%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV041+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 : 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 09:00:24 AM UTC 2026 % Result : Theorem 0.37s 0.71s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV041+1 : TPTP v9.2.1. Bugfixed v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n003.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 19:53:29 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.71 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.71 % SZS status Theorem % 0.37/0.71 % SZS output start Proof % 0.37/0.71 ( % 0.37/0.71 (declare-sort $$unsorted 0) % 0.37/0.71 (declare-const tptp.n330 $$unsorted) % 0.37/0.71 (declare-const tptp.init $$unsorted) % 0.37/0.71 (declare-const tptp.def $$unsorted) % 0.37/0.71 (declare-const tptp.use $$unsorted) % 0.37/0.71 (declare-const tptp.true Bool) % 0.37/0.71 (declare-const tptp.tptp_update2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.a_select3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.37/0.71 (declare-const tptp.uniform_int_rnd (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.uninit $$unsorted) % 0.37/0.71 (declare-const tptp.n3 $$unsorted) % 0.37/0.71 (declare-const tptp.tptp_const_array1 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.pred (-> $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.tptp_minus_1 $$unsorted) % 0.37/0.71 (declare-const tptp.n0 $$unsorted) % 0.37/0.71 (declare-const tptp.tptp_msub (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.n1 $$unsorted) % 0.37/0.71 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.n5 $$unsorted) % 0.37/0.71 (declare-const tptp.n410 $$unsorted) % 0.37/0.71 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.37/0.71 (declare-const tptp.tptp_update3 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.minus (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.tptp_const_array2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.37/0.71 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.37/0.71 (declare-const tptp.trans (-> $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.a_select2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.inv (-> $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.dim (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.plus (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.tptp_madd (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.sum (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.tptp_mmul (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.71 (declare-const tptp.tptp_float_0_0 $$unsorted) % 0.37/0.71 (declare-const tptp.n4 $$unsorted) % 0.37/0.71 (declare-const tptp.n2 $$unsorted) % 0.37/0.71 (define @t1 () (@var "Y" $$unsorted)) % 0.37/0.71 (define @t2 () (@var "X" $$unsorted)) % 0.37/0.71 (define @t3 () (= @t2 @t1)) % 0.37/0.71 (define @t4 () (tptp.gt @t1 @t2)) % 0.37/0.71 (define @t5 () (tptp.gt @t2 @t1)) % 0.37/0.71 (define @t6 () (@list @t2 @t1)) % 0.37/0.71 (define @t7 () (@var "Z" $$unsorted)) % 0.37/0.71 (define @t8 () (@list @t2 @t1 @t7)) % 0.37/0.71 (define @t9 () (@list @t2)) % 0.37/0.71 (define @t10 () (tptp.leq @t2 @t7)) % 0.37/0.71 (define @t11 () (tptp.leq @t1 @t7)) % 0.37/0.71 (define @t12 () (tptp.leq @t2 @t1)) % 0.37/0.71 (define @t13 () (and @t12 @t11)) % 0.37/0.71 (define @t14 () (forall @t8 (=> @t13 @t10))) % 0.37/0.71 (define @t15 () (forall @t6 (=> @t4 @t12))) % 0.37/0.71 (define @t16 () (tptp.succ @t2)) % 0.37/0.71 (define @t17 () (tptp.succ @t1)) % 0.37/0.71 (define @t18 () (@var "C" $$unsorted)) % 0.37/0.71 (define @t19 () (tptp.uniform_int_rnd @t18 @t2)) % 0.37/0.71 (define @t20 () (tptp.leq tptp.n0 @t2)) % 0.37/0.71 (define @t21 () (@list @t2 @t18)) % 0.37/0.71 (define @t22 () (@var "Val" $$unsorted)) % 0.37/0.71 (define @t23 () (@var "I" $$unsorted)) % 0.37/0.71 (define @t24 () (@var "U" $$unsorted)) % 0.37/0.71 (define @t25 () (@var "L" $$unsorted)) % 0.37/0.71 (define @t26 () (tptp.leq @t23 @t24)) % 0.37/0.71 (define @t27 () (@var "J" $$unsorted)) % 0.37/0.71 (define @t28 () (@var "U2" $$unsorted)) % 0.37/0.71 (define @t29 () (@var "L2" $$unsorted)) % 0.37/0.71 (define @t30 () (@var "U1" $$unsorted)) % 0.37/0.71 (define @t31 () (@var "L1" $$unsorted)) % 0.37/0.71 (define @t32 () (@var "A" $$unsorted)) % 0.37/0.71 (define @t33 () (tptp.trans @t32)) % 0.37/0.71 (define @t34 () (@var "N" $$unsorted)) % 0.37/0.71 (define @t35 () (tptp.leq @t27 @t34)) % 0.37/0.71 (define @t36 () (tptp.leq tptp.n0 @t27)) % 0.37/0.71 (define @t37 () (tptp.leq @t23 @t34)) % 0.37/0.71 (define @t38 () (tptp.leq tptp.n0 @t23)) % 0.37/0.71 (define @t39 () (and @t38 @t37 @t36 @t35)) % 0.37/0.71 (define @t40 () (@list @t23 @t27)) % 0.37/0.71 (define @t41 () (forall @t40 (=> @t39 (= (tptp.a_select3 @t32 @t23 @t27) (tptp.a_select3 @t32 @t27 @t23))))) % 0.37/0.71 (define @t42 () (@list @t32 @t34)) % 0.37/0.71 (define @t43 () (tptp.inv @t32)) % 0.37/0.71 (define @t44 () (@var "VAL" $$unsorted)) % 0.37/0.71 (define @t45 () (@var "K" $$unsorted)) % 0.37/0.71 (define @t46 () (tptp.tptp_update3 @t32 @t45 @t45 @t44)) % 0.37/0.71 (define @t47 () (@var "B" $$unsorted)) % 0.37/0.71 (define @t48 () (tptp.tptp_madd @t32 @t47)) % 0.37/0.71 (define @t49 () (= (tptp.a_select3 @t47 @t23 @t27) (tptp.a_select3 @t47 @t27 @t23))) % 0.37/0.71 (define @t50 () (forall @t40 (=> @t39 @t49))) % 0.37/0.71 (define @t51 () (and @t41 @t50)) % 0.37/0.71 (define @t52 () (@list @t32 @t47 @t34)) % 0.37/0.71 (define @t53 () (tptp.tptp_msub @t32 @t47)) % 0.37/0.71 (define @t54 () (tptp.tptp_mmul @t32 (tptp.tptp_mmul @t47 @t33))) % 0.37/0.71 (define @t55 () (forall @t40 (=> @t39 (= (tptp.a_select3 @t54 @t23 @t27) (tptp.a_select3 @t54 @t27 @t23))))) % 0.37/0.71 (define @t56 () (@var "M" $$unsorted)) % 0.37/0.71 (define @t57 () (and @t38 (tptp.leq @t23 @t56) @t36 (tptp.leq @t27 @t56))) % 0.37/0.71 (define @t58 () (@var "E" $$unsorted)) % 0.37/0.71 (define @t59 () (@var "F" $$unsorted)) % 0.37/0.71 (define @t60 () (@var "D" $$unsorted)) % 0.37/0.71 (define @t61 () (tptp.tptp_madd @t32 (tptp.tptp_mmul @t47 (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul @t18 (tptp.tptp_mmul @t60 (tptp.trans @t18))) (tptp.tptp_mmul @t58 (tptp.tptp_mmul @t59 (tptp.trans @t58)))) (tptp.trans @t47))))) % 0.37/0.71 (define @t62 () (@var "Body" $$unsorted)) % 0.37/0.71 (define @t63 () (tptp.sum tptp.n0 tptp.tptp_minus_1 @t62)) % 0.37/0.71 (define @t64 () (@list @t62)) % 0.37/0.71 (define @t65 () (tptp.succ tptp.tptp_minus_1)) % 0.37/0.71 (define @t66 () (tptp.succ @t16)) % 0.37/0.71 (define @t67 () (tptp.succ @t66)) % 0.37/0.71 (define @t68 () (tptp.succ @t67)) % 0.37/0.71 (define @t69 () (tptp.succ @t68)) % 0.37/0.71 (define @t70 () (tptp.plus tptp.n5 @t2)) % 0.37/0.71 (define @t71 () (forall @t9 (= @t70 @t69))) % 0.37/0.71 (define @t72 () (tptp.pred @t2)) % 0.37/0.71 (define @t73 () (tptp.pred @t16)) % 0.37/0.71 (define @t74 () (forall @t9 (= @t73 @t2))) % 0.37/0.71 (define @t75 () (@var "V" $$unsorted)) % 0.37/0.71 (define @t76 () (tptp.tptp_update3 @t2 @t24 @t75 @t44)) % 0.37/0.71 (define @t77 () (@var "VAL2" $$unsorted)) % 0.37/0.71 (define @t78 () (not (= @t23 @t24))) % 0.37/0.71 (define @t79 () (@var "J0" $$unsorted)) % 0.37/0.71 (define @t80 () (@var "I0" $$unsorted)) % 0.37/0.71 (define @t81 () (tptp.leq @t80 @t24)) % 0.37/0.71 (define @t82 () (tptp.leq