%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV158+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 : n021.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 09:00:37 AM UTC 2026 % Result : Theorem 0.37s 0.62s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV158+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 % 0.17/0.34 % Computer : n021.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 19:59:05 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.62 % SZS status Theorem % 0.37/0.62 % SZS output start Proof % 0.37/0.62 ( % 0.37/0.62 (declare-sort $$unsorted 0) % 0.37/0.62 (declare-const tptp.q $$unsorted) % 0.37/0.62 (declare-const tptp.pv47 $$unsorted) % 0.37/0.62 (declare-const tptp.pv84 $$unsorted) % 0.37/0.62 (declare-const tptp.exp (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.x $$unsorted) % 0.37/0.62 (declare-const tptp.rho $$unsorted) % 0.37/0.62 (declare-const tptp.times (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.sigma $$unsorted) % 0.37/0.62 (declare-const tptp.tptp_sum_index $$unsorted) % 0.37/0.62 (declare-const tptp.def $$unsorted) % 0.37/0.62 (declare-const tptp.use $$unsorted) % 0.37/0.62 (declare-const tptp.true Bool) % 0.37/0.62 (declare-const tptp.tptp_update2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.divide (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.a_select3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.sqrt (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.uniform_int_rnd (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.mu $$unsorted) % 0.37/0.62 (declare-const tptp.n3 $$unsorted) % 0.37/0.62 (declare-const tptp.tptp_const_array1 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.pred (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.tptp_minus_1 $$unsorted) % 0.37/0.62 (declare-const tptp.n0 $$unsorted) % 0.37/0.62 (declare-const tptp.tptp_msub (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.n1 $$unsorted) % 0.37/0.62 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.n5 $$unsorted) % 0.37/0.62 (declare-const tptp.pv10 $$unsorted) % 0.37/0.62 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.tptp_update3 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.minus (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.tptp_minus_2 $$unsorted) % 0.37/0.62 (declare-const tptp.tptp_const_array2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.trans (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.a_select2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.inv (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.dim (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.plus (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.n135299 $$unsorted) % 0.37/0.62 (declare-const tptp.tptp_madd (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.sum (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.tptp_mmul (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.tptp_float_0_0 $$unsorted) % 0.37/0.62 (declare-const tptp.tptp_pi $$unsorted) % 0.37/0.62 (declare-const tptp.n4 $$unsorted) % 0.37/0.62 (declare-const tptp.n2 $$unsorted) % 0.37/0.62 (define @t1 () (@var "Y" $$unsorted)) % 0.37/0.62 (define @t2 () (@var "X" $$unsorted)) % 0.37/0.62 (define @t3 () (= @t2 @t1)) % 0.37/0.62 (define @t4 () (tptp.gt @t1 @t2)) % 0.37/0.62 (define @t5 () (tptp.gt @t2 @t1)) % 0.37/0.62 (define @t6 () (@list @t2 @t1)) % 0.37/0.62 (define @t7 () (@var "Z" $$unsorted)) % 0.37/0.62 (define @t8 () (@list @t2 @t1 @t7)) % 0.37/0.62 (define @t9 () (@list @t2)) % 0.37/0.62 (define @t10 () (tptp.leq @t2 @t1)) % 0.37/0.62 (define @t11 () (tptp.succ @t2)) % 0.37/0.62 (define @t12 () (tptp.succ @t1)) % 0.37/0.62 (define @t13 () (@var "C" $$unsorted)) % 0.37/0.62 (define @t14 () (tptp.uniform_int_rnd @t13 @t2)) % 0.37/0.62 (define @t15 () (tptp.leq tptp.n0 @t2)) % 0.37/0.62 (define @t16 () (@list @t2 @t13)) % 0.37/0.62 (define @t17 () (@var "Val" $$unsorted)) % 0.37/0.62 (define @t18 () (@var "I" $$unsorted)) % 0.37/0.62 (define @t19 () (@var "U" $$unsorted)) % 0.37/0.62 (define @t20 () (@var "L" $$unsorted)) % 0.37/0.62 (define @t21 () (tptp.leq @t18 @t19)) % 0.37/0.62 (define @t22 () (@var "J" $$unsorted)) % 0.37/0.62 (define @t23 () (@var "U2" $$unsorted)) % 0.37/0.62 (define @t24 () (@var "L2" $$unsorted)) % 0.37/0.62 (define @t25 () (@var "U1" $$unsorted)) % 0.37/0.62 (define @t26 () (@var "L1" $$unsorted)) % 0.37/0.62 (define @t27 () (@var "A" $$unsorted)) % 0.37/0.62 (define @t28 () (tptp.trans @t27)) % 0.37/0.62 (define @t29 () (@var "N" $$unsorted)) % 0.37/0.62 (define @t30 () (tptp.leq @t22 @t29)) % 0.37/0.62 (define @t31 () (tptp.leq tptp.n0 @t22)) % 0.37/0.62 (define @t32 () (tptp.leq @t18 @t29)) % 0.37/0.62 (define @t33 () (tptp.leq tptp.n0 @t18)) % 0.37/0.62 (define @t34 () (and @t33 @t32 @t31 @t30)) % 0.37/0.62 (define @t35 () (@list @t18 @t22)) % 0.37/0.62 (define @t36 () (forall @t35 (=> @t34 (= (tptp.a_select3 @t27 @t18 @t22) (tptp.a_select3 @t27 @t22 @t18))))) % 0.37/0.62 (define @t37 () (@list @t27 @t29)) % 0.37/0.62 (define @t38 () (tptp.inv @t27)) % 0.37/0.62 (define @t39 () (@var "VAL" $$unsorted)) % 0.37/0.62 (define @t40 () (@var "K" $$unsorted)) % 0.37/0.62 (define @t41 () (tptp.tptp_update3 @t27 @t40 @t40 @t39)) % 0.37/0.62 (define @t42 () (@var "B" $$unsorted)) % 0.37/0.62 (define @t43 () (tptp.tptp_madd @t27 @t42)) % 0.37/0.62 (define @t44 () (= (tptp.a_select3 @t42 @t18 @t22) (tptp.a_select3 @t42 @t22 @t18))) % 0.37/0.62 (define @t45 () (forall @t35 (=> @t34 @t44))) % 0.37/0.62 (define @t46 () (and @t36 @t45)) % 0.37/0.62 (define @t47 () (@list @t27 @t42 @t29)) % 0.37/0.62 (define @t48 () (tptp.tptp_msub @t27 @t42)) % 0.37/0.62 (define @t49 () (tptp.tptp_mmul @t27 (tptp.tptp_mmul @t42 @t28))) % 0.37/0.62 (define @t50 () (forall @t35 (=> @t34 (= (tptp.a_select3 @t49 @t18 @t22) (tptp.a_select3 @t49 @t22 @t18))))) % 0.37/0.62 (define @t51 () (@var "M" $$unsorted)) % 0.37/0.62 (define @t52 () (and @t33 (tptp.leq @t18 @t51) @t31 (tptp.leq @t22 @t51))) % 0.37/0.62 (define @t53 () (@var "E" $$unsorted)) % 0.37/0.62 (define @t54 () (@var "F" $$unsorted)) % 0.37/0.62 (define @t55 () (@var "D" $$unsorted)) % 0.37/0.62 (define @t56 () (tptp.tptp_madd @t27 (tptp.tptp_mmul @t42 (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul @t13 (tptp.tptp_mmul @t55 (tptp.trans @t13))) (tptp.tptp_mmul @t53 (tptp.tptp_mmul @t54 (tptp.trans @t53)))) (tptp.trans @t42))))) % 0.37/0.62 (define @t57 () (@var "Body" $$unsorted)) % 0.37/0.62 (define @t58 () (tptp.sum tptp.n0 tptp.tptp_minus_1 @t57)) % 0.37/0.62 (define @t59 () (@list @t57)) % 0.37/0.62 (define @t60 () (tptp.succ @t11)) % 0.37/0.62 (define @t61 () (tptp.succ @t60)) % 0.37/0.62 (define @t62 () (tptp.succ @t61)) % 0.37/0.62 (define @t63 () (tptp.succ @t62)) % 0.37/0.62 (define @t64 () (tptp.pred @t2)) % 0.37/0.62 (define @t65 () (@var "V" $$unsorted)) % 0.37/0.62 (define @t66 () (tptp.tptp_update3 @t2 @t19 @t65 @t39)) % 0.37/0.62 (define @t67 () (@var "VAL2" $$unsorted)) % 0.37/0.62 (define @t68 () (not (= @t18 @t19))) % 0.37/0.62 (define @t69 () (@var "J0" $$unsorted)) % 0.37/0.62 (define @t70 () (@var "I0" $$unsorted)) % 0.37/0.62 (define @t71 () (tptp.leq @t70 @t19)) % 0.37/0.62 (define @t72 () (tptp.leq tptp.n0 @t70)) % 0.37/0.62 (define @t73 () (tptp.tptp_update2 @t2 @t19 @t39)) % 0.37/0.62 (define @t74 () (tptp.a_select2 tptp.sigma tptp.tptp_sum_index)) % 0.37/0.62 (define @t75 () (tptp.sqrt (tptp.times tptp.n2 tptp.tptp_pi))) % 0.37/0.62 (define @t76 () (tptp.a_select2 tptp.x tptp.pv10)) % 0.37/0.62 (define @t77 () (tptp.minus @t76 (tptp.a_select2 tptp.mu tptp.tptp_sum_index))) % 0.37/0.62 (define @t78 () (tptp.sum tptp.n0 tptp.n4 (tptp.divide (tptp.times (tptp.exp (tptp.divide (tptp.divide (tptp.times @t77 @t77) tptp.tptp_minus_2) (tptp.times @t74 @t74))) (tptp.a_select2 tptp.rho tptp.tptp_sum_index)) (tptp.times @t75 @t74)))) % 0.37/0.62 (define @t79 () (tptp.a_select2 tptp.sigma @t13)) % 0.37/0.62 (define @t80 () (tptp.minus @t76 (tptp.a_select2 tptp.mu @t13))) % 0.37/0.62 (define @t81 () (tptp.a_select2 tptp.sigma tptp.pv47)) % 0.37/0.62 (define @t82 () (tptp.minus @t76 (tptp.a_select2 tptp.mu tptp.pv47))) % 0.37/0.62 (define @t83 () (tptp.divide (tptp.times (tptp.exp (tptp.divide (tptp.divide (tptp.times @t82 @t82) tptp.tptp_minus_2) (tptp.times @t81 @t81))) (tptp.a_select2 tptp.rho tptp.pv47)) (tptp.times @t75 @t81))) % 0.37/0.62 (define @t84 () (tptp.divide @t83 tptp.pv84)) % 0.37/0.62 (define @t85 () (= @t84 (tptp.divide (tptp.divide (tptp.times (tptp.exp (tptp.divide (tptp.divide (tptp.times @t80 @t80) tptp.tptp_minus_2) (tptp.times @t79 @t79))) (tptp.a_select2 tptp.rho @t13)) (tptp.times @t75 @t79)) @t78))) % 0.37/0.62 (define @t86 () (=> (= tptp.pv47 @t13) @t85)) % 0.37/0.62 (define @t87 () (tptp.leq @t13 tptp.pv47)) % 0.37/0.62 (define @t88 () (tptp.leq tptp.n0 @t13)) % 0.37/0.62 (define @t89 () (and @t88 @t87)) % 0.37/0.62 (define @t90 () (=> @t89 @t86)) % 0.37/0.62 (define @t91 () (@list @t13)) % 0.37/0.62 (define @t92 () (forall @t91 @t90)) % 0.37/0.62 (define @t93 () (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q @t42 tptp.tptp_sum_index))) % 0.37/0.62 (define @t94 () (tptp.leq @t42 (tptp.pred tptp.pv10))) % 0.37/0.62 (define @t95 () (tptp.leq tptp.n0 @t42)) % 0.37/0.62 (define @t96 () (and @t95 @t94)) % 0.37/0.62 (define @t97 () (=> @t96 (= @t93 tptp.n1))) % 0.37/0.62 (define @t98 () (@list @t42)) % 0.37/0.62 (define @t99 () (forall @t98 @t97)) % 0.37/0.62 (define @t100 () (tptp.a_select2 tptp.sigma @t27)) % 0.37/0.62 (define @t101 () (tptp.minus @t76 (tptp.a_select2 tptp.mu @t27))) % 0.37/0.62 (define @t102 () (= (tptp.a_select3 tptp.q tptp.pv10 @t27) (tptp.divide (tptp.divide (tptp.times (tptp.exp (tptp.divide (tptp.divide (tptp.times @t101 @t101) tptp.tptp_minus_2) (tptp.times @t100 @t100))) (tptp.a_select2 tptp.rho @t27)) (tptp.times @t75 @t100)) @t78))) % 0.37/0.62 (define @t103 () (tptp.leq @t27 (tptp.pred tptp.pv47))) % 0.37/0.62 (define @t104 () (tptp.leq tptp.n0 @t27)) % 0.37/0.62 (define @t105 () (and @t104 @t103)) % 0.37/0.62 (define @t106 () (forall (@list @t27) (=> @t105 @t102))) % 0.37/0.62 (define @t107 () (tptp.leq tptp.pv47 tptp.n4)) % 0.37/0.62 (define @t108 () (tptp.leq tptp.pv10 tptp.n135299)) % 0.37/0.62 (define @t109 () (tptp.leq tptp.n0 tptp.pv47)) % 0.37/0.62 (define @t110 () (tptp.leq tptp.n0 tptp.pv10)) % 0.37/0.62 (define @t111 () (= tptp.pv84 @t78)) % 0.37/0.62 (define @t112 () (and @t111 @t110 @t109 @t108 @t107 @t106 @t99)) % 0.37/0.62 (define @t113 () (=> @t112 @t92)) % 0.37/0.62 (define @t114 () (not @t113)) % 0.37/0.62 (define @t115 () (= @t2 tptp.n4)) % 0.37/0.62 (define @t116 () (= @t2 tptp.n3)) % 0.37/0.62 (define @t117 () (= @t2 tptp.n2)) % 0.37/0.62 (define @t118 () (= @t2 tptp.n1)) % 0.37/0.62 (define @t119 () (= @t2 tptp.n0)) % 0.37/0.62 (define @t120 () (tptp.succ tptp.n0)) % 0.37/0.62 (define @t121 () (tptp.succ @t120)) % 0.37/0.62 (define @t122 () (tptp.succ @t121)) % 0.37/0.62 (define @t123 () (tptp.succ @t122)) % 0.37/0.62 (define @t124 () (= @t84 (tptp.divide @t83 @t78))) % 0.37/0.62 (define @t125 () (not (tptp.leq tptp.pv47 tptp.pv47))) % 0.37/0.62 (define @t126 () (not @t109)) % 0.37/0.62 (define @t127 () (not (= tptp.pv47 tptp.pv47))) % 0.37/0.62 (define @t128 () (or @t126 @t125 @t127 @t124)) % 0.37/0.62 (define @t129 () (= @t13 tptp.pv47)) % 0.37/0.62 (define @t130 () (not @t129)) % 0.37/0.62 (define @t131 () (not @t87)) % 0.37/0.62 (define @t132 () (not @t88)) % 0.37/0.62 (define @t133 () (or @t130 @t132 @t131 @t130 @t85)) % 0.37/0.62 (define @t134 () (or @t132 @t131 @t130 @t85)) % 0.37/0.62 (define @t135 () (=> @t129 @t85)) % 0.37/0.62 (define @t136 () (= tptp.n1 @t93)) % 0.37/0.62 (define @t137 () (not @t94)) % 0.37/0.62 (define @t138 () (not @t95)) % 0.37/0.62 (define @t139 () (not @t103)) % 0.37/0.62 (define @t140 () (not @t104)) % 0.37/0.62 (assume @p1 (forall @t6 (or @t5 @t4 @t3))) % 0.37/0.62 (assume @p2 (forall @t8 (=> (and @t5 (tptp.gt @t1 @t7)) (tptp.gt @t2 @t7)))) % 0.37/0.62 (assume @p3 (forall @t9 (not (tptp.gt @t2 @t2)))) % 0.37/0.62 (assume @p4 (forall @t9 (tptp.leq @t2 @t2))) % 0.37/0.62 (assume @p5 (forall @t8 (=> (and @t10 (tptp.leq @t1 @t7)) (tptp.leq @t2 @t7)))) % 0.37/0.62 (assume @p6 (forall @t6 (= (tptp.lt @t2 @t1) @t4))) % 0.37/0.62 (assume @p7 (forall @t6 (= (tptp.geq @t2 @t1) (tptp.leq @t1 @t2)))) % 0.37/0.62 (assume @p8 (forall @t6 (=> @t4 @t10))) % 0.37/0.62 (assume @p9 (forall @t6 (=> (and @t10 (not @t3)) @t4))) % 0.37/0.62 (assume @p10 (forall @t6 (= (tptp.leq @t2 (tptp.pred @t1)) @t4))) % 0.37/0.62 (assume @p11 (forall @t9 (tptp.gt @t11 @t2))) % 0.37/0.62 (assume @p12 (forall @t6 (=> @t10 (tptp.leq @t2 @t12)))) % 0.37/0.62 (assume @p13 (forall @t6 (= @t10 (tptp.gt @t12 @t2)))) % 0.37/0.62 (assume @p14 (forall @t16 (=> @t15 (tptp.leq @t14 @t2)))) % 0.37/0.62 (assume @p15 (forall @t16 (=> @t15 (tptp.leq tptp.n0 @t14)))) % 0.37/0.62 (assume @p16 (forall (@list @t18 @t20 @t19 @t17) (=> (and (tptp.leq @t20 @t18) @t21) (= (tptp.a_select2 (tptp.tptp_const_array1 (tptp.dim @t20 @t19) @t17) @t18) @t17)))) % 0.37/0.62 (assume @p17 (forall (@list @t18 @t26 @t25 @t22 @t24 @t23 @t17) (=> (and (tptp.leq @t26 @t18) (tptp.leq @t18 @t25) (tptp.leq @t24 @t22) (tptp.leq @t22 @t23)) (= (tptp.a_select3 (tptp.tptp_const_array2 (tptp.dim @t26 @t25) (tptp.dim @t24 @t23) @t17) @t18 @t22) @t17)))) % 0.37/0.62 (assume @p18 (forall @t37 (=> @t36 (forall @t35 (=> @t34 (= (tptp.a_select3 @t28 @t18 @t22) (tptp.a_select3 @t28 @t22 @t18))))))) % 0.37/0.62 (assume @p19 (forall @t37 (=> @t36 (forall @t35 (=> @t34 (= (tptp.a_select3 @t38 @t18 @t22) (tptp.a_select3 @t38 @t22 @t18))))))) % 0.37/0.62 (assume @p20 (forall @t37 (=> @t36 (forall (@list @t18 @t22 @t40 @t39) (=> (and @t33 @t32 @t31 @t30 (tptp.leq tptp.n0 @t40) (tptp.leq @t40 @t29)) (= (tptp.a_select3 @t41 @t18 @t22) (tptp.a_select3 @t41 @t22 @t18))))))) % 0.37/0.62 (assume @p21 (forall @t47 (=> @t46 (forall @t35 (=> @t34 (= (tptp.a_select3 @t43 @t18 @t22) (tptp.a_select3 @t43 @t22 @t18))))))) % 0.37/0.62 (assume @p22 (forall @t47 (=> @t46 (forall @t35 (=> @t34 (= (tptp.a_select3 @t48 @t18 @t22) (tptp.a_select3 @t48 @t22 @t18))))))) % 0.37/0.62 (assume @p23 (forall @t47 (=> @t45 @t50))) % 0.37/0.62 (assume @p24 (forall (@list @t27 @t42 @t29 @t51) (=> (forall @t35 (=> @t52 @t44)) @t50))) % 0.37/0.62 (assume @p25 (forall (@list @t27 @t42 @t13 @t55 @t53 @t54 @t29 @t51) (=> (and (forall @t35 (=> @t52 (= (tptp.a_select3 @t55 @t18 @t22) (tptp.a_select3 @t55 @t22 @t18)))) @t36 (forall @t35 (=> @t34 (= (tptp.a_select3 @t54 @t18 @t22) (tptp.a_select3 @t54 @t22 @t18))))) (forall @t35 (=> @t34 (= (tptp.a_select3 @t56 @t18 @t22) (tptp.a_select3 @t56 @t22 @t18))))))) % 0.37/0.62 (assume @p26 (forall @t59 (= @t58 tptp.n0))) % 0.37/0.62 (assume @p27 (forall @t59 (= tptp.tptp_float_0_0 @t58))) % 0.37/0.62 (assume @p28 (= (tptp.succ tptp.tptp_minus_1) tptp.n0)) % 0.37/0.62 (assume @p29 (forall @t9 (= (tptp.plus @t2 tptp.n1) @t11))) % 0.37/0.62 (assume @p30 (forall @t9 (= (tptp.plus tptp.n1 @t2) @t11))) % 0.37/0.62 (assume @p31 (forall @t9 (= (tptp.plus @t2 tptp.n2) @t60))) % 0.37/0.62 (assume @p32 (forall @t9 (= (tptp.plus tptp.n2 @t2) @t60))) % 0.37/0.62 (assume @p33 (forall @t9 (= (tptp.plus @t2 tptp.n3) @t61))) % 0.37/0.62 (assume @p34 (forall @t9 (= (tptp.plus tptp.n3 @t2) @t61))) % 0.37/0.62 (assume @p35 (forall @t9 (= (tptp.plus @t2 tptp.n4) @t62))) % 0.37/0.62 (assume @p36 (forall @t9 (= (tptp.plus tptp.n4 @t2) @t62))) % 0.37/0.62 (assume @p37 (forall @t9 (= (tptp.plus @t2 tptp.n5) @t63))) % 0.37/0.62 (assume @p38 (forall @t9 (= (tptp.plus tptp.n5 @t2) @t63))) % 0.37/0.62 (assume @p39 (forall @t9 (= (tptp.minus @t2 tptp.n1) @t64))) % 0.37/0.62 (assume @p40 (forall @t9 (= (tptp.pred @t11) @t2))) % 0.37/0.62 (assume @p41 (forall @t9 (= (tptp.succ @t64) @t2))) % 0.37/0.62 (assume @p42 (forall @t6 (= (tptp.leq @t11 @t12) @t10))) % 0.37/0.62 (assume @p43 (forall @t6 (=> (tptp.leq @t11 @t1) @t4))) % 0.37/0.62 (assume @p44 (forall @t6 (=> (tptp.leq (tptp.minus @t2 @t1) @t2) (tptp.leq tptp.n0 @t1)))) % 0.37/0.62 (assume @p45 (forall (@list @t2 @t19 @t65 @t39) (= (tptp.a_select3 @t66 @t19 @t65) @t39))) % 0.37/0.62 (assume @p46 (forall (@list @t18 @t22 @t19 @t65 @t2 @t39 @t67) (=> (and @t68 (= @t22 @t65) (= (tptp.a_select3 @t2 @t19 @t65) @t39)) (= (tptp.a_select3 (tptp.tptp_update3 @t2 @t18 @t22 @t67) @t19 @t65) @t39)))) % 0.37/0.62 (assume @p47 (forall (@list @t18 @t22 @t19 @t65 @t2 @t39) (=> (and (forall (@list @t70 @t69) (=> (and @t72 (tptp.leq tptp.n0 @t69) @t71 (tptp.leq @t69 @t65)) (= (tptp.a_select3 @t2 @t70 @t69) @t39))) @t33 @t21 @t31 (tptp.leq @t22 @t65)) (= (tptp.a_select3 @t66 @t18 @t22) @t39)))) % 0.37/0.62 (assume @p48 (forall (@list @t2 @t19 @t39) (= (tptp.a_select2 @t73 @t19) @t39))) % 0.37/0.62 (assume @p49 (forall (@list @t18 @t19 @t2 @t39 @t67) (=> (and @t68 (= (tptp.a_select2 @t2 @t19) @t39)) (= (tptp.a_select2 (tptp.tptp_update2 @t2 @t18 @t67) @t19) @t39)))) % 0.37/0.62 (assume @p50 (forall (@list @t18 @t19 @t2 @t39) (=> (and (forall (@list @t70) (=> (and @t72 @t71) (= (tptp.a_select2 @t2 @t70) @t39))) @t33 @t21) (= (tptp.a_select2 @t73 @t18) @t39)))) % 0.37/0.62 (assume @p51 tptp.true) % 0.37/0.62 (assume @p52 (not (= tptp.def tptp.use))) % 0.37/0.62 (assume @p53 @t114) % 0.37/0.62 (assume @p54 (tptp.gt tptp.n5 tptp.n4)) % 0.37/0.62 (assume @p55 (tptp.gt tptp.n135299 tptp.n4)) % 0.37/0.62 (assume @p56 (tptp.gt tptp.n135299 tptp.n5)) % 0.37/0.62 (assume @p57 (tptp.gt tptp.n4 tptp.tptp_minus_1)) % 0.37/0.62 (assume @p58 (tptp.gt tptp.n5 tptp.tptp_minus_1)) % 0.37/0.62 (assume @p59 (tptp.gt tptp.n135299 tptp.tptp_minus_1)) % 0.37/0.62 (assume @p60 (tptp.gt tptp.n0 tptp.tptp_minus_1)) % 0.37/0.62 (assume @p61 (tptp.gt tptp.n1 tptp.tptp_minus_1)) % 0.37/0.62 (assume @p62 (tptp.gt tptp.n2 tptp.tptp_minus_1)) % 0.37/0.62 (assume @p63 (tptp.gt tptp.n3 tptp.tptp_minus_1)) % 0.37/0.62 (assume @p64 (tptp.gt tptp.n4 tptp.tptp_minus_2)) % 0.37/0.62 (assume @p65 (tptp.gt tptp.n5 tptp.tptp_minus_2)) % 0.37/0.62 (assume @p66 (tptp.gt tptp.tptp_minus_1 tptp.tptp_minus_2)) % 0.37/0.62 (assume @p67 (tptp.gt tptp.n135299 tptp.tptp_minus_2)) % 0.37/0.62 (assume @p68 (tptp.gt tptp.n0 tptp.tptp_minus_2)) % 0.37/0.62 (assume @p69 (tptp.gt tptp.n1 tptp.tptp_minus_2)) % 0.37/0.62 (assume @p70 (tptp.gt tptp.n2 tptp.tptp_minus_2)) % 0.37/0.62 (assume @p71 (tptp.gt tptp.n3 tptp.tptp_minus_2)) % 0.37/0.62 (assume @p72 (tptp.gt tptp.n4 tptp.n0)) % 0.37/0.62 (assume @p73 (tptp.gt tptp.n5 tptp.n0)) % 0.37/0.62 (assume @p74 (tptp.gt tptp.n135299 tptp.n0)) % 0.37/0.62 (assume @p75 (tptp.gt tptp.n1 tptp.n0)) % 0.37/0.62 (assume @p76 (tptp.gt tptp.n2 tptp.n0)) % 0.37/0.62 (assume @p77 (tptp.gt tptp.n3 tptp.n0)) % 0.37/0.62 (assume @p78 (tptp.gt tptp.n4 tptp.n1)) % 0.37/0.62 (assume @p79 (tptp.gt tptp.n5 tptp.n1)) % 0.37/0.62 (assume @p80 (tptp.gt tptp.n135299 tptp.n1)) % 0.37/0.62 (assume @p81 (tptp.gt tptp.n2 tptp.n1)) % 0.37/0.62 (assume @p82 (tptp.gt tptp.n3 tptp.n1)) % 0.37/0.62 (assume @p83 (tptp.gt tptp.n4 tptp.n2)) % 0.37/0.62 (assume @p84 (tptp.gt tptp.n5 tptp.n2)) % 0.37/0.62 (assume @p85 (tptp.gt