%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV164+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 : n010.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 0.47s 0.69s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV164+1 : TPTP v9.2.1. Bugfixed v3.3.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n010.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 19:57:55 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.47/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.47/0.69 % SZS status Theorem % 0.47/0.69 % SZS output start Proof % 0.47/0.69 ( % 0.47/0.69 (declare-sort $$unsorted 0) % 0.47/0.69 (declare-const tptp.divide (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.x $$unsorted) % 0.47/0.69 (declare-const tptp.pv10 $$unsorted) % 0.47/0.69 (declare-const tptp.tptp_minus_2 $$unsorted) % 0.47/0.69 (declare-const tptp.sqrt (-> $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.tptp_pi $$unsorted) % 0.47/0.69 (declare-const tptp.sigma $$unsorted) % 0.47/0.69 (declare-const tptp.tptp_sum_index $$unsorted) % 0.47/0.69 (declare-const tptp.def $$unsorted) % 0.47/0.69 (declare-const tptp.use $$unsorted) % 0.47/0.69 (declare-const tptp.true Bool) % 0.47/0.69 (declare-const tptp.tptp_update2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.times (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.a_select3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.rho $$unsorted) % 0.47/0.69 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.47/0.69 (declare-const tptp.uniform_int_rnd (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.q $$unsorted) % 0.47/0.69 (declare-const tptp.n3 $$unsorted) % 0.47/0.69 (declare-const tptp.tptp_const_array1 (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.pred (-> $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.tptp_minus_1 $$unsorted) % 0.47/0.69 (declare-const tptp.n0 $$unsorted) % 0.47/0.69 (declare-const tptp.tptp_msub (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.n1 $$unsorted) % 0.47/0.69 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.n5 $$unsorted) % 0.47/0.69 (declare-const tptp.n135299 $$unsorted) % 0.47/0.69 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.47/0.69 (declare-const tptp.tptp_update3 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.minus (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.mu $$unsorted) % 0.47/0.69 (declare-const tptp.tptp_const_array2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.47/0.69 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.47/0.69 (declare-const tptp.trans (-> $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.a_select2 (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.inv (-> $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.dim (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.plus (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.tptp_madd (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.sum (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.tptp_mmul (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.tptp_float_0_0 $$unsorted) % 0.47/0.69 (declare-const tptp.exp (-> $$unsorted $$unsorted)) % 0.47/0.69 (declare-const tptp.n4 $$unsorted) % 0.47/0.69 (declare-const tptp.n2 $$unsorted) % 0.47/0.69 (define @t1 () (@var "Y" $$unsorted)) % 0.47/0.69 (define @t2 () (@var "X" $$unsorted)) % 0.47/0.69 (define @t3 () (= @t2 @t1)) % 0.47/0.69 (define @t4 () (tptp.gt @t1 @t2)) % 0.47/0.69 (define @t5 () (tptp.gt @t2 @t1)) % 0.47/0.69 (define @t6 () (@list @t2 @t1)) % 0.47/0.69 (define @t7 () (@var "Z" $$unsorted)) % 0.47/0.69 (define @t8 () (@list @t2 @t1 @t7)) % 0.47/0.69 (define @t9 () (@list @t2)) % 0.47/0.69 (define @t10 () (tptp.leq @t2 @t7)) % 0.47/0.69 (define @t11 () (tptp.leq @t1 @t7)) % 0.47/0.69 (define @t12 () (tptp.leq @t2 @t1)) % 0.47/0.69 (define @t13 () (and @t12 @t11)) % 0.47/0.69 (define @t14 () (forall @t8 (=> @t13 @t10))) % 0.47/0.69 (define @t15 () (forall @t6 (=> @t4 @t12))) % 0.47/0.69 (define @t16 () (tptp.succ @t2)) % 0.47/0.69 (define @t17 () (tptp.succ @t1)) % 0.47/0.69 (define @t18 () (@var "C" $$unsorted)) % 0.47/0.69 (define @t19 () (tptp.uniform_int_rnd @t18 @t2)) % 0.47/0.69 (define @t20 () (tptp.leq tptp.n0 @t2)) % 0.47/0.69 (define @t21 () (@list @t2 @t18)) % 0.47/0.69 (define @t22 () (@var "Val" $$unsorted)) % 0.47/0.69 (define @t23 () (@var "I" $$unsorted)) % 0.47/0.69 (define @t24 () (@var "U" $$unsorted)) % 0.47/0.69 (define @t25 () (@var "L" $$unsorted)) % 0.47/0.69 (define @t26 () (tptp.leq @t23 @t24)) % 0.47/0.69 (define @t27 () (@var "J" $$unsorted)) % 0.47/0.69 (define @t28 () (@var "U2" $$unsorted)) % 0.47/0.69 (define @t29 () (@var "L2" $$unsorted)) % 0.47/0.69 (define @t30 () (@var "U1" $$unsorted)) % 0.47/0.69 (define @t31 () (@var "L1" $$unsorted)) % 0.47/0.69 (define @t32 () (@var "A" $$unsorted)) % 0.47/0.69 (define @t33 () (tptp.trans @t32)) % 0.47/0.69 (define @t34 () (@var "N" $$unsorted)) % 0.47/0.69 (define @t35 () (tptp.leq @t27 @t34)) % 0.47/0.69 (define @t36 () (tptp.leq tptp.n0 @t27)) % 0.47/0.69 (define @t37 () (tptp.leq @t23 @t34)) % 0.47/0.69 (define @t38 () (tptp.leq tptp.n0 @t23)) % 0.47/0.69 (define @t39 () (and @t38 @t37 @t36 @t35)) % 0.47/0.69 (define @t40 () (@list @t23 @t27)) % 0.47/0.69 (define @t41 () (forall @t40 (=> @t39 (= (tptp.a_select3 @t32 @t23 @t27) (tptp.a_select3 @t32 @t27 @t23))))) % 0.47/0.69 (define @t42 () (@list @t32 @t34)) % 0.47/0.69 (define @t43 () (tptp.inv @t32)) % 0.47/0.69 (define @t44 () (@var "VAL" $$unsorted)) % 0.47/0.69 (define @t45 () (@var "K" $$unsorted)) % 0.47/0.69 (define @t46 () (tptp.tptp_update3 @t32 @t45 @t45 @t44)) % 0.47/0.69 (define @t47 () (@var "B" $$unsorted)) % 0.47/0.69 (define @t48 () (tptp.tptp_madd @t32 @t47)) % 0.47/0.69 (define @t49 () (= (tptp.a_select3 @t47 @t23 @t27) (tptp.a_select3 @t47 @t27 @t23))) % 0.47/0.69 (define @t50 () (forall @t40 (=> @t39 @t49))) % 0.47/0.69 (define @t51 () (and @t41 @t50)) % 0.47/0.69 (define @t52 () (@list @t32 @t47 @t34)) % 0.47/0.69 (define @t53 () (tptp.tptp_msub @t32 @t47)) % 0.47/0.69 (define @t54 () (tptp.tptp_mmul @t32 (tptp.tptp_mmul @t47 @t33))) % 0.47/0.69 (define @t55 () (forall @t40 (=> @t39 (= (tptp.a_select3 @t54 @t23 @t27) (tptp.a_select3 @t54 @t27 @t23))))) % 0.47/0.69 (define @t56 () (@var "M" $$unsorted)) % 0.47/0.69 (define @t57 () (and @t38 (tptp.leq @t23 @t56) @t36 (tptp.leq @t27 @t56))) % 0.47/0.69 (define @t58 () (@var "E" $$unsorted)) % 0.47/0.69 (define @t59 () (@var "F" $$unsorted)) % 0.47/0.69 (define @t60 () (@var "D" $$unsorted)) % 0.47/0.69 (define @t61 () (tptp.tptp_madd @t32 (tptp.tptp_mmul @t47 (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul @t18 (tptp.tptp_mmul @t60 (tptp.trans @t18))) (tptp.tptp_mmul @t58 (tptp.tptp_mmul @t59 (tptp.trans @t58)))) (tptp.trans @t47))))) % 0.47/0.69 (define @t62 () (@var "Body" $$unsorted)) % 0.47/0.69 (define @t63 () (tptp.sum tptp.n0 tptp.tptp_minus_1 @t62)) % 0.47/0.69 (define @t64 () (@list @t62)) % 0.47/0.69 (define @t65 () (tptp.succ tptp.tptp_minus_1)) % 0.47/0.69 (define @t66 () (tptp.succ @t16)) % 0.47/0.69 (define @t67 () (tptp.succ @t66)) % 0.47/0.69 (define @t68 () (tptp.succ @t67)) % 0.47/0.69 (define @t69 () (tptp.succ @t68)) % 