tptp.n0 @t80)) % 0.37/0.71 (define @t83 () (tptp.tptp_update2 @t2 @t24 @t44)) % 0.37/0.71 (define @t84 () (tptp.tptp_const_array2 (tptp.dim tptp.n0 tptp.n3) (tptp.dim tptp.n0 tptp.n2) tptp.uninit)) % 0.37/0.71 (define @t85 () (tptp.a_select3 @t84 @t47 @t32)) % 0.37/0.71 (define @t86 () (tptp.minus tptp.n0 tptp.n1)) % 0.37/0.71 (define @t87 () (tptp.leq @t47 @t86)) % 0.37/0.71 (define @t88 () (tptp.leq tptp.n0 @t47)) % 0.37/0.71 (define @t89 () (and @t88 @t87)) % 0.37/0.71 (define @t90 () (=> @t89 (= @t85 tptp.init))) % 0.37/0.71 (define @t91 () (@list @t47)) % 0.37/0.71 (define @t92 () (forall @t91 @t90)) % 0.37/0.71 (define @t93 () (tptp.leq @t32 tptp.n2)) % 0.37/0.71 (define @t94 () (tptp.leq tptp.n0 @t32)) % 0.37/0.71 (define @t95 () (and @t94 @t93)) % 0.37/0.71 (define @t96 () (=> @t95 @t92)) % 0.37/0.71 (define @t97 () (@list @t32)) % 0.37/0.71 (define @t98 () (forall @t97 @t96)) % 0.37/0.71 (define @t99 () (and (tptp.geq (tptp.minus tptp.n330 tptp.n1) tptp.n0) (tptp.geq (tptp.minus tptp.n410 tptp.n1) tptp.n0))) % 0.37/0.71 (define @t100 () (=> @t99 @t98)) % 0.37/0.71 (define @t101 () (not @t100)) % 0.37/0.71 (define @t102 () (tptp.gt tptp.n5 tptp.n4)) % 0.37/0.71 (define @t103 () (tptp.gt tptp.n0 tptp.tptp_minus_1)) % 0.37/0.71 (define @t104 () (= @t2 tptp.n4)) % 0.37/0.71 (define @t105 () (= @t2 tptp.n3)) % 0.37/0.71 (define @t106 () (= @t2 tptp.n2)) % 0.37/0.71 (define @t107 () (= @t2 tptp.n1)) % 0.37/0.71 (define @t108 () (= @t2 tptp.n0)) % 0.37/0.71 (define @t109 () (tptp.leq @t2 tptp.n0)) % 0.37/0.71 (define @t110 () (and @t20 @t109)) % 0.37/0.71 (define @t111 () (forall @t9 (=> @t110 @t108))) % 0.37/0.71 (define @t112 () (tptp.succ tptp.n0)) % 0.37/0.71 (define @t113 () (tptp.succ @t112)) % 0.37/0.71 (define @t114 () (tptp.succ @t113)) % 0.37/0.71 (define @t115 () (tptp.succ @t114)) % 0.37/0.71 (define @t116 () (tptp.succ @t65)) % 0.37/0.71 (define @t117 () (tptp.succ @t116)) % 0.37/0.71 (define @t118 () (tptp.succ @t117)) % 0.37/0.71 (define @t119 () (@list tptp.tptp_minus_1)) % 0.37/0.71 (define @t120 () (@list tptp.n0)) % 0.37/0.71 (define @t121 () (not @t109)) % 0.37/0.71 (define @t122 () (not @t20)) % 0.37/0.71 (define @t123 () (or @t122 @t121 @t108)) % 0.37/0.71 (define @t124 () (tptp.leq @t86 tptp.n0)) % 0.37/0.71 (define @t125 () (not @t124)) % 0.37/0.71 (define @t126 () (tptp.leq tptp.n0 @t86)) % 0.37/0.71 (define @t127 () (not @t126)) % 0.37/0.71 (define @t128 () (or @t127 @t125 (= @t86 tptp.n0))) % 0.37/0.71 (define @t129 () (forall @t9 @t123)) % 0.37/0.71 (define @t130 () (= tptp.n0 @t86)) % 0.37/0.71 (define @t131 () (or @t127 @t125 @t130)) % 0.37/0.71 (define @t132 () (not @t11)) % 0.37/0.71 (define @t133 () (not @t12)) % 0.37/0.71 (define @t134 () (@var "BOUND_VARIABLE_8387" $$unsorted)) % 0.37/0.71 (define @t135 () (= tptp.init (tptp.a_select3 @t84 @t134 @t32))) % 0.37/0.71 (define @t136 () (not (tptp.leq @t134 @t86))) % 0.37/0.71 (define @t137 () (not (tptp.leq tptp.n0 @t134))) % 0.37/0.71 (define @t138 () (not @t93)) % 0.37/0.71 (define @t139 () (not @t94)) % 0.37/0.71 (define @t140 () (or @t139 @t138 @t137 @t136 @t135)) % 0.37/0.71 (define @t141 () (@list @t32 @t134)) % 0.37/0.71 (define @t142 () (forall @t141 @t140)) % 0.37/0.71 (define @t143 () (@quantifiers_skolemize @t142 1)) % 0.37/0.71 (define @t144 () (or @t137 @t136 @t135)) % 0.37/0.71 (define @t145 () (or @t139 @t138 @t144)) % 0.37/0.71 (define @t146 () (forall @t141 @t145)) % 0.37/0.71 (define @t147 () (@list @t134)) % 0.37/0.71 (define @t148 () (forall @t147 @t145)) % 0.37/0.71 (define @t149 () (forall @t147 @t144)) % 0.37/0.71 (define @t150 () (or @t139 @t138 @t149)) % 0.37/0.71 (define @t151 () (= tptp.init @t85)) % 0.37/0.71 (define @t152 () (not @t87)) % 0.37/0.71 (define @t153 () (not @t88)) % 0.37/0.71 (define @t154 () (or @t153 @t152 @t151)) % 0.37/0.71 (define @t155 () (forall @t91 @t154)) % 0.37/0.71 (define @t156 () (or @t139 @t138 @t155)) % 0.37/0.71 (define @t157 () (tptp.leq @t143 @t86)) % 0.37/0.71 (define @t158 () (@quantifiers_skolemize @t142 0)) % 0.37/0.71 (define @t159 () (not @t157)) % 0.37/0.71 (define @t160 () (tptp.leq tptp.n0 @t143)) % 0.37/0.71 (define @t161 () (not @t160)) % 0.37/0.71 (define @t162 () (or (not (tptp.leq tptp.n0 @t158)) (not (tptp.leq @t158 tptp.n2)) @t161 @t159 (= tptp.init (tptp.a_select3 @t84 @t143 @t158)))) % 0.37/0.71 (define @t163 () (@list true)) % 0.37/0.71 (define @t164 () (@list @t162)) % 0.37/0.71 (define @t165 () (or @t161 @t159 @t126)) % 0.37/0.71 (define @t166 () (@list false false false)) % 0.37/0.71 (define @t167 () (tptp.leq tptp.tptp_minus_1 tptp.n0)) % 0.37/0.71 (define @t168 () (not @t103)) % 0.37/0.71 (define @t169 () (or @t168 @t167)) % 0.37/0.71 (assume @p1 (forall @t6 (or @t5 @t4 @t3))) % 0.37/0.71 (assume @p2 (forall @t8 (=> (and @t5 (tptp.gt @t1 @t7)) (tptp.gt @t2 @t7)))) % 0.37/0.71 (assume @p3 (forall @t9 (not (tptp.gt @t2 @t2)))) % 0.37/0.71 (assume @p4 (forall @t9 (tptp.leq @t2 @t2))) % 0.37/0.71 (assume @p5 @t14) % 0.37/0.71 (assume @p6 (forall @t6 (= (tptp.lt @t2 @t1) @t4))) % 0.37/0.71 (assume @p7 (forall @t6 (= (tptp.geq @t2 @t1) (tptp.leq @t1 @t2)))) % 0.37/0.71 (assume @p8 @t15) % 0.37/0.71 (assume @p9 (forall @t6 (=> (and @t12 (not @t3)) @t4))) % 0.37/0.71 (assume @p10 (forall @t6 (= (tptp.leq @t2 (tptp.pred @t1)) @t4))) % 0.37/0.71 (assume @p11 (forall @t9 (tptp.gt @t16 @t2))) % 0.37/0.71 (assume @p12 (forall @t6 (=> @t12 (tptp.leq @t2 @t17)))) % 0.37/0.71 (assume @p13 (forall @t6 (= @t12 (tptp.gt @t17 @t2)))) % 0.37/0.71 (assume @p14 (forall @t21 (=> @t20 (tptp.leq @t19 @t2)))) % 0.37/0.71 (assume @p15 (forall @t21 (=> @t20 (tptp.leq tptp.n0 @t19)))) % 0.37/0.71 (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)))) % 0.37/0.71 (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)))) % 0.37/0.71 (assume @p18 (forall @t42 (=> @t41 (forall @t40 (=> @t39 (= (tptp.a_select3 @t33 @t23 @t27) (tptp.a_select3 @t33 @t27 @t23))))))) % 0.37/0.71 (assume @p19 (forall @t42 (=> @t41 (forall @t40 (=> @t39 (= (tptp.a_select3 @t43 @t23 @t27) (tptp.a_select3 @t43 @t27 @t23))))))) % 0.37/0.71 (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))))))) % 0.37/0.71 (assume @p21 (forall @t52 (=> @t51 (forall @t40 (=> @t39 (= (tptp.a_select3 @t48 @t23 @t27) (tptp.a_select3 @t48 @t27 @t23))))))) % 0.37/0.71 (assume @p22 (forall @t52 (=> @t51 (forall @t40 (=> @t39 (= (tptp.a_select3 @t53 @t23 @t27) (tptp.a_select3 @t53 @t27 @t23))))))) % 0.37/0.71 (assume @p23 (forall @t52 (=> @t50 @t55))) % 0.37/0.71 (assume @p24 (forall (@list @t32 @t47 @t34 @t56) (=> (forall @t40 (=> @t57 @t49)) @t55))) % 0.37/0.71 (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))))))) % 0.37/0.71 (assume @p26 (forall @t64 (= @t63 tptp.n0))) % 0.37/0.71 (assume @p27 (forall @t64 (= tptp.tptp_float_0_0 @t63))) % 0.37/0.71 (assume @p28 (= @t65 tptp.n0)) % 0.37/0.71 (assume @p29 (forall @t9 (= (tptp.plus @t2 tptp.n1) @t16))) % 0.37/0.71 (assume @p30 (forall @t9 (= (tptp.plus tptp.n1 @t2) @t16))) % 0.37/0.71 (assume @p31 (forall @t9 (= (tptp.plus @t2 tptp.n2) @t66))) % 0.37/0.71 (assume @p32 (forall @t9 (= (tptp.plus tptp.n2 @t2) @t66))) % 0.37/0.71 (assume @p33 (forall @t9 (= (tptp.plus @t2 tptp.n3) @t67))) % 0.37/0.71 (assume @p34 (forall @t9 (= (tptp.plus tptp.n3 @t2) @t67))) % 0.37/0.71 (assume @p35 (forall @t9 (= (tptp.plus @t2 tptp.n4) @t68))) % 0.37/0.71 (assume @p36 (forall @t9 (= (tptp.plus tptp.n4 @t2) @t68))) % 0.37/0.71 (assume @p37 (forall @t9 (= (tptp.plus @t2 tptp.n5) @t69))) % 0.37/0.71 (assume @p38 @t71) % 0.37/0.71 (assume @p39 (forall @t9 (= (tptp.minus @t2 tptp.n1) @t72))) % 0.37/0.71 (assume @p40 @t74) % 0.37/0.71 (assume @p41 (forall @t9 (= (tptp.succ @t72) @t2))) % 0.37/0.71 (assume @p42 (forall @t6 (= (tptp.leq @t16 @t17) @t12))) % 0.37/0.71 (assume @p43 (forall @t6 (=> (tptp.leq @t16 @t1) @t4))) % 0.37/0.71 (assume @p44 (forall @t6 (=> (tptp.leq (tptp.minus @t2 @t1) @t2) (tptp.leq tptp.n0 @t1)))) % 0.37/0.71 (assume @p45 (forall (@list @t2 @t24 @t75 @t44) (= (tptp.a_select3 @t76 @t24 @t75) @t44))) % 0.37/0.71 (assume @p46 (forall (@list @t23 @t27 @t24 @t75 @t2 @t44 @t77) (=> (and @t78 (= @t27 @t75) (= (tptp.a_select3 @t2 @t24 @t75) @t44)) (= (tptp.a_select3 (tptp.tptp_update3 @t2 @t23 @t27 @t77) @t24 @t75) @t44)))) % 0.37/0.71 (assume @p47 (forall (@list @t23 @t27 @t24 @t75 @t2 @t44) (=> (and (forall (@list @t80 @t79) (=> (and @t82 (tptp.leq tptp.n0 @t79) @t81 (tptp.leq @t79 @t75)) (= (tptp.a_select3 @t2 @t80 @t79) @t44))) @t38 @t26 @t36 (tptp.leq @t27 @t75)) (= (tptp.a_select3 @t76 @t23 @t27) @t44)))) % 0.37/0.71 (assume @p48 (forall (@list @t2 @t24 @t44) (= (tptp.a_select2 @t83 @t24) @t44))) % 0.37/0.71 (assume @p49 (forall (@list @t23 @t24 @t2 @t44 @t77) (=> (and @t78 (= (tptp.a_select2 @t2 @t24) @t44)) (= (tptp.a_select2 (tptp.tptp_update2 @t2 @t23 @t77) @t24) @t44)))) % 0.37/0.71 (assume @p50 (forall (@list @t23 @t24 @t2 @t44) (=> (and (forall (@list @t80) (=> (and @t82 @t81) (= (tptp.a_select2 @t2 @t80) @t44))) @t38 @t26) (= (tptp.a_select2 @t83 @t23) @t44)))) % 0.37/0.71 (assume @p51 tptp.true) % 0.37/0.71 (assume @p52 (not (= tptp.def tptp.use))) % 0.37/0.71 (assume @p53 @t101) % 0.37/0.71 (assume @p54 @t102) % 0.37/0.71 (assume @p55 (tptp.gt tptp.n330 tptp.n4)) % 0.37/0.71 (assume @p56 (tptp.gt tptp.n410 tptp.n4)) % 0.37/0.71 (assume @p57 (tptp.gt tptp.n330 tptp.n5)) % 0.37/0.71 (assume @p58 (tptp.gt tptp.n410 tptp.n5)) % 0.37/0.71 (assume @p59 (tptp.gt tptp.n410 tptp.n330)) % 0.37/0.71 (assume @p60 (tptp.gt tptp.n4 tptp.tptp_minus_1)) % 0.37/0.71 (assume @p61 (tptp.gt tptp.n5 tptp.tptp_minus_1)) % 0.37/0.71 (assume @p62 (tptp.gt tptp.n330 tptp.tptp_minus_1)) % 0.37/0.71 (assume @p63 (tptp.gt tptp.n410 tptp.tptp_minus_1)) % 0.37/0.71 (assume @p64 @t103) % 0.37/0.71 (assume @p65 (tptp.gt tptp.n1 tptp.tptp_minus_1)) % 0.37/0.71 (assume @p66 (tptp.gt tptp.n2 tptp.tptp_minus_1)) % 0.37/0.71 (assume @p67 (tptp.gt tptp.n3 tptp.tptp_minus_1)) % 0.37/0.71 (assume @p68 (tptp.gt tptp.n4 tptp.n0)) % 0.37/0.71 (assume @p69 (tptp.gt tptp.n5 tptp.n0)) % 0.37/0.71 (assume @p70 (tptp.gt tptp.n330 tptp.n0)) % 0.37/0.71 (assume @p71 (tptp.gt tptp.n410 tptp.n0)) % 0.37/0.71 (assume @p72 (tptp.gt tptp.n1 tptp.n0)) % 0.37/0.71 (assume @p73 (tptp.gt tptp.n2 tptp.n0)) % 0.37/0.71 (assume @p74 (tptp.gt tptp.n3 tptp.n0)) % 0.37/0.71 (assume @p75 (tptp.gt tptp.n4 tptp.n1)) % 0.37/0.71 (assume @p76 (tptp.gt tptp.n5 tptp.n1)) % 0.37/0.71 (assume @p77 (tptp.gt tptp.n330 tptp.n1)) % 0.37/0.71 (assume @p78 (tptp.gt tptp.n410 tptp.n1)) % 0.37/0.71 (assume @p79 (tptp.gt tptp.n2 tptp.n1)) % 0.37/0.71 (assume @p80 (tptp.gt tptp.n3 tptp.n1)) % 0.37/0.71 (assume @p81 (tptp.gt tptp.n4 tptp.n2)) % 0.37/0.71 (assume @p82 (tptp.gt tptp.n5 tptp.n2)) % 0.37/0.71 (assume @p83 (tptp.gt tptp.n330 tptp.n2)) % 0.37/0.71 (assume @p84 (tptp.gt tptp.n410 tptp.n2)) % 0.37/0.71 (assume @p85 (tptp.gt tptp.n3 tptp.n2)) % 0.37/0.71 (assume @p86 (tptp.gt tptp.n4 tptp.n3)) % 0.37/0.71 (assume @p87 (tptp.gt tptp.n5 tptp.n3)) % 0.37/0.71 (assume @p88 (tptp.gt tptp.n330 tptp.n3)) % 0.37/0.71 (assume @p89 (tptp.gt tptp.n410 tptp.n3)) % 0.37/0.71 (assume @p90 (forall @t9 (=> (and @t20 (tptp.leq @t2 tptp.n4)) (or @t108 @t107 @t106 @t105 @t104)))) % 0.37/0.71 (assume @p91 (forall @t9 (=> (and @t20 (tptp.leq @t2 tptp.n5)) (or @t108 @t107 @t106 @t105 @t104 (= @t2 tptp.n5))))) % 0.37/0.71 (assume @p92 @t111) % 0.37/0.71 (assume @p93 (forall @t9 (=> (and @t20 (tptp.leq @t2 tptp.n1)) (or @t108 @t107)))) % 0.37/0.71 (assume @p94 (forall @t9 (=> (and @t20 (tptp.leq @t2 tptp.n2)) (or @t108 @t107 @t106)))) % 0.37/0.71 (assume @p95 (forall @t9 (=> (and @t20 (tptp.leq @t2 tptp.n3)) (or @t108 @t107 @t106 @t105)))) % 0.37/0.71 (assume @p96 (= @t115 tptp.n4)) % 0.37/0.71 (assume @p97 (= (tptp.succ @t115) tptp.n5)) % 0.37/0.71 (assume @p98 (= @t112 tptp.n1)) % 0.37/0.71 (assume @p99 (= @t113 tptp.n2)) % 0.37/0.71 (assume @p100 (= @t114 tptp.n3)) % 0.37/0.71 (assume @p101 true) % 0.37/0.71 (step @p102 :rule evaluate :args ((= true false))) % 0.37/0.71 (step @p103 :rule instantiate :premises (@p3) :args ((@list tptp.n4))) % 0.37/0.71 (step @p104 :rule false_intro :premises (@p103)) % 0.37/0.71 (step @p105 :rule refl :args (tptp.n4)) % 0.37/0.71 (step @p106 :rule cong :premises (@p28) :args (@t116)) % 0.37/0.71 (step @p107 :rule cong :premises (@p106) :args (@t117)) % 0.37/0.71 (step @p108 :rule cong :premises (@p107) :args (@t118)) % 0.37/0.71 (step @p109 :rule cong :premises (@p108) :args ((tptp.succ @t118))) % 0.37/0.71 (step @p110 :rule eq-symm :args (@t70 @t69)) % 0.37/0.71 (step @p111 :rule cong :premises (@p110) :args (@t71)) % 0.37/0.71 (step @p112 :rule eq_resolve :premises (@p38 @p111)) % 0.37/0.71 (step @p113 :rule instantiate :premises (@p112) :args (@t119)) % 0.37/0.71 (step @p114 :rule symm :premises (@p113)) % 0.37/0.71 (step @p115 :rule eq-symm :args (@t73 @t2)) % 0.37/0.71 (step @p116 :rule cong :premises (@p115) :args (@t74)) % 0.37/0.71 (step @p117 :rule eq_resolve :premises (@p40 @p116)) % 0.37/0.71 (step @p118 :rule instantiate :premises (@p117) :args (@t119)) % 0.37/0.71 (step @p119 :rule symm :premises (@p118)) % 0.37/0.71 (step @p120 :rule symm :premises (@p28)) % 0.37/0.71 (step @p121 :rule cong :premises (@p120) :args ((tptp.pred tptp.n0))) % 0.37/0.71 (step @p122 :rule instantiate :premises (@p39) :args (@t120)) % 0.37/0.71 (step @p123 :rule aci_norm :args ((= (or (or @t122 @t121) @t108) @t123))) % 0.37/0.71 (step @p124 :rule refl :args (@t108)) % 0.37/0.71 (step @p125 :rule bool-and-de-morgan :args (@t20 @t109 true)) % 0.37/0.71 (step @p126 :rule nary_cong :premises (@p125 @p124) :args ((or (not @t110) @t108))) % 0.37/0.71 (step @p127 :rule trans :premises (@p126 @p123)) % 0.37/0.71 (step @p128 :rule bool-impl-elim :args (@t110 @t108)) % 0.37/0.71 (step @p129 :rule trans :premises (@p128 @p127)) % 0.37/0.71 (step @p130 :rule cong :premises (@p129) :args (@t111)) % 0.37/0.71 (step @p131 :rule eq_resolve :premises (@p92 @p130)) % 0.37/0.71 (step @p132 :rule eq-symm :args (@t86 tptp.n0)) % 0.37/0.71 (step @p133 :rule refl :args (@t125)) % 0.37/0.71 (step @p134 :rule refl :args (@t127)) % 0.37/0.71 (step @p135 :rule nary_cong :premises (@p134 @p133 @p132) :args (@t128)) % 0.37/0.71 (step @p136 :rule refl :args (@t129)) % 0.37/0.71 (step @p137 :rule cong :premises (@p136 @p135) :args ((=> @t129 @t128))) % 0.37/0.71 (assume-push @p243 @t129) % 0.37/0.71 (step @p139 :rule instantiate :premises (@p131) :args ((@list @t86))) % 0.37/0.71 (step-pop @p244 :rule scope :premises (@p139)) % 0.37/0.71 (step @p140 :rule process_scope :premises (@p244) :args (@t128)) % 0.37/0.71 (step @p142 :rule eq_resolve :premises (@p140 @p137)) % 0.37/0.71 (step @p143 :rule implies_elim :premises (@p142)) % 