%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV175+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 : n022.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 09:00:39 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 : SWV175+1 : TPTP v9.2.1. Bugfixed v3.3.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n022.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 19:58:38 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.50 %----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 $$unsorted 0) % 0.45/0.65 (declare-const tptp.muold_init $$unsorted) % 0.45/0.65 (declare-const tptp.rhoold_init $$unsorted) % 0.45/0.65 (declare-const tptp.loopcounter $$unsorted) % 0.45/0.65 (declare-const tptp.q_init $$unsorted) % 0.45/0.65 (declare-const tptp.pv28 $$unsorted) % 0.45/0.65 (declare-const tptp.init $$unsorted) % 0.45/0.65 (declare-const tptp.def $$unsorted) % 0.45/0.65 (declare-const tptp.use $$unsorted) % 0.45/0.65 (declare-const tptp.true Bool) % 0.45/0.65 (declare-const tptp.tptp_update2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.center_init $$unsorted) % 0.45/0.65 (declare-const tptp.a_select3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.uniform_int_rnd (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.n135299 $$unsorted) % 0.45/0.65 (declare-const tptp.n3 $$unsorted) % 0.45/0.65 (declare-const tptp.tptp_const_array1 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.pred (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.tptp_minus_1 $$unsorted) % 0.45/0.65 (declare-const tptp.n0 $$unsorted) % 0.45/0.65 (declare-const tptp.tptp_msub (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.n1 $$unsorted) % 0.45/0.65 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.n5 $$unsorted) % 0.45/0.65 (declare-const tptp.pv30 $$unsorted) % 0.45/0.65 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.tptp_update3 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.minus (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.rho_init $$unsorted) % 0.45/0.65 (declare-const tptp.tptp_const_array2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.trans (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.a_select2 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.inv (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.dim (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.plus (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.tptp_madd (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.sum (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.tptp_mmul (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.tptp_float_0_0 $$unsorted) % 0.45/0.65 (declare-const tptp.sigmaold_init $$unsorted) % 0.45/0.65 (declare-const tptp.n4 $$unsorted) % 0.45/0.65 (declare-const tptp.n2 $$unsorted) % 0.45/0.65 (define @t1 () (@var "Y" $$unsorted)) % 0.45/0.65 (define @t2 () (@var "X" $$unsorted)) % 0.45/0.65 (define @t3 () (= @t2 @t1)) % 0.45/0.65 (define @t4 () (tptp.gt @t1 @t2)) % 0.45/0.65 (define @t5 () (tptp.gt @t2 @t1)) % 0.45/0.65 (define @t6 () (@list @t2 @t1)) % 0.45/0.65 (define @t7 () (@var "Z" $$unsorted)) % 0.45/0.65 (define @t8 () (@list @t2 @t1 @t7)) % 0.45/0.65 (define @t9 () (@list @t2)) % 0.45/0.65 (define @t10 () (tptp.leq @t2 @t1)) % 0.45/0.65 (define @t11 () (tptp.succ @t2)) % 0.45/0.65 (define @t12 () (tptp.succ @t1)) % 0.45/0.65 (define @t13 () (@var "C" $$unsorted)) % 0.45/0.65 (define @t14 () (tptp.uniform_int_rnd @t13 @t2)) % 0.45/0.65 (define @t15 () (tptp.leq tptp.n0 @t2)) % 0.45/0.65 (define @t16 () (@list @t2 @t13)) % 0.45/0.65 (define @t17 () (@var "Val" $$unsorted)) % 0.45/0.65 (define @t18 () (@var "I" $$unsorted)) % 0.45/0.65 (define @t19 () (@var "U" $$unsorted)) % 0.45/0.65 (define @t20 () (@var "L" $$unsorted)) % 0.45/0.65 (define @t21 () (tptp.leq @t18 @t19)) % 0.45/0.65 (define @t22 () (@var "J" $$unsorted)) % 0.45/0.65 (define @t23 () (@var "U2" $$unsorted)) % 0.45/0.65 (define @t24 () (@var "L2" $$unsorted)) % 0.45/0.65 (define @t25 () (@var "U1" $$unsorted)) % 0.45/0.65 (define @t26 () (@var "L1" $$unsorted)) % 0.45/0.65 (define @t27 () (@var "A" $$unsorted)) % 0.45/0.65 (define @t28 () (tptp.trans @t27)) % 0.45/0.65 (define @t29 () (@var "N" $$unsorted)) % 0.45/0.65 (define @t30 () (tptp.leq @t22 @t29)) % 0.45/0.65 (define @t31 () (tptp.leq tptp.n0 @t22)) % 0.45/0.65 (define @t32 () (tptp.leq @t18 @t29)) % 0.45/0.65 (define @t33 () (tptp.leq tptp.n0 @t18)) % 0.45/0.65 (define @t34 () (and @t33 @t32 @t31 @t30)) % 0.45/0.65 (define @t35 () (@list @t18 @t22)) % 0.45/0.65 (define @t36 () (forall @t35 (=> @t34 (= (tptp.a_select3 @t27 @t18 @t22) (tptp.a_select3 @t27 @t22 @t18))))) % 0.45/0.65 (define @t37 () (@list @t27 @t29)) % 0.45/0.65 (define @t38 () (tptp.inv @t27)) % 0.45/0.65 (define @t39 () (@var "VAL" $$unsorted)) % 0.45/0.65 (define @t40 () (@var "K" $$unsorted)) % 0.45/0.65 (define @t41 () (tptp.tptp_update3 @t27 @t40 @t40 @t39)) % 0.45/0.65 (define @t42 () (@var "B" $$unsorted)) % 0.45/0.65 (define @t43 () (tptp.tptp_madd @t27 @t42)) % 0.45/0.65 (define @t44 () (= (tptp.a_select3 @t42 @t18 @t22) (tptp.a_select3 @t42 @t22 @t18))) % 0.45/0.65 (define @t45 () (forall @t35 (=> @t34 @t44))) % 0.45/0.65 (define @t46 () (and @t36 @t45)) % 0.45/0.65 (define @t47 () (@list @t27 @t42 @t29)) % 0.45/0.65 (define @t48 () (tptp.tptp_msub @t27 @t42)) % 0.45/0.65 (define @t49 () (tptp.tptp_mmul @t27 (tptp.tptp_mmul @t42 @t28))) % 0.45/0.65 (define @t50 () (forall @t35 (=> @t34 (= (tptp.a_select3 @t49 @t18 @t22) (tptp.a_select3 @t49 @t22 @t18))))) % 0.45/0.65 (define @t51 () (@var "M" $$unsorted)) % 0.45/0.65 (define @t52 () (and @t33 (tptp.leq @t18 @t51) @t31 (tptp.leq @t22 @t51))) % 0.45/0.65 (define @t53 () (@var "E" $$unsorted)) % 0.45/0.65 (define @t54 () (@var "F" $$unsorted)) % 0.45/0.65 (define @t55 () (@var "D" $$unsorted)) % 0.45/0.65 (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))))) % 0.45/0.65 (define @t57 () (@var "Body" $$unsorted)) % 0.45/0.65 (define @t58 () (tptp.sum tptp.n0 tptp.tptp_minus_1 @t57)) % 0.45/0.65 (define @t59 () (@list @t57)) % 0.45/0.65 (define @t60 () (tptp.succ @t11)) % 0.45/0.65 (define @t61 () (tptp.succ @t60)) % 0.45/0.65 (define @t62 () (tptp.succ @t61)) % 0.45/0.65 (define @t63 () (tptp.succ @t62)) % 0.45/0.65 (define @t64 () (tptp.pred @t2)) % 0.45/0.65 (define @t65 () (@var "V" $$unsorted)) % 0.45/0.65 (define @t66 () (tptp.tptp_update3 @t2 @t19 @t65 @t39)) % 0.45/0.65 (define @t67 () (@var "VAL2" $$unsorted)) % 0.45/0.65 (define @t68 () (not (= @t18 @t19))) % 0.45/0.65 (define @t69 () (@var "J0" $$unsorted)) % 0.45/0.65 (define @t70 () (@var "I0" $$unsorted)) % 0.45/0.65 (define @t71 () (tptp.leq @t70 @t19)) % 0.45/0.65 (define @t72 () (tptp.leq tptp.n0 @t70)) % 0.45/0.65 (define @t73 () (tptp.tptp_update2 @t2 @t19 @t39)) % 0.45/0.65 (define @t74 () (tptp.a_select3 tptp.q_init tptp.pv30 tptp.pv28)) % 0.45/0.65 (define @t75 () (@var "G" $$unsorted)) % 0.45/0.65 (define @t76 () (tptp.a_select2 tptp.sigmaold_init @t75)) % 0.45/0.65 (define @t77 () (tptp.leq @t75 tptp.n4)) % 0.45/0.65 (define @t78 () (tptp.leq tptp.n0 @t75)) % 0.45/0.65 (define @t79 () (and @t78 @t77)) % 0.45/0.65 (define @t80 () (=> @t79 (= @t76 tptp.init))) % 