0.47/0.69 (define @t70 () (tptp.plus tptp.n5 @t2)) % 0.47/0.69 (define @t71 () (forall @t9 (= @t70 @t69))) % 0.47/0.69 (define @t72 () (tptp.pred @t2)) % 0.47/0.69 (define @t73 () (@var "V" $$unsorted)) % 0.47/0.69 (define @t74 () (tptp.tptp_update3 @t2 @t24 @t73 @t44)) % 0.47/0.69 (define @t75 () (@var "VAL2" $$unsorted)) % 0.47/0.69 (define @t76 () (not (= @t23 @t24))) % 0.47/0.69 (define @t77 () (@var "J0" $$unsorted)) % 0.47/0.69 (define @t78 () (@var "I0" $$unsorted)) % 0.47/0.70 (define @t79 () (tptp.leq @t78 @t24)) % 0.47/0.70 (define @t80 () (tptp.leq tptp.n0 @t78)) % 0.47/0.70 (define @t81 () (tptp.tptp_update2 @t2 @t24 @t44)) % 0.47/0.70 (define @t82 () (tptp.a_select2 tptp.sigma tptp.tptp_sum_index)) % 0.47/0.70 (define @t83 () (tptp.sqrt (tptp.times tptp.n2 tptp.tptp_pi))) % 0.47/0.70 (define @t84 () (tptp.a_select2 tptp.x tptp.pv10)) % 0.47/0.70 (define @t85 () (tptp.minus @t84 (tptp.a_select2 tptp.mu tptp.tptp_sum_index))) % 0.47/0.70 (define @t86 () (tptp.sum tptp.n0 tptp.n4 (tptp.divide (tptp.times (tptp.exp (tptp.divide (tptp.divide (tptp.times @t85 @t85) tptp.tptp_minus_2) (tptp.times @t82 @t82))) (tptp.a_select2 tptp.rho tptp.tptp_sum_index)) (tptp.times @t83 @t82)))) % 0.47/0.70 (define @t87 () (tptp.a_select2 tptp.sigma @t47)) % 0.47/0.70 (define @t88 () (tptp.minus @t84 (tptp.a_select2 tptp.mu @t47))) % 0.47/0.70 (define @t89 () (= (tptp.a_select3 tptp.q tptp.pv10 @t47) (tptp.divide (tptp.divide (tptp.times (tptp.exp (tptp.divide (tptp.divide (tptp.times @t88 @t88) tptp.tptp_minus_2) (tptp.times @t87 @t87))) (tptp.a_select2 tptp.rho @t47)) (tptp.times @t83 @t87)) @t86))) % 0.47/0.70 (define @t90 () (tptp.leq @t47 tptp.tptp_minus_1)) % 0.47/0.70 (define @t91 () (tptp.leq tptp.n0 @t47)) % 0.47/0.70 (define @t92 () (and @t91 @t90)) % 0.47/0.70 (define @t93 () (@list @t47)) % 0.47/0.70 (define @t94 () (forall @t93 (=> @t92 @t89))) % 0.47/0.70 (define @t95 () (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q @t32 tptp.tptp_sum_index))) % 0.47/0.70 (define @t96 () (tptp.leq @t32 (tptp.pred tptp.pv10))) % 0.47/0.70 (define @t97 () (tptp.leq tptp.n0 @t32)) % 0.47/0.70 (define @t98 () (and @t97 @t96)) % 0.47/0.70 (define @t99 () (=> @t98 (= @t95 tptp.n1))) % 0.47/0.70 (define @t100 () (@list @t32)) % 0.47/0.70 (define @t101 () (forall @t100 @t99)) % 0.47/0.70 (define @t102 () (tptp.leq tptp.pv10 tptp.n135299)) % 0.47/0.70 (define @t103 () (tptp.leq tptp.n0 tptp.pv10)) % 0.47/0.70 (define @t104 () (and @t103 @t102 @t101)) % 0.47/0.70 (define @t105 () (=> @t104 @t94)) % 0.47/0.70 (define @t106 () (not @t105)) % 0.47/0.70 (define @t107 () (tptp.gt tptp.n5 tptp.n4)) % 0.47/0.70 (define @t108 () (tptp.gt tptp.n0 tptp.tptp_minus_1)) % 0.47/0.70 (define @t109 () (= @t2 tptp.n4)) % 0.47/0.70 (define @t110 () (= @t2 tptp.n3)) % 0.47/0.70 (define @t111 () (= @t2 tptp.n2)) % 0.47/0.70 (define @t112 () (= @t2 tptp.n1)) % 0.47/0.70 (define @t113 () (= @t2 tptp.n0)) % 0.47/0.70 (define @t114 () (tptp.leq @t2 tptp.n0)) % 0.47/0.70 (define @t115 () (and @t20 @t114)) % 0.47/0.70 (define @t116 () (forall @t9 (=> @t115 @t113))) % 0.47/0.70 (define @t117 () (tptp.succ tptp.n0)) % 0.47/0.70 (define @t118 () (tptp.succ @t117)) % 0.47/0.70 (define @t119 () (tptp.succ @t118)) % 0.47/0.70 (define @t120 () (tptp.succ @t119)) % 0.47/0.70 (define @t121 () (tptp.succ @t65)) % 0.47/0.70 (define @t122 () (tptp.succ @t121)) % 0.47/0.70 (define @t123 () (tptp.succ @t122)) % 0.47/0.70 (define @t124 () (@list tptp.tptp_minus_1)) % 0.47/0.70 (define @t125 () (not @t114)) % 0.47/0.70 (define @t126 () (not @t20)) % 0.47/0.70 (define @t127 () (or @t126 @t125 @t113)) % 0.47/0.70 (define @t128 () (tptp.leq tptp.tptp_minus_1 tptp.n0)) % 0.47/0.70 (define @t129 () (not @t128)) % 0.47/0.70 (define @t130 () (tptp.leq tptp.n0 tptp.tptp_minus_1)) % 0.47/0.70 (define @t131 () (not @t130)) % 0.47/0.70 (define @t132 () (or @t131 @t129 (= tptp.tptp_minus_1 tptp.n0))) % 0.47/0.70 (define @t133 () (forall @t9 @t127)) % 0.47/0.70 (define @t134 () (= tptp.n0 tptp.tptp_minus_1)) % 0.47/0.70 (define @t135 () (or @t131 @t129 @t134)) % 0.47/0.70 (define @t136 () (not @t108)) % 0.47/0.70 (define @t137 () (or @t136 @t128)) % 0.47/0.70 (define @t138 () (not @t11)) % 0.47/0.70 (define @t139 () (not @t12)) % 0.47/0.70 (define @t140 () (not @t90)) % 0.47/0.70 (define @t141 () (not @t91)) % 0.47/0.70 (define @t142 () (or @t141 @t140 @t89)) % 0.47/0.70 (define @t143 () (@quantifiers_skolemize (forall @t93 @t142) 0)) % 0.47/0.70 (define @t144 () (= tptp.n1 @t95)) % 0.47/0.70 (define @t145 () (not @t96)) % 0.47/0.70 (define @t146 () (not @t97)) % 0.47/0.70 (define @t147 () (tptp.leq @t143 tptp.tptp_minus_1)) % 0.47/0.70 (define @t148 () (tptp.a_select2 tptp.sigma @t143)) % 0.47/0.70 (define @t149 () (tptp.minus @t84 (tptp.a_select2 tptp.mu @t143))) % 0.47/0.70 (define @t150 () (not @t147)) % 0.47/0.70 (define @t151 () (tptp.leq tptp.n0 @t143)) % 0.47/0.70 (define @t152 () (not @t151)) % 0.47/0.70 (define @t153 () (or @t152 @t150 (= (tptp.a_select3 tptp.q tptp.pv10 @t143) (tptp.divide (tptp.divide (tptp.times (tptp.exp (tptp.divide (tptp.divide (tptp.times @t149 @t149) tptp.tptp_minus_2) (tptp.times @t148 @t148))) (tptp.a_select2 tptp.rho @t143)) (tptp.times @t83 @t148)) @t86)))) % 0.47/0.70 (define @t154 () (@list true)) % 0.47/0.70 (define @t155 () (@list @t153)) % 0.47/0.70 (define @t156 () (or @t152 @t150 @t130)) % 0.47/0.70 (define @t157 () (@list false false false)) % 0.47/0.70 (assume @p1 (forall @t6 (or @t5 @t4 @t3))) % 0.47/0.70 (assume @p2 (forall @t8 (=> (and @t5 (tptp.gt @t1 @t7)) (tptp.gt @t2 @t7)))) % 0.47/0.70 (assume @p3 (forall @t9 (not (tptp.gt @t2 @t2)))) % 0.47/0.70 (assume @p4 (forall @t9 (tptp.leq @t2 @t2))) % 0.47/0.70 (assume @p5 @t14) % 0.47/0.70 (assume @p6 (forall @t6 (= (tptp.lt @t2 @t1) @t4))) % 0.47/0.70 (assume @p7 (forall @t6 (= (tptp.geq @t2 @t1) (tptp.leq @t1 @t2)))) % 0.47/0.70 (assume @p8 @t15) % 0.47/0.70 (assume @p9 (forall @t6 (=> (and @t12 (not @t3)) @t4))) % 0.47/0.70 (assume @p10 (forall @t6 (= (tptp.leq @t2 (tptp.pred @t1)) @t4))) % 0.47/0.70 (assume @p11 (forall @t9 (tptp.gt @t16 @t2))) % 0.47/0.70 (assume @p12 (forall @t6 (=> @t12 (tptp.leq @t2 @t17)))) % 0.47/0.70 (assume @p13 (forall @t6 (= @t12 (tptp.gt @t17 @t2)))) % 0.47/0.70 (assume @p14 (forall @t21 (=> @t20 (tptp.leq @t19 @t2)))) % 0.47/0.70 (assume @p15 (forall @t21 (=> @t20 (tptp.leq tptp.n0 @t19)))) % 0.47/0.70 (assume @p16 (forall (@list @t23 @t25 @t24 @t22) (=> (and (tptp.leq @t25 @t23) @t26) (= (tptp.a_select2 (tptp.tptp_const_array1 (tptp.dim @t25 @t24) @t22) @t23) @t22)))) % 0.47/0.70 (assume @p17 (forall (@list @t23 @t31 @t30 @t27 @t29 @t28 @t22) (=> (and (tptp.leq @t31 @t23) (tptp.leq @t23 @t30) (tptp.leq @t29 @t27) (tptp.leq @t27 @t28)) (= (tptp.a_select3 (tptp.tptp_const_array2 (tptp.dim @t31 @t30) (tptp.dim @t29 @t28) @t22) @t23 @t27) @t22)))) % 0.47/0.70 (assume @p18 (forall @t42 (=> @t41 (forall @t40 (=> @t39 (= (tptp.a_select3 @t33 @t23 @t27) (tptp.a_select3 @t33 @t27 @t23))))))) % 0.47/0.70 (assume @p19 (forall @t42 (=> @t41 (forall @t40 (=> @t39 (= (tptp.a_select3 @t43 @t23 @t27) (tptp.a_select3 @t43 @t27 @t23))))))) % 0.47/0.70 (assume @p20 (forall @t42 (=> @t41 (forall (@list @t23 @t27 @t45 @t44) (=> (and @t38 @t37 @t36 @t35 (tptp.leq tptp.n0 @t45) (tptp.leq @t45 @t34)) (= (tptp.a_select3 @t46 @t23 @t27) (tptp.a_select3 @t46 @t27 @t23))))))) % 0.47/0.70 (assume @p21 (forall @t52 (=> @t51 (forall @t40 (=> @t39 (= (tptp.a_select3 @t48 @t23 @t27) (tptp.a_select3 @t48 @t27 @t23))))))) % 0.47/0.70 (assume @p22 (forall @t52 (=> @t51 (forall @t40 (=> @t39 (= (tptp.a_select3 @t53 @t23 @t27) (tptp.a_select3 @t53 @t27 @t23))))))) % 0.47/0.70 (assume @p23 (forall @t52 (=> @t50 @t55))) % 0.47/0.70 (assume @p24 (forall (@list @t32 @t47 @t34 @t56) (=> (forall @t40 (=> @t57 @t49)) @t55))) % 0.47/0.70 (assume @p25 (forall (@list @t32 @t47 @t18 @t60 @t58 @t59 @t34 @t56) (=> (and (forall @t40 (=> @t57 (= (tptp.a_select3 @t60 @t23 @t27) (tptp.a_select3 @t60 @t27 @t23)))) @t41 (forall @t40 (=> @t39 (= (tptp.a_select3 @t59 @t23 @t27) (tptp.a_select3 @t59 @t27 @t23))))) (forall @t40 (=> @t39 (= (tptp.a_select3 @t61 @t23 @t27) (tptp.a_select3 @t61 @t27 @t23))))))) % 0.47/0.70 (assume @p26 (forall @t64 (= @t63 tptp.n0))) % 0.47/0.70 (assume @p27 (forall @t64 (= tptp.tptp_float_0_0 @t63))) % 0.47/0.70 (assume @p28 (= @t65 tptp.n0)) % 0.47/0.70 (assume @p29 (forall @t9 (= (tptp.plus @t2 tptp.n1) @t16))) % 0.47/0.70 (assume @p30 (forall @t9 (= (tptp.plus tptp.n1 @t2) @t16))) % 0.47/0.70 (assume @p31 (forall @t9 (= (tptp.plus @t2 tptp.n2) @t66))) % 0.47/0.70 (assume @p32 (forall @t9 (= (tptp.plus tptp.n2 @t2) @t66))) % 0.47/0.70 (assume @p33 (forall @t9 (= (tptp.plus @t2 tptp.n3) @t67))) % 0.47/0.70 (assume @p34 (forall @t9 (= (tptp.plus tptp.n3 @t2) @t67))) % 0.47/0.70 (assume @p35 (forall @t9 (= (tptp.plus @t2 tptp.n4) @t68))) % 0.47/0.70 (assume @p36 (forall @t9 (= (tptp.plus tptp.n4 @t2) @t68))) % 0.47/0.70 (assume @p37 (forall @t9 (= (tptp.plus @t2 tptp.n5) @t69))) % 0.47/0.70 (assume @p38 @t71) % 0.47/0.70 (assume @p39 (forall @t9 (= (tptp.minus @t2 tptp.n1) @t72))) % 0.47/0.70 (assume @p40 (forall @t9 (= (tptp.pred @t16) @t2))) % 0.47/0.70 (assume @p41 (forall @t9 (= (tptp.succ @t72) @t2))) % 0.47/0.70 (assume @p42 (forall @t6 (= (tptp.leq @t16 @t17) @t12))) % 0.47/0.70 (assume @p43 (forall @t6 (=> (tptp.leq @t16 @t1) @t4))) % 0.47/0.70 (assume @p44 (forall @t6 (=> (tptp.leq (tptp.minus @t2 @t1) @t2) (tptp.leq tptp.n0 @t1)))) % 0.47/0.70 (assume @p45 (forall (@list @t2 @t24 @t73 @t44) (= (tptp.a_select3 @t74 @t24 @t73) @t44))) % 0.47/0.70 (assume @p46 (forall (@list @t23 @t27 @t24 @t73 @t2 @t44 @t75) (=> (and @t76 (= @t27 @t73) (= (tptp.a_select3 @t2 @t24 @t73) @t44)) (= (tptp.a_select3 (tptp.tptp_update3 @t2 @t23 @t27 @t75) @t24 @t73) @t44)))) % 0.47/0.70 (assume @p47 (forall (@list @t23 @t27 @t24 @t73 @t2 @t44) (=> (and (forall (@list @t78 @t77) (=> (and @t80 (tptp.leq tptp.n0 @t77) @t79 (tptp.leq @t77 @t73)) (= (tptp.a_select3 @t2 @t78 @t77) @t44))) @t38 @t26 @t36 (tptp.leq @t27 @t73)) (= (tptp.a_select3 @t74 @t23 @t27) @t44)))) % 0.47/0.70 (assume @p48 (forall (@list @t2 @t24 @t44) (= (tptp.a_select2 @t81 @t24) @t44))) % 0.47/0.70 (assume @p49 (forall (@list @t23 @t24 @t2 @t44 @t75) (=> (and @t76 (= (tptp.a_select2 @t2 @t24) @t44)) (= (tptp.a_select2 (tptp.tptp_update2 @t2 @t23 @t75) @t24) @t44)))) % 0.47/0.70 (assume @p50 (forall (@list @t23 @t24 @t2 @t44) (=> (and (forall (@list @t78) (=> (and @t80 @t79) (= (tptp.a_select2 @t2 @t78) @t44))) @t38 @t26) (= (tptp.a_select2 @t81 @t23) @t44)))) % 0.47/0.70 (assume @p51 tptp.true) % 0.47/0.70 (assume @p52 (not (= tptp.def tptp.use))) % 0.47/0.70 (assume @p53 @t106) % 0.47/0.70 (assume @p54 @t107) % 0.47/0.70 (assume @p55 (tptp.gt tptp.n135299 tptp.n4)) % 0.47/0.70 (assume @p56 (tptp.gt tptp.n135299 tptp.n5)) % 