tptp.n135299 tptp.n2)) % 0.37/0.62 (assume @p86 (tptp.gt tptp.n3 tptp.n2)) % 0.37/0.62 (assume @p87 (tptp.gt tptp.n4 tptp.n3)) % 0.37/0.62 (assume @p88 (tptp.gt tptp.n5 tptp.n3)) % 0.37/0.62 (assume @p89 (tptp.gt tptp.n135299 tptp.n3)) % 0.37/0.62 (assume @p90 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n4)) (or @t119 @t118 @t117 @t116 @t115)))) % 0.37/0.62 (assume @p91 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n5)) (or @t119 @t118 @t117 @t116 @t115 (= @t2 tptp.n5))))) % 0.37/0.62 (assume @p92 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n0)) @t119))) % 0.37/0.62 (assume @p93 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n1)) (or @t119 @t118)))) % 0.37/0.62 (assume @p94 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n2)) (or @t119 @t118 @t117)))) % 0.37/0.62 (assume @p95 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n3)) (or @t119 @t118 @t117 @t116)))) % 0.37/0.62 (assume @p96 (= @t123 tptp.n4)) % 0.37/0.62 (assume @p97 (= (tptp.succ @t123) tptp.n5)) % 0.37/0.62 (assume @p98 (= @t120 tptp.n1)) % 0.37/0.62 (assume @p99 (= @t121 tptp.n2)) % 0.37/0.62 (assume @p100 (= @t122 tptp.n3)) % 0.37/0.62 (assume @p101 true) % 0.37/0.62 (step @p102 :rule aci_norm :args ((= (or @t126 @t125 false @t124) (or @t126 @t125 @t124)))) % 0.37/0.62 (step @p103 :rule refl :args (@t124)) % 0.37/0.62 (step @p104 :rule evaluate :args ((not true))) % 0.37/0.62 (step @p105 :rule eq-refl :args (tptp.pv47)) % 0.37/0.62 (step @p106 :rule cong :premises (@p105) :args (@t127)) % 0.37/0.62 (step @p107 :rule trans :premises (@p106 @p104)) % 0.37/0.62 (step @p108 :rule refl :args (@t125)) % 0.37/0.62 (step @p109 :rule refl :args (@t126)) % 0.37/0.62 (step @p110 :rule nary_cong :premises (@p109 @p108 @p107 @p103) :args (@t128)) % 0.37/0.62 (step @p111 :rule trans :premises (@p110 @p102)) % 0.37/0.62 (step @p112 :rule quant-var-elim-eq :args ((= (forall @t91 @t133) @t128))) % 0.37/0.62 (step @p113 :rule aci_norm :args ((= @t134 @t133))) % 0.37/0.62 (step @p114 :rule cong :premises (@p113) :args ((forall @t91 @t134))) % 0.37/0.62 (step @p115 :rule trans :premises (@p114 @p112)) % 0.37/0.62 (step @p116 :rule trans :premises (@p115 @p111)) % 0.37/0.62 (step @p117 :rule aci_norm :args ((= (or (or @t132 @t131) (or @t130 @t85)) @t134))) % 0.37/0.62 (step @p118 :rule bool-impl-elim :args (@t129 @t85)) % 0.37/0.62 (step @p119 :rule bool-and-de-morgan :args (@t88 @t87 true)) % 0.37/0.62 (step @p120 :rule nary_cong :premises (@p119 @p118) :args ((or (not @t89) @t135))) % 0.37/0.62 (step @p121 :rule trans :premises (@p120 @p117)) % 0.37/0.62 (step @p122 :rule bool-impl-elim :args (@t89 @t135)) % 0.37/0.62 (step @p123 :rule trans :premises (@p122 @p121)) % 0.37/0.62 (step @p124 :rule cong :premises (@p123) :args ((forall @t91 (=> @t89 @t135)))) % 0.37/0.62 (step @p125 :rule trans :premises (@p124 @p116)) % 0.37/0.62 (step @p126 :rule refl :args (@t85)) % 0.37/0.62 (step @p127 :rule eq-symm :args (tptp.pv47 @t13)) % 0.37/0.62 (step @p128 :rule cong :premises (@p127 @p126) :args (@t86)) % 0.37/0.62 (step @p129 :rule refl :args (@t89)) % 0.37/0.62 (step @p130 :rule cong :premises (@p129 @p128) :args (@t90)) % 0.37/0.62 (step @p131 :rule cong :premises (@p130) :args (@t92)) % 0.37/0.62 (step @p132 :rule trans :premises (@p131 @p125)) % 0.37/0.62 (step @p133 :rule aci_norm :args ((= (or (or @t138 @t137) @t136) (or @t138 @t137 @t136)))) % 0.37/0.62 (step @p134 :rule refl :args (@t136)) % 0.37/0.62 (step @p135 :rule bool-and-de-morgan :args (@t95 @t94 true)) % 0.37/0.62 (step @p136 :rule nary_cong :premises (@p135 @p134) :args ((or (not @t96) @t136))) % 0.37/0.62 (step @p137 :rule trans :premises (@p136 @p133)) % 0.37/0.62 (step @p138 :rule bool-impl-elim :args (@t96 @t136)) % 0.37/0.62 (step @p139 :rule trans :premises (@p138 @p137)) % 0.37/0.62 (step @p140 :rule cong :premises (@p139) :args ((forall @t98 (=> @t96 @t136)))) % 0.37/0.62 (step @p141 :rule eq-symm :args (@t93 tptp.n1)) % 0.37/0.62 (step @p142 :rule refl :args (@t96)) % 0.37/0.62 (step @p143 :rule cong :premises (@p142 @p141) :args (@t97)) % 0.37/0.62 (step @p144 :rule cong :premises (@p143) :args (@t99)) % 0.37/0.62 (step @p145 :rule trans :premises (@p144 @p140)) % 0.37/0.62 (step @p146 :rule aci_norm :args ((= (or (or @t140 @t139) @t102) (or @t140 @t139 @t102)))) % 0.37/0.62 (step @p147 :rule refl :args (@t102)) % 0.37/0.62 (step @p148 :rule bool-and-de-morgan :args (@t104 @t103 true)) % 0.37/0.62 (step @p149 :rule nary_cong :premises (@p148 @p147) :args ((or (not @t105) @t102))) % 0.37/0.62 (step @p150 :rule trans :premises (@p149 @p146)) % 0.37/0.62 (step @p151 :rule bool-impl-elim :args (@t105 @t102)) % 0.37/0.62 (step @p152 :rule trans :premises (@p151 @p150)) % 0.37/0.62 (step @p153 :rule cong :premises (@p152) :args (@t106)) % 0.37/0.62 (step @p154 :rule refl :args (@t107)) % 0.37/0.62 (step @p155 :rule refl :args (@t108)) % 0.37/0.62 (step @p156 :rule refl :args (@t109)) % 0.37/0.62 (step @p157 :rule refl :args (@t110)) % 0.37/0.62 (step @p158 :rule refl :args (@t111)) % 0.37/0.62 (step @p159 :rule nary_cong :premises (@p158 @p157 @p156 @p155 @p154 @p153 @p145) :args (@t112)) % 0.37/0.62 (step @p160 :rule cong :premises (@p159 @p132) :args (@t113)) % 0.37/0.62 (step @p161 :rule cong :premises (@p160) :args (@t114)) % 0.37/0.62 (step @p162 :rule eq_resolve :premises (@p53 @p161)) % 0.37/0.62 (step @p163 :rule not_implies_elim1 :premises (@p162)) % 0.37/0.62 (step @p164 :rule and_elim :premises (@p163) :args (0)) % 0.37/0.62 (step @p165 :rule not_implies_elim2 :premises (@p162)) % 0.37/0.62 (step @p166 :rule not_or_elim :premises (@p165) :args (2)) % 0.37/0.62 (assume-push @p175 @t111) % 0.37/0.62 (step @p168 :rule refl :args (@t83)) % 0.37/0.62 (step @p169 :rule cong :premises (@p168 @p164) :args (@t84)) % 0.37/0.62 (step-pop @p176 :rule scope :premises (@p169)) % 0.37/0.62 (step @p170 :rule process_scope :premises (@p176) :args (@t124)) % 0.37/0.62 (step @p172 :rule implies_elim :premises (@p170)) % 0.37/0.62 (step @p173 :rule reordering :premises (@p172) :args ((or @t124 (not @t111)))) % 0.37/0.62 (step @p174 false :rule chain_m_resolution :premises (@p173 @p166 @p164) :args (false (@list true false) (@list @t124 @t111))) % 0.37/0.62 ) % 0.37/0.62 % SZS output end Proof % 0.37/0.62 % cvc5 exiting %------------------------------------------------------------------------------