%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV160+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 09:00:38 AM UTC 2026 % Result : Theorem 0.35s 0.70s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWV160+1 : TPTP v9.2.1. Bugfixed v3.3.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n003.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 19:57:29 EDT 2026 % 0.16/0.35 % CPUTime : % 0.26/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.35/0.70 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.35/0.70 % SZS status Theorem % 0.35/0.70 % SZS output start Proof % 0.35/0.70 ( % 0.35/0.70 (declare-sort $$unsorted 0) % 0.35/0.70 (declare-const tptp.tptp_term_equals (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.exp (-> $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.x $$unsorted) % 0.35/0.70 (declare-const tptp.rho $$unsorted) % 0.35/0.70 (declare-const tptp.times (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.sigma $$unsorted) % 0.35/0.70 (declare-const tptp.pv47 $$unsorted) % 0.35/0.70 (declare-const tptp.pv84 $$unsorted) % 0.35/0.70 (declare-const tptp.q $$unsorted) % 0.35/0.70 (declare-const tptp.tptp_sum_index $$unsorted) % 0.35/0.70 (declare-const tptp.def $$unsorted) % 0.35/0.70 (declare-const tptp.use $$unsorted) % 0.35/0.70 (declare-const tptp.true Bool) % 0.35/0.70 (declare-const tptp.tptp_update2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.divide (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.a_select3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.sqrt (-> $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.35/0.70 (declare-const tptp.uniform_int_rnd (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.mu $$unsorted) % 0.35/0.70 (declare-const tptp.n3 $$unsorted) % 0.35/0.70 (declare-const tptp.tptp_const_array1 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.cond (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.pred (-> $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.tptp_minus_1 $$unsorted) % 0.35/0.70 (declare-const tptp.n0 $$unsorted) % 0.35/0.70 (declare-const tptp.tptp_msub (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.n1 $$unsorted) % 0.35/0.70 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.n5 $$unsorted) % 0.35/0.70 (declare-const tptp.pv10 $$unsorted) % 0.35/0.70 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.35/0.70 (declare-const tptp.tptp_update3 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.minus (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.tptp_minus_2 $$unsorted) % 0.35/0.70 (declare-const tptp.tptp_const_array2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.35/0.70 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.35/0.70 (declare-const tptp.trans (-> $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.a_select2 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.inv (-> $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.dim (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.plus (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.n135299 $$unsorted) % 0.35/0.70 (declare-const tptp.tptp_madd (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.sum (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.tptp_mmul (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.70 (declare-const tptp.tptp_float_0_0 $$unsorted) % 0.35/0.70 (declare-const