0.37/0.71 (step @p144 :rule chain_m_resolution :premises (@p143 @p131) :args (@t131 (@list false) (@list @t129))) % 0.37/0.71 (step @p145 :rule aci_norm :args ((= (or (or @t133 @t132) @t10) (or @t133 @t132 @t10)))) % 0.37/0.71 (step @p146 :rule refl :args (@t10)) % 0.37/0.71 (step @p147 :rule bool-and-de-morgan :args (@t12 @t11 true)) % 0.37/0.71 (step @p148 :rule nary_cong :premises (@p147 @p146) :args ((or (not @t13) @t10))) % 0.37/0.71 (step @p149 :rule trans :premises (@p148 @p145)) % 0.37/0.71 (step @p150 :rule bool-impl-elim :args (@t13 @t10)) % 0.37/0.71 (step @p151 :rule trans :premises (@p150 @p149)) % 0.37/0.71 (step @p152 :rule cong :premises (@p151) :args (@t14)) % 0.37/0.71 (step @p153 :rule eq_resolve :premises (@p5 @p152)) % 0.37/0.71 (step @p154 :rule instantiate :premises (@p153) :args ((@list tptp.n0 @t143 @t86))) % 0.37/0.71 (step @p155 :rule aci_norm :args ((= @t145 @t140))) % 0.37/0.71 (step @p156 :rule cong :premises (@p155) :args (@t146)) % 0.37/0.71 (step @p157 :rule quant-merge-prenex :args ((= (forall @t97 @t148) @t146))) % 0.37/0.71 (step @p158 :rule alpha_equiv :args (@t149 (@list @t134) (@list @t47))) % 0.37/0.71 (step @p159 :rule refl :args (@t138)) % 0.37/0.71 (step @p160 :rule refl :args (@t139)) % 0.37/0.71 (step @p161 :rule nary_cong :premises (@p160 @p159 @p158) :args (@t150)) % 0.37/0.71 (step @p162 :rule quant-miniscope-or :args ((= @t148 @t150))) % 0.37/0.71 (step @p163 :rule trans :premises (@p162 @p161)) % 0.37/0.71 (step @p164 :rule symm :premises (@p163)) % 0.37/0.71 (step @p165 :rule cong :premises (@p164) :args ((forall @t97 @t156))) % 0.37/0.71 (step @p166 :rule trans :premises (@p165 @p157)) % 0.37/0.71 (step @p167 :rule trans :premises (@p166 @p156)) % 0.37/0.71 (step @p168 :rule aci_norm :args ((= (or (or @t139 @t138) @t155) @t156))) % 0.37/0.71 (step @p169 :rule refl :args (@t155)) % 0.37/0.71 (step @p170 :rule bool-and-de-morgan :args (@t94 @t93 true)) % 0.37/0.71 (step @p171 :rule nary_cong :premises (@p170 @p169) :args ((or (not @t95) @t155))) % 0.37/0.71 (step @p172 :rule trans :premises (@p171 @p168)) % 0.37/0.71 (step @p173 :rule bool-impl-elim :args (@t95 @t155)) % 0.37/0.71 (step @p174 :rule trans :premises (@p173 @p172)) % 0.37/0.71 (step @p175 :rule cong :premises (@p174) :args ((forall @t97 (=> @t95 @t155)))) % 0.37/0.71 (step @p176 :rule trans :premises (@p175 @p167)) % 0.37/0.71 (step @p177 :rule aci_norm :args ((= (or (or @t153 @t152) @t151) @t154))) % 0.37/0.71 (step @p178 :rule refl :args (@t151)) % 0.37/0.71 (step @p179 :rule bool-and-de-morgan :args (@t88 @t87 true)) % 0.37/0.71 (step @p180 :rule nary_cong :premises (@p179 @p178) :args ((or (not @t89) @t151))) % 0.37/0.71 (step @p181 :rule trans :premises (@p180 @p177)) % 0.37/0.71 (step @p182 :rule bool-impl-elim :args (@t89 @t151)) % 0.37/0.71 (step @p183 :rule trans :premises (@p182 @p181)) % 0.37/0.71 (step @p184 :rule cong :premises (@p183) :args ((forall @t91 (=> @t89 @t151)))) % 0.37/0.71 (step @p185 :rule eq-symm :args (@t85 tptp.init)) % 0.37/0.71 (step @p186 :rule refl :args (@t89)) % 0.37/0.71 (step @p187 :rule cong :premises (@p186 @p185) :args (@t90)) % 0.37/0.71 (step @p188 :rule cong :premises (@p187) :args (@t92)) % 0.37/0.71 (step @p189 :rule trans :premises (@p188 @p184)) % 0.37/0.71 (step @p190 :rule refl :args (@t95)) % 0.37/0.71 (step @p191 :rule cong :premises (@p190 @p189) :args (@t96)) % 0.37/0.71 (step @p192 :rule cong :premises (@p191) :args (@t98)) % 0.37/0.71 (step @p193 :rule trans :premises (@p192 @p176)) % 0.37/0.71 (step @p194 :rule refl :args (@t99)) % 0.37/0.71 (step @p195 :rule cong :premises (@p194 @p193) :args (@t100)) % 0.37/0.71 (step @p196 :rule cong :premises (@p195) :args (@t101)) % 0.37/0.71 (step @p197 :rule eq_resolve :premises (@p53 @p196)) % 0.37/0.71 (step @p198 :rule not_implies_elim2 :premises (@p197)) % 0.37/0.71 (step @p199 :rule skolemize :premises (@p198)) % 0.37/0.71 (step @p200 :rule bool-double-not-elim :args (@t157)) % 0.37/0.71 (step @p201 :rule refl :args (@t162)) % 0.37/0.71 (step @p202 :rule nary_cong :premises (@p201 @p200) :args ((or @t162 (not @t159)))) % 0.37/0.71 (step @p203 :rule cnf_or_neg :args (@t162 3)) % 0.37/0.71 (step @p204 :rule eq_resolve :premises (@p203 @p202)) % 0.37/0.71 (step @p205 :rule reordering :premises (@p204) :args ((or @t157 @t162))) % 0.37/0.71 (step @p206 :rule chain_m_resolution :premises (@p205 @p199) :args (@t157 @t163 @t164)) % 0.37/0.71 (step @p207 :rule bool-double-not-elim :args (@t160)) % 0.37/0.71 (step @p208 :rule nary_cong :premises (@p201 @p207) :args ((or @t162 (not @t161)))) % 0.37/0.71 (step @p209 :rule cnf_or_neg :args (@t162 2)) % 0.37/0.71 (step @p210 :rule eq_resolve :premises (@p209 @p208)) % 0.37/0.71 (step @p211 :rule reordering :premises (@p210) :args ((or @t160 @t162))) % 0.37/0.71 (step @p212 :rule chain_m_resolution :premises (@p211 @p199) :args (@t160 @t163 @t164)) % 0.37/0.71 (step @p213 :rule cnf_or_pos :args (@t165)) % 0.37/0.71 (step @p214 :rule reordering :premises (@p213) :args ((or @t161 @t159 @t126 (not @t165)))) % 0.37/0.71 (step @p215 :rule chain_m_resolution :premises (@p214 @p212 @p206 @p154) :args (@t126 @t166 (@list @t160 @t157 @t165))) % 0.37/0.71 (step @p216 :rule bool-impl-elim :args (@t4 @t12)) % 0.37/0.71 (step @p217 :rule cong :premises (@p216) :args (@t15)) % 0.37/0.71 (step @p218 :rule eq_resolve :premises (@p8 @p217)) % 0.37/0.71 (step @p219 :rule instantiate :premises (@p218) :args ((@list tptp.tptp_minus_1 tptp.n0))) % 0.37/0.71 (step @p220 :rule cnf_or_pos :args (@t169)) % 0.37/0.71 (step @p221 :rule reordering :premises (@p220) :args ((or @t168 @t167 (not @t169)))) % 0.37/0.71 (step @p222 :rule chain_m_resolution :premises (@p221 @p64 @p219) :args (@t167 (@list false false) (@list @t103 @t169))) % 0.37/0.71 (step @p223 :rule true_intro :premises (@p222)) % 0.37/0.71 (step @p224 :rule refl :args (tptp.n0)) % 0.37/0.71 (step @p225 :rule trans :premises (@p122 @p121 @p119)) % 0.37/0.71 (step @p226 :rule cong :premises (@p225 @p224) :args (@t124)) % 0.37/0.71 (step @p227 :rule trans :premises (@p226 @p223)) % 0.37/0.71 (step @p228 :rule true_elim :premises (@p227)) % 0.37/0.71 (step @p229 :rule cnf_or_pos :args (@t131)) % 0.37/0.71 (step @p230 :rule reordering :premises (@p229) :args ((or @t125 @t127 @t130 (not @t131)))) % 0.37/0.71 (step @p231 :rule chain_m_resolution :premises (@p230 @p228 @p215 @p144) :args (@t130 @t166 (@list @t124 @t126 @t131))) % 0.37/0.71 (step @p232 :rule trans :premises (@p231 @p122 @p121 @p119)) % 0.37/0.71 (step @p233 :rule refl :args (tptp.n5)) % 0.37/0.71 (step @p234 :rule cong :premises (@p233 @p232) :args ((tptp.plus tptp.n5 tptp.n0))) % 0.37/0.71 (step @p235 :rule instantiate :premises (@p112) :args (@t120)) % 0.37/0.71 (step @p236 :rule symm :premises (@p97)) % 0.37/0.71 (step @p237 :rule trans :premises (@p236 @p235 @p234 @p114 @p109 @p96)) % 0.37/0.71 (step @p238 :rule cong :premises (@p237 @p105) :args (@t102)) % 0.37/0.71 (step @p239 :rule true_intro :premises (@p54)) % 0.37/0.71 (step @p240 :rule symm :premises (@p239)) % 0.37/0.71 (step @p241 :rule trans :premises (@p240 @p238 @p104)) % 0.37/0.71 (step @p242 false :rule eq_resolve :premises (@p241 @p102)) % 0.37/0.71 ) % 0.37/0.71 % SZS output end Proof % 0.37/0.71 % cvc5 exiting %------------------------------------------------------------------------------