0.47/0.70 (assume @p57 (tptp.gt tptp.n4 tptp.tptp_minus_1)) % 0.47/0.70 (assume @p58 (tptp.gt tptp.n5 tptp.tptp_minus_1)) % 0.47/0.70 (assume @p59 (tptp.gt tptp.n135299 tptp.tptp_minus_1)) % 0.47/0.70 (assume @p60 @t108) % 0.47/0.70 (assume @p61 (tptp.gt tptp.n1 tptp.tptp_minus_1)) % 0.47/0.70 (assume @p62 (tptp.gt tptp.n2 tptp.tptp_minus_1)) % 0.47/0.70 (assume @p63 (tptp.gt tptp.n3 tptp.tptp_minus_1)) % 0.47/0.70 (assume @p64 (tptp.gt tptp.n4 tptp.tptp_minus_2)) % 0.47/0.70 (assume @p65 (tptp.gt tptp.n5 tptp.tptp_minus_2)) % 0.47/0.70 (assume @p66 (tptp.gt tptp.tptp_minus_1 tptp.tptp_minus_2)) % 0.47/0.70 (assume @p67 (tptp.gt tptp.n135299 tptp.tptp_minus_2)) % 0.47/0.70 (assume @p68 (tptp.gt tptp.n0 tptp.tptp_minus_2)) % 0.47/0.70 (assume @p69 (tptp.gt tptp.n1 tptp.tptp_minus_2)) % 0.47/0.70 (assume @p70 (tptp.gt tptp.n2 tptp.tptp_minus_2)) % 0.47/0.70 (assume @p71 (tptp.gt tptp.n3 tptp.tptp_minus_2)) % 0.47/0.70 (assume @p72 (tptp.gt tptp.n4 tptp.n0)) % 0.47/0.70 (assume @p73 (tptp.gt tptp.n5 tptp.n0)) % 0.47/0.70 (assume @p74 (tptp.gt tptp.n135299 tptp.n0)) % 0.47/0.70 (assume @p75 (tptp.gt tptp.n1 tptp.n0)) % 0.47/0.70 (assume @p76 (tptp.gt tptp.n2 tptp.n0)) % 0.47/0.70 (assume @p77 (tptp.gt tptp.n3 tptp.n0)) % 0.47/0.70 (assume @p78 (tptp.gt tptp.n4 tptp.n1)) % 0.47/0.70 (assume @p79 (tptp.gt tptp.n5 tptp.n1)) % 0.47/0.70 (assume @p80 (tptp.gt tptp.n135299 tptp.n1)) % 0.47/0.70 (assume @p81 (tptp.gt tptp.n2 tptp.n1)) % 0.47/0.70 (assume @p82 (tptp.gt tptp.n3 tptp.n1)) % 0.47/0.70 (assume @p83 (tptp.gt tptp.n4 tptp.n2)) % 0.47/0.70 (assume @p84 (tptp.gt tptp.n5 tptp.n2)) % 0.47/0.70 (assume @p85 (tptp.gt tptp.n135299 tptp.n2)) % 0.47/0.70 (assume @p86 (tptp.gt tptp.n3 tptp.n2)) % 0.47/0.70 (assume @p87 (tptp.gt tptp.n4 tptp.n3)) % 0.47/0.70 (assume @p88 (tptp.gt tptp.n5 tptp.n3)) % 0.47/0.70 (assume @p89 (tptp.gt tptp.n135299 tptp.n3)) % 0.47/0.70 (assume @p90 (forall @t9 (=> (and @t20 (tptp.leq @t2 tptp.n4)) (or @t113 @t112 @t111 @t110 @t109)))) % 0.47/0.70 (assume @p91 (forall @t9 (=> (and @t20 (tptp.leq @t2 tptp.n5)) (or @t113 @t112 @t111 @t110 @t109 (= @t2 tptp.n5))))) % 0.47/0.70 (assume @p92 @t116) % 0.47/0.70 (assume @p93 (forall @t9 (=> (and @t20 (tptp.leq @t2 tptp.n1)) (or @t113 @t112)))) % 0.47/0.70 (assume @p94 (forall @t9 (=> (and @t20 (tptp.leq @t2 tptp.n2)) (or @t113 @t112 @t111)))) % 0.47/0.70 (assume @p95 (forall @t9 (=> (and @t20 (tptp.leq @t2 tptp.n3)) (or @t113 @t112 @t111 @t110)))) % 0.47/0.70 (assume @p96 (= @t120 tptp.n4)) % 0.47/0.70 (assume @p97 (= (tptp.succ @t120) tptp.n5)) % 0.47/0.70 (assume @p98 (= @t117 tptp.n1)) % 0.47/0.70 (assume @p99 (= @t118 tptp.n2)) % 0.47/0.70 (assume @p100 (= @t119 tptp.n3)) % 0.47/0.70 (assume @p101 true) % 0.47/0.70 (step @p102 :rule evaluate :args ((= true false))) % 0.47/0.70 (step @p103 :rule instantiate :premises (@p3) :args ((@list tptp.n4))) % 0.47/0.70 (step @p104 :rule false_intro :premises (@p103)) % 0.47/0.70 (step @p105 :rule refl :args (tptp.n4)) % 0.47/0.70 (step @p106 :rule cong :premises (@p28) :args (@t121)) % 0.47/0.70 (step @p107 :rule cong :premises (@p106) :args (@t122)) % 0.47/0.70 (step @p108 :rule cong :premises (@p107) :args (@t123)) % 0.47/0.70 (step @p109 :rule cong :premises (@p108) :args ((tptp.succ @t123))) % 0.47/0.70 (step @p110 :rule eq-symm :args (@t70 @t69)) % 0.47/0.70 (step @p111 :rule cong :premises (@p110) :args (@t71)) % 0.47/0.70 (step @p112 :rule eq_resolve :premises (@p38 @p111)) % 0.47/0.70 (step @p113 :rule instantiate :premises (@p112) :args (@t124)) % 0.47/0.70 (step @p114 :rule symm :premises (@p113)) % 0.47/0.70 (step @p115 :rule