/0.62 (define @t61 () (tptp.succ @t60)) % 0.36/0.62 (define @t62 () (tptp.succ @t61)) % 0.36/0.62 (define @t63 () (tptp.succ @t62)) % 0.36/0.62 (define @t64 () (tptp.pred @t2)) % 0.36/0.62 (define @t65 () (@var "V" $$unsorted)) % 0.36/0.62 (define @t66 () (tptp.tptp_update3 @t2 @t19 @t65 @t39)) % 0.36/0.62 (define @t67 () (@var "VAL2" $$unsorted)) % 0.36/0.62 (define @t68 () (not (= @t18 @t19))) % 0.36/0.62 (define @t69 () (@var "J0" $$unsorted)) % 0.36/0.62 (define @t70 () (@var "I0" $$unsorted)) % 0.36/0.62 (define @t71 () (tptp.leq @t70 @t19)) % 0.36/0.62 (define @t72 () (tptp.leq tptp.n0 @t70)) % 0.36/0.62 (define @t73 () (tptp.tptp_update2 @t2 @t19 @t39)) % 0.36/0.62 (define @t74 () (@var "H" $$unsorted)) % 0.36/0.62 (define @t75 () (tptp.a_select2 tptp.sigmaold_init @t74)) % 0.36/0.62 (define @t76 () (tptp.leq @t74 tptp.n4)) % 0.36/0.62 (define @t77 () (tptp.leq tptp.n0 @t74)) % 0.36/0.62 (define @t78 () (and @t77 @t76)) % 0.36/0.62 (define @t79 () (=> @t78 (= @t75 tptp.init))) % 0.36/0.62 (define @t80 () (@list @t74)) % 0.36/0.62 (define @t81 () (forall @t80 @t79)) % 0.36/0.62 (define @t82 () (@var "G" $$unsorted)) % 0.36/0.62 (define @t83 () (tptp.a_select2 tptp.sigmaold_init @t82)) % 0.36/0.62 (define @t84 () (tptp.leq @t82 tptp.n4)) % 0.36/0.62 (define @t85 () (tptp.leq tptp.n0 @t82)) % 0.36/0.62 (define @t86 () (and @t85 @t84)) % 0.36/0.62 (define @t87 () (=> @t86 (= @t83 tptp.init))) % 0.36/0.62 (define @t88 () (@list @t82)) % 0.36/0.62 (define @t89 () (forall @t88 @t87)) % 0.36/0.62 (define @t90 () (tptp.gt tptp.loopcounter tptp.n1)) % 0.36/0.62 (define @t91 () (=> @t90 @t89)) % 0.36/0.62 (define @t92 () (tptp.a_select2 tptp.rhoold_init @t54)) % 0.36/0.62 (define @t93 () (tptp.leq @t54 tptp.n4)) % 0.36/0.62 (define @t94 () (tptp.leq tptp.n0 @t54)) % 0.36/0.62 (define @t95 () (and @t94 @t93)) % 0.36/0.62 (define @t96 () (=> @t95 (= @t92 tptp.init))) % 0.36/0.62 (define @t97 () (@list @t54)) % 0.36/0.62 (define @t98 () (forall @t97 @t96)) % 0.36/0.62 (define @t99 () (=> @t90 @t98)) % 0.36/0.62 (define @t100 () (tptp.a_select2 tptp.muold_init @t53)) % 0.36/0.62 (define @t101 () (tptp.leq @t53 tptp.n4)) % 0.36/0.62 (define @t102 () (tptp.leq tptp.n0 @t53)) % 0.36/0.62 (define @t103 () (and @t102 @t101)) % 0.36/0.62 (define @t104 () (=> @t103 (= @t100 tptp.init))) % 0.36/0.62 (define @t105 () (@list @t53)) % 0.36/0.62 (define @t106 () (forall @t105 @t104)) % 0.36/0.62 (define @t107 () (=> @t90 @t106)) % 0.36/0.62 (define @t108 () (tptp.a_select3 tptp.center_init @t55 tptp.n0)) % 0.36/0.62 (define @t109 () (tptp.leq @t55 tptp.n4)) % 0.36/0.62 (define @t110 () (tptp.leq tptp.n0 @t55)) % 0.36/0.62 (define @t111 () (and @t110 @t109)) % 0.36/0.62 (define @t112 () (=> @t111 (= @t108 tptp.init))) % 0.36/0.62 (define @t113 () (@list @t55)) % 0.36/0.62 (define @t114 () (forall @t113 @t112)) % 0.36/0.62 (define @t115 () (tptp.a_select2 tptp.rho_init @t13)) % 0.36/0.62 (define @t116 () (tptp.leq @t13 tptp.n4)) % 0.36/0.62 (define @t117 () (tptp.leq tptp.n0 @t13)) % 0.36/0.62 (define @t118 () (and @t117 @t116)) % 0.36/0.62 (define @t119 () (=> @t118 (= @t115 tptp.init))) % 0.36/0.62 (define @t120 () (@list @t13)) % 0.36/0.62 (define @t121 () (forall @t120 @t119)) % 0.36/0.62 (define @t122 () (tptp.a_select3 tptp.q_init @t27 @t42)) % 0.36/0.62 (define @t123 () (tptp.leq @t42 tptp.n4)) % 0.36/0.62 (define @t124 () (tptp.leq tptp.n0 @t42)) % 0.36/0.62 (define @t125 () (and @t124 @t123)) % 0.36/0.62 (define @t126 () (=> @t125 (= @t122 tptp.init))) % 0.36/0.62 (define @t127 () (@list @t42)) % 0.36/0.62 (define @t128 () (forall @t127 @t126)) % 0.36/0.62 (define @t129 () (tptp.leq @t27 tptp.n135299)) % 0.36/0.62 (define @t130 () (tptp.leq tptp.n0 @t27)) % 0.36/0.62 (define @t131 () (and @t130 @t129)) % 0.36/0.62 (define @t132 () (=> @t131 @t128)) % 0.36/0.62 (define @t133 () (@list @t27)) % 0.36/0.62 (define @t134 () (forall @t133 @t132)) % 0.36/0.62 (define @t135 () (and @t90 @t134 @t121 @t114 @t107 @t99 @t91)) % 0.36/0.62 (define @t136 () (=> @t135 @t81)) % 0.36/0.62 (define @t137 () (not @t136)) % 0.36/0.62 (define @t138 () (= @t2 tptp.n4)) % 0.36/0.62 (define @t139 () (= @t2 tptp.n3)) % 0.36/0.62 (define @t140 () (= @t2 tptp.n2)) % 0.36/0.62 (define @t141 () (= @t2 tptp.n1)) % 0.36/0.62 (define @t142 () (= @t2 tptp.n0)) % 0.36/0.62 (define @t143 () (tptp.succ tptp.n0)) % 0.36/0.62 (define @t144 () (tptp.succ @t143)) % 0.36/0.62 (define @t145 () (tptp.succ @t144)) % 0.36/0.62 (define @t146 () (tptp.succ @t145)) % 0.36/0.62 (define @t147 () (= tptp.init @t75)) % 0.36/0.62 (define @t148 () (not @t76)) % 0.36/0.62 (define @t149 () (not @t77)) % 0.36/0.62 (define @t150 () (or @t149 @t148 @t147)) % 0.36/0.62 (define @t151 () (= tptp.init @t83)) % 0.36/0.62 (define @t152 () (not @t84)) % 0.36/0.62 (define @t153 () (not @t85)) % 0.36/0.62 (define @t154 () (or @t153 @t152 @t151)) % 0.36/0.62 (define @t155 () (= tptp.init @t92)) % 0.36/0.62 (define @t156 () (not @t93)) % 0.36/0.62 (define @t157 () (not @t94)) % 0.36/0.62 (define @t158 () (= tptp.init @t100)) % 0.36/0.62 (define @t159 () (not @t101)) % 0.36/0.62 (define @t160 () (not @t102)) % 0.36/0.62 (define @t161 () (= tptp.init @t108)) % 0.36/0.62 (define @t162 () (not @t109)) % 0.36/0.62 (define @t163 () (not @t110)) % 0.36/0.62 (define @t164 () (= tptp.init @t115)) % 0.36/0.62 (define @t165 () (not @t116)) % 0.36/0.62 (define @t166 () (not @t117)) % 0.36/0.62 (define @t167 () (@var "BOUND_VARIABLE_8430" $$unsorted)) % 0.36/0.62 (define @t168 () (= tptp.init (tptp.a_select3 tptp.q_init @t27 @t167))) % 0.36/0.62 (define @t169 () (not (tptp.leq @t167 tptp.n4))) % 0.36/0.62 (define @t170 () (not (tptp.leq tptp.n0 @t167))) % 0.36/0.62 (define @t171 () (not @t129)) % 0.36/0.62 (define @t172 () (not @t130)) % 0.36/0.62 (define @t173 () (or @t170 @t169 @t168)) % 0.36/0.62 (define @t174 () (or @t172 @t171 @t173)) % 0.36/0.62 (define @t175 () (forall (@list @t27 @t167) @t174)) % 0.36/0.62 (define @t176 () (@list @t167)) % 0.36/0.62 (define @t177 () (forall @t176 @t174)) % 0.36/0.62 (define @t178 () (forall @t176 @t173)) % 0.36/0.62 (define @t179 () (or @t172 @t171 @t178)) % 0.36/0.62 (define @t180 () (= tptp.init @t122)) % 0.36/0.62 (define @t181 () (not @t123)) % 0.36/0.62 (define @t182 () (not @t124)) % 0.36/0.62 (define @t183 () (or @t182 @t181 @t180)) % 0.36/0.62 (define @t184 () (forall @t127 @t183)) % 0.36/0.62 (define @t185 () (or @t172 @t171 @t184)) % 0.36/0.62 (define @t186 () (forall @t88 @t154)) % 0.36/0.62 (define @t187 () (@list false)) % 0.36/0.62 (define @t188 () (forall @t80 @t150)) % 0.36/0.62 (assume @p1 (forall @t6 (or @t5 @t4 @t3))) % 0.36/0.62 (assume @p2 (forall @t8 (=> (and @t5 (tptp.gt @t1 @t7)) (tptp.gt @t2 @t7)))) % 0.36/0.62 (assume @p3 (forall @t9 (not (tptp.gt @t2 @t2)))) % 0.36/0.62 (assume @p4 (forall @t9 (tptp.leq @t2 @t2))) % 0.36/0.62 (assume @p5 (forall @t8 (=> (and @t10 (tptp.leq @t1 @t7)) (tptp.leq @t2 @t7)))) % 0.36/0.62 (assume @p6 (forall @t6 (= (tptp.lt @t2 @t1) @t4))) % 0.36/0.62 (assume @p7 (forall @t6 (= (tptp.geq @t2 @t1) (tptp.leq @t1 @t2)))) % 0.36/0.62 (assume @p8 (forall @t6 (=> @t4 @t10))) % 0.36/0.62 (assume @p9 (forall @t6 (=> (and @t10 (not @t3)) @t4))) % 0.36/0.62 (assume @p10 (forall @t6 (= (tptp.leq @t2 (tptp.pred @t1)) @t4))) % 0.36/0.62 (assume @p11 (forall @t9 (tptp.gt @t11 @t2))) % 0.36/0.62 (assume @p12 (forall @t6 (=> @t10 (tptp.leq @t2 @t12)))) % 0.36/0.62 (assume @p13 (forall @t6 (= @t10 (tptp.gt @t12 @t2)))) % 0.36/0.62 (assume @p14 (forall @t16 (=> @t15 (tptp.leq @t14 @t2)))) % 0.36/0.62 (assume @p15 (forall @t16 (=> @t15 (tptp.leq tptp.n0 @t14)))) % 0.36/0.62 (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)))) % 0.36/0.62 (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)))) % 0.36/0.62 (assume @p18 (forall @t37 (=> @t36 (forall @t35 (=> @t34 (= (tptp.a_select3 @t28 @t18 @t22) (tptp.a_select3 @t28 @t22 @t18))))))) % 0.36/0.62 (assume @p19 (forall @t37 (=> @t36 (forall @t35 (=> @t34 (= (tptp.a_select3 @t38 @t18 @t22) (tptp.a_select3 @t38 @t22 @t18))))))) % 0.36/0.62 (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))))))) % 0.36/0.62 (assume @p21 (forall @t47 (=> @t46 (forall @t35 (=> @t34 (= (tptp.a_select3 @t43 @t18 @t22) (tptp.a_select3 @t43 @t22 @t18))))))) % 0.36/0.62 (assume @p22 (forall @t47 (=> @t46 (forall @t35 (=> @t34 (= (tptp.a_select3 @t48 @t18 @t22) (tptp.a_select3 @t48 @t22 @t18))))))) % 0.36/0.62 (assume @p23 (forall @t47 (=> @t45 @t50))) % 0.36/0.62 (assume @p24 (forall (@list @t27 @t42 @t29 @t51) (=> (forall @t35 (=> @t52 @t44)) @t50))) % 0.36/0.62 (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))))))) % 0.36/0.62 (assume @p26 (forall @t59 (= @t58 tptp.n0))) % 0.36/0.62 (assume @p27 (forall @t59 (= tptp.tptp_float_0_0 @t58))) % 0.36/0.62 (assume @p28 (= (tptp.succ tptp.tptp_minus_1) tptp.n0)) % 0.36/0.62 (assume @p29 (forall @t9 (= (tptp.plus @t2 tptp.n1) @t11))) % 0.36/0.62 (assume @p30 (forall @t9 (= (tptp.plus tptp.n1 @t2) @t11))) % 0.36/0.62 (assume @p31 (forall @t9 (= (tptp.plus @t2 tptp.n2) @t60))) % 0.36/0.62 (assume @p32 (forall @t9 (= (tptp.plus tptp.n2 @t2) @t60))) % 0.36/0.62 (assume @p33 (forall @t9 (= (tptp.plus @t2 tptp.n3) @t61))) % 0.36/0.62 (assume @p34 (forall @t9 (= (tptp.plus tptp.n3 @t2) @t61))) % 0.36/0.62 (assume @p35 (forall @t9 (= (tptp.plus @t2 tptp.n4) @t62))) % 0.36/0.62 (assume @p36 (forall @t9 (= (tptp.plus tptp.n4 @t2) @t62))) % 0.36/0.62 (assume @p37 (forall @t9 (= (tptp.plus @t2 tptp.n5) @t63))) % 0.36/0.62 (assume @p38 (forall @t9 (= (tptp.plus tptp.n5 @t2) @t63))) % 0.36/0.62 (assume @p39 (forall @t9 (= (tptp.minus @t2 tptp.n1) @t64))) % 0.36/0.62 (assume @p40 (forall @t9 (= (tptp.pred @t11) @t2))) % 0.36/0.62 (assume @p41 (forall @t9 (= (tptp.succ @t64) @t2))) % 0.36/0.62 (assume @p42 (forall @t6 (= (tptp.leq @t11 @t12) @t10))) % 0.36/0.62 (assume @p43 (forall @t6 (=> (tptp.leq @t11 @t1) @t4))) % 0.36/0.62 (assume @p44 (forall @t6 (=> (tptp.leq (tptp.minus @t2 @t1) @t2) (tptp.leq tptp.n0 @t1)))) % 0.36/0.62 (assume @p45 (forall (@list @t2 @t19 @t65 @t39) (= (tptp.a_select3 @t66 @t19 @t65) @t39))) % 0.36/0.62 (assume @p46 (forall (@list @t18 @t22 @t19 @t65 @t2 @t39 @t67) (=> (and @t68 (= @t22 @t65) (= (tptp.a_select3 @t2 @t19 @t65) @t39)) (= (tptp.a_select3 (tptp.tptp_update3 @t2 @t18 @t22 @t67) @t19 @t65) @t39)))) % 0.36/0.62 (assume @p47 (forall (@list @t18 @t22 @t19 @t65 @t2 @t39) (=> (and (forall (@list @t70 @t69) (=> (and @t72 (tptp.leq tptp.n0 @t69) @t71 (tptp.leq @t69 @t65)) (= (tptp.a_select3 @t2 @t70 @t69) @t39))) @t33 @t21 @t31 (tptp.leq @t22 @t65)) (= (tptp.a_select3 @t66 @t18 @t22) @t39)))) % 0.36/0.62 (assume @p48 (forall (@list @t2 @t19 @t39) (= (tptp.a_select2 @t73 @t19) @t39))) % 0.36/0.62 (assume @p49 (forall (@list @t18 @t19 @t2 @t39 @t67) (=> (and @t68 (= (tptp.a_select2 @t2 @t19) @t39)) (= (tptp.a_select2 (tptp.tptp_update2 @t2 @t18 @t67) @t19) @t39)))) % 0.36/0.62 (assume @p50 (forall (@list @t18 @t19 @t2 @t39) (=> (and (forall (@list @t70) (=> (and @t72 @t71) (= (tptp.a_select2 @t2 @t70) @t39))) @t33 @t21) (= (tptp.a_select2 @t73 @t18) @t39)))) % 0.36/0.62 (assume @p51 tptp.true) % 0.36/0.62 (assume @p52 (not (= tptp.def tptp.use))) % 0.36/0.62 (assume @p53 @t137) % 0.36/0.62 (assume @p54 (tptp.gt tptp.n5 tptp.n4)) % 0.36/0.62 (assume @p55 (tptp.gt tptp.n135299 tptp.n4)) % 0.36/0.62 (assume @p56 (tptp.gt tptp.n135299 tptp.n5)) % 0.36/0.62 (assume @p57 (tptp.gt tptp.n4 tptp.tptp_minus_1)) % 0.36/0.62 (assume @p58 (tptp.gt tptp.n5 tptp.tptp_minus_1)) % 0.36/0.62 (assume @p59 (tptp.gt tptp.n135299 tptp.tptp_minus_1)) % 0.36/0.62 (assume @p60 (tptp.gt tptp.n0 tptp.tptp_minus_1)) % 0.36/0.62 (assume @p61 (tptp.gt tptp.n1 tptp.tptp_minus_1)) % 0.36/0.62 (assume @p62 (tptp.gt tptp.n2 tptp.tptp_minus_1)) % 0.36/0.62 (assume @p63 (tptp.gt tptp.n3 tptp.tptp_minus_1)) % 0.36/0.62 (assume @p64 (tptp.gt tptp.n4 tptp.n0)) % 0.36/0.62 (assume @p65 (tptp.gt tptp.n5 tptp.n0)) % 0.36/0.62 (assume @p66 (tptp.gt tptp.n135299 tptp.n0)) % 0.36/0.62 (assume @p67 (tptp.gt tptp.n1 tptp.n0)) % 0.36/0.62 (assume @p68 (tptp.gt tptp.n2 tptp.n0)) % 0.36/0.62 (assume @p69 (tptp.gt tptp.n3 tptp.n0)) % 0.36/0.62 (assume @p70 (tptp.gt tptp.n4 tptp.n1)) % 0.36/0.62 (assume @p71 (tptp.gt tptp.n5 tptp.n1)) % 0.36/0.62 (assume @p72 (tptp.gt tptp.n135299 tptp.n1)) % 0.36/0.62 (assume @p73 (tptp.gt tptp.n2 tptp.n1)) % 0.36/0.62 (assume @p74 (tptp.gt tptp.n3 tptp.n1)) % 0.36/0.62 (assume @p75 (tptp.gt tptp.n4 tptp.n2)) % 0.36/0.62 (assume @p76 (tptp.gt tptp.n5 tptp.n2)) % 0.36/0.62 (assume @p77 (tptp.gt tptp.n135299 tptp.n2)) % 0.36/0.62 (assume @p78 (tptp.gt tptp.n3 tptp.n2)) % 0.36/0.62 (assume @p79 (tptp.gt tptp.n4 tptp.n3)) % 0.36/0.62 (assume @p80 (tptp.gt tptp.n5 tptp.n3)) % 0.36/0.62 (assume @p81 (tptp.gt tptp.n135299 tptp.n3)) % 0.36/0.62 (assume @p82 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n4)) (or @t142 @t141 @t140 @t139 @t138)))) % 0.36/0.62 (assume @p83 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n5)) (or @t142 @t141 @t140 @t139 @t138 (= @t2 tptp.n5))))) % 0.36/0.62 (assume @p84 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n0)) @t142))) % 0.36/0.62 (assume @p85 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n1)) (or @t142 @t141)))) % 0.36/0.62 (assume @p86 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n2)) (or @t142 @t141 @t140)))) % 0.36/0.62 (assume @p87 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n3)) (or @t142 @t141 @t140 @t139)))) % 0.36/0.62 (assume @p88 (= @t146 tptp.n4)) % 0.36/0.62 (assume @p89 (= (tptp.succ @t146) tptp.n5)) % 0.36/0.62 (assume @p90 (= @t143 tptp.n1)) % 0.36/0.62 (assume @p91 (= @t144 tptp.n2)) % 0.36/0.62 (assume @p92 (= @t145 tptp.n3)) % 0.36/0.62 (assume @p93 true) % 0.36/0.62 (step @p94 :rule aci_norm :args ((= (or (or @t149 @t148) @t147) @t150))) % 0.36/0.62 (step @p95 :rule refl :args (@t147)) % 0.36/0.62 (step @p96 :rule bool-and-de-morgan :args (@t77 @t76 true)) % 0.36/0.62 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or (not @t78) @t147))) % 0.36/0.62 (step @p98 :rule trans :premises (@p97 @p94)) % 0.36/0.62 (step @p99 :rule bool-impl-elim :args (@t78 @t147)) % 0.36/0.62 (step @p100 :rule trans :premises (@p99 @p98)) % 0.36/0.62 (step @p101 :rule cong :premises (@p100) :args ((forall @t80 (=> @t78 @t147)))) % 0.36/0.62 (step @p102 :rule eq-symm :args (@t75 tptp.init)) % 0.36/0.62 (step @p103 :rule refl :args (@t78)) % 0.36/0.62 (step @p104 :rule cong :premises (@p103 @p102) :args (@t79)) % 0.36/0.62 (step @p105 :rule cong :premises (@p104) :args (@t81)) % 0.36/0.62 (step @p106 :rule trans :premises (@p105 @p101)) % 0.36/0.62 (step @p107 :rule aci_norm :args ((= (or (or @t153 @t152) @t151) @t154))) % 0.36/0.62 (step @p108 :rule refl :args (@t151)) % 0.36/0.62 (step @p109 :rule bool-and-de-morgan :args (@t85 @t84 true)) % 0.36/0.62 (step @p110 :rule nary_cong :premises (@p109 @p108) :args ((or (not @t86) @t151))) % 0.36/0.62 (step @p111 :rule trans :premises (@p110 @p107)) % 0.36/0.62 (step @p112 :rule bool-impl-elim :args (@t86 @t151)) % 0.36/0.62 (step @p113 :rule trans :premises (@p112 @p111)) % 0.36/0.62 (step @p114 :rule cong :premises (@p113) :args ((forall @t88 (=> @t86 @t151)))) % 0.36/0.62 (step @p115 :rule eq-symm :args (@t83 tptp.init)) % 0.36/0.62 (step @p116 :rule refl :args (@t86)) % 0.36/0.62 (step @p117 :rule cong :premises (@p116 @p115) :args (@t87)) % 0.36/0.62 (step @p118 :rule cong :premises (@p117) :args (@t89)) % 0.36/0.62 (step @p119 :rule trans :premises (@p118 @p114)) % 0.36/0.62 (step @p120 :rule refl :args (@t90)) % 0.36/0.62 (step @p121 :rule cong :premises (@p120 @p119) :args (@t91)) % 0.36/0.62 (step @p122 :rule aci_norm :args ((= (or (or @t157 @t156) @t155) (or @t157 @t156 @t155)))) % 0.36/0.62 (step @p123 :rule refl :args (@t155)) % 0.36/0.62 (step @p124 :rule bool-and-de-morgan :args (@t94 @t93 true)) % 0.36/0.62 (step @p125 :rule nary_cong :premises (@p124 @p123) :args ((or (not @t95) @t155))) % 0.36/0.62 (step @p126 :rule trans :premises (@p125 @p122)) % 0.36/0.62 (step @p127 :rule bool-impl-elim :args (@t95 @t155)) % 0.36/0.62 (step @p128 :rule trans :premises (@p127 @p126)) % 0.36/0.62 (step @p129 :rule cong :premises (@p128) :args ((forall @t97 (=> @t95 @t155)))) % 0.36/0.62 (step @p130 :rule eq-symm :args (@t92 tptp.init)) % 0.36/0.62 (step @p131 :rule refl :args (@t95)) % 0.36/0.62 (step @p132 :rule cong :premises (@p131 @p130) :args (@t96)) % 0.36/0.62 (step @p133 :rule cong :premises (@p132) :args (@t98)) % 0.36/0.62 (step @p134 :rule trans :premises (@p133 @p129)) % 0.36/0.62 (step @p135 :rule cong :premises (@p120 @p134) :args (@t99)) % 0.36/0.62 (step @p136 :rule aci_norm :args ((= (or (or @t160 @t159) @t158) (or @t160 @t159 @t158)))) % 0.36/0.62 (step @p137 :rule refl :args (@t158)) % 0.36/0.62 (step @p138 :rule bool-and-de-morgan :args (@t102 @t101 true)) % 0.36/0.62 (step @p139 :rule nary_cong :premises (@p138 @p137) :args ((or (not @t103) @t158))) % 0.36/0.62 (step @p140 :rule trans :premises (@p139 @p136)) % 0.36/0.62 (step @p141 :rule bool-impl-elim :args (@t103 @t158)) % 0.36/0.62 (step @p142 :rule trans :premises (@p141 @p140)) % 0.36/0.62 (step @p143 :rule cong :premises (@p142) :args ((forall @t105 (=> @t103 @t158)))) % 0.36/0.62 (step @p144 :rule eq-symm :args (@t100 tptp.init)) % 0.36/0.62 (step @p145 :rule refl :args (@t103)) % 0.36/0.62 (step @p146 :rule cong :premises (@p145 @p144) :args (@t104)) % 0.36/0.62 (step @p147 :rule cong :premises (@p146) :args (@t106)) % 0.36/0.62 (step @p148 :rule trans :premises (@p147 @p143)) % 0.36/0.62 (step @p149 :rule cong :premises (@p120 @p148) :args (@t107)) % 0.36/0.62 (step @p150 :rule aci_norm :args ((= (or (or @t163 @t162) @t161) (or @t163 @t162 @t161)))) % 0.36/0.62 (step @p151 :rule refl :args (@t161)) % 0.36/0.62 (step @p152 :rule bool-and-de-morgan :args (@t110 @t109 true)) % 0.36/0.62 (step @p153 :rule nary_cong :premises (@p152 @p151) :args ((or (not @t111) @t161))) % 0.36/0.62 (step @p154 :rule trans :premises (@p153 @p150)) % 0.36/0.62 (step @p155 :rule bool-impl-elim :args (@t111 @t161)) % 0.36/0.62 (step @p156 :rule trans :premises (@p155 @p154)) % 0.36/0.62 (step @p157 :rule cong :premises (@p156) :args ((forall @t113 (=> @t111 @t161)))) % 0.36/0.62 (step @p158 :rule eq-symm :args (@t108 tptp.init)) % 0.36/0.62 (step @p159 :rule refl :args (@t111)) % 0.36/0.62 (step @p160 :rule cong :premises (@p159 @p158) :args (@t112)) % 0.36/0.62 (step @p161 :rule cong :premises (@p160) :args (@t114)) % 0.36/0.62 (step @p162 :rule trans :premises (@p161 @p157)) % 0.36/0.62 (step @p163 :rule aci_norm :args ((= (or (or @t166 @t165) @t164) (or @t166 @t165 @t164)))) % 0.36/0.62 (step @p164 :rule refl :args (@t164)) % 0.36/0.62 (step @p165 :rule bool-and-de-morgan :args (@t117 @t116 true)) % 0.36/0.62 (step @p166 :rule nary_cong :premises (@p165 @p164) :args ((or (not @t118) @t164))) % 0.36/0.62 (step @p167 :rule trans :premises (@p166 @p163)) % 0.36/0.62 (step @p168 :rule bool-impl-elim :args (@t118 @t164)) % 0.36/0.62 (step @p169 :rule trans :premises (@p168 @p167)) % 0.36/0.62 (step @p170 :rule cong :premises (@p169) :args ((forall @t120 (=> @t118 @t164)))) % 0.36/0.62 (step @p171 :rule eq-symm :args (@t115 tptp.init)) % 0.36/0.62 (step @p172 :rule refl :args (@t118)) % 0.36/0.62 (step @p173 :rule cong :premises (@p172 @p171) :args (@t119)) % 0.36/0.62 (step @p174 :rule cong :premises (@p173) :args (@t121)) % 0.36/0.62 (step @p175 :rule trans :premises (@p174 @p170)) % 0.36/0.62 (step @p176 :rule aci_norm :args ((= @t174 (or @t172 @t171 @t170 @t169 @t168)))) % 0.36/0.62 (step @p177 :rule cong :premises (@p176) :args (@t175)) % 0.36/0.62 (step @p178 :rule quant-merge-prenex :args ((= (forall @t133 @t177) @t175))) % 0.36/0.62 (step @p179 :rule alpha_equiv :args (@t178 (@list @t167) (@list @t42))) % 0.36/0.62 (step @p180 :rule refl :args (@t171)) % 0.36/0.62 (step @p181 :rule refl :args (@t172)) % 0.36/0.62 (step @p182 :rule nary_cong :premises (@p181 @p180 @p179) :args (@t179)) % 0.36/0.62 (step @p183 :rule quant-miniscope-or :args ((= @t177 @t179))) % 0.36/0.62 (step @p184 :rule trans :premises (@p183 @p182)) % 0.36/0.62 (step @p185 :rule symm :premises (@p184)) % 0.36/0.62 (step @p186 :rule cong :premises (@p185) :args ((forall @t133 @t185))) % 0.36/0.62 (step @p187 :rule trans :premises (@p186 @p178)) % 0.36/0.62 (step @p188 :rule trans :premises (@p187 @p177)) % 0.36/0.62 (step @p189 :rule aci_norm :args ((= (or (or @t172 @t171) @t184) @t185))) % 0.36/0.62 (step @p190 :rule refl :args (@t184)) % 0.36/0.62 (step @p191 :rule bool-and-de-morgan :args (@t130 @t129 true)) % 0.36/0.62 (step @p192 :rule nary_cong :premises (@p191 @p190) :args ((or (not @t131) @t184))) % 0.36/0.62 (step @p193 :rule trans :premises (@p192 @p189)) % 0.36/0.62 (step @p194 :rule bool-impl-elim :args (@t131 @t184)) % 0.36/0.62 (step @p195 :rule trans :premises (@p194 @p193)) % 0.36/0.62 (step @p196 :rule cong :premises (@p195) :args ((forall @t133 (=> @t131 @t184)))) % 0.36/0.62 (step @p197 :rule trans :premises (@p196 @p188)) % 0.36/0.62 (step @p198 :rule aci_norm :args ((= (or (or @t182 @t181) @t180) @t183))) % 0.36/0.62 (step @p199 :rule refl :args (@t180)) % 0.36/0.62 (step @p200 :rule bool-and-de-morgan :args (@t124 @t123 true)) % 0.36/0.62 (step @p201 :rule nary_cong :premises (@p200 @p199) :args ((or (not @t125) @t180))) % 0.36/0.62 (step @p202 :rule trans :premises (@p201 @p198)) % 0.36/0.62 (step @p203 :rule bool-impl-elim :args (@t125 @t180)) % 0.36/0.62 (step @p204 :rule trans :premises (@p203 @p202)) % 0.36/0.62 (step @p205 :rule cong :premises (@p204) :args ((forall @t127 (=> @t125 @t180)))) % 0.36/0.62 (step @p206 :rule eq-symm :args (@t122 tptp.init)) % 0.36/0.62 (step @p207 :rule refl :args (@t125)) % 0.36/0.62 (step @p208 :rule cong :premises (@p207 @p206) :args (@t126)) % 0.36/0.62 (step @p209 :rule cong :premises (@p208) :args (@t128)) % 0.36/0.62 (step @p210 :rule trans :premises (@p209 @p205)) % 0.36/0.62 (step @p211 :rule refl :args (@t131)) % 0.36/0.62 (step @p212 :rule cong :premises (@p211 @p210) :args (@t132)) % 0.36/0.62 (step @p213 :rule cong :premises (@p212) :args (@t134)) % 0.36/0.62 (step @p214 :rule trans :premises (@p213 @p197)) % 0.36/0.62 (step @p215 :rule nary_cong :premises (@p120 @p214 @p175 @p162 @p149 @p135 @p121) :args (@t135)) % 0.36/0.62 (step @p216 :rule cong :premises (@p215 @p106) :args (@t136)) % 0.36/0.62 (step @p217 :rule cong :premises (@p216) :args (@t137)) % 0.36/0.62 (step @p218 :rule eq_resolve :premises (@p53 @p217)) % 0.36/0.62 (step @p219 :rule not_implies_elim1 :premises (@p218)) % 0.36/0.62 (step @p220 :rule and_elim :premises (@p219) :args (0)) % 0.36/0.62 (step @p221 :rule and_elim :premises (@p219) :args (6)) % 0.36/0.62 (step @p222 :rule implies_elim :premises (@p221)) % 0.36/0.62 (step @p223 :rule reordering :premises (@p222) :args ((or @t186 (not @t90)))) % 0.36/0.62 (step @p224 :rule chain_m_resolution :premises (@p223 @p220) :args (@t186 @t187 (@list @t90))) % 0.36/0.62 (step @p225 :rule alpha_equiv :args (@t186 (@list @t82) (@list @t74))) % 0.36/0.62 (step @p226 :rule equiv_elim1 :premises (@p225)) % 0.36/0.62 (step @p227 :rule reordering :premises (@p226) :args ((or @t188 (not @t186)))) % 0.36/0.62 (step @p228 :rule chain_m_resolution :premises (@p227 @p224) :args (@t188 @t187 (@list @t186))) % 0.36/0.62 (step @p229 :rule not_implies_elim2 :premises (@p218)) % 0.36/0.62 (step @p230 false :rule chain_m_resolution :premises (@p229 @p228) :args (false @t187 (@list @t188))) % 0.36/0.62 ) % 0.36/0.62 % SZS output end Proof % 0.36/0.62 % cvc5 exiting %------------------------------------------------------------------------------