%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV191+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 : n008.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 09:00:41 AM UTC 2026 % Result : Theorem 0.39s 0.69s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SWV191+1 : TPTP v9.2.1. Bugfixed v3.3.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n008.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 19:59:03 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.69 % SZS status Theorem % 0.39/0.69 % SZS output start Proof % 0.39/0.69 ( % 0.39/0.69 (declare-sort $$unsorted 0) % 0.39/0.69 (declare-const tptp.rho_defuse $$unsorted) % 0.39/0.69 (declare-const tptp.xinit_defuse $$unsorted) % 0.39/0.69 (declare-const tptp.xinit_mean_defuse $$unsorted) % 0.39/0.69 (declare-const tptp.def $$unsorted) % 0.39/0.69 (declare-const tptp.use $$unsorted) % 0.39/0.69 (declare-const tptp.true Bool) % 0.39/0.69 (declare-const tptp.tptp_update2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.z_defuse $$unsorted) % 0.39/0.69 (declare-const tptp.a_select3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.39/0.69 (declare-const tptp.uniform_int_rnd (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.u_defuse $$unsorted) % 0.39/0.69 (declare-const tptp.n3 $$unsorted) % 0.39/0.69 (declare-const tptp.tptp_const_array1 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.pred (-> $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.tptp_minus_1 $$unsorted) % 0.39/0.69 (declare-const tptp.n0 $$unsorted) % 0.39/0.69 (declare-const tptp.tptp_msub (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.n1 $$unsorted) % 0.39/0.69 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.n5 $$unsorted) % 0.39/0.69 (declare-const tptp.sigma_defuse $$unsorted) % 0.39/0.69 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.39/0.69 (declare-const tptp.tptp_update3 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.minus (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.xinit_noise_defuse $$unsorted) % 0.39/0.69 (declare-const tptp.tptp_const_array2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.39/0.69 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.39/0.69 (declare-const tptp.trans (-> $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.a_select2 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.inv (-> $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.dim (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.plus (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.tptp_madd (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.sum (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.tptp_mmul (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.69 (declare-const tptp.tptp_float_0_0 $$unsorted) % 0.39/0.69 (declare-const tptp.n4 $$unsorted) % 0.39/0.69 (declare-const tptp.n2 $$unsorted) % 0.39/0.69 (define @t1 () (@var "Y" $$unsorted)) % 0.39/0.69 (define @t2 () (@var "X" $$unsorted)) % 0.39/0.69 (define @t3 () (= @t2 @t1)) % 0.39/0.69 (define @t4 () (tptp.gt @t1 @t2)) % 0.39/0.69 (define @t5 () (tptp.gt @t2 @t1)) % 0.39/0.69 (define @t6 () (@list @t2 @t1)) % 0.39/0.69 (define @t7 () (@var "Z" $$unsorted)) % 0.39/0.69 (define @t8 () (@list @t2 @t1 @t7)) % 0.39/0.69 (define @t9 () (@list @t2)) % 0.39/0.69 (define @t10 () (forall @t9 (not (tptp.gt @t2 @t2)))) % 0.39/0.69 (define @t11 () (tptp.leq @t2 @t7)) % 0.39/0.69 (define @t12 () (tptp.leq @t1 @t7)) % 0.39/0.69 (define @t13 () (tptp.leq @t2 @t1)) % 0.39/0.69 (define @t14 () (and @t13 @t12)) % 0.39/0.69 (define @t15 () (forall @t8 (=> @t14 @t11))) % 0.39/0.69 (define @t16 () (forall @t6 (=> @t4 @t13))) % 0.39/0.69 (define @t17 () (tptp.succ @t2)) % 0.39/0.69 (define @t18 () (tptp.succ @t1)) % 0.39/0.69 (define @t19 () (@var "C" $$unsorted)) % 0.39/0.69 (define @t20 () (tptp.uniform_int_rnd @t19 @t2)) % 0.39/0.69 (define @t21 () (tptp.leq tptp.n0 @t2)) % 0.39/0.69 (define @t22 () (@list @t2 @t19)) % 0.39/0.69 (define @t23 () (@var "Val" $$unsorted)) % 0.39/0.69 (define @t24 () (@var "I" $$unsorted)) % 0.39/0.69 (define @t25 () (@var "U" $$unsorted)) % 0.39/0.69 (define @t26 () (@var "L" $$unsorted)) % 0.39/0.69 (define @t27 () (tptp.leq @t24 @t25)) % 0.39/0.69 (define @t28 () (@var "J" $$unsorted)) % 0.39/0.69 (define @t29 () (@var "U2" $$unsorted)) % 0.39/0.69 (define @t30 () (@var "L2" $$unsorted)) % 0.39/0.69 (define @t31 () (@var "U1" $$unsorted)) % 0.39/0.69 (define @t32 () (@var "L1" $$unsorted)) % 0.39/0.69 (define @t33 () (@var "A" $$unsorted)) % 0.39/0.69 (define @t34 () (tptp.trans @t33)) % 0.39/0.69 (define @t35 () (@var "N" $$unsorted)) % 0.39/0.69 (define @t36 () (tptp.leq @t28 @t35)) % 0.39/0.69 (define @t37 () (tptp.leq tptp.n0 @t28)) % 0.39/0.69 (define @t38 () (tptp.leq @t24 @t35)) % 0.39/0.69 (define @t39 () (tptp.leq tptp.n0 @t24)) % 0.39/0.69 (define @t40 () (and @t39 @t38 @t37 @t36)) % 0.39/0.69 (define @t41 () (@list @t24 @t28)) % 0.39/0.69 (define @t42 () (forall @t41 (=> @t40 (= (tptp.a_select3 @t33 @t24 @t28) (tptp.a_select3 @t33 @t28 @t24))))) % 0.39/0.69 (define @t43 () (@list @t33 @t35)) % 0.39/0.69 (define @t44 () (tptp.inv @t33)) % 0.39/0.69 (define @t45 () (@var "VAL" $$unsorted)) % 0.39/0.69 (define @t46 () (@var "K" $$unsorted)) % 0.39/0.69 (define @t47 () (tptp.tptp_update3 @t33 @t46 @t46 @t45)) % 0.39/0.69 (define @t48 () (@var "B" $$unsorted)) % 0.39/0.69 (define @t49 () (tptp.tptp_madd @t33 @t48)) % 0.39/0.69 (define @t50 () (= (tptp.a_select3 @t48 @t24 @t28) (tptp.a_select3 @t48 @t28 @t24))) % 0.39/0.69 (define @t51 () (forall @t41 (=> @t40 @t50))) % 0.39/0.69 (define @t52 () (and @t42 @t51)) % 0.39/0.69 (define @t53 () (@list @t33 @t48 @t35)) % 0.39/0.69 (define @t54 () (tptp.tptp_msub @t33 @t48)) % 0.39/0.69 (define @t55 () (tptp.tptp_mmul @t33 (tptp.tptp_mmul @t48 @t34))) % 0.39/0.69 (define @t56 () (forall @t41 (=> @t40 (= (tptp.a_select3 @t55 @t24 @t28) (tptp.a_select3 @t55 @t28 @t24))))) % 0.39/0.69 (define @t57 () (@var "M" $$unsorted)) % 0.39/0.69 (define @t58 () (and @t39 (tptp.leq @t24 @t57) @t37 (tptp.leq @t28 @t57))) % 0.39/0.69 (define @t59 () (@var "E" $$unsorted)) % 0.39/0.69 (define @t60 () (@var "F" $$unsorted)) % 0.39/0.69 (define @t61 () (@var "D" $$unsorted)) % 0.39/0.69 (define @t62 () (tptp.tptp_madd @t33 (tptp.tptp_mmul @t48 (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul @t19 (tptp.tptp_mmul @t61 (tptp.trans @t19))) (tptp.tptp_mmul @t59 (tptp.tptp_mmul @t60 (tptp.trans @t59)))) (tptp.trans @t48))))) % 0.39/0.69 (define @t63 () (@var "Body" $$unsorted)) % 0.39/0.69 (define @t64 () (tptp.sum tptp.n0 tptp.tptp_minus_1 @t63)) % 0.39/0.69 (define @t65 () (@list @t63)) % 0.39/0.69 (define @t66 () (tptp.succ @t17)) % 0.39/0.69 (define @t67 () (tptp.succ @t66)) % 0.39/0.69 (define @t68 () (tptp.succ @t67)) % 0.39/0.69 (define @t69 () (tptp.succ @t68)) % 0.39/0.69 (define @t70 () (tptp.plus tptp.n5 @t2)) % 0.39/0.69 (define @t71 () (forall @t9 (= @t70 @t69))) % 0.39/0.69 (define @t72 () (tptp.pred @t2)) % 0.39/0.69 (define @t73 () (@var "V" $$unsorted)) % 0.39/0.69 (define @t74 () (tptp.tptp_update3 @t2 @t25 @t73 @t45)) % 0.39/0.69 (define @t75 () (@var "VAL2" $$unsorted)) % 0.39/0.69 (define @t76 () (not (= @t24 @t25))) % 0.39/0.69 (define @t77 () (@var "J0" $$unsorted)) % 0.39/0.69 (define @t78 () (@var "I0" $$unsorted)) % 0.39/0.69 (define @t79 () (tptp.leq @t78 @t25)) % 0.39/0.69 (define @t80 () (tptp.leq tptp.n0 @t78)) % 0.39/0.69 (define @t81 () (tptp.tptp_update2 @t2 @t25 @t45)) % 0.39/0.69 (define @t82 () (tptp.a_select3 tptp.z_defuse @t33 @t48)) % 0.39/0.69 (define @t83 () (tptp.leq @t48 tptp.tptp_minus_1)) % 0.39/0.69 (define @t84 () (tptp.leq @t33 tptp.n2)) % 0.39/0.69 (define @t85 () (tptp.leq tptp.n0 @t48)) % 0.39/0.69 (define @t86 () (tptp.leq tptp.n0 @t33)) % 0.39/0.69 (define @t87 () (and @t86 @t85 @t84 @t83)) % 0.39/0.69 (define @t88 () (=> @t87 (= @t82 tptp.use))) % 0.39/0.69 (define @t89 () (@list @t33 @t48)) % 0.39/0.69 (define @t90 () (forall @t89 @t88)) % 0.39/0.69 (define @t91 () (tptp.a_select2 tptp.xinit_noise_defuse tptp.n5)) % 0.39/0.69 (define @t92 () (tptp.a_select2 tptp.xinit_noise_defuse tptp.n4)) % 0.39/0.69 (define @t93 () (tptp.a_select2 tptp.xinit_noise_defuse tptp.n3)) % 0.39/0.69 (define @t94 () (tptp.a_select2 tptp.xinit_noise_defuse tptp.n2)) % 0.39/0.69 (define @t95 () (tptp.a_select2 tptp.xinit_noise_defuse tptp.n1)) % 0.39/0.69 (define @t96 () (tptp.a_select2 tptp.xinit_noise_defuse tptp.n0)) % 0.39/0.69 (define @t97 () (tptp.a_select2 tptp.xinit_mean_defuse tptp.n5)) % 0.39/0.69 (define @t98 () (tptp.a_select2 tptp.xinit_mean_defuse tptp.n4)) % 0.39/0.69 (define @t99 () (tptp.a_select2 tptp.xinit_mean_defuse tptp.n3)) % 0.39/0.69 (define @t100 () (tptp.a_select2 tptp.xinit_mean_defuse tptp.n2)) % 0.39/0.69 (define @t101 () (tptp.a_select2 tptp.xinit_mean_defuse tptp.n1)) % 0.39/0.69 (define @t102 () (tptp.a_select2 tptp.xinit_mean_defuse tptp.n0)) % 0.39/0.69 (define @t103 () (tptp.a_select2 tptp.xinit_defuse tptp.n5)) % 0.39/0.69 (define @t104 () (tptp.a_select2 tptp.xinit_defuse tptp.n4)) % 0.39/0.69 (define @t105 () (tptp.a_select2 tptp.xinit_defuse tptp.n3)) % 0.39/0.69 (define @t106 () (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0)) % 0.39/0.69 (define @t107 () (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0)) % 0.39/0.69 (define @t108 () (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0)) % 0.39/0.69 (define @t109 () (tptp.a_select2 tptp.sigma_defuse tptp.n5)) % 0.39/0.69 (define @t110 () (tptp.a_select2 tptp.sigma_defuse tptp.n4)) % 0.39/0.69 (define @t111 () (tptp.a_select2 tptp.sigma_defuse tptp.n3)) % 0.39/0.69 (define @t112 () (tptp.a_select2 tptp.sigma_defuse tptp.n2)) % 0.39/0.69 (define @t113 () (tptp.a_select2 tptp.sigma_defuse tptp.n1)) % 0.39/0.69 (define @t114 () (tptp.a_select2 tptp.sigma_defuse tptp.n0)) % 0.39/0.69 (define @t115 () (tptp.a_select2 tptp.rho_defuse tptp.n2)) % 0.39/0.69 (define @t116 () (tptp.a_select2 tptp.rho_defuse tptp.n1)) % 0.39/0.69 (define @t117 () (tptp.a_select2 tptp.rho_defuse tptp.n0)) % 0.39/0.69 (define @t118 () (and (= @t117 tptp.use) (= @t116 tptp.use) (= @t115 tptp.use) (= @t114 tptp.use) (= @t113 tptp.use) (= @t112 tptp.use) (= @t111 tptp.use) (= @t110 tptp.use) (= @t109 tptp.use) (= @t108 tptp.use) (= @t107 tptp.use) (= @t106 tptp.use) (= @t105 tptp.use) (= @t104 tptp.use) (= @t103 tptp.use) (= @t102 tptp.use) (= @t101 tptp.use) (= @t100 tptp.use) (= @t99 tptp.use) (= @t98 tptp.use) (= @t97 tptp.use) (= @t96 tptp.use) (= @t95 tptp.use) (= @t94 tptp.use) (= @t93 tptp.use) (= @t92 tptp.use) (= @t91 tptp.use))) % 0.39/0.69 (define @t119 () (=> @t118 @t90)) % 0.39/0.69 (define @t120 () (not @t119)) % 0.39/0.69 (define @t121 () (tptp.gt tptp.n0 tptp.tptp_minus_1)) % 0.39/0.69 (define @t122 () (= @t2 tptp.n4)) % 0.39/0.69 (define @t123 () (= @t2 tptp.n3)) % 0.39/0.69 (define @t124 () (= @t2 tptp.n2)) % 0.39/0.69 (define @t125 () (= @t2 tptp.n1)) % 0.39/0.69 (define @t126 () (= @t2 tptp.n0)) % 0.39/0.69 (define @t127 () (tptp.leq @t2 tptp.n0)) % 0.39/0.69 (define @t128 () (and @t21 @t127)) % 0.39/0.69 (define @t129 () (forall @t9 (=> @t128 @t126))) % 0.39/0.69 (define @t130 () (tptp.succ tptp.n0)) % 0.39/0.69 (define @t131 () (tptp.succ @t130)) % 0.39/0.69 (define @t132 () (tptp.succ @t131)) % 0.39/0.69 (define @t133 () (tptp.succ @t132)) % 0.39/0.69 (define @t134 () (not @t127)) % 0.39/0.69 (define @t135 () (not @t21)) % 0.39/0.69 (define @t136 () (or @t135 @t134 @t126)) % 0.39/0.69 (define @t137 () (tptp.leq tptp.tptp_minus_1 tptp.n0)) % 