aci_norm :args ((= (or (or @t126 @t125) @t113) @t127))) % 0.47/0.70 (step @p116 :rule refl :args (@t113)) % 0.47/0.70 (step @p117 :rule bool-and-de-morgan :args (@t20 @t114 true)) % 0.47/0.70 (step @p118 :rule nary_cong :premises (@p117 @p116) :args ((or (not @t115) @t113))) % 0.47/0.70 (step @p119 :rule trans :premises (@p118 @p115)) % 0.47/0.70 (step @p120 :rule bool-impl-elim :args (@t115 @t113)) % 0.47/0.70 (step @p121 :rule trans :premises (@p120 @p119)) % 0.47/0.70 (step @p122 :rule cong :premises (@p121) :args (@t116)) % 0.47/0.70 (step @p123 :rule eq_resolve :premises (@p92 @p122)) % 0.47/0.70 (step @p124 :rule eq-symm :args (tptp.tptp_minus_1 tptp.n0)) % 0.47/0.70 (step @p125 :rule refl :args (@t129)) % 0.47/0.70 (step @p126 :rule refl :args (@t131)) % 0.47/0.70 (step @p127 :rule nary_cong :premises (@p126 @p125 @p124) :args (@t132)) % 0.47/0.70 (step @p128 :rule refl :args (@t133)) % 0.47/0.70 (step @p129 :rule cong :premises (@p128 @p127) :args ((=> @t133 @t132))) % 0.47/0.70 (assume-push @p212 @t133) % 0.47/0.70 (step @p131 :rule instantiate :premises (@p123) :args (@t124)) % 0.47/0.70 (step-pop @p213 :rule scope :premises (@p131)) % 0.47/0.70 (step @p132 :rule process_scope :premises (@p213) :args (@t132)) % 0.47/0.70 (step @p134 :rule eq_resolve :premises (@p132 @p129)) % 0.47/0.70 (step @p135 :rule implies_elim :premises (@p134)) % 0.47/0.70 (step @p136 :rule chain_m_resolution :premises (@p135 @p123) :args (@t135 (@list false) (@list @t133))) % 0.47/0.70 (step @p137 :rule bool-impl-elim :args (@t4 @t12)) % 0.47/0.70 (step @p138 :rule cong :premises (@p137) :args (@t15)) % 0.47/0.70 (step @p139 :rule eq_resolve :premises (@p8 @p138)) % 0.47/0.70 (step @p140 :rule instantiate :premises (@p139) :args ((@list tptp.tptp_minus_1 tptp.n0))) % 0.47/0.70 (step @p141 :rule cnf_or_pos :args (@t137)) % 0.47/0.70 (step @p142 :rule reordering :premises (@p141) :args ((or @t136 @t128 (not @t137)))) % 0.47/0.70 (step @p143 :rule chain_m_resolution :premises (@p142 @p60 @p140) :args (@t128 (@list false false) (@list @t108 @t137))) % 0.47/0.70 (step @p144 :rule aci_norm :args ((= (or (or @t139 @t138) @t10) (or @t139 @t138 @t10)))) % 0.47/0.70 (step @p145 :rule refl :args (@t10)) % 0.47/0.70 (step @p146 :rule bool-and-de-morgan :args (@t12 @t11 true)) % 0.47/0.70 (step @p147 :rule nary_cong :premises (@p146 @p145) :args ((or (not @t13) @t10))) % 0.47/0.70 (step @p148 :rule trans :premises (@p147 @p144)) % 0.47/0.70 (step @p149 :rule bool-impl-elim :args (@t13 @t10)) % 0.47/0.70 (step @p150 :rule trans :premises (@p149 @p148)) % 0.47/0.70 (step @p151 :rule cong :premises (@p150) :args (@t14)) % 0.47/0.70 (step @p152 :rule eq_resolve :premises (@p5 @p151)) % 0.47/0.70 (step @p153 :rule instantiate :premises (@p152) :args ((@list tptp.n0 @t143 tptp.tptp_minus_1))) % 0.47/0.70 (step @p154 :rule aci_norm :args ((= (or (or @t141 @t140) @t89) @t142))) % 0.47/0.70 (step @p155 :rule refl :args (@t89)) % 0.47/0.70 (step @p156 :rule bool-and-de-morgan :args (@t91 @t90 true)) % 0.47/0.70 (step @p157 :rule nary_cong :premises (@p156 @p155) :args ((or (not @t92) @t89))) % 0.47/0.70 (step @p158 :rule trans :premises (@p157 @p154)) % 0.47/0.70 (step @p159 :rule bool-impl-elim :args (@t92 @t89)) % 0.37/0.70 (step @p160 :rule trans :premises (@p159 @p158)) % 0.37/0.70 (step @p161 :rule cong :premises (@p160) :args (@t94)) % 0.37/0.70 (step @p162 :rule aci_norm :args ((= (or (or @t146 @t145) @t144) (or @t146 @t145 @t144)))) % 0.37/0.70 (step @p163 :rule refl :args (@t144)) % 0.37/0.70 (step @p164 :rule bool-and-de-morgan :args (@t97 @t96 true)) % 0.37/0.70 (step @p165 :rule nary_cong :premises (@p164 @p163) :args ((or (not @t98) @t144))) % 0.37/0.70 (step @p166 :rule trans :premises (@p165 @p162)) % 0.37/0.70 (step @p167 :rule bool-impl-elim :args (@t98 @t144)) % 0.37/0.70 (step @p168 :rule trans :premises (@p167 @p166)) % 0.37/0.70 (step @p169 :rule cong :premises (@p168) :args ((forall @t100 (=> @t98 @t144)))) % 0.37/0.70 (step @p170 :rule eq-symm :args (@t95 tptp.n1)) % 0.37/0.70 (step @p171 :rule refl :args (@t98)) % 0.37/0.70 (step @p172 :rule cong :premises (@p171 @p170) :args (@t99)) % 0.37/0.70 (step @p173 :rule cong :premises (@p172) :args (@t101)) % 0.37/0.70 (step @p174 :rule trans :premises (@p173 @p169)) % 0.37/0.70 (step @p175 :rule refl :args (@t102)) % 0.37/0.70 (step @p176 :rule refl :args (@t103)) % 0.37/0.70 (step @p177 :rule nary_cong :premises (@p176 @p175 @p174) :args (@t104)) % 0.37/0.70 (step @p178 :rule cong :premises (@p177 @p161) :args (@t105)) % 0.37/0.70 (step @p179 :rule cong :premises (@p178) :args (@t106)) % 0.37/0.70 (step @p180 :rule eq_resolve :premises (@p53 @p179)) % 0.37/0.70 (step @p181 :rule not_implies_elim2 :premises (@p180)) % 0.37/0.70 (step @p182 :rule skolemize :premises (@p181)) % 0.37/0.70 (step @p183 :rule bool-double-not-elim :args (@t147)) % 0.37/0.70 (step @p184 :rule refl :args (@t153)) % 0.37/0.70 (step @p185 :rule nary_cong :premises (@p184 @p183) :args ((or @t153 (not @t150)))) % 0.37/0.70 (step @p186 :rule cnf_or_neg :args (@t153 1)) % 0.37/0.70 (step @p187 :rule eq_resolve :premises (@p186 @p185)) % 0.37/0.70 (step @p188 :rule reordering :premises (@p187) :args ((or @t147 @t153))) % 0.37/0.70 (step @p189 :rule chain_m_resolution :premises (@p188 @p182) :args (@t147 @t154 @t155)) % 0.37/0.70 (step @p190 :rule bool-double-not-elim :args (@t151)) % 0.37/0.70 (step @p191 :rule nary_cong :premises (@p184 @p190) :args ((or @t153 (not @t152)))) % 0.37/0.70 (step @p192 :rule cnf_or_neg :args (@t153 0)) % 0.37/0.70 (step @p193 :rule eq_resolve :premises (@p192 @p191)) % 0.37/0.70 (step @p194 :rule reordering :premises (@p193) :args ((or @t151 @t153))) % 0.37/0.70 (step @p195 :rule chain_m_resolution :premises (@p194 @p182) :args (@t151 @t154 @t155)) % 0.37/0.70 (step @p196 :rule cnf_or_pos :args (@t156)) % 0.37/0.70 (step @p197 :rule reordering :premises (@p196) :args ((or @t152 @t150 @t130 (not @t156)))) % 0.37/0.70 (step @p198 :rule chain_m_resolution :premises (@p197 @p195 @p189 @p153) :args (@t130 @t157 (@list @t151 @t147 @t156))) % 0.37/0.70 (step @p199 :rule cnf_or_pos :args (@t135)) % 0.37/0.70 (step @p200 :rule reordering :premises (@p199) :args ((or @t131 @t129 @t134 (not @t135)))) % 0.37/0.70 (step @p201 :rule chain_m_resolution :premises (@p200 @p198 @p143 @p136) :args (@t134 @t157 (@list @t130 @t128 @t135))) % 0.37/0.70 (step @p202 :rule refl :args (tptp.n5)) % 0.37/0.70 (step @p203 :rule cong :premises (@p202 @p201) :args ((tptp.plus tptp.n5 tptp.n0))) % 0.37/0.70 (step @p204 :rule instantiate :premises (@p112) :args ((@list tptp.n0))) % 0.37/0.70 (step @p205 :rule symm :premises (@p97)) % 0.37/0.70 (step @p206 :rule trans :premises (@p205 @p204 @p203 @p114 @p109 @p96)) % 0.37/0.70 (step @p207 :rule cong :premises (@p206 @p105) :args (@t107)) % 0.37/0.70 (step @p208 :rule true_intro :premises (@p54)) % 0.37/0.70 (step @p209 :rule symm :premises (@p208)) % 0.37/0.70 (step @p210 :rule trans :premises (@p209 @p207 @p104)) % 0.37/0.70 (step @p211 false :rule eq_resolve :premises (@p210 @p102)) % 0.37/0.70 ) % 0.37/0.70 % SZS output end Proof % 0.37/0.70 % cvc5 exiting %------------------------------------------------------------------------------