tptp.tptp_pi $$unsorted) % 0.35/0.70 (declare-const tptp.n4 $$unsorted) % 0.35/0.70 (declare-const tptp.n2 $$unsorted) % 0.35/0.70 (define @t1 () (@var "Y" $$unsorted)) % 0.35/0.70 (define @t2 () (@var "X" $$unsorted)) % 0.35/0.70 (define @t3 () (= @t2 @t1)) % 0.35/0.70 (define @t4 () (tptp.gt @t1 @t2)) % 0.35/0.70 (define @t5 () (tptp.gt @t2 @t1)) % 0.35/0.70 (define @t6 () (@list @t2 @t1)) % 0.35/0.70 (define @t7 () (@var "Z" $$unsorted)) % 0.35/0.70 (define @t8 () (@list @t2 @t1 @t7)) % 0.35/0.70 (define @t9 () (@list @t2)) % 0.35/0.70 (define @t10 () (forall @t9 (not (tptp.gt @t2 @t2)))) % 0.35/0.70 (define @t11 () (tptp.leq @t2 @t1)) % 0.35/0.70 (define @t12 () (tptp.leq @t2 (tptp.pred @t1))) % 0.35/0.70 (define @t13 () (forall @t6 (= @t12 @t4))) % 0.35/0.70 (define @t14 () (tptp.succ @t2)) % 0.35/0.70 (define @t15 () (tptp.succ @t1)) % 0.35/0.70 (define @t16 () (@var "C" $$unsorted)) % 0.35/0.70 (define @t17 () (tptp.uniform_int_rnd @t16 @t2)) % 0.35/0.70 (define @t18 () (tptp.leq tptp.n0 @t2)) % 0.35/0.70 (define @t19 () (@list @t2 @t16)) % 0.35/0.70 (define @t20 () (@var "Val" $$unsorted)) % 0.35/0.70 (define @t21 () (@var "I" $$unsorted)) % 0.35/0.70 (define @t22 () (@var "U" $$unsorted)) % 0.35/0.70 (define @t23 () (@var "L" $$unsorted)) % 0.35/0.70 (define @t24 () (tptp.leq @t21 @t22)) % 0.35/0.70 (define @t25 () (@var "J" $$unsorted)) % 0.35/0.70 (define @t26 () (@var "U2" $$unsorted)) % 0.35/0.70 (define @t27 () (@var "L2" $$unsorted)) % 0.35/0.70 (define @t28 () (@var "U1" $$unsorted)) % 0.35/0.70 (define @t29 () (@var "L1" $$unsorted)) % 0.35/0.70 (define @t30 () (@var "A" $$unsorted)) % 0.35/0.70 (define @t31 () (tptp.trans @t30)) % 0.35/0.70 (define @t32 () (@var "N" $$unsorted)) % 0.35/0.70 (define @t33 () (tptp.leq @t25 @t32)) % 0.35/0.70 (define @t34 () (tptp.leq tptp.n0 @t25)) % 0.35/0.70 (define @t35 () (tptp.leq @t21 @t32)) % 0.35/0.70 (define @t36 () (tptp.leq tptp.n0 @t21)) % 0.35/0.70 (define @t37 () (and @t36 @t35 @t34 @t33)) % 0.35/0.70 (define @t38 () (@list @t21 @t25)) % 0.35/0.70 (define @t39 () (forall @t38 (=> @t37 (= (tptp.a_select3 @t30 @t21 @t25) (tptp.a_select3 @t30 @t25 @t21))))) % 0.35/0.70 (define @t40 () (@list @t30 @t32)) % 0.35/0.70 (define @t41 () (tptp.inv @t30)) % 0.35/0.70 (define @t42 () (@var "VAL" $$unsorted)) % 0.35/0.70 (define @t43 () (@var "K" $$unsorted)) % 0.35/0.70 (define @t44 () (tptp.tptp_update3 @t30 @t43 @t43 @t42)) % 0.35/0.70 (define @t45 () (@var "B" $$unsorted)) % 0.35/0.70 (define @t46 () (tptp.tptp_madd @t30 @t45)) % 0.35/0.70 (define @t47 () (= (tptp.a_select3 @t45 @t21 @t25) (tptp.a_select3 @t45 @t25 @t21))) % 0.35/0.70 (define @t48 () (forall @t38 (=> @t37 @t47))) % 0.35/0.70 (define @t49 () (and @t39 @t48)) % 0.35/0.70 (define @t50 () (@list @t30 @t45 @t32)) % 0.35/0.70 (define @t51 () (tptp.tptp_msub @t30 @t45)) % 0.35/0.70 (define @t52 () (tptp.tptp_mmul @t30 (tptp.tptp_mmul @t45 @t31))) % 0.35/0.70 (define @t53 () (forall @t38 (=> @t37 (= (tptp.a_select3 @t52 @t21 @t25) (tptp.a_select3 @t52 @t25 @t21))))) % 0.35/0.70 (define @t54 () (@var "M" $$unsorted)) % 0.35/0.70 (define @t55 () (and @t36 (tptp.leq @t21 @t54) @t34 (tptp.leq @t25 @t54))) % 0.35/0.70 (define @t56 () (@var "E" $$unsorted)) % 0.35/0.70 (define @t57 () (@var "F" $$unsorted)) % 0.35/0.70 (define @t58 () (@var "D" $$unsorted)) % 0.35/0.70 (define @t59 () (tptp.tptp_madd @t30 (tptp.tptp_mmul @t45 (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul @t16 (tptp.tptp_mmul @t58 (tptp.trans @t16))) (tptp.tptp_mmul @t56 (tptp.tptp_mmul @t57 (tptp.trans @t56)))) (tptp.trans @t45))))) % 0.35/0.70 (define @t60 () (@var "Body" $$unsorted)) % 0.35/0.70 (define @t61 () (tptp.sum tptp.n0 tptp.tptp_minus_1 @t60)) % 0.35/0.70 (define @t62 () (@list @t60)) % 0.35/0.70 (define @t63 () (tptp.succ @t14)) % 0.35/0.70 (define @t64 () (tptp.succ @t63)) % 0.35/0.70 (define @t65 () (tptp.succ @t64)) % 0.35/0.70 (define @t66 () (tptp.succ @t65)) % 0.35/0.70 (define @t67 () (tptp.pred @t2)) % 0.35/0.70 (define @t68 () (@var "V" $$unsorted)) % 0.35/0.70 (define @t69 () (tptp.tptp_update3 @t2 @t22 @t68 @t42)) % 0.35/0.70 (define @t70 () (@var "VAL2" $$unsorted)) % 0.35/0.70 (define @t71 () (not (= @t21 @t22))) % 0.35/0.70 (define @t72 () (@var "J0" $$unsorted)) % 0.35/0.70 (define @t73 () (@var "I0" $$unsorted)) % 0.35/0.70 (define @t74 () (tptp.leq @t73 @t22)) % 0.35/0.70 (define @t75 () (tptp.leq tptp.n0 @t73)) % 0.35/0.70 (define @t76 () (tptp.tptp_update2 @t2 @t22 @t42)) % 0.35/0.70 (define @t77 () (tptp.a_select2 tptp.sigma tptp.pv47)) % 0.35/0.70 (define @t78 () (tptp.sqrt (tptp.times tptp.n2 tptp.tptp_pi))) % 0.35/0.70 (define @t79 () (tptp.a_select2 tptp.x tptp.pv10)) % 0.35/0.70 (define @t80 () (tptp.minus @t79 (tptp.a_select2 tptp.mu tptp.pv47))) % 0.35/0.70 (define @t81 () (tptp.divide (tptp.divide (tptp.times (tptp.exp (tptp.divide (tptp.divide (tptp.times @t80 @t80) tptp.tptp_minus_2) (tptp.times @t77 @t77))) (tptp.a_select2 tptp.rho tptp.pv47)) (tptp.times @t78 @t77)) tptp.pv84)) % 0.35/0.70 (define @t82 () (tptp.tptp_term_equals tptp.pv47 tptp.tptp_sum_index)) % 0.35/0.70 (define @t83 () (tptp.sum tptp.n0 tptp.n4 (tptp.cond @t82 @t81 (tptp.a_select3 tptp.q @t16 tptp.tptp_sum_index)))) % 0.35/0.70 (define @t84 () (=> (= tptp.pv10 @t16) (= @t83 tptp.n1))) % 0.35/0.70 (define @t85 () (tptp.pred tptp.pv10)) % 0.35/0.70 (define @t86 () (tptp.leq @t16 @t85)) % 0.35/0.70 (define @t87 () (tptp.leq tptp.n0 @t16)) % 0.35/0.70 (define @t88 () (and @t87 @t86)) % 0.35/0.70 (define @t89 () (=> @t88 @t84)) % 0.35/0.70 (define @t90 () (@list @t16)) % 0.35/0.70 (define @t91 () (forall @t90 @t89)) % 0.35/0.70 (define @t92 () (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q @t45 tptp.tptp_sum_index))) % 0.35/0.70 (define @t93 () (tptp.leq @t45 @t85)) % 0.35/0.70 (define @t94 () (tptp.leq tptp.n0 @t45)) % 0.35/0.70 (define @t95 () (and @t94 @t93)) % 0.35/0.70 (define @t96 () (=> @t95 (= @t92 tptp.n1))) % 0.35/0.70 (define @t97 () (@list @t45)) % 0.35/0.70 (define @t98 () (forall @t97 @t96)) % 0.35/0.70 (define @t99 () (tptp.a_select2 tptp.sigma tptp.tptp_sum_index)) % 0.35/0.70 (define @t100 () (tptp.minus @t79 (tptp.a_select2 tptp.mu tptp.tptp_sum_index))) % 0.35/0.70 (define @t101 () (tptp.sum tptp.n0 tptp.n4 (tptp.divide (tptp.times (tptp.exp (tptp.divide (tptp.divide (tptp.times @t100 @t100) tptp.tptp_minus_2) (tptp.times @t99 @t99))) (tptp.a_select2 tptp.rho tptp.tptp_sum_index)) (tptp.times @t78 @t99)))) % 0.35/0.70 (define @t102 () (tptp.a_select2 tptp.sigma @t30)) % 0.35/0.70 (define @t103 () (tptp.minus @t79 (tptp.a_select2 tptp.mu @t30))) % 0.35/0.70 (define @t104 () (= (tptp.a_select3 tptp.q tptp.pv10 @t30) (tptp.divide (tptp.divide (tptp.times (tptp.exp (tptp.divide (tptp.divide (tptp.times @t103 @t103) tptp.tptp_minus_2) (tptp.times @t102 @t102))) (tptp.a_select2 tptp.rho @t30)) (tptp.times @t78 @t102)) @t101))) % 0.35/0.70 (define @t105 () (tptp.leq @t30 (tptp.pred tptp.pv47))) % 0.35/0.70 (define @t106 () (tptp.leq tptp.n0 @t30)) % 0.35/0.70 (define @t107 () (and @t106 @t105)) % 0.35/0.70 (define @t108 () (forall (@list @t30) (=> @t107 @t104))) % 0.35/0.70 (define @t109 () (tptp.leq tptp.pv47 tptp.n4)) % 0.35/0.70 (define @t110 () (tptp.leq tptp.pv10 tptp.n135299)) % 0.35/0.70 (define @t111 () (tptp.leq tptp.n0 tptp.pv47)) % 0.35/0.70 (define @t112 () (tptp.leq tptp.n0 tptp.pv10)) % 0.35/0.70 (define @t113 () (= tptp.pv84 @t101)) % 0.35/0.70 (define @t114 () (and @t113 @t112 @t111 @t110 @t109 @t108 @t98)) % 0.35/0.70 (define @t115 () (=> @t114 @t91)) % 0.35/0.70 (define @t116 () (not @t115)) % 0.35/0.70 (define @t117 () (= @t2 tptp.n4)) % 0.35/0.70 (define @t118 () (= @t2 tptp.n3)) % 0.35/0.70 (define @t119 () (= @t2 tptp.n2)) % 0.35/0.70 (define @t120 () (= @t2 tptp.n1)) % 0.35/0.70 (define @t121 () (= @t2 tptp.n0)) % 0.35/0.70 (define @t122 () (tptp.succ tptp.n0)) % 0.35/0.70 (define @t123 () (tptp.succ @t122)) % 0.35/0.70 (define @t124 () (tptp.succ @t123)) % 0.35/0.70 (define @t125 () (tptp.succ @t124)) % 0.35/0.70 (define @t126 () (tptp.gt tptp.pv10 tptp.pv10)) % 0.35/0.70 (define @t127 () (tptp.leq tptp.pv10 @t85)) % 0.35/0.70 (define @t128 () (forall @t6 (= @t4 @t12))) % 0.35/0.70 (define @t129 () (= @t126 @t127)) % 0.35/0.70 (define @t130 () (= @t127 @t126)) % 0.35/0.70 (define @t131 () (= tptp.n1 (tptp.sum tptp.n0 tptp.n4 (tptp.cond @t82 @t81 (tptp.a_select3 tptp.q tptp.pv10 tptp.tptp_sum_index))))) % 0.35/0.70 (define @t132 () (not @t127)) % 0.35/0.70 (define @t133 () (not @t112)) % 0.35/0.70 (define @t134 () (not (= tptp.pv10 tptp.pv10))) % 0.35/0.70 (define @t135 () (or @t133 @t132 @t134 @t131)) % 0.35/0.70 (define @t136 () (= tptp.n1 @t83)) % 0.35/0.70 (define @t137 () (= @t16 tptp.pv10)) % 0.35/0.70 (define @t138 () (not @t137)) % 0.35/0.70 (define @t139 () (not @t86)) % 0.35/0.70 (define @t140 () (not @t87)) % 0.35/0.70 (define @t141 () (or @t138 @t140 @t139 @t138 @t136)) % 0.35/0.70 (define @t142 () (or @t140 @t139 @t138 @t136)) % 0.35/0.70 (define @t143 () (=> @t137 @t136)) % 0.35/0.70 (define @t144 () (= tptp.n1 @t92)) % 0.35/0.70 (define @t145 () (not @t93)) % 0.35/0.70 (define @t146 () (not @t94)) % 0.35/0.70 (define @t147 () (not @t105)) % 0.35/0.70 (define @t148 () (not @t106)) % 0.35/0.70 (define @t149 () (@list false false)) % 0.35/0.70 (assume @p1 (forall @t6 (or @t5 @t4 @t3))) % 0.35/0.70 (assume @p2 (forall @t8 (=> (and @t5 (tptp.gt @t1 @t7)) (tptp.gt @t2 @t7)))) % 0.35/0.70 (assume @p3 @t10) % 0.35/0.70 (assume @p4 (forall @t9 (tptp.leq @t2 @t2))) % 0.35/0.70 (assume @p5 (forall @t8 (=> (and @t11 (tptp.leq @t1 @t7)) (tptp.leq @t2 @t7)))) % 0.35/0.70 (assume @p6 (forall @t6 (= (tptp.lt @t2 @t1) @t4))) % 0.35/0.70 (assume @p7 (forall @t6 (= (tptp.geq @t2 @t1) (tptp.leq @t1 @t2)))) % 0.35/0.70 (assume @p8 (forall @t6 (=> @t4 @t11))) % 0.35/0.70 (assume @p9 (forall @t6 (=> (and @t11 (not @t3)) @t4))) % 0.35/0.70 (assume @p10 @t13) % 0.35/0.70 (assume @p11 (forall @t9 (tptp.gt @t14 @t2))) % 0.35/0.70 (assume @p12 (forall @t6 (=> @t11 (tptp.leq @t2 @t15)))) % 0.35/0.70 (assume @p13 (forall @t6 (= @t11 (tptp.gt @t15 @t2)))) % 0.35/0.70 (assume @p14 (forall @t19 (=> @t18 (tptp.leq @t17 @t2)))) % 0.35/0.70 (assume @p15 (forall @t19 (=> @t18 (tptp.leq tptp.n0 @t17)))) % 0.35/0.70 (assume @p16 (forall (@list @t21 @t23 @t22 @t20) (=> (and (tptp.leq @t23 @t21) @t24) (= (tptp.a_select2 (tptp.tptp_const_array1 (tptp.dim @t23 @t22) @t20) @t21) @t20)))) % 0.35/0.70 (assume @p17 (forall (@list @t21 @t29 @t28 @t25 @t27 @t26 @t20) (=> (and (tptp.leq @t29 @t21) (tptp.leq @t21 @t28) (tptp.leq @t27 @t25) (tptp.leq @t25 @t26)) (= (tptp.a_select3 (tptp.tptp_const_array2 (tptp.dim @t29 @t28) (tptp.dim @t27 @t26) @t20) @t21 @t25) @t20)))) % 0.35/0.70 (assume @p18 (forall @t40 (=> @t39 (forall @t38 (=> @t37 (= (tptp.a_select3 @t31 @t21 @t25) (tptp.a_select3 @t31 @t25 @t21))))))) % 0.35/0.70 (assume @p19 (forall @t40 (=> @t39 (forall @t38 (=> @t37 (= (tptp.a_select3 @t41 @t21 @t25) (tptp.a_select3 @t41 @t25 @t21))))))) % 0.35/0.70 (assume @p20 (forall @t40 (=> @t39 (forall (@list @t21 @t25 @t43 @t42) (=> (and @t36 @t35 @t34 @t33 (tptp.leq tptp.n0 @t43) (tptp.leq @t43 @t32)) (= (tptp.a_select3 @t44 @t21 @t25) (tptp.a_select3 @t44 @t25 @t21))))))) % 0.35/0.70 (assume @p21 (forall @t50 (=> @t49 (forall @t38 (=> @t37 (= (tptp.a_select3 @t46 @t21 @t25) (tptp.a_select3 @t46 @t25 @t21))))))) % 0.35/0.70 (assume @p22 (forall @t50 (=> @t49 (forall @t38 (=> @t37 (= (tptp.a_select3 @t51 @t21 @t25) (tptp.a_select3 @t51 @t25 @t21))))))) % 0.35/0.70 (assume @p23 (forall @t50 (=> @t48 @t53))) % 0.35/0.70 (assume @p24 (forall (@list @t30 @t45 @t32 @t54) (=> (forall @t38 (=> @t55 @t47)) @t53))) % 0.35/0.70 (assume @p25 (forall (@list @t30 @t45 @t16 @t58 @t56 @t57 @t32 @t54) (=> (and (forall @t38 (=> @t55 (= (tptp.a_select3 @t58 @t21 @t25) (tptp.a_select3 @t58 @t25 @t21)))) @t39 (forall @t38 (=> @t37 (= (tptp.a_select3 @t57 @t21 @t25) (tptp.a_select3 @t57 @t25 @t21))))) (forall @t38 (=> @t37 (= (tptp.a_select3 @t59 @t21 @t25) (tptp.a_select3 @t59 @t25 @t21))))))) % 0.35/0.70 (assume @p26 (forall @t62 (= @t61 tptp.n0))) % 0.35/0.70 (assume @p27 (forall @t62 (= tptp.tptp_float_0_0 @t61))) % 0.35/0.70 (assume @p28 (= (tptp.succ tptp.tptp_minus_1) tptp.n0)) % 0.35/0.70 (assume @p29 (forall @t9 (= (tptp.plus @t2 tptp.n1) @t14))) % 0.35/0.70 (assume @p30 (forall @t9 (= (tptp.plus tptp.n1 @t2) @t14))) % 0.35/0.70 (assume @p31 (forall @t9 (= (tptp.plus @t2 tptp.n2) @t63))) % 0.35/0.70 (assume @p32 (forall @t9 (= (tptp.plus tptp.n2 @t2) @t63))) % 0.35/0.70 (assume @p33 (forall @t9 (= (tptp.plus @t2 tptp.n3) @t64))) % 0.35/0.70 (assume @p34 (forall @t9 (= (tptp.plus tptp.n3 @t2) @t64))) % 0.35/0.70 (assume @p35 (forall @t9 (= (tptp.plus @t2 tptp.n4) @t65))) % 0.35/0.70 (assume @p36 (forall @t9 (= (tptp.plus tptp.n4 @t2) @t65))) % 0.35/0.70 (assume @p37 (forall @t9 (= (tptp.plus @t2 tptp.n5) @t66))) % 0.35/0.70 (assume @p38 (forall @t9 (= (tptp.plus tptp.n5 @t2) @t66))) % 0.35/0.70 (assume @p39 (forall @t9 (= (tptp.minus @t2 tptp.n1) @t67))) % 0.35/0.70 (assume @p40 (forall @t9 (= (tptp.pred @t14) @t2))) % 0.35/0.70 (assume @p41 (forall @t9 (= (tptp.succ @t67) @t2))) % 0.35/0.70 (assume @p42 (forall @t6 (= (tptp.leq @t14 @t15) @t11))) % 0.35/0.70 (assume @p43 (forall @t6 (=> (tptp.leq @t14 @t1) @t4))) % 0.35/0.70 (assume @p44 (forall @t6 (=> (tptp.leq (tptp.minus @t2 @t1) @t2) (tptp.leq tptp.n0 @t1)))) % 0.35/0.70 (assume @p45 (forall (@list @t2 @t22 @t68 @t42) (= (tptp.a_select3 @t69 @t22 @t68) @t42))) % 0.35/0.70 (assume @p46 (forall (@list @t21 @t25 @t22 @t68 @t2 @t42 @t70) (=> (and @t71 (= @t25 @t68) (= (tptp.a_select3 @t2 @t22 @t68) @t42)) (= (tptp.a_select3 (tptp.tptp_update3 @t2 @t21 @t25 @t70) @t22 @t68) @t42)))) % 0.35/0.70 (assume @p47 (forall (@list @t21 @t25 @t22 @t68 @t2 @t42) (=> (and (forall (@list @t73 @t72) (=> (and @t75 (tptp.leq tptp.n0 @t72) @t74 (tptp.leq @t72 @t68)) (= (tptp.a_select3 @t2 @t73 @t72) @t42))) @t36 @t24 @t34 (tptp.leq @t25 @t68)) (= (tptp.a_select3 @t69 @t21 @t25) @t42)))) % 0.35/0.70 (assume @p48 (forall (@list @t2 @t22 @t42) (= (tptp.a_select2 @t76 @t22) @t42))) % 0.35/0.70 (assume @p49 (forall (@list @t21 @t22 @t2 @t42 @t70) (=> (and @t71 (= (tptp.a_select2 @t2 @t22) @t42)) (= (tptp.a_select2 (tptp.tptp_update2 @t2 @t21 @t70) @t22) @t42)))) % 0.35/0.70 (assume @p50 (forall (@list @t21 @t22 @t2 @t42) (=> (and (forall (@list @t73) (=> (and @t75 @t74) (= (tptp.a_select2 @t2 @t73) @t42))) @t36 @t24) (= (tptp.a_select2 @t76 @t21) @t42)))) % 0.35/0.70 (assume @p51 tptp.true) % 0.35/0.70 (assume @p52 (not (= tptp.def tptp.use))) % 0.35/0.70 (assume @p53 @t116) % 0.35/0.70 (assume @p54 (tptp.gt tptp.n5 tptp.n4)) % 0.35/0.70 (assume @p55 (tptp.gt tptp.n135299 tptp.n4)) % 0.35/0.70 (assume @p56 (tptp.gt tptp.n135299 tptp.n5)) % 0.35/0.70 (assume @p57 (tptp.gt tptp.n4 tptp.tptp_minus_1)) % 0.35/0.70 (assume @p58 (tptp.gt tptp.n5 tptp.tptp_minus_1)) % 0.35/0.70 (assume @p59 (tptp.gt tptp.n135299 tptp.tptp_minus_1)) % 0.35/0.70 (assume @p60 (tptp.gt tptp.n0 tptp.tptp_minus_1)) % 0.35/0.70 (assume @p61 (tptp.gt tptp.n1 tptp.tptp_minus_1)) % 0.35/0.70 (assume @p62 (tptp.gt tptp.n2 tptp.tptp_minus_1)) % 0.35/0.70 (assume @p63 (tptp.gt tptp.n3 tptp.tptp_minus_1)) % 0.35/0.70 (assume @p64 (tptp.gt tptp.n4 tptp.tptp_minus_2)) % 0.35/0.70 (assume @p65 (tptp.gt tptp.n5 tptp.tptp_minus_2)) % 0.35/0.70 (assume @p66 (tptp.gt tptp.tptp_minus_1 tptp.tptp_minus_2)) % 0.35/0.70 (assume @p67 (tptp.gt tptp.n135299 tptp.tptp_minus_2)) % 0.35/0.70 (assume @p68 (tptp.gt tptp.n0 tptp.tptp_minus_2)) % 0.35/0.70 (assume @p69 (tptp.gt tptp.n1 tptp.tptp_minus_2)) % 0.35/0.70 (assume @p70 (tptp.gt tptp.n2 tptp.tptp_minus_2)) % 0.35/0.70 (assume @p71 (tptp.gt tptp.n3 tptp.tptp_minus_2)) % 0.35/0.70 (assume @p72 (tptp.gt tptp.n4 tptp.n0)) % 0.35/0.70 (assume @p73 (tptp.gt tptp.n5 tptp.n0)) % 0.35/0.70 (assume @p74 (tptp.gt tptp.n135299 tptp.n0)) % 0.35/0.70 (assume @p75 (tptp.gt tptp.n1 tptp.n0)) % 0.35/0.70 (assume @p76 (tptp.gt tptp.n2 tptp.n0)) % 0.35/0.70 (assume @p77 (tptp.gt tptp.n3 tptp.n0)) % 0.35/0.70 (assume @p78 (tptp.gt tptp.n4 tptp.n1)) % 0.35/0.70 (assume @p79 (tptp.gt tptp.n5 tptp.n1)) % 0.35/0.70 (assume @p80 (tptp.gt tptp.n135299 tptp.n1)) % 0.35/0.70 (assume @p81 (tptp.gt tptp.n2 tptp.n1)) % 0.35/0.70 (assume @p82 (tptp.gt tptp.n3 tptp.n1)) % 0.35/0.70 (assume @p83 (tptp.gt tptp.n4 tptp.n2)) % 0.35/0.70 (assume @p84 (tptp.gt tptp.n5 tptp.n2)) % 0.35/0.70 (assume @p85 (tptp.gt tptp.n135299 tptp.n2)) % 0.35/0.70 (assume @p86 (tptp.gt tptp.n3 tptp.n2)) % 0.35/0.70 (assume @p87 (tptp.gt tptp.n4 tptp.n3)) % 0.35/0.70 (assume @p88 (tptp.gt tptp.n5 tptp.n3)) % 0.35/0.70 (assume @p89 (tptp.gt tptp.n135299 tptp.n3)) % 0.35/0.70 (assume @p90 (forall @t9 (=> (and @t18 (tptp.leq @t2 tptp.n4)) (or @t121 @t120 @t119 @t118 @t117)))) % 0.35/0.70 (assume @p91 (forall @t9 (=> (and @t18 (tptp.leq @t2 tptp.n5)) (or @t121 @t120 @t119 @t118 @t117 (= @t2 tptp.n5))))) % 0.35/0.70 (assume @p92 (forall @t9 (=> (and @t18 (tptp.leq @t2 tptp.n0)) @t121))) % 0.35/0.70 (assume @p93 (forall @t9 (=> (and @t18 (tptp.leq @t2 tptp.n1)) (or @t121 @t120)))) % 0.35/0.70 (assume @p94 (forall @t9 (=> (and @t18 (tptp.leq @t2 tptp.n2)) (or @t121 @t120 @t119)))) % 0.35/0.70 (assume @p95 (forall @t9 (=> (and @t18 (tptp.leq @t2 tptp.n3)) (or @t121 @t120 @t119 @t118)))) % 0.35/0.70 (assume @p96 (= @t125 tptp.n4)) % 0.35/0.70 (assume @p97 (= (tptp.succ @t125) tptp.n5)) % 0.35/0.70 (assume @p98 (= @t122 tptp.n1)) % 0.35/0.70 (assume @p99 (= @t123 tptp.n2)) % 0.35/0.70 (assume @p100 (= @t124 tptp.n3)) % 0.35/0.70 (assume @p101 true) % 0.35/0.70 (step @p102 :rule eq-symm :args (@t12 @t4)) % 0.35/0.70 (step @p103 :rule cong :premises (@p102) :args (@t13)) % 0.35/0.70 (step @p104 :rule eq_resolve :premises (@p10 @p103)) % 0.35/0.70 (step @p105 :rule eq-symm :args (@t126 @t127)) % 0.35/0.70 (step @p106 :rule refl :args (@t128)) % 0.35/0.70 (step @p107 :rule cong :premises (@p106 @p105) :args ((=> @t128 @t129))) % 0.35/0.70 (assume-push @p188 @t128) % 0.35/0.70 (step @p109 :rule instantiate :premises (@p104) :args ((@list tptp.pv10 tptp.pv10))) % 0.35/0.70 (step-pop @p189 :rule scope :premises (@p109)) % 0.35/0.70 (step @p110 :rule process_scope :premises (@p189) :args (@t129)) % 0.35/0.70 (step @p112 :rule eq_resolve :premises (@p110 @p107)) % 0.35/0.70 (step @p113 :rule implies_elim :premises (@p112)) % 0.35/0.70 (step @p114 :rule chain_m_resolution :premises (@p113 @p104) :args (@t130 (@list false) (@list @t128))) % 0.35/0.70 (step @p115 :rule aci_norm :args ((= (or @t133 @t132 false @t131) (or @t133 @t132 @t131)))) % 0.35/0.70 (step @p116 :rule refl :args (@t131)) % 0.35/0.70 (step @p117 :rule evaluate :args ((not true))) % 0.35/0.70 (step @p118 :rule eq-refl :args (tptp.pv10)) % 0.35/0.70 (step @p119 :rule cong :premises (@p118) :args (@t134)) % 0.35/0.70 (step @p120 :rule trans :premises (@p119 @p117)) % 0.35/0.70 (step @p121 :rule refl :args (@t132)) % 0.35/0.70 (step @p122 :rule refl :args (@t133)) % 0.35/0.70 (step @p123 :rule nary_cong :premises (@p122 @p121 @p120 @p116) :args (@t135)) % 0.35/0.70 (step @p124 :rule trans :premises (@p123 @p115)) % 0.35/0.70 (step @p125 :rule quant-var-elim-eq :args ((= (forall @t90 @t141) @t135))) % 0.35/0.70 (step @p126 :rule aci_norm :args ((= @t142 @t141))) % 0.35/0.70 (step @p127 :rule cong :premises (@p126) :args ((forall @t90 @t142))) % 0.35/0.70 (step @p128 :rule trans :premises (@p127 @p125)) % 0.35/0.70 (step @p129 :rule trans :premises (@p128 @p124)) % 0.35/0.70 (step @p130 :rule aci_norm :args ((= (or (or @t140 @t139) (or @t138 @t136)) @t142))) % 0.35/0.70 (step @p131 :rule bool-impl-elim :args (@t137 @t136)) % 0.35/0.70 (step @p132 :rule bool-and-de-morgan :args (@t87 @t86 true)) % 0.35/0.70 (step @p133 :rule nary_cong :premises (@p132 @p131) :args ((or (not @t88) @t143))) % 0.35/0.70 (step @p134 :rule trans :premises (@p133 @p130)) % 0.35/0.70 (step @p135 :rule bool-impl-elim :args (@t88 @t143)) % 0.35/0.70 (step @p136 :rule trans :premises (@p135 @p134)) % 0.35/0.70 (step @p137 :rule cong :premises (@p136) :args ((forall @t90 (=> @t88 @t143)))) % 0.35/0.70 (step @p138 :rule trans :premises (@p137 @p129)) % 0.35/0.70 (step @p139 :rule eq-symm :args (@t83 tptp.n1)) % 0.35/0.70 (step @p140 :rule eq-symm :args (tptp.pv10 @t16)) % 0.35/0.70 (step @p141 :rule cong :premises (@p140 @p139) :args (@t84)) % 