0.39/0.69 (define @t138 () (not @t137)) % 0.39/0.69 (define @t139 () (tptp.leq tptp.n0 tptp.tptp_minus_1)) % 0.39/0.69 (define @t140 () (not @t139)) % 0.39/0.69 (define @t141 () (or @t140 @t138 (= tptp.tptp_minus_1 tptp.n0))) % 0.39/0.69 (define @t142 () (forall @t9 @t136)) % 0.39/0.69 (define @t143 () (@list tptp.tptp_minus_1)) % 0.39/0.69 (define @t144 () (= tptp.n0 tptp.tptp_minus_1)) % 0.39/0.69 (define @t145 () (or @t140 @t138 @t144)) % 0.39/0.69 (define @t146 () (not @t121)) % 0.39/0.69 (define @t147 () (or @t146 @t137)) % 0.39/0.69 (define @t148 () (@list false false)) % 0.39/0.69 (define @t149 () (not @t12)) % 0.39/0.69 (define @t150 () (not @t13)) % 0.39/0.69 (define @t151 () (= tptp.use @t82)) % 0.39/0.69 (define @t152 () (not @t83)) % 0.39/0.69 (define @t153 () (not @t84)) % 0.39/0.69 (define @t154 () (not @t85)) % 0.39/0.69 (define @t155 () (not @t86)) % 0.39/0.69 (define @t156 () (or @t155 @t154 @t153 @t152 @t151)) % 0.39/0.69 (define @t157 () (forall @t89 @t156)) % 0.39/0.69 (define @t158 () (@quantifiers_skolemize @t157 1)) % 0.39/0.69 (define @t159 () (or @t155 @t154 @t153 @t152)) % 0.39/0.69 (define @t160 () (tptp.leq @t158 tptp.tptp_minus_1)) % 0.39/0.69 (define @t161 () (@quantifiers_skolemize @t157 0)) % 0.39/0.69 (define @t162 () (not @t160)) % 0.39/0.69 (define @t163 () (tptp.leq tptp.n0 @t158)) % 0.39/0.69 (define @t164 () (not @t163)) % 0.39/0.69 (define @t165 () (or (not (tptp.leq tptp.n0 @t161)) @t164 (not (tptp.leq @t161 tptp.n2)) @t162 (= tptp.use (tptp.a_select3 tptp.z_defuse @t161 @t158)))) % 0.39/0.69 (define @t166 () (@list true)) % 0.39/0.69 (define @t167 () (@list @t165)) % 0.39/0.69 (define @t168 () (or @t164 @t162 @t139)) % 0.39/0.69 (define @t169 () (@list false false false)) % 0.39/0.69 (define @t170 () (tptp.gt tptp.n4 tptp.n4)) % 0.39/0.69 (assume @p1 (forall @t6 (or @t5 @t4 @t3))) % 0.39/0.69 (assume @p2 (forall @t8 (=> (and @t5 (tptp.gt @t1 @t7)) (tptp.gt @t2 @t7)))) % 0.39/0.69 (assume @p3 @t10) % 0.39/0.69 (assume @p4 (forall @t9 (tptp.leq @t2 @t2))) % 0.39/0.69 (assume @p5 @t15) % 0.39/0.69 (assume @p6 (forall @t6 (= (tptp.lt @t2 @t1) @t4))) % 0.39/0.69 (assume @p7 (forall @t6 (= (tptp.geq @t2 @t1) (tptp.leq @t1 @t2)))) % 0.39/0.69 (assume @p8 @t16) % 0.39/0.69 (assume @p9 (forall @t6 (=> (and @t13 (not @t3)) @t4))) % 0.39/0.69 (assume @p10 (forall @t6 (= (tptp.leq @t2 (tptp.pred @t1)) @t4))) % 0.39/0.69 (assume @p11 (forall @t9 (tptp.gt @t17 @t2))) % 0.39/0.69 (assume @p12 (forall @t6 (=> @t13 (tptp.leq @t2 @t18)))) % 0.39/0.69 (assume @p13 (forall @t6 (= @t13 (tptp.gt @t18 @t2)))) % 0.39/0.69 (assume @p14 (forall @t22 (=> @t21 (tptp.leq @t20 @t2)))) % 0.39/0.69 (assume @p15 (forall @t22 (=> @t21 (tptp.leq tptp.n0 @t20)))) % 0.39/0.69 (assume @p16 (forall (@list @t24 @t26 @t25 @t23) (=> (and (tptp.leq @t26 @t24) @t27) (= (tptp.a_select2 (tptp.tptp_const_array1 (tptp.dim @t26 @t25) @t23) @t24) @t23)))) % 0.39/0.69 (assume @p17 (forall (@list @t24 @t32 @t31 @t28 @t30 @t29 @t23) (=> (and (tptp.leq @t32 @t24) (tptp.leq @t24 @t31) (tptp.leq @t30 @t28) (tptp.leq @t28 @t29)) (= (tptp.a_select3 (tptp.tptp_const_array2 (tptp.dim @t32 @t31) (tptp.dim @t30 @t29) @t23) @t24 @t28) @t23)))) % 0.39/0.69 (assume @p18 (forall @t43 (=> @t42 (forall @t41 (=> @t40 (= (tptp.a_select3 @t34 @t24 @t28) (tptp.a_select3 @t34 @t28 @t24))))))) % 0.39/0.69 (assume @p19 (forall @t43 (=> @t42 (forall @t41 (=> @t40 (= (tptp.a_select3 @t44 @t24 @t28) (tptp.a_select3 @t44 @t28 @t24))))))) % 0.39/0.69 (assume @p20 (forall @t43 (=> @t42 (forall (@list @t24 @t28 @t46 @t45) (=> (and @t39 @t38 @t37 @t36 (tptp.leq tptp.n0 @t46) (tptp.leq @t46 @t35)) (= (tptp.a_select3 @t47 @t24 @t28) (tptp.a_select3 @t47 @t28 @t24))))))) % 0.39/0.69 (assume @p21 (forall @t53 (=> @t52 (forall @t41 (=> @t40 (= (tptp.a_select3 @t49 @t24 @t28) (tptp.a_select3 @t49 @t28 @t24))))))) % 0.39/0.69 (assume @p22 (forall @t53 (=> @t52 (forall @t41 (=> @t40 (= (tptp.a_select3 @t54 @t24 @t28) (tptp.a_select3 @t54 @t28 @t24))))))) % 0.39/0.69 (assume @p23 (forall @t53 (=> @t51 @t56))) % 0.39/0.69 (assume @p24 (forall (@list @t33 @t48 @t35 @t57) (=> (forall @t41 (=> @t58 @t50)) @t56))) % 0.39/0.69 (assume @p25 (forall (@list @t33 @t48 @t19 @t61 @t59 @t60 @t35 @t57) (=> (and (forall @t41 (=> @t58 (= (tptp.a_select3 @t61 @t24 @t28) (tptp.a_select3 @t61 @t28 @t24)))) @t42 (forall @t41 (=> @t40 (= (tptp.a_select3 @t60 @t24 @t28) (tptp.a_select3 @t60 @t28 @t24))))) (forall @t41 (=> @t40 (= (tptp.a_select3 @t62 @t24 @t28) (tptp.a_select3 @t62 @t28 @t24))))))) % 0.39/0.69 (assume @p26 (forall @t65 (= @t64 tptp.n0))) % 0.39/0.69 (assume @p27 (forall @t65 (= tptp.tptp_float_0_0 @t64))) % 0.39/0.69 (assume @p28 (= (tptp.succ tptp.tptp_minus_1) tptp.n0)) % 0.39/0.69 (assume @p29 (forall @t9 (= (tptp.plus @t2 tptp.n1) @t17))) % 0.39/0.69 (assume @p30 (forall @t9 (= (tptp.plus tptp.n1 @t2) @t17))) % 0.39/0.69 (assume @p31 (forall @t9 (= (tptp.plus @t2 tptp.n2) @t66))) % 0.39/0.69 (assume @p32 (forall @t9 (= (tptp.plus tptp.n2 @t2) @t66))) % 0.39/0.69 (assume @p33 (forall @t9 (= (tptp.plus @t2 tptp.n3) @t67))) % 0.39/0.69 (assume @p34 (forall @t9 (= (tptp.plus tptp.n3 @t2) @t67))) % 0.39/0.69 (assume @p35 (forall @t9 (= (tptp.plus @t2 tptp.n4) @t68))) % 0.39/0.69 (assume @p36 (forall @t9 (= (tptp.plus tptp.n4 @t2) @t68))) % 0.39/0.69 (assume @p37 (forall @t9 (= (tptp.plus @t2 tptp.n5) @t69))) % 0.39/0.69 (assume @p38 @t71) % 0.39/0.69 (assume @p39 (forall @t9 (= (tptp.minus @t2 tptp.n1) @t72))) % 0.39/0.69 (assume @p40 (forall @t9 (= (tptp.pred @t17) @t2))) % 0.39/0.69 (assume @p41 (forall @t9 (= (tptp.succ @t72) @t2))) % 0.39/0.69 (assume @p42 (forall @t6 (= (tptp.leq @t17 @t18) @t13))) % 0.39/0.69 (assume @p43 (forall @t6 (=> (tptp.leq @t17 @t1) @t4))) % 0.39/0.69 (assume @p44 (forall @t6 (=> (tptp.leq (tptp.minus @t2 @t1) @t2) (tptp.leq tptp.n0 @t1)))) % 0.39/0.69 (assume @p45 (forall (@list @t2 @t25 @t73 @t45) (= (tptp.a_select3 @t74 @t25 @t73) @t45))) % 0.39/0.69 (assume @p46 (forall (@list @t24 @t28 @t25 @t73 @t2 @t45 @t75) (=> (and @t76 (= @t28 @t73) (= (tptp.a_select3 @t2 @t25 @t73) @t45)) (= (tptp.a_select3 (tptp.tptp_update3 @t2 @t24 @t28 @t75) @t25 @t73) @t45)))) % 0.39/0.69 (assume @p47 (forall (@list @t24 @t28 @t25 @t73 @t2 @t45) (=> (and (forall (@list @t78 @t77) (=> (and @t80 (tptp.leq tptp.n0 @t77) @t79 (tptp.leq @t77 @t73)) (= (tptp.a_select3 @t2 @t78 @t77) @t45))) @t39 @t27 @t37 (tptp.leq @t28 @t73)) (= (tptp.a_select3 @t74 @t24 @t28) @t45)))) % 0.39/0.69 (assume @p48 (forall (@list @t2 @t25 @t45) (= (tptp.a_select2 @t81 @t25) @t45))) % 0.39/0.69 (assume @p49 (forall (@list @t24 @t25 @t2 @t45 @t75) (=> (and @t76 (= (tptp.a_select2 @t2 @t25) @t45)) (= (tptp.a_select2 (tptp.tptp_update2 @t2 @t24 @t75) @t25) @t45)))) % 0.39/0.69 (assume @p50 (forall (@list @t24 @t25 @t2 @t45) (=> (and (forall (@list @t78) (=> (and @t80 @t79) (= (tptp.a_select2 @t2 @t78) @t45))) @t39 @t27) (= (tptp.a_select2 @t81 @t24) @t45)))) % 0.39/0.69 (assume @p51 tptp.true) % 0.39/0.69 (assume @p52 (not (= tptp.def tptp.use))) % 0.39/0.69 (assume @p53 @t120) % 0.39/0.69 (assume @p54 (tptp.gt tptp.n5 tptp.n4)) % 0.39/0.69 (assume @p55 (tptp.gt tptp.n4 tptp.tptp_minus_1)) % 0.39/0.69 (assume @p56 (tptp.gt tptp.n5 tptp.tptp_minus_1)) % 0.39/0.69 (assume @p57 @t121) % 0.39/0.69 (assume @p58 (tptp.gt tptp.n1 tptp.tptp_minus_1)) % 0.39/0.69 (assume @p59 (tptp.gt tptp.n2 tptp.tptp_minus_1)) % 0.39/0.69 (assume @p60 (tptp.gt tptp.n3 tptp.tptp_minus_1)) % 0.39/0.69 (assume @p61 (tptp.gt tptp.n4 tptp.n0)) % 0.39/0.69 (assume @p62 (tptp.gt tptp.n5 tptp.n0)) % 0.39/0.69 (assume @p63 (tptp.gt tptp.n1 tptp.n0)) % 0.39/0.69 (assume @p64 (tptp.gt tptp.n2 tptp.n0)) % 0.39/0.69 (assume @p65 (tptp.gt tptp.n3 tptp.n0)) % 