%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV053+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 : n018.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 09:00:25 AM UTC 2026 % Result : Theorem 0.36s 0.69s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SWV053+1 : TPTP v9.2.1. Bugfixed v3.3.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.36 % Computer : n018.cluster.edu % 0.17/0.36 % Model : x86_64 x86_64 % 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.36 % Memory : 8042.1875MB % 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.36 % CPULimit : 300 % 0.17/0.36 % WCLimit : 300 % 0.17/0.36 % DateTime : Tue Jun 2 19:53:35 EDT 2026 % 0.17/0.36 % CPUTime : % 0.28/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.69 % SZS status Theorem % 0.36/0.69 % SZS output start Proof % 0.36/0.69 ( % 0.36/0.69 (declare-sort $$unsorted 0) % 0.36/0.69 (declare-const tptp.pv71 $$unsorted) % 0.36/0.69 (declare-const tptp.divide (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.sqrt (-> $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.center $$unsorted) % 0.36/0.69 (declare-const tptp.pv10 $$unsorted) % 0.36/0.69 (declare-const tptp.q $$unsorted) % 0.36/0.69 (declare-const tptp.def $$unsorted) % 0.36/0.69 (declare-const tptp.use $$unsorted) % 0.36/0.69 (declare-const tptp.true Bool) % 0.36/0.69 (declare-const tptp.tptp_update2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.times (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.a_select3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.36/0.69 (declare-const tptp.uniform_int_rnd (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.n135300 $$unsorted) % 0.36/0.69 (declare-const tptp.n3 $$unsorted) % 0.36/0.69 (declare-const tptp.tptp_const_array1 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.pred (-> $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.tptp_minus_1 $$unsorted) % 0.36/0.69 (declare-const tptp.n0 $$unsorted) % 0.36/0.69 (declare-const tptp.tptp_msub (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.n1 $$unsorted) % 0.36/0.69 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.n5 $$unsorted) % 0.36/0.69 (declare-const tptp.pv12 $$unsorted) % 0.36/0.69 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.36/0.69 (declare-const tptp.tptp_update3 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.minus (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.x $$unsorted) % 0.36/0.69 (declare-const tptp.tptp_const_array2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.36/0.69 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.36/0.69 (declare-const tptp.trans (-> $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.a_select2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.inv (-> $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.dim (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.plus (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.tptp_madd (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.sum (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.tptp_mmul (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.69 (declare-const tptp.tptp_float_0_0 $$unsorted) % 0.36/0.69 (declare-const tptp.n4 $$unsorted) % 0.36/0.69 (declare-const tptp.n2 $$unsorted) % 0.36/0.69 (define @t1 () (@var "Y" $$unsorted)) % 0.36/0.69 (define @t2 () (@var "X" $$unsorted)) % 0.36/0.69 (define @t3 () (= @t2 @t1)) % 0.36/0.69 (define @t4 () (tptp.gt @t1 @t2)) % 0.36/0.69 (define @t5 () (tptp.gt @t2 @t1)) % 0.36/0.69 (define @t6 () (@list @t2 @t1)) % 0.36/0.69 (define @t7 () (@var "Z" $$unsorted)) % 0.36/0.69 (define @t8 () (@list @t2 @t1 @t7)) % 0.36/0.69 (define @t9 () (@list @t2)) % 0.36/0.69 (define @t10 () (tptp.leq @t2 @t1)) % 0.36/0.69 (define @t11 () (tptp.succ @t2)) % 0.36/0.69 (define @t12 () (tptp.succ @t1)) % 0.36/0.69 (define @t13 () (@var "C" $$unsorted)) % 0.36/0.69 (define @t14 () (tptp.uniform_int_rnd @t13 @t2)) % 0.36/0.69 (define @t15 () (tptp.leq tptp.n0 @t2)) % 0.36/0.69 (define @t16 () (@list @t2 @t13)) % 0.36/0.69 (define @t17 () (@var "Val" $$unsorted)) % 0.36/0.69 (define @t18 () (@var "I" $$unsorted)) % 0.36/0.69 (define @t19 () (@var "U" $$unsorted)) % 0.36/0.69 (define @t20 () (@var "L" $$unsorted)) % 0.36/0.69 (define @t21 () (tptp.leq @t18 @t19)) % 0.36/0.69 (define @t22 () (@var "J" $$unsorted)) % 0.36/0.69 (define @t23 () (@var "U2" $$unsorted)) % 0.36/0.69 (define @t24 () (@var "L2" $$unsorted)) % 0.36/0.69 (define @t25 () (@var "U1" $$unsorted)) % 0.36/0.69 (define @t26 () (@var "L1" $$unsorted)) % 0.36/0.69 (define @t27 () (@var "A" $$unsorted)) % 0.36/0.69 (define @t28 () (tptp.trans @t27)) % 0.36/0.69 (define @t29 () (@var "N" $$unsorted)) % 0.36/0.69 (define @t30 () (tptp.leq @t22 @t29)) % 0.36/0.69 (define @t31 () (tptp.leq tptp.n0 @t22)) % 0.36/0.69 (define @t32 () (tptp.leq @t18 @t29)) % 0.36/0.69 (define @t33 () (tptp.leq tptp.n0 @t18)) % 0.36/0.69 (define @t34 () (and @t33 @t32 @t31 @t30)) % 0.36/0.69 (define @t35 () (@list @t18 @t22)) % 0.36/0.69 (define @t36 () (forall @t35 (=> @t34 (= (tptp.a_select3 @t27 @t18 @t22) (tptp.a_select3 @t27 @t22 @t18))))) % 0.36/0.69 (define @t37 () (@list @t27 @t29)) % 0.36/0.69 (define @t38 () (tptp.inv @t27)) % 0.36/0.69 (define @t39 () (@var "VAL" $$unsorted)) % 0.36/0.69 (define @t40 () (@var "K" $$unsorted)) % 0.36/0.69 (define @t41 () (tptp.tptp_update3 @t27 @t40 @t40 @t39)) % 0.36/0.69 (define @t42 () (@var "B" $$unsorted)) % 0.36/0.69 (define @t43 () (tptp.tptp_madd @t27 @t42)) % 0.36/0.69 (define @t44 () (= (tptp.a_select3 @t42 @t18 @t22) (tptp.a_select3 @t42 @t22 @t18))) % 0.36/0.69 (define @t45 () (forall @t35 (=> @t34 @t44))) % 0.36/0.69 (define @t46 () (and @t36 @t45)) % 0.36/0.69 (define @t47 () (@list @t27 @t42 @t29)) % 0.36/0.69 (define @t48 () (tptp.tptp_msub @t27 @t42)) % 0.36/0.69 (define @t49 () (tptp.tptp_mmul @t27 (tptp.tptp_mmul @t42 @t28))) % 0.36/0.69 (define @t50 () (forall @t35 (=> @t34 (= (tptp.a_select3 @t49 @t18 @t22) (tptp.a_select3 @t49 @t22 @t18))))) % 0.36/0.69 (define @t51 () (@var "M" $$unsorted)) % 0.36/0.69 (define @t52 () (and @t33 (tptp.leq @t18 @t51) @t31 (tptp.leq @t22 @t51))) % 0.36/0.69 (define @t53 () (@var "E" $$unsorted)) % 0.36/0.69 (define @t54 () (@var "F" $$unsorted)) % 0.36/0.69 (define @t55 () (@var "D" $$unsorted)) % 0.36/0.69 (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))))) % 0.36/0.69 (define @t57 () (@var "Body" $$unsorted)) % 0.36/0.69 (define @t58 () (tptp.sum tptp.n0 tptp.tptp_minus_1 @t57)) % 0.36/0.69 (define @t59 () (@list @t57)) % 0.36/0.69 (define @t60 () (forall @t59 (= @t58 tptp.n0))) % 0.36/0.69 (define @t61 () (tptp.succ tptp.tptp_minus_1)) % 0.36/0.69 (define @t62 () (tptp.succ @t11)) % 0.36/0.69 (define @t63 () (tptp.succ @t62)) % 0.36/0.69 (define @t64 () (tptp.succ @t63)) % 0.36/0.69 (define @t65 () (tptp.succ @t64)) % 0.36/0.69 (define @t66 () (tptp.pred @t2)) % 0.36/0.69 (define @t67 () (tptp.pred @t11)) % 0.36/0.69 (define @t68 () (forall @t9 (= @t67 @t2))) % 0.36/0.69 (define @t69 () (@var "V" $$unsorted)) % 0.36/0.69 (define @t70 () (tptp.tptp_update3 @t2 @t19 @t69 @t39)) % 0.36/0.69 (define @t71 () (@var "VAL2" $$unsorted)) % 0.36/0.69 (define @t72 () (not (= @t18 @t19))) % 0.36/0.69 (define @t73 () (@var "J0" $$unsorted)) % 0.36/0.69 (define @t74 () (@var "I0" $$unsorted)) % 0.36/0.69 (define @t75 () (tptp.leq @t74 @t19)) % 0.36/0.69 (define @t76 () (tptp.leq tptp.n0 @t74)) % 0.36/0.69 (define @t77 () (tptp.tptp_update2 @t2 @t19 @t39)) % 0.36/0.69 (define @t78 () (@var "H" $$unsorted)) % 0.36/0.69 (define @t79 () (@var "G" $$unsorted)) % 0.36/0.69 (define @t80 () (tptp.minus tptp.n5 tptp.n1)) % 0.36/0.69 (define @t81 () (tptp.sum tptp.n0 @t80 (tptp.a_select3 tptp.q @t79 @t78))) % 0.36/0.69 (define @t82 () (tptp.minus tptp.pv10 tptp.n1)) % 0.36/0.69 (define @t83 () (tptp.leq @t79 @t82)) % 0.36/0.69 (define @t84 () (tptp.leq tptp.n0 @t79)) % 0.36/0.69 (define @t85 () (and @t84 @t83)) % 0.36/0.69 (define @t86 () (=> @t85 (= @t81 tptp.n1))) % 0.36/0.69 (define @t87 () (@list @t79 @t78)) % 0.36/0.69 (define @t88 () (forall @t87 @t86)) % 0.36/0.69 (define @t89 () (tptp.a_select2 tptp.x tptp.pv10)) % 0.36/0.69 (define @t90 () (tptp.minus (tptp.a_select3 tptp.center @t54 tptp.n0) @t89)) % 0.36/0.69 (define @t91 () (tptp.minus (tptp.a_select3 tptp.center @t53 tptp.n0) @t89)) % 0.36/0.69 (define @t92 () (= (tptp.a_select3 tptp.q tptp.pv10 @t53) (tptp.divide (tptp.sqrt (tptp.times @t91 @t91)) (tptp.sum tptp.n0 @t80 (tptp.sqrt (tptp.times @t90 @t90)))))) % 0.36/0.69 (define @t93 () (tptp.minus tptp.pv12 tptp.n1)) % 0.36/0.69 (define @t94 () (tptp.leq @t53 @t93)) % 0.36/0.69 (define @t95 () (tptp.leq tptp.n0 @t53)) % 0.36/0.69 (define @t96 () (and @t95 @t94)) % 0.36/0.69 (define @t97 () (@list @t53 @t54)) % 0.36/0.69 (define @t98 () (forall @t97 (=> @t96 @t92))) % 0.36/0.69 (define @t99 () (tptp.leq tptp.pv12 @t80)) % 0.36/0.69 (define @t100 () (tptp.leq tptp.pv10 (tptp.minus tptp.n135300 tptp.n1))) % 0.36/0.69 (define @t101 () (tptp.leq tptp.n0 tptp.pv12)) % 0.36/0.69 (define @t102 () (tptp.leq tptp.n0 tptp.pv10)) % 0.36/0.69 (define @t103 () (tptp.minus (tptp.a_select3 tptp.center tptp.pv71 tptp.n0) @t89)) % 0.36/0.69 (define @t104 () (tptp.sqrt (tptp.times @t103 @t103))) % 0.36/0.69 (define @t105 () (tptp.minus tptp.n0 tptp.n1)) % 0.36/0.69 (define @t106 () (= tptp.n0 (tptp.sum tptp.n0 @t105 @t104))) % 0.36/0.69 (define @t107 () (and @t106 @t102 @t101 @t100 @t99 @t98 @t88)) % 0.36/0.69 (define @t108 () (tptp.sum tptp.n0 @t80 (tptp.a_select3 tptp.q @t13 @t55))) % 0.36/0.69 (define @t109 () (tptp.leq @t13 @t82)) % 0.36/0.69 (define @t110 () (tptp.leq tptp.n0 @t13)) % 0.36/0.69 (define @t111 () (and @t110 @t109)) % 0.36/0.69 (define @t112 () (=> @t111 (= @t108 tptp.n1))) % 0.36/0.69 (define @t113 () (@list @t13 @t55)) % 0.36/0.69 (define @t114 () (forall @t113 @t112)) % 0.36/0.69 (define @t115 () (tptp.minus (tptp.a_select3 tptp.center @t42 tptp.n0) @t89)) % 0.36/0.69 (define @t116 () (tptp.minus (tptp.a_select3 tptp.center @t27 tptp.n0) @t89)) % 0.36/0.69 (define @t117 () (= (tptp.a_select3 tptp.q tptp.pv10 @t27) (tptp.divide (tptp.sqrt (tptp.times @t116 @t116)) (tptp.sum tptp.n0 @t80 (tptp.sqrt (tptp.times @t115 @t115)))))) % 0.36/0.69 (define @t118 () (tptp.leq @t27 @t93)) % 0.36/0.69 (define @t119 () (tptp.leq tptp.n0 @t27)) % 0.36/0.69 (define @t120 () (and @t119 @t118)) % 0.36/0.69 (define @t121 () (@list @t27 @t42)) % 0.36/0.69 (define @t122 () (forall @t121 (=> @t120 @t117))) % 0.36/0.69 (define @t123 () (and @t102 @t101 @t100 @t99 @t122 @t114)) % 0.36/0.69 (define @t124 () (=> @t123 @t107)) % 0.36/0.69 (define @t125 () (not @t124)) % 0.36/0.69 (define @t126 () (= @t2 tptp.n4)) % 0.36/0.69 (define @t127 () (= @t2 tptp.n3)) % 0.36/0.69 (define @t128 () (= @t2 tptp.n2)) % 0.36/0.69 (define @t129 () (= @t2 tptp.n1)) % 0.36/0.69 (define @t130 () (= @t2 tptp.n0)) % 0.36/0.69 (define @t131 () (tptp.succ tptp.n0)) % 0.36/0.69 (define @t132 () (tptp.succ @t131)) % 0.36/0.69 (define @t133 () (tptp.succ @t132)) % 0.36/0.69 (define @t134 () (tptp.succ @t133)) % 0.36/0.69 (define @t135 () (= tptp.n1 @t81)) % 0.36/0.69 (define @t136 () (not @t83)) % 0.36/0.69 (define @t137 () (not @t84)) % 0.36/0.69 (define @t138 () (or @t137 @t136 @t135)) % 0.36/0.69 (define @t139 () (not @t94)) % 0.36/0.69 (define @t140 () (not @t95)) % 0.36/0.69 (define @t141 () (or @t140 @t139 @t92)) % 0.36/0.69 (define @t142 () (= tptp.n1 @t108)) % 0.36/0.69 (define @t143 () (not @t109)) % 0.36/0.69 (define @t144 () (not @t110)) % 0.36/0.69 (define @t145 () (or @t144 @t143 @t142)) % 0.36/0.69 (define @t146 () (not @t118)) % 0.36/0.69 (define @t147 () (not @t119)) % 0.36/0.69 (define @t148 () (or @t147 @t146 @t117)) % 0.36/0.69 (define @t149 () (forall @t113 @t145)) % 0.36/0.69 (define @t150 () (forall @t87 @t138)) % 0.36/0.69 (define @t151 () (@list false)) % 0.36/0.69 (define @t152 () (forall @t121 @t148)) % 0.36/0.69 (define @t153 () (forall @t97 @t141)) % 0.36/0.69 (define @t154 () (not @t106)) % 0.36/0.69 (define @t155 () (tptp.sum tptp.n0 tptp.tptp_minus_1 @t104)) % 0.36/0.69 (define @t156 () (= tptp.n0 @t155)) % 0.36/0.69 (define @t157 () (not @t156)) % 0.36/0.69 (define @t158 () (tptp.pred @t61)) % 0.36/0.69 (define @t159 () (= tptp.tptp_minus_1 @t158)) % 0.36/0.69 (define @t160 () (not @t159)) % 0.36/0.69 (define @t161 () (= @t105 (tptp.pred tptp.n0))) % 0.36/0.69 (define @t162 () (not @t161)) % 0.36/0.69 (define @t163 () (= tptp.n0 @t61)) % 0.36/0.69 (define @t164 () (not @t163)) % 0.36/0.69 (define @t165 () (and @t157 @t156)) % 0.36/0.69 (assume @p1 (forall @t6 (or @t5 @t4 @t3))) % 0.36/0.69 (assume @p2 (forall @t8 (=> (and @t5 (tptp.gt @t1 @t7)) (tptp.gt @t2 @t7)))) % 0.36/0.69 (assume @p3 (forall @t9 (not (tptp.gt @t2 @t2)))) % 0.36/0.69 (assume @p4 (forall @t9 (tptp.leq @t2 @t2))) % 0.36/0.69 (assume @p5 (forall @t8 (=> (and @t10 (tptp.leq @t1 @t7)) (tptp.leq @t2 @t7)))) % 0.36/0.69 (assume @p6 (forall @t6 (= (tptp.lt @t2 @t1) @t4))) % 0.36/0.69 (assume @p7 (forall @t6 (= (tptp.geq @t2 @t1) (tptp.leq @t1 @t2)))) % 0.36/0.69 (assume @p8 (forall @t6 (=> @t4 @t10))) % 0.36/0.69 (assume @p9 (forall @t6 (=> (and @t10 (not @t3)) @t4))) % 0.36/0.69 (assume @p10 (forall @t6 (= (tptp.leq @t2 (tptp.pred @t1)) @t4))) % 0.36/0.69 (assume @p11 (forall @t9 (tptp.gt @t11 @t2))) % 0.36/0.69 (assume @p12 (forall @t6 (=> @t10 (tptp.leq @t2 @t12)))) % 0.36/0.69 (assume @p13 (forall @t6 (= @t10 (tptp.gt @t12 @t2)))) % 0.36/0.69 (assume @p14 (forall @t16 (=> @t15 (tptp.leq @t14 @t2)))) % 0.36/0.69 (assume @p15 (forall @t16 (=> @t15 (tptp.leq tptp.n0 @t14)))) % 0.36/0.69 (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)))) % 0.36/0.69 (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)))) % 0.36/0.69 (assume @p18 (forall @t37 (=> @t36 (forall @t35 (=> @t34 (= (tptp.a_select3 @t28 @t18 @t22) (tptp.a_select3 @t28 @t22 @t18))))))) % 0.36/0.69 (assume @p19 (forall @t37 (=> @t36 (forall @t35 (=> @t34 (= (tptp.a_select3 @t38 @t18 @t22) (tptp.a_select3 @t38 @t22 @t18))))))) % 0.36/0.69 (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))))))) % 0.36/0.69 (assume @p21 (forall @t47 (=> @t46 (forall @t35 (=> @t34 (= (tptp.a_select3 @t43 @t18 @t22) (tptp.a_select3 @t43 @t22 @t18))))))) % 0.36/0.69 (assume @p22 (forall @t47 (=> @t46 (forall @t35 (=> @t34 (= (tptp.a_select3 @t48 @t18 @t22) (tptp.a_select3 @t48 @t22 @t18))))))) % 0.36/0.69 (assume @p23 (forall @t47 (=> @t45 @t50))) % 0.36/0.69 (assume @p24 (forall (@list @t27 @t42 @t29 @t51) (=> (forall @t35 (=> @t52 @t44)) @t50))) % 0.36/0.69 (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))))))) % 0.36/0.69 (assume @p26 @t60) % 0.36/0.69 (assume @p27 (forall @t59 (= tptp.tptp_float_0_0 @t58))) % 0.36/0.69 (assume @p28 (= @t61 tptp.n0)) % 0.36/0.69 (assume @p29 (forall @t9 (= (tptp.plus @t2 tptp.n1) @t11))) % 0.36/0.69 (assume @p30 (forall @t9 (= (tptp.plus tptp.n1 @t2) @t11))) % 0.36/0.69 (assume @p31 (forall @t9 (= (tptp.plus @t2 tptp.n2) @t62))) % 0.36/0.69 (assume @p32 (forall @t9 (= (tptp.plus tptp.n2 @t2) @t62))) % 0.36/0.69 (assume @p33 (forall @t9 (= (tptp.plus @t2 tptp.n3) @t63))) % 0.36/0.69 (assume @p34 (forall @t9 (= (tptp.plus tptp.n3 @t2) @t63))) % 0.36/0.69 (assume @p35 (forall @t9 (= (tptp.plus @t2 tptp.n4) @t64))) % 0.36/0.69 (assume @p36 (forall @t9 (= (tptp.plus tptp.n4 @t2) @t64))) % 0.36/0.69 (assume @p37 (forall @t9 (= (tptp.plus @t2 tptp.n5) @t65))) % 0.36/0.69 (assume @p38 (forall @t9 (= (tptp.plus tptp.n5 @t2) @t65))) % 0.36/0.69 (assume @p39 (forall @t9 (= (tptp.minus @t2 tptp.n1) @t66))) % 0.36/0.69 (assume @p40 @t68) % 0.36/0.69 (assume @p41 (forall @t9 (= (tptp.succ @t66) @t2))) % 0.36/0.69 (assume @p42 (forall @t6 (= (tptp.leq @t11 @t12) @t10))) % 0.36/0.69 (assume @p43 (forall @t6 (=> (tptp.leq @t11 @t1) @t4))) % 0.36/0.69 (assume @p44 (forall @t6 (=> (tptp.leq (tptp.minus @t2 @t1) @t2) (tptp.leq tptp.n0 @t1)))) % 0.36/0.69 (assume @p45 (forall (@list @t2 @t19 @t69 @t39) (= (tptp.a_select3 @t70 @t19 @t69) @t39))) % 0.36/0.69 (assume @p46 (forall (@list @t18 @t22 @t19 @t69 @t2 @t39 @t71) (=> (and @t72 (= @t22 @t69) (= (tptp.a_select3 @t2 @t19 @t69) @t39)) (= (tptp.a_select3 (tptp.tptp_update3 @t2 @t18 @t22 @t71) @t19 @t69) @t39)))) % 0.36/0.69 (assume @p47 (forall (@list @t18 @t22 @t19 @t69 @t2 @t39) (=> (and (forall (@list @t74 @t73) (=> (and @t76 (tptp.leq tptp.n0 @t73) @t75 (tptp.leq @t73 @t69)) (= (tptp.a_select3 @t2 @t74 @t73) @t39))) @t33 @t21 @t31 (tptp.leq @t22 @t69)) (= (tptp.a_select3 @t70 @t18 @t22) @t39)))) % 0.36/0.69 (assume @p48 (forall (@list @t2 @t19 @t39) (= (tptp.a_select2 @t77 @t19) @t39))) % 0.36/0.69 (assume @p49 (forall (@list @t18 @t19 @t2 @t39 @t71) (=> (and @t72 (= (tptp.a_select2 @t2 @t19) @t39)) (= (tptp.a_select2 (tptp.tptp_update2 @t2 @t18 @t71) @t19) @t39)))) % 0.36/0.69 (assume @p50 (forall (@list @t18 @t19 @t2 @t39) (=> (and (forall (@list @t74) (=> (and @t76 @t75) (= (tptp.a_select2 @t2 @t74) @t39))) @t33 @t21) (= (tptp.a_select2 @t77 @t18) @t39)))) % 0.36/0.69 (assume @p51 tptp.true) % 0.36/0.69 (assume @p52 (not (= tptp.def tptp.use))) % 0.36/0.69 (assume @p53 @t125) % 0.36/0.69 (assume @p54 (tptp.gt tptp.n5 tptp.n4)) % 0.36/0.69 (assume @p55 (tptp.gt tptp.n135300 tptp.n4)) % 0.36/0.69 (assume @p56 (tptp.gt tptp.n135300 tptp.n5)) % 0.36/0.69 (assume @p57 (tptp.gt tptp.n4 tptp.tptp_minus_1)) % 0.36/0.69 (assume @p58 (tptp.gt tptp.n5 tptp.tptp_minus_1)) % 0.36/0.69 (assume @p59 (tptp.gt tptp.n135300 tptp.tptp_minus_1)) % 0.36/0.69 (assume @p60 (tptp.gt tptp.n0 tptp.tptp_minus_1)) % 0.36/0.69 (assume @p61 (tptp.gt tptp.n1 tptp.tptp_minus_1)) % 0.36/0.69 (assume @p62 (tptp.gt tptp.n2 tptp.tptp_minus_1)) % 0.36/0.69 (assume @p63 (tptp.gt tptp.n3 tptp.tptp_minus_1)) % 0.36/0.69 (assume @p64 (tptp.gt tptp.n4 tptp.n0)) % 0.36/0.69 (assume @p65 (tptp.gt tptp.n5 tptp.n0)) % 0.36/0.69 (assume @p66 (tptp.gt tptp.n135300 tptp.n0)) % 0.36/0.69 (assume @p67 (tptp.gt tptp.n1 tptp.n0)) % 0.36/0.69 (assume @p68 (tptp.gt tptp.n2 tptp.n0)) % 0.36/0.69 (assume @p69 (tptp.gt tptp.n3 tptp.n0)) % 0.36/0.69 (assume @p70 (tptp.gt tptp.n4 tptp.n1)) % 0.36/0.69 (assume @p71 (tptp.gt tptp.n5 tptp.n1)) % 0.36/0.69 (assume @p72 (tptp.gt