0.35/0.70 (step @p142 :rule refl :args (@t88)) % 0.35/0.70 (step @p143 :rule cong :premises (@p142 @p141) :args (@t89)) % 0.35/0.70 (step @p144 :rule cong :premises (@p143) :args (@t91)) % 0.35/0.70 (step @p145 :rule trans :premises (@p144 @p138)) % 0.35/0.70 (step @p146 :rule aci_norm :args ((= (or (or @t146 @t145) @t144) (or @t146 @t145 @t144)))) % 0.35/0.70 (step @p147 :rule refl :args (@t144)) % 0.35/0.70 (step @p148 :rule bool-and-de-morgan :args (@t94 @t93 true)) % 0.35/0.70 (step @p149 :rule nary_cong :premises (@p148 @p147) :args ((or (not @t95) @t144))) % 0.35/0.70 (step @p150 :rule trans :premises (@p149 @p146)) % 0.35/0.70 (step @p151 :rule bool-impl-elim :args (@t95 @t144)) % 0.35/0.70 (step @p152 :rule trans :premises (@p151 @p150)) % 0.35/0.70 (step @p153 :rule cong :premises (@p152) :args ((forall @t97 (=> @t95 @t144)))) % 0.35/0.70 (step @p154 :rule eq-symm :args (@t92 tptp.n1)) % 0.35/0.70 (step @p155 :rule refl :args (@t95)) % 0.35/0.70 (step @p156 :rule cong :premises (@p155 @p154) :args (@t96)) % 0.35/0.70 (step @p157 :rule cong :premises (@p156) :args (@t98)) % 0.35/0.71 (step @p158 :rule trans :premises (@p157 @p153)) % 0.35/0.71 (step @p159 :rule aci_norm :args ((= (or (or @t148 @t147) @t104) (or @t148 @t147 @t104)))) % 0.35/0.71 (step @p160 :rule refl :args (@t104)) % 0.35/0.71 (step @p161 :rule bool-and-de-morgan :args (@t106 @t105 true)) % 0.35/0.71 (step @p162 :rule nary_cong :premises (@p161 @p160) :args ((or (not @t107) @t104))) % 0.35/0.71 (step @p163 :rule trans :premises (@p162 @p159)) % 0.35/0.71 (step @p164 :rule bool-impl-elim :args (@t107 @t104)) % 0.35/0.71 (step @p165 :rule trans :premises (@p164 @p163)) % 0.35/0.71 (step @p166 :rule cong :premises (@p165) :args (@t108)) % 0.35/0.71 (step @p167 :rule refl :args (@t109)) % 0.35/0.71 (step @p168 :rule refl :args (@t110)) % 0.35/0.71 (step @p169 :rule refl :args (@t111)) % 0.35/0.71 (step @p170 :rule refl :args (@t112)) % 0.35/0.71 (step @p171 :rule refl :args (@t113)) % 0.35/0.71 (step @p172 :rule nary_cong :premises (@p171 @p170 @p169 @p168 @p167 @p166 @p158) :args (@t114)) % 0.35/0.71 (step @p173 :rule cong :premises (@p172 @p145) :args (@t115)) % 0.35/0.71 (step @p174 :rule cong :premises (@p173) :args (@t116)) % 0.35/0.71 (step @p175 :rule eq_resolve :premises (@p53 @p174)) % 0.35/0.71 (step @p176 :rule not_implies_elim2 :premises (@p175)) % 0.35/0.71 (step @p177 :rule not_or_elim :premises (@p176) :args (1)) % 0.35/0.71 (step @p178 :rule not_not_elim :premises (@p177)) % 0.35/0.71 (step @p179 :rule cnf_equiv_pos1 :args (@t130)) % 0.35/0.71 (step @p180 :rule reordering :premises (@p179) :args ((or @t132 @t126 (not @t130)))) % 0.35/0.71 (step @p181 :rule chain_m_resolution :premises (@p180 @p178 @p114) :args (@t126 @t149 (@list @t127 @t130))) % 0.35/0.71 (assume-push @p190 @t10) % 0.35/0.71 (step @p183 :rule instantiate :premises (@p3) :args ((@list tptp.pv10))) % 0.35/0.71 (step-pop @p191 :rule scope :premises (@p183)) % 0.35/0.71 (step @p184 :rule process_scope :premises (@p191) :args ((not @t126))) % 0.35/0.71 (step @p186 :rule implies_elim :premises (@p184)) % 0.35/0.71 (step @p187 false :rule chain_m_resolution :premises (@p186 @p181 @p3) :args (false @t149 (@list @t126 @t10))) % 0.35/0.71 ) % 0.35/0.71 % SZS output end Proof % 0.35/0.71 % cvc5 exiting %------------------------------------------------------------------------------