0.39/0.69 (assume @p66 (tptp.gt tptp.n4 tptp.n1)) % 0.39/0.69 (assume @p67 (tptp.gt tptp.n5 tptp.n1)) % 0.39/0.69 (assume @p68 (tptp.gt tptp.n2 tptp.n1)) % 0.39/0.69 (assume @p69 (tptp.gt tptp.n3 tptp.n1)) % 0.39/0.69 (assume @p70 (tptp.gt tptp.n4 tptp.n2)) % 0.39/0.69 (assume @p71 (tptp.gt tptp.n5 tptp.n2)) % 0.39/0.69 (assume @p72 (tptp.gt tptp.n3 tptp.n2)) % 0.39/0.69 (assume @p73 (tptp.gt tptp.n4 tptp.n3)) % 0.39/0.69 (assume @p74 (tptp.gt tptp.n5 tptp.n3)) % 0.39/0.69 (assume @p75 (forall @t9 (=> (and @t21 (tptp.leq @t2 tptp.n4)) (or @t126 @t125 @t124 @t123 @t122)))) % 0.39/0.69 (assume @p76 (forall @t9 (=> (and @t21 (tptp.leq @t2 tptp.n5)) (or @t126 @t125 @t124 @t123 @t122 (= @t2 tptp.n5))))) % 0.39/0.69 (assume @p77 @t129) % 0.39/0.69 (assume @p78 (forall @t9 (=> (and @t21 (tptp.leq @t2 tptp.n1)) (or @t126 @t125)))) % 0.39/0.69 (assume @p79 (forall @t9 (=> (and @t21 (tptp.leq @t2 tptp.n2)) (or @t126 @t125 @t124)))) % 0.39/0.69 (assume @p80 (forall @t9 (=> (and @t21 (tptp.leq @t2 tptp.n3)) (or @t126 @t125 @t124 @t123)))) % 0.39/0.69 (assume @p81 (= @t133 tptp.n4)) % 0.39/0.69 (assume @p82 (= (tptp.succ @t133) tptp.n5)) % 0.39/0.69 (assume @p83 (= @t130 tptp.n1)) % 0.39/0.69 (assume @p84 (= @t131 tptp.n2)) % 0.39/0.69 (assume @p85 (= @t132 tptp.n3)) % 0.39/0.69 (assume @p86 true) % 0.39/0.69 (step @p87 :rule true_intro :premises (@p54)) % 0.39/0.69 (step @p88 :rule refl :args (tptp.n4)) % 0.39/0.69 (step @p89 :rule eq-symm :args (@t70 @t69)) % 0.39/0.69 (step @p90 :rule cong :premises (@p89) :args (@t71)) % 0.39/0.69 (step @p91 :rule eq_resolve :premises (@p38 @p90)) % 0.39/0.69 (step @p92 :rule instantiate :premises (@p91) :args ((@list tptp.n0))) % 0.39/0.69 (step @p93 :rule symm :premises (@p92)) % 0.39/0.69 (step @p94 :rule aci_norm :args ((= (or (or @t135 @t134) @t126) @t136))) % 0.39/0.69 (step @p95 :rule refl :args (@t126)) % 0.39/0.69 (step @p96 :rule bool-and-de-morgan :args (@t21 @t127 true)) % 0.39/0.69 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or (not @t128) @t126))) % 0.39/0.69 (step @p98 :rule trans :premises (@p97 @p94)) % 0.39/0.69 (step @p99 :rule bool-impl-elim :args (@t128 @t126)) % 0.39/0.69 (step @p100 :rule trans :premises (@p99 @p98)) % 0.39/0.69 (step @p101 :rule cong :premises (@p100) :args (@t129)) % 0.39/0.69 (step @p102 :rule eq_resolve :premises (@p77 @p101)) % 0.39/0.69 (step @p103 :rule eq-symm :args (tptp.tptp_minus_1 tptp.n0)) % 0.39/0.69 (step @p104 :rule refl :args (@t138)) % 0.39/0.69 (step @p105 :rule refl :args (@t140)) % 0.39/0.69 (step @p106 :rule nary_cong :premises (@p105 @p104 @p103) :args (@t141)) % 0.39/0.69 (step @p107 :rule refl :args (@t142)) % 0.39/0.69 (step @p108 :rule cong :premises (@p107 @p106) :args ((=> @t142 @t141))) % 0.39/0.69 (assume-push @p228 @t142) % 0.39/0.69 (step @p110 :rule instantiate :premises (@p102) :args (@t143)) % 0.39/0.69 (step-pop @p229 :rule scope :premises (@p110)) % 0.39/0.69 (step @p111 :rule process_scope :premises (@p229) :args (@t141)) % 0.39/0.69 (step @p113 :rule eq_resolve :premises (@p111 @p108)) % 0.39/0.69 (step @p114 :rule implies_elim :premises (@p113)) % 0.39/0.69 (step @p115 :rule chain_m_resolution :premises (@p114 @p102) :args (@t145 (@list false) (@list @t142))) % 0.39/0.69 (step @p116 :rule bool-impl-elim :args (@t4 @t13)) % 0.39/0.69 (step @p117 :rule cong :premises (@p116) :args (@t16)) % 0.39/0.69 (step @p118 :rule eq_resolve :premises (@p8 @p117)) % 0.39/0.69 (step @p119 :rule instantiate :premises (@p118) :args ((@list tptp.tptp_minus_1 tptp.n0))) % 0.39/0.69 (step @p120 :rule cnf_or_pos :args (@t147)) % 0.39/0.69 (step @p121 :rule reordering :premises (@p120) :args ((or @t146 @t137 (not @t147)))) % 0.39/0.69 (step @p122 :rule chain_m_resolution :premises (@p121 @p57 @p119) :args (@t137 @t148 (@list @t121 @t147))) % 0.39/0.69 (step @p123 :rule aci_norm :args ((= (or (or @t150 @t149) @t11) (or @t150 @t149 @t11)))) % 0.39/0.69 (step @p124 :rule refl :args (@t11)) % 0.39/0.69 (step @p125 :rule bool-and-de-morgan :args (@t13 @t12 true)) % 0.39/0.69 (step @p126 :rule nary_cong :premises (@p125 @p124) :args ((or (not @t14) @t11))) % 0.39/0.69 (step @p127 :rule trans :premises (@p126 @p123)) % 0.39/0.69 (step @p128 :rule bool-impl-elim :args (@t14 @t11)) % 0.39/0.69 (step @p129 :rule trans :premises (@p128 @p127)) % 0.39/0.69 (step @p130 :rule cong :premises (@p129) :args (@t15)) % 0.39/0.69 (step @p131 :rule eq_resolve :premises (@p5 @p130)) % 0.39/0.69 (step @p132 :rule instantiate :premises (@p131) :args ((@list tptp.n0 @t158 tptp.tptp_minus_1))) % 0.39/0.69 (step @p133 :rule aci_norm :args ((= (or @t159 @t151) @t156))) % 0.39/0.69 (step @p134 :rule refl :args (@t151)) % 0.39/0.69 (step @p135 :rule aci_norm :args ((= (or @t155 (or @t154 (or @t153 @t152))) @t159))) % 0.39/0.69 (step @p136 :rule bool-and-de-morgan :args (@t84 @t83 true)) % 0.39/0.69 (step @p137 :rule refl :args (@t154)) % 0.39/0.69 (step @p138 :rule nary_cong :premises (@p137 @p136) :args ((or @t154 (not (and @t84 @t83))))) % 0.39/0.69 (step @p139 :rule bool-and-de-morgan :args (@t85 @t84 (and @t83))) % 0.39/0.69 (step @p140 :rule trans :premises (@p139 @p138)) % 0.39/0.69 (step @p141 :rule refl :args (@t155)) % 0.39/0.69 (step @p142 :rule nary_cong :premises (@p141 @p140) :args ((or @t155 (not (and @t85 @t84 @t83))))) % 0.39/0.69 (step @p143 :rule bool-and-de-morgan :args (@t86 @t85 (and @t84 @t83))) % 0.39/0.69 (step @p144 :rule trans :premises (@p143 @p142)) % 0.39/0.69 (step @p145 :rule trans :premises (@p144 @p135)) % 0.39/0.69 (step @p146 :rule nary_cong :premises (@p145 @p134) :args ((or (not @t87) @t151))) % 0.39/0.69 (step @p147 :rule trans :premises (@p146 @p133)) % 0.39/0.69 (step @p148 :rule bool-impl-elim :args (@t87 @t151)) % 0.39/0.69 (step @p149 :rule trans :premises (@p148 @p147)) % 0.39/0.69 (step @p150 :rule cong :premises (@p149) :args ((forall @t89 (=> @t87 @t151)))) % 0.39/0.69 (step @p151 :rule eq-symm :args (@t82 tptp.use)) % 0.39/0.69 (step @p152 :rule refl :args (@t87)) % 0.39/0.69 (step @p153 :rule cong :premises (@p152 @p151) :args (@t88)) % 0.39/0.69 (step @p154 :rule cong :premises (@p153) :args (@t90)) % 0.39/0.69 (step @p155 :rule trans :premises (@p154 @p150)) % 0.39/0.69 (step @p156 :rule eq-symm :args (@t91 tptp.use)) % 0.39/0.69 (step @p157 :rule eq-symm :args (@t92 tptp.use)) % 0.39/0.69 (step @p158 :rule eq-symm :args (@t93 tptp.use)) % 0.39/0.69 (step @p159 :rule eq-symm :args (@t94 tptp.use)) % 0.39/0.69 (step @p160 :rule eq-symm :args (@t95 tptp.use)) % 0.39/0.69 (step @p161 :rule eq-symm :args (@t96 tptp.use)) % 0.39/0.69 (step @p162 :rule eq-symm :args (@t97 tptp.use)) % 0.39/0.69 (step @p163 :rule eq-symm :args (@t98 tptp.use)) % 0.39/0.69 (step @p164 :rule eq-symm :args (@t99 tptp.use)) % 0.39/0.69 (step @p165 :rule eq-symm :args (@t100 tptp.use)) % 0.39/0.69 (step @p166 :rule eq-symm :args (@t101 tptp.use)) % 0.39/0.69 (step @p167 :rule eq-symm :args (@t102 tptp.use)) % 0.39/0.69 (step @p168 :rule eq-symm :args (@t103 tptp.use)) % 0.39/0.69 (step @p169 :rule eq-symm :args (@t104 tptp.use)) % 0.39/0.69 (step @p170 :rule eq-symm :args (@t105 tptp.use)) % 0.39/0.69 (step @p171 :rule eq-symm :args (@t106 tptp.use)) % 0.39/0.69 (step @p172 :rule eq-symm :args (@t107 tptp.use)) % 0.39/0.69 (step @p173 :rule eq-symm :args (@t108 tptp.use)) % 0.39/0.69 (step @p174 :rule eq-symm :args (@t109 tptp.use)) % 0.39/0.69 (step @p175 :rule eq-symm :args (@t110 tptp.use)) % 0.39/0.69 (step @p176 :rule eq-symm :args (@t111 tptp.use)) % 0.39/0.69 (step @p177 :rule eq-symm :args (@t112 tptp.use)) % 0.39/0.69 (step @p178 :rule eq-symm :args (@t113 tptp.use)) % 0.39/0.69 (step @p179 :rule eq-symm :args (@t114 tptp.use)) % 0.39/0.69 (step @p180 :rule eq-symm :args (@t115 tptp.use)) % 0.39/0.69 (step @p181 :rule eq-symm :args (@t116 tptp.use)) % 0.39/0.69 (step @p182 :rule eq-symm :args (@t117 tptp.use)) % 0.39/0.69 (step @p183 :rule nary_cong :premises (@p182 @p181 @p180 @p179 @p178 @p177 @p176 @p175 @p174 @p173 @p172 @p171 @p170 @p169 @p168 @p167 @p166 @p165 @p164 @p163 @p162 @p161 @p160 @p159 @p158 @p157 @p156) :args (@t118)) % 0.39/0.69 (step @p184 :rule cong :premises (@p183 @p155) :args (@t119)) % 0.39/0.69 (step @p185 :rule cong :premises (@p184) :args (@t120)) % 0.39/0.69 (step @p186 :rule eq_resolve :premises (@p53 @p185)) % 0.39/0.69 (step @p187 :rule not_implies_elim2 :premises (@p186)) % 0.39/0.69 (step @p188 :rule skolemize :premises (@p187)) % 0.39/0.69 (step @p189 :rule bool-double-not-elim :args (@t160)) % 0.39/0.69 (step @p190 :rule refl :args (@t165)) % 0.39/0.69 (step @p191 :rule nary_cong :premises (@p190 @p189) :args ((or @t165 (not @t162)))) % 0.39/0.69 (step @p192 :rule cnf_or_neg :args (@t165 3)) % 0.39/0.69 (step @p193 :rule eq_resolve :premises (@p192 @p191)) % 0.39/0.69 (step @p194 :rule reordering :premises (@p193) :args ((or @t160 @t165))) % 0.39/0.69 (step @p195 :rule chain_m_resolution :premises (@p194 @p188) :args (@t160 @t166 @t167)) % 0.39/0.69 (step @p196 :rule bool-double-not-elim :args (@t163)) % 0.39/0.69 (step @p197 :rule nary_cong :premises (@p190 @p196) :args ((or @t165 (not @t164)))) % 0.39/0.69 (step @p198 :rule cnf_or_neg :args (@t165 1)) % 0.39/0.69 (step @p199 :rule eq_resolve :premises (@p198 @p197)) % 0.39/0.69 (step @p200 :rule reordering :premises (@p199) :args ((or @t163 @t165))) % 0.39/0.69 (step @p201 :rule chain_m_resolution :premises (@p200 @p188) :args (@t163 @t166 @t167)) % 0.39/0.69 (step @p202 :rule cnf_or_pos :args (@t168)) % 0.39/0.69 (step @p203 :rule reordering :premises (@p202) :args ((or @t164 @t162 @t139 (not @t168)))) % 0.39/0.69 (step @p204 :rule chain_m_resolution :premises (@p203 @p201 @p195 @p132) :args (@t139 @t169 (@list @t163 @t160 @t168))) % 0.39/0.69 (step @p205 :rule cnf_or_pos :args (@t145)) % 0.39/0.69 (step @p206 :rule reordering :premises (@p205) :args ((or @t140 @t138 @t144 (not @t145)))) % 0.39/0.69 (step @p207 :rule chain_m_resolution :premises (@p206 @p204 @p122 @p115) :args (@t144 @t169 (@list @t139 @t137 @t145))) % 0.39/0.69 (step @p208 :rule symm :premises (@p207)) % 0.39/0.69 (step @p209 :rule refl :args (tptp.n5)) % 0.39/0.69 (step @p210 :rule cong :premises (@p209 @p208) :args ((tptp.plus tptp.n5 tptp.tptp_minus_1))) % 0.39/0.69 (step @p211 :rule instantiate :premises (@p91) :args (@t143)) % 0.39/0.69 (step @p212 :rule symm :premises (@p28)) % 0.39/0.69 (step @p213 :rule cong :premises (@p212) :args (@t130)) % 0.39/0.69 (step @p214 :rule cong :premises (@p213) :args (@t131)) % 0.39/0.69 (step @p215 :rule cong :premises (@p214) :args (@t132)) % 0.39/0.69 (step @p216 :rule cong :premises (@p215) :args (@t133)) % 0.39/0.69 (step @p217 :rule symm :premises (@p81)) % 0.39/0.69 (step @p218 :rule trans :premises (@p217 @p216 @p211 @p210 @p93 @p82)) % 0.39/0.69 (step @p219 :rule cong :premises (@p218 @p88) :args (@t170)) % 0.39/0.69 (step @p220 :rule trans :premises (@p219 @p87)) % 0.39/0.69 (step @p221 :rule true_elim :premises (@p220)) % 0.39/0.69 (assume-push @p230 @t10) % 0.39/0.69 (step @p223 :rule instantiate :premises (@p3) :args ((@list tptp.n4))) % 0.39/0.69 (step-pop @p231 :rule scope :premises (@p223)) % 0.39/0.69 (step @p224 :rule process_scope :premises (@p231) :args ((not @t170))) % 0.39/0.69 (step @p226 :rule implies_elim :premises (@p224)) % 0.39/0.69 (step @p227 false :rule chain_m_resolution :premises (@p226 @p221 @p3) :args (false @t148 (@list @t170 @t10))) % 0.39/0.69 ) % 0.39/0.69 % SZS output end Proof % 0.39/0.69 % cvc5 exiting %------------------------------------------------------------------------------