0.45/0.65 (define @t81 () (@list @t75)) % 0.45/0.65 (define @t82 () (forall @t81 @t80)) % 0.45/0.65 (define @t83 () (tptp.gt tptp.loopcounter tptp.n1)) % 0.45/0.65 (define @t84 () (=> @t83 @t82)) % 0.45/0.65 (define @t85 () (tptp.a_select2 tptp.rhoold_init @t54)) % 0.45/0.65 (define @t86 () (tptp.leq @t54 tptp.n4)) % 0.45/0.65 (define @t87 () (tptp.leq tptp.n0 @t54)) % 0.45/0.65 (define @t88 () (and @t87 @t86)) % 0.45/0.65 (define @t89 () (=> @t88 (= @t85 tptp.init))) % 0.45/0.65 (define @t90 () (@list @t54)) % 0.45/0.65 (define @t91 () (forall @t90 @t89)) % 0.45/0.65 (define @t92 () (=> @t83 @t91)) % 0.45/0.65 (define @t93 () (tptp.a_select2 tptp.muold_init @t53)) % 0.45/0.65 (define @t94 () (tptp.leq @t53 tptp.n4)) % 0.45/0.65 (define @t95 () (tptp.leq tptp.n0 @t53)) % 0.45/0.65 (define @t96 () (and @t95 @t94)) % 0.45/0.65 (define @t97 () (=> @t96 (= @t93 tptp.init))) % 0.45/0.65 (define @t98 () (@list @t53)) % 0.45/0.65 (define @t99 () (forall @t98 @t97)) % 0.45/0.65 (define @t100 () (=> @t83 @t99)) % 0.45/0.65 (define @t101 () (tptp.a_select3 tptp.center_init @t55 tptp.n0)) % 0.45/0.65 (define @t102 () (tptp.leq @t55 tptp.n4)) % 0.45/0.65 (define @t103 () (tptp.leq tptp.n0 @t55)) % 0.45/0.65 (define @t104 () (and @t103 @t102)) % 0.45/0.65 (define @t105 () (=> @t104 (= @t101 tptp.init))) % 0.45/0.65 (define @t106 () (@list @t55)) % 0.45/0.65 (define @t107 () (forall @t106 @t105)) % 0.45/0.65 (define @t108 () (tptp.a_select2 tptp.rho_init @t13)) % 0.45/0.65 (define @t109 () (tptp.leq @t13 (tptp.pred tptp.pv28))) % 0.45/0.65 (define @t110 () (tptp.leq tptp.n0 @t13)) % 0.45/0.65 (define @t111 () (and @t110 @t109)) % 0.45/0.65 (define @t112 () (=> @t111 (= @t108 tptp.init))) % 0.45/0.65 (define @t113 () (@list @t13)) % 0.45/0.65 (define @t114 () (forall @t113 @t112)) % 0.45/0.65 (define @t115 () (tptp.a_select3 tptp.q_init @t27 @t42)) % 0.45/0.65 (define @t116 () (tptp.leq @t42 tptp.n4)) % 0.45/0.65 (define @t117 () (tptp.leq tptp.n0 @t42)) % 0.45/0.65 (define @t118 () (and @t117 @t116)) % 0.45/0.65 (define @t119 () (=> @t118 (= @t115 tptp.init))) % 0.45/0.65 (define @t120 () (@list @t42)) % 0.45/0.65 (define @t121 () (forall @t120 @t119)) % 0.45/0.65 (define @t122 () (tptp.leq @t27 tptp.n135299)) % 0.45/0.65 (define @t123 () (tptp.leq tptp.n0 @t27)) % 0.45/0.65 (define @t124 () (and @t123 @t122)) % 0.45/0.65 (define @t125 () (=> @t124 @t121)) % 0.45/0.65 (define @t126 () (@list @t27)) % 0.45/0.65 (define @t127 () (forall @t126 @t125)) % 0.45/0.65 (define @t128 () (tptp.leq tptp.pv30 tptp.n135299)) % 0.45/0.65 (define @t129 () (tptp.leq tptp.pv28 tptp.n4)) % 0.45/0.65 (define @t130 () (tptp.leq tptp.n0 tptp.pv30)) % 0.45/0.65 (define @t131 () (tptp.leq tptp.n0 tptp.pv28)) % 0.45/0.65 (define @t132 () (and @t131 @t130 @t129 @t128 @t127 @t114 @t107 @t100 @t92 @t84)) % 0.45/0.65 (define @t133 () (=> @t132 (= @t74 tptp.init))) % 0.45/0.65 (define @t134 () (not @t133)) % 0.45/0.65 (define @t135 () (= @t2 tptp.n4)) % 0.45/0.65 (define @t136 () (= @t2 tptp.n3)) % 0.45/0.65 (define @t137 () (= @t2 tptp.n2)) % 0.45/0.65 (define @t138 () (= @t2 tptp.n1)) % 0.45/0.65 (define @t139 () (= @t2 tptp.n0)) % 0.45/0.65 (define @t140 () (tptp.succ tptp.n0)) % 0.45/0.65 (define @t141 () (tptp.succ @t140)) % 0.45/0.65 (define @t142 () (tptp.succ @t141)) % 0.45/0.65 (define @t143 () (tptp.succ @t142)) % 0.45/0.65 (define @t144 () (= tptp.init @t76)) % 0.45/0.65 (define @t145 () (not @t77)) % 0.45/0.65 (define @t146 () (not @t78)) % 0.45/0.65 (define @t147 () (= tptp.init @t85)) % 0.45/0.65 (define @t148 () (not @t86)) % 0.45/0.65 (define @t149 () (not @t87)) % 0.45/0.65 (define @t150 () (= tptp.init @t93)) % 0.45/0.65 (define @t151 () (not @t94)) % 0.45/0.65 (define @t152 () (not @t95)) % 0.45/0.65 (define @t153 () (= tptp.init @t101)) % 0.45/0.65 (define @t154 () (not @t102)) % 0.45/0.65 (define @t155 () (not @t103)) % 0.45/0.65 (define @t156 () (= tptp.init @t108)) % 0.45/0.65 (define @t157 () (not @t109)) % 0.45/0.65 (define @t158 () (not @t110)) % 0.45/0.65 (define @t159 () (@var "BOUND_VARIABLE_8430" $$unsorted)) % 0.45/0.65 (define @t160 () (= tptp.init (tptp.a_select3 tptp.q_init @t27 @t159))) % 0.45/0.65 (define @t161 () (not (tptp.leq @t159 tptp.n4))) % 0.45/0.65 (define @t162 () (not (tptp.leq tptp.n0 @t159))) % 0.45/0.65 (define @t163 () (not @t122)) % 0.45/0.65 (define @t164 () (not @t123)) % 0.45/0.65 (define @t165 () (or @t164 @t163 @t162 @t161 @t160)) % 0.45/0.65 (define @t166 () (or @t162 @t161 @t160)) % 0.45/0.65 (define @t167 () (or @t164 @t163 @t166)) % 0.45/0.65 (define @t168 () (@list @t27 @t159)) % 0.45/0.65 (define @t169 () (forall @t168 @t167)) % 0.45/0.65 (define @t170 () (@list @t159)) % 0.45/0.65 (define @t171 () (forall @t170 @t167)) % 0.45/0.65 (define @t172 () (forall @t170 @t166)) % 0.45/0.65 (define @t173 () (or @t164 @t163 @t172)) % 0.45/0.65 (define @t174 () (= tptp.init @t115)) % 0.45/0.65 (define @t175 () (not @t116)) % 0.45/0.65 (define @t176 () (not @t117)) % 0.45/0.65 (define @t177 () (or @t176 @t175 @t174)) % 0.45/0.65 (define @t178 () (forall @t120 @t177)) % 0.45/0.65 (define @t179 () (or @t164 @t163 @t178)) % 0.45/0.65 (define @t180 () (= tptp.init @t74)) % 0.45/0.65 (define @t181 () (not @t129)) % 0.45/0.65 (define @t182 () (not @t131)) % 0.45/0.65 (define @t183 () (not @t128)) % 0.45/0.65 (define @t184 () (not @t130)) % 0.45/0.65 (define @t185 () (or @t184 @t183 @t182 @t181 @t180)) % 0.45/0.65 (define @t186 () (not @t185)) % 0.45/0.65 (define @t187 () (forall @t168 @t165)) % 0.45/0.65 (assume @p1 (forall @t6 (or @t5 @t4 @t3))) % 0.45/0.65 (assume @p2 (forall @t8 (=> (and @t5 (tptp.gt @t1 @t7)) (tptp.gt @t2 @t7)))) % 0.45/0.65 (assume @p3 (forall @t9 (not (tptp.gt @t2 @t2)))) % 0.45/0.65 (assume @p4 (forall @t9 (tptp.leq @t2 @t2))) % 0.45/0.65 (assume @p5 (forall @t8 (=> (and @t10 (tptp.leq @t1 @t7)) (tptp.leq @t2 @t7)))) % 0.45/0.65 (assume @p6 (forall @t6 (= (tptp.lt @t2 @t1) @t4))) % 0.45/0.65 (assume @p7 (forall @t6 (= (tptp.geq @t2 @t1) (tptp.leq @t1 @t2)))) % 0.45/0.65 (assume @p8 (forall @t6 (=> @t4 @t10))) % 0.45/0.65 (assume @p9 (forall @t6 (=> (and @t10 (not @t3)) @t4))) % 0.45/0.65 (assume @p10 (forall @t6 (= (tptp.leq @t2 (tptp.pred @t1)) @t4))) % 0.45/0.65 (assume @p11 (forall @t9 (tptp.gt @t11 @t2))) % 0.45/0.65 (assume @p12 (forall @t6 (=> @t10 (tptp.leq @t2 @t12)))) % 0.45/0.65 (assume @p13 (forall @t6 (= @t10 (tptp.gt @t12 @t2)))) % 0.45/0.65 (assume @p14 (forall @t16 (=> @t15 (tptp.leq @t14 @t2)))) % 0.45/0.65 (assume @p15 (forall @t16 (=> @t15 (tptp.leq tptp.n0 @t14)))) % 0.45/0.65 (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)))) % 0.45/0.65 (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)))) % 0.45/0.65 (assume @p18 (forall @t37 (=> @t36 (forall @t35 (=> @t34 (= (tptp.a_select3 @t28 @t18 @t22) (tptp.a_select3 @t28 @t22 @t18))))))) % 0.45/0.65 (assume @p19 (forall @t37 (=> @t36 (forall @t35 (=> @t34 (= (tptp.a_select3 @t38 @t18 @t22) (tptp.a_select3 @t38 @t22 @t18))))))) % 0.45/0.65 (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))))))) % 0.45/0.65 (assume @p21 (forall @t47 (=> @t46 (forall @t35 (=> @t34 (= (tptp.a_select3 @t43 @t18 @t22) (tptp.a_select3 @t43 @t22 @t18))))))) % 0.45/0.65 (assume @p22 (forall @t47 (=> @t46 (forall @t35 (=> @t34 (= (tptp.a_select3 @t48 @t18 @t22) (tptp.a_select3 @t48 @t22 @t18))))))) % 0.45/0.65 (assume @p23 (forall @t47 (=> @t45 @t50))) % 0.45/0.65 (assume @p24 (forall (@list @t27 @t42 @t29 @t51) (=> (forall @t35 (=> @t52 @t44)) @t50))) % 0.45/0.65 (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))))))) % 0.45/0.65 (assume @p26 (forall @t59 (= @t58 tptp.n0))) % 0.45/0.65 (assume @p27 (forall @t59 (= tptp.tptp_float_0_0 @t58))) % 0.45/0.65 (assume @p28 (= (tptp.succ tptp.tptp_minus_1) tptp.n0)) % 0.45/0.65 (assume @p29 (forall @t9 (= (tptp.plus @t2 tptp.n1) @t11))) % 0.45/0.65 (assume @p30 (forall @t9 (= (tptp.plus tptp.n1 @t2) @t11))) % 0.45/0.65 (assume @p31 (forall @t9 (= (tptp.plus @t2 tptp.n2) @t60))) % 0.45/0.65 (assume @p32 (forall @t9 (= (tptp.plus tptp.n2 @t2) @t60))) % 0.45/0.65 (assume @p33 (forall @t9 (= (tptp.plus @t2 tptp.n3) @t61))) % 0.45/0.65 (assume @p34 (forall @t9 (= (tptp.plus tptp.n3 @t2) @t61))) % 0.45/0.65 (assume @p35 (forall @t9 (= (tptp.plus @t2 tptp.n4) @t62))) % 0.45/0.65 (assume @p36 (forall @t9 (= (tptp.plus tptp.n4 @t2) @t62))) % 0.45/0.65 (assume @p37 (forall @t9 (= (tptp.plus @t2 tptp.n5) @t63))) % 0.45/0.65 (assume @p38 (forall @t9 (= (tptp.plus tptp.n5 @t2) @t63))) % 0.45/0.65 (assume @p39 (forall @t9 (= (tptp.minus @t2 tptp.n1) @t64))) % 0.45/0.65 (assume @p40 (forall @t9 (= (tptp.pred @t11) @t2))) % 0.45/0.65 (assume @p41 (forall @t9 (= (tptp.succ @t64) @t2))) % 0.45/0.65 (assume @p42 (forall @t6 (= (tptp.leq @t11 @t12) @t10))) % 0.45/0.65 (assume @p43 (forall @t6 (=> (tptp.leq @t11 @t1) @t4))) % 0.45/0.65 (assume @p44 (forall @t6 (=> (tptp.leq (tptp.minus @t2 @t1) @t2) (tptp.leq tptp.n0 @t1)))) % 0.45/0.65 (assume @p45 (forall (@list @t2 @t19 @t65 @t39) (= (tptp.a_select3 @t66 @t19 @t65) @t39))) % 0.45/0.65 (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)))) % 0.45/0.65 (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)))) % 0.45/0.65 (assume @p48 (forall (@list @t2 @t19 @t39) (= (tptp.a_select2 @t73 @t19) @t39))) % 0.45/0.65 (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)))) % 0.45/0.65 (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)))) % 0.45/0.65 (assume @p51 tptp.true) % 0.45/0.65 (assume @p52 (not (= tptp.def tptp.use))) % 0.45/0.65 (assume @p53 @t134) % 0.45/0.65 (assume @p54 (tptp.gt tptp.n5 tptp.n4)) % 0.45/0.65 (assume @p55 (tptp.gt tptp.n135299 tptp.n4)) % 0.45/0.65 (assume @p56 (tptp.gt tptp.n135299 tptp.n5)) % 0.45/0.65 (assume @p57 (tptp.gt tptp.n4 tptp.tptp_minus_1)) % 0.45/0.65 (assume @p58 (tptp.gt tptp.n5 tptp.tptp_minus_1)) % 0.45/0.65 (assume @p59 (tptp.gt tptp.n135299 tptp.tptp_minus_1)) % 0.45/0.65 (assume @p60 (tptp.gt tptp.n0 tptp.tptp_minus_1)) % 0.45/0.65 (assume @p61 (tptp.gt tptp.n1 tptp.tptp_minus_1)) % 0.45/0.65 (assume @p62 (tptp.gt tptp.n2 tptp.tptp_minus_1)) % 0.45/0.65 (assume @p63 (tptp.gt tptp.n3 tptp.tptp_minus_1)) % 0.45/0.65 (assume @p64 (tptp.gt tptp.n4 tptp.n0)) % 0.45/0.65 (assume @p65 (tptp.gt tptp.n5 tptp.n0)) % 0.45/0.65 (assume @p66 (tptp.gt tptp.n135299 tptp.n0)) % 0.45/0.65 (assume @p67 (tptp.gt tptp.n1 tptp.n0)) % 0.45/0.65 (assume @p68 (tptp.gt tptp.n2 tptp.n0)) % 0.45/0.65 (assume @p69 (tptp.gt tptp.n3 tptp.n0)) % 0.45/0.65 (assume @p70 (tptp.gt tptp.n4 tptp.n1)) % 0.45/0.65 (assume @p71 (tptp.gt tptp.n5 tptp.n1)) % 0.45/0.65 (assume @p72 (tptp.gt tptp.n135299 tptp.n1)) % 0.45/0.65 (assume @p73 (tptp.gt tptp.n2 tptp.n1)) % 0.45/0.65 (assume @p74 (tptp.gt tptp.n3 tptp.n1)) % 0.45/0.65 (assume @p75 (tptp.gt tptp.n4 tptp.n2)) % 0.45/0.65 (assume @p76 (tptp.gt tptp.n5 