tptp.n135300 tptp.n1)) % 0.36/0.69 (assume @p73 (tptp.gt tptp.n2 tptp.n1)) % 0.36/0.69 (assume @p74 (tptp.gt tptp.n3 tptp.n1)) % 0.36/0.69 (assume @p75 (tptp.gt tptp.n4 tptp.n2)) % 0.36/0.69 (assume @p76 (tptp.gt tptp.n5 tptp.n2)) % 0.36/0.69 (assume @p77 (tptp.gt tptp.n135300 tptp.n2)) % 0.36/0.69 (assume @p78 (tptp.gt tptp.n3 tptp.n2)) % 0.36/0.69 (assume @p79 (tptp.gt tptp.n4 tptp.n3)) % 0.36/0.69 (assume @p80 (tptp.gt tptp.n5 tptp.n3)) % 0.36/0.69 (assume @p81 (tptp.gt tptp.n135300 tptp.n3)) % 0.36/0.69 (assume @p82 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n4)) (or @t130 @t129 @t128 @t127 @t126)))) % 0.36/0.69 (assume @p83 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n5)) (or @t130 @t129 @t128 @t127 @t126 (= @t2 tptp.n5))))) % 0.36/0.69 (assume @p84 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n0)) @t130))) % 0.36/0.69 (assume @p85 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n1)) (or @t130 @t129)))) % 0.36/0.69 (assume @p86 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n2)) (or @t130 @t129 @t128)))) % 0.36/0.69 (assume @p87 (forall @t9 (=> (and @t15 (tptp.leq @t2 tptp.n3)) (or @t130 @t129 @t128 @t127)))) % 0.36/0.69 (assume @p88 (= @t134 tptp.n4)) % 0.36/0.69 (assume @p89 (= (tptp.succ @t134) tptp.n5)) % 0.36/0.69 (assume @p90 (= @t131 tptp.n1)) % 0.36/0.69 (assume @p91 (= @t132 tptp.n2)) % 0.36/0.69 (assume @p92 (= @t133 tptp.n3)) % 0.36/0.69 (assume @p93 true) % 0.36/0.69 (step @p94 :rule symm :premises (@p28)) % 0.36/0.69 (step @p95 :rule aci_norm :args ((= (or (or @t137 @t136) @t135) @t138))) % 0.36/0.69 (step @p96 :rule refl :args (@t135)) % 0.36/0.69 (step @p97 :rule bool-and-de-morgan :args (@t84 @t83 true)) % 0.36/0.69 (step @p98 :rule nary_cong :premises (@p97 @p96) :args ((or (not @t85) @t135))) % 0.36/0.69 (step @p99 :rule trans :premises (@p98 @p95)) % 0.36/0.69 (step @p100 :rule bool-impl-elim :args (@t85 @t135)) % 0.36/0.69 (step @p101 :rule trans :premises (@p100 @p99)) % 0.36/0.69 (step @p102 :rule cong :premises (@p101) :args ((forall @t87 (=> @t85 @t135)))) % 0.36/0.69 (step @p103 :rule eq-symm :args (@t81 tptp.n1)) % 0.36/0.69 (step @p104 :rule refl :args (@t85)) % 0.36/0.69 (step @p105 :rule cong :premises (@p104 @p103) :args (@t86)) % 0.36/0.69 (step @p106 :rule cong :premises (@p105) :args (@t88)) % 0.36/0.69 (step @p107 :rule trans :premises (@p106 @p102)) % 0.36/0.69 (step @p108 :rule aci_norm :args ((= (or (or @t140 @t139) @t92) @t141))) % 0.36/0.69 (step @p109 :rule refl :args (@t92)) % 0.36/0.69 (step @p110 :rule bool-and-de-morgan :args (@t95 @t94 true)) % 0.36/0.69 (step @p111 :rule nary_cong :premises (@p110 @p109) :args ((or (not @t96) @t92))) % 0.36/0.69 (step @p112 :rule trans :premises (@p111 @p108)) % 0.36/0.69 (step @p113 :rule bool-impl-elim :args (@t96 @t92)) % 0.36/0.69 (step @p114 :rule trans :premises (@p113 @p112)) % 0.36/0.69 (step @p115 :rule cong :premises (@p114) :args (@t98)) % 0.36/0.69 (step @p116 :rule refl :args (@t99)) % 0.36/0.69 (step @p117 :rule refl :args (@t100)) % 0.36/0.69 (step @p118 :rule refl :args (@t101)) % 0.36/0.69 (step @p119 :rule refl :args (@t102)) % 0.36/0.69 (step @p120 :rule refl :args (@t106)) % 0.36/0.69 (step @p121 :rule nary_cong :premises (@p120 @p119 @p118 @p117 @p116 @p115 @p107) :args (@t107)) % 0.36/0.69 (step @p122 :rule aci_norm :args ((= (or (or @t144 @t143) @t142) @t145))) % 0.36/0.69 (step @p123 :rule refl :args (@t142)) % 0.36/0.69 (step @p124 :rule bool-and-de-morgan :args (@t110 @t109 true)) % 0.36/0.69 (step @p125 :rule nary_cong :premises (@p124 @p123) :args ((or (not @t111) @t142))) % 0.36/0.69 (step @p126 :rule trans :premises (@p125 @p122)) % 0.36/0.69 (step @p127 :rule bool-impl-elim :args (@t111 @t142)) % 0.36/0.69 (step @p128 :rule trans :premises (@p127 @p126)) % 0.36/0.69 (step @p129 :rule cong :premises (@p128) :args ((forall @t113 (=> @t111 @t142)))) % 0.36/0.69 (step @p130 :rule eq-symm :args (@t108 tptp.n1)) % 0.36/0.69 (step @p131 :rule refl :args (@t111)) % 0.36/0.69 (step @p132 :rule cong :premises (@p131 @p130) :args (@t112)) % 0.36/0.69 (step @p133 :rule cong :premises (@p132) :args (@t114)) % 0.36/0.69 (step @p134 :rule trans :premises (@p133 @p129)) % 0.36/0.69 (step @p135 :rule aci_norm :args ((= (or (or @t147 @t146) @t117) @t148))) % 0.36/0.69 (step @p136 :rule refl :args (@t117)) % 0.36/0.69 (step @p137 :rule bool-and-de-morgan :args (@t119 @t118 true)) % 0.36/0.69 (step @p138 :rule nary_cong :premises (@p137 @p136) :args ((or (not @t120) @t117))) % 0.36/0.69 (step @p139 :rule trans :premises (@p138 @p135)) % 0.36/0.69 (step @p140 :rule bool-impl-elim :args (@t120 @t117)) % 0.36/0.69 (step @p141 :rule trans :premises (@p140 @p139)) % 0.36/0.69 (step @p142 :rule cong :premises (@p141) :args (@t122)) % 0.36/0.69 (step @p143 :rule nary_cong :premises (@p119 @p118 @p117 @p116 @p142 @p134) :args (@t123)) % 0.36/0.69 (step @p144 :rule cong :premises (@p143 @p121) :args (@t124)) % 0.36/0.69 (step @p145 :rule cong :premises (@p144) :args (@t125)) % 0.36/0.69 (step @p146 :rule eq_resolve :premises (@p53 @p145)) % 0.36/0.69 (step @p147 :rule not_implies_elim1 :premises (@p146)) % 0.36/0.69 (step @p148 :rule and_elim :premises (@p147) :args (5)) % 0.36/0.69 (step @p149 :rule alpha_equiv :args (@t149 (@list @t13 @t55) (@list @t79 @t78))) % 0.36/0.69 (step @p150 :rule equiv_elim1 :premises (@p149)) % 0.36/0.69 (step @p151 :rule reordering :premises (@p150) :args ((or @t150 (not @t149)))) % 0.36/0.69 (step @p152 :rule chain_m_resolution :premises (@p151 @p148) :args (@t150 @t151 (@list @t149))) % 0.36/0.69 (step @p153 :rule and_elim :premises (@p147) :args (4)) % 0.36/0.69 (step @p154 :rule alpha_equiv :args (@t152 (@list @t27 @t42) (@list @t53 @t54))) % 0.36/0.69 (step @p155 :rule equiv_elim1 :premises (@p154)) % 0.36/0.69 (step @p156 :rule reordering :premises (@p155) :args ((or @t153 (not @t152)))) % 0.36/0.69 (step @p157 :rule chain_m_resolution :premises (@p156 @p153) :args (@t153 @t151 (@list @t152))) % 0.36/0.69 (step @p158 :rule and_elim :premises (@p147) :args (3)) % 0.36/0.69 (step @p159 :rule and_elim :premises (@p147) :args (2)) % 0.36/0.70 (step @p160 :rule and_elim :premises (@p147) :args (1)) % 0.36/0.70 (step @p161 :rule and_elim :premises (@p147) :args (0)) % 0.36/0.70 (step @p162 :rule not_implies_elim2 :premises (@p146)) % 0.36/0.70 (step @p163 :rule not_and :premises (@p162)) % 0.36/0.70 (step @p164 :rule reordering :premises (@p163) :args ((or (not @t102) (not @t101) (not @t100) (not @t99) @t154 (not @t153) (not @t150)))) % 0.36/0.70 (step @p165 :rule chain_m_resolution :premises (@p164 @p161 @p160 @p159 @p158 @p157 @p152) :args (@t154 (@list false false false false false false) (@list @t102 @t101 @t100 @t99 @t153 @t150))) % 0.36/0.70 (step @p166 :rule instantiate :premises (@p39) :args ((@list tptp.n0))) % 0.36/0.70 (step @p167 :rule eq-symm :args (@t67 @t2)) % 0.36/0.70 (step @p168 :rule cong :premises (@p167) :args (@t68)) % 0.36/0.70 (step @p169 :rule eq_resolve :premises (@p40 @p168)) % 0.36/0.70 (step @p170 :rule instantiate :premises (@p169) :args ((@list tptp.tptp_minus_1))) % 0.36/0.70 (step @p171 :rule eq-symm :args (@t58 tptp.n0)) % 0.36/0.70 (step @p172 :rule cong :premises (@p171) :args (@t60)) % 0.36/0.70 (step @p173 :rule eq_resolve :premises (@p26 @p172)) % 0.36/0.70 (step @p174 :rule instantiate :premises (@p173) :args ((@list @t104))) % 0.36/0.70 (step @p175 :rule refl :args (@t157)) % 0.36/0.70 (step @p176 :rule refl :args (@t160)) % 0.36/0.70 (step @p177 :rule refl :args (@t162)) % 0.36/0.70 (step @p178 :rule bool-double-not-elim :args (@t106)) % 0.36/0.70 (step @p179 :rule refl :args (@t164)) % 0.36/0.70 (step @p180 :rule nary_cong :premises (@p179 @p178 @p177 @p176 @p175) :args ((or @t164 (not @t154) @t162 @t160 @t157))) % 0.36/0.70 (assume-push @p220 @t157) % 0.36/0.70 (assume-push @p221 @t156) % 0.36/0.70 (step @p183 :rule evaluate :args ((= false true))) % 0.36/0.70 (step @p184 :rule true_intro :premises (@p174)) % 0.36/0.70 (step @p185 :rule false_intro :premises (@p165)) % 0.36/0.70 (step @p186 :rule refl :args (@t104)) % 0.36/0.70 (step @p187 :rule symm :premises (@p166)) % 0.36/0.70 (step @p188 :rule cong :premises (@p28) :args (@t158)) % 0.36/0.70 (step @p189 :rule trans :premises (@p170 @p188 @p187)) % 0.36/0.70 (step @p190 :rule refl :args (tptp.n0)) % 0.36/0.70 (step @p191 :rule cong :premises (@p190 @p189 @p186) :args (@t155)) % 0.36/0.70 (step @p192 :rule cong :premises (@p190 @p191) :args (@t156)) % 0.36/0.70 (step @p193 :rule trans :premises (@p192 @p185)) % 0.36/0.70 (step @p194 :rule symm :premises (@p193)) % 0.36/0.70 (step @p195 :rule trans :premises (@p194 @p184)) % 0.36/0.70 (step @p196 false :rule eq_resolve :premises (@p195 @p183)) % 0.36/0.70 (step-pop @p222 :rule scope :premises (@p196)) % 0.36/0.70 (step-pop @p223 :rule scope :premises (@p222)) % 0.36/0.70 (step @p197 :rule process_scope :premises (@p223) :args (false)) % 0.36/0.70 (assume-push @p224 @t163) % 0.36/0.70 (assume-push @p225 @t154) % 0.36/0.70 (assume-push @p226 @t161) % 0.36/0.70 (assume-push @p227 @t159) % 0.36/0.70 (assume-push @p228 @t156) % 0.36/0.70 (step @p185 :rule false_intro :premises (@p165)) % 0.36/0.70 (step @p186 :rule refl :args (@t104)) % 0.36/0.70 (step @p187 :rule symm :premises (@p166)) % 0.36/0.70 (step @p188 :rule cong :premises (@p28) :args (@t158)) % 0.36/0.70 (step @p189 :rule trans :premises (@p170 @p188 @p187)) % 0.36/0.70 (step @p190 :rule refl :args (tptp.n0)) % 0.36/0.70 (step @p191 :rule cong :premises (@p190 @p189 @p186) :args (@t155)) % 0.36/0.70 (step @p192 :rule cong :premises (@p190 @p191) :args (@t156)) % 0.36/0.70 (step @p205 :rule trans :premises (@p192 @p185)) % 0.36/0.70 (step @p206 :rule false_elim :premises (@p205)) % 0.36/0.70 (step @p207 :rule and_intro :premises (@p206 @p174)) % 0.36/0.70 (step-pop @p229 :rule scope :premises (@p207)) % 0.36/0.70 (step-pop @p230 :rule scope :premises (@p229)) % 0.36/0.70 (step-pop @p231 :rule scope :premises (@p230)) % 0.36/0.70 (step-pop @p232 :rule scope :premises (@p231)) % 0.36/0.70 (step-pop @p233 :rule scope :premises (@p232)) % 0.36/0.70 (step @p208 :rule process_scope :premises (@p233) :args (@t165)) % 0.36/0.70 (step @p214 :rule implies_elim :premises (@p208)) % 0.36/0.70 (step @p215 :rule resolution :premises (@p214 @p197) :args (true @t165)) % 0.36/0.70 (step @p216 :rule not_and :premises (@p215)) % 0.36/0.70 (step @p217 :rule eq_resolve :premises (@p216 @p180)) % 0.36/0.70 (step @p218 :rule reordering :premises (@p217) :args ((or @t106 @t164 @t162 @t160 @t157))) % 0.36/0.70 (step @p219 false :rule chain_m_resolution :premises (@p218 @p174 @p170 @p166 @p165 @p94) :args (false (@list false false false true false) (@list @t156 @t159 @t161 @t106 @t163))) % 0.36/0.70 ) % 0.36/0.70 % SZS output end Proof % 0.36/0.70 % cvc5 exiting %------------------------------------------------------------------------------