tptp.n2)) % 0.45/0.65 (assume @p77 (tptp.gt tptp.n135299 tptp.n2)) % 0.45/0.65 (assume @p78 (tptp.gt tptp.n3 tptp.n2)) % 0.45/0.65 (assume @p79 (tptp.gt tptp.n4 tptp.n3)) % 0.45/0.65 (assume @p80 (tptp.gt tptp.n5 tptp.n3)) % 0.45/0.65 (assume @p81 (tptp.gt tptp.n135299 tptp.n3)) % 0.45/0.65 (assume @p82 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n4)) (or @t139 @t138 @t137 @t136 @t135)))) % 0.45/0.65 (assume @p83 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n5)) (or @t139 @t138 @t137 @t136 @t135 (= @t2 tptp.n5))))) % 0.45/0.65 (assume @p84 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n0)) @t139))) % 0.45/0.65 (assume @p85 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n1)) (or @t139 @t138)))) % 0.45/0.65 (assume @p86 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n2)) (or @t139 @t138 @t137)))) % 0.45/0.65 (assume @p87 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n3)) (or @t139 @t138 @t137 @t136)))) % 0.45/0.65 (assume @p88 (= @t143 tptp.n4)) % 0.45/0.65 (assume @p89 (= (tptp.succ @t143) tptp.n5)) % 0.45/0.65 (assume @p90 (= @t140 tptp.n1)) % 0.45/0.65 (assume @p91 (= @t141 tptp.n2)) % 0.45/0.65 (assume @p92 (= @t142 tptp.n3)) % 0.45/0.65 (assume @p93 true) % 0.45/0.65 (step @p94 :rule eq-symm :args (@t74 tptp.init)) % 0.45/0.65 (step @p95 :rule aci_norm :args ((= (or (or @t146 @t145) @t144) (or @t146 @t145 @t144)))) % 0.45/0.65 (step @p96 :rule refl :args (@t144)) % 0.45/0.65 (step @p97 :rule bool-and-de-morgan :args (@t78 @t77 true)) % 0.45/0.65 (step @p98 :rule nary_cong :premises (@p97 @p96) :args ((or (not @t79) @t144))) % 0.45/0.65 (step @p99 :rule trans :premises (@p98 @p95)) % 0.45/0.65 (step @p100 :rule bool-impl-elim :args (@t79 @t144)) % 0.45/0.65 (step @p101 :rule trans :premises (@p100 @p99)) % 0.45/0.65 (step @p102 :rule cong :premises (@p101) :args ((forall @t81 (=> @t79 @t144)))) % 0.45/0.65 (step @p103 :rule eq-symm :args (@t76 tptp.init)) % 0.45/0.65 (step @p104 :rule refl :args (@t79)) % 0.45/0.65 (step @p105 :rule cong :premises (@p104 @p103) :args (@t80)) % 0.45/0.65 (step @p106 :rule cong :premises (@p105) :args (@t82)) % 0.45/0.65 (step @p107 :rule trans :premises (@p106 @p102)) % 0.45/0.65 (step @p108 :rule refl :args (@t83)) % 0.45/0.65 (step @p109 :rule cong :premises (@p108 @p107) :args (@t84)) % 0.45/0.65 (step @p110 :rule aci_norm :args ((= (or (or @t149 @t148) @t147) (or @t149 @t148 @t147)))) % 0.45/0.65 (step @p111 :rule refl :args (@t147)) % 0.45/0.65 (step @p112 :rule bool-and-de-morgan :args (@t87 @t86 true)) % 0.45/0.65 (step @p113 :rule nary_cong :premises (@p112 @p111) :args ((or (not @t88) @t147))) % 0.45/0.65 (step @p114 :rule trans :premises (@p113 @p110)) % 0.45/0.65 (step @p115 :rule bool-impl-elim :args (@t88 @t147)) % 0.45/0.65 (step @p116 :rule trans :premises (@p115 @p114)) % 0.45/0.65 (step @p117 :rule cong :premises (@p116) :args ((forall @t90 (=> @t88 @t147)))) % 0.45/0.65 (step @p118 :rule eq-symm :args (@t85 tptp.init)) % 0.45/0.65 (step @p119 :rule refl :args (@t88)) % 0.45/0.65 (step @p120 :rule cong :premises (@p119 @p118) :args (@t89)) % 0.45/0.65 (step @p121 :rule cong :premises (@p120) :args (@t91)) % 0.45/0.65 (step @p122 :rule trans :premises (@p121 @p117)) % 0.45/0.65 (step @p123 :rule cong :premises (@p108 @p122) :args (@t92)) % 0.45/0.65 (step @p124 :rule aci_norm :args ((= (or (or @t152 @t151) @t150) (or @t152 @t151 @t150)))) % 0.45/0.65 (step @p125 :rule refl :args (@t150)) % 0.45/0.65 (step @p126 :rule bool-and-de-morgan :args (@t95 @t94 true)) % 0.45/0.65 (step @p127 :rule nary_cong :premises (@p126 @p125) :args ((or (not @t96) @t150))) % 0.45/0.65 (step @p128 :rule trans :premises (@p127 @p124)) % 0.45/0.65 (step @p129 :rule bool-impl-elim :args (@t96 @t150)) % 0.45/0.65 (step @p130 :rule trans :premises (@p129 @p128)) % 0.45/0.65 (step @p131 :rule cong :premises (@p130) :args ((forall @t98 (=> @t96 @t150)))) % 0.45/0.65 (step @p132 :rule eq-symm :args (@t93 tptp.init)) % 0.45/0.65 (step @p133 :rule refl :args (@t96)) % 0.45/0.65 (step @p134 :rule cong :premises (@p133 @p132) :args (@t97)) % 0.45/0.65 (step @p135 :rule cong :premises (@p134) :args (@t99)) % 0.45/0.65 (step @p136 :rule trans :premises (@p135 @p131)) % 0.45/0.65 (step @p137 :rule cong :premises (@p108 @p136) :args (@t100)) % 0.45/0.65 (step @p138 :rule aci_norm :args ((= (or (or @t155 @t154) @t153) (or @t155 @t154 @t153)))) % 0.45/0.65 (step @p139 :rule refl :args (@t153)) % 0.45/0.65 (step @p140 :rule bool-and-de-morgan :args (@t103 @t102 true)) % 0.45/0.65 (step @p141 :rule nary_cong :premises (@p140 @p139) :args ((or (not @t104) @t153))) % 0.45/0.65 (step @p142 :rule trans :premises (@p141 @p138)) % 0.45/0.65 (step @p143 :rule bool-impl-elim :args (@t104 @t153)) % 0.45/0.65 (step @p144 :rule trans :premises (@p143 @p142)) % 0.45/0.65 (step @p145 :rule cong :premises (@p144) :args ((forall @t106 (=> @t104 @t153)))) % 0.45/0.65 (step @p146 :rule eq-symm :args (@t101 tptp.init)) % 0.45/0.65 (step @p147 :rule refl :args (@t104)) % 0.45/0.65 (step @p148 :rule cong :premises (@p147 @p146) :args (@t105)) % 0.45/0.65 (step @p149 :rule cong :premises (@p148) :args (@t107)) % 0.45/0.65 (step @p150 :rule trans :premises (@p149 @p145)) % 0.45/0.65 (step @p151 :rule aci_norm :args ((= (or (or @t158 @t157) @t156) (or @t158 @t157 @t156)))) % 0.45/0.65 (step @p152 :rule refl :args (@t156)) % 0.45/0.65 (step @p153 :rule bool-and-de-morgan :args (@t110 @t109 true)) % 0.45/0.65 (step @p154 :rule nary_cong :premises (@p153 @p152) :args ((or (not @t111) @t156))) % 0.45/0.65 (step @p155 :rule trans :premises (@p154 @p151)) % 0.45/0.65 (step @p156 :rule bool-impl-elim :args (@t111 @t156)) % 0.45/0.65 (step @p157 :rule trans :premises (@p156 @p155)) % 0.45/0.65 (step @p158 :rule cong :premises (@p157) :args ((forall @t113 (=> @t111 @t156)))) % 0.45/0.65 (step @p159 :rule eq-symm :args (@t108 tptp.init)) % 0.45/0.65 (step @p160 :rule refl :args (@t111)) % 0.45/0.65 (step @p161 :rule cong :premises (@p160 @p159) :args (@t112)) % 0.45/0.65 (step @p162 :rule cong :premises (@p161) :args (@t114)) % 0.45/0.65 (step @p163 :rule trans :premises (@p162 @p158)) % 0.45/0.65 (step @p164 :rule aci_norm :args ((= @t167 @t165))) % 0.45/0.65 (step @p165 :rule cong :premises (@p164) :args (@t169)) % 0.45/0.65 (step @p166 :rule quant-merge-prenex :args ((= (forall @t126 @t171) @t169))) % 0.45/0.65 (step @p167 :rule alpha_equiv :args (@t172 (@list @t159) (@list @t42))) % 0.45/0.65 (step @p168 :rule refl :args (@t163)) % 0.45/0.65 (step @p169 :rule refl :args (@t164)) % 0.45/0.65 (step @p170 :rule nary_cong :premises (@p169 @p168 @p167) :args (@t173)) % 0.45/0.65 (step @p171 :rule quant-miniscope-or :args ((= @t171 @t173))) % 0.45/0.65 (step @p172 :rule trans :premises (@p171 @p170)) % 0.45/0.65 (step @p173 :rule symm :premises (@p172)) % 0.45/0.65 (step @p174 :rule cong :premises (@p173) :args ((forall @t126 @t179))) % 0.45/0.65 (step @p175 :rule trans :premises (@p174 @p166)) % 0.45/0.65 (step @p176 :rule trans :premises (@p175 @p165)) % 0.45/0.65 (step @p177 :rule aci_norm :args ((= (or (or @t164 @t163) @t178) @t179))) % 0.45/0.65 (step @p178 :rule refl :args (@t178)) % 0.45/0.65 (step @p179 :rule bool-and-de-morgan :args (@t123 @t122 true)) % 0.45/0.65 (step @p180 :rule nary_cong :premises (@p179 @p178) :args ((or (not @t124) @t178))) % 0.45/0.65 (step @p181 :rule trans :premises (@p180 @p177)) % 0.45/0.65 (step @p182 :rule bool-impl-elim :args (@t124 @t178)) % 0.45/0.65 (step @p183 :rule trans :premises (@p182 @p181)) % 0.45/0.65 (step @p184 :rule cong :premises (@p183) :args ((forall @t126 (=> @t124 @t178)))) % 0.45/0.65 (step @p185 :rule trans :premises (@p184 @p176)) % 0.45/0.65 (step @p186 :rule aci_norm :args ((= (or (or @t176 @t175) @t174) @t177))) % 0.45/0.65 (step @p187 :rule refl :args (@t174)) % 0.45/0.65 (step @p188 :rule bool-and-de-morgan :args (@t117 @t116 true)) % 0.45/0.66 (step @p189 :rule nary_cong :premises (@p188 @p187) :args ((or (not @t118) @t174))) % 0.45/0.66 (step @p190 :rule trans :premises (@p189 @p186)) % 0.45/0.66 (step @p191 :rule bool-impl-elim :args (@t118 @t174)) % 0.45/0.66 (step @p192 :rule trans :premises (@p191 @p190)) % 0.45/0.66 (step @p193 :rule cong :premises (@p192) :args ((forall @t120 (=> @t118 @t174)))) % 0.45/0.66 (step @p194 :rule eq-symm :args (@t115 tptp.init)) % 0.45/0.66 (step @p195 :rule refl :args (@t118)) % 0.45/0.66 (step @p196 :rule cong :premises (@p195 @p194) :args (@t119)) % 0.45/0.66 (step @p197 :rule cong :premises (@p196) :args (@t121)) % 0.45/0.66 (step @p198 :rule trans :premises (@p197 @p193)) % 0.45/0.66 (step @p199 :rule refl :args (@t124)) % 0.45/0.66 (step @p200 :rule cong :premises (@p199 @p198) :args (@t125)) % 0.45/0.66 (step @p201 :rule cong :premises (@p200) :args (@t127)) % 0.45/0.66 (step @p202 :rule trans :premises (@p201 @p185)) % 0.45/0.66 (step @p203 :rule refl :args (@t128)) % 0.45/0.66 (step @p204 :rule refl :args (@t129)) % 0.45/0.66 (step @p205 :rule refl :args (@t130)) % 0.45/0.66 (step @p206 :rule refl :args (@t131)) % 0.45/0.66 (step @p207 :rule nary_cong :premises (@p206 @p205 @p204 @p203 @p202 @p163 @p150 @p137 @p123 @p109) :args (@t132)) % 0.45/0.66 (step @p208 :rule cong :premises (@p207 @p94) :args (@t133)) % 0.45/0.66 (step @p209 :rule cong :premises (@p208) :args (@t134)) % 0.45/0.66 (step @p210 :rule eq_resolve :premises (@p53 @p209)) % 0.45/0.66 (step @p211 :rule not_implies_elim1 :premises (@p210)) % 0.45/0.66 (step @p212 :rule and_elim :premises (@p211) :args (4)) % 0.45/0.66 (step @p213 :rule and_elim :premises (@p211) :args (3)) % 0.45/0.66 (step @p214 :rule and_elim :premises (@p211) :args (2)) % 0.45/0.66 (step @p215 :rule and_elim :premises (@p211) :args (1)) % 0.45/0.66 (step @p216 :rule and_elim :premises (@p211) :args (0)) % 0.45/0.66 (step @p217 :rule not_implies_elim2 :premises (@p210)) % 0.45/0.66 (step @p218 :rule cnf_or_pos :args (@t185)) % 0.45/0.66 (step @p219 :rule reordering :premises (@p218) :args ((or @t180 @t182 @t184 @t181 @t183 @t186))) % 0.45/0.66 (step @p220 :rule chain_m_resolution :premises (@p219 @p217 @p216 @p215 @p214 @p213) :args (@t186 (@list true false false false false) (@list @t180 @t131 @t130 @t129 @t128))) % 0.45/0.66 (assume-push @p227 @t187) % 0.45/0.66 (step @p222 :rule instantiate :premises (@p212) :args ((@list tptp.pv30 tptp.pv28))) % 0.45/0.66 (step-pop @p228 :rule scope :premises (@p222)) % 0.45/0.66 (step @p223 :rule process_scope :premises (@p228) :args (@t185)) % 0.45/0.66 (step @p225 :rule implies_elim :premises (@p223)) % 0.45/0.66 (step @p226 false :rule chain_m_resolution :premises (@p225 @p220 @p212) :args (false (@list true false) (@list @t185 @t187))) % 0.45/0.66 ) % 0.45/0.66 % SZS output end Proof % 0.45/0.66 % cvc5 exiting %------------------------------------------------------------------------------