%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM516+3 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n013.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 08:39:41 AM UTC 2026 % Result : Theorem 1.42s 1.64s % Output : Proof 1.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM516+3 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n013.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 11:26:30 EDT 2026 % 0.16/0.35 % CPUTime : % 0.27/0.52 %----Proving TF0_NAR, FOF, or CNF % 1.42/1.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 1.42/1.64 % SZS status Theorem % 1.42/1.64 % SZS output start Proof % 1.42/1.64 ( % 1.42/1.64 (declare-sort $$unsorted 0) % 1.42/1.64 (declare-const tptp.xr $$unsorted) % 1.42/1.64 (declare-const tptp.xk $$unsorted) % 1.42/1.64 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 1.42/1.64 (declare-const tptp.xm $$unsorted) % 1.42/1.64 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.42/1.64 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 1.42/1.64 (declare-const tptp.xn $$unsorted) % 1.42/1.64 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 1.42/1.64 (declare-const tptp.sz00 $$unsorted) % 1.42/1.64 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.42/1.64 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.42/1.64 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.42/1.64 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 1.42/1.64 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 1.42/1.64 (declare-const tptp.sz10 $$unsorted) % 1.42/1.64 (declare-const tptp.xp $$unsorted) % 1.42/1.64 (define @t1 () (@var "W0" $$unsorted)) % 1.42/1.64 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 1.42/1.64 (define @t3 () (@list @t1)) % 1.42/1.64 (define @t4 () (@var "W1" $$unsorted)) % 1.42/1.64 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 1.42/1.64 (define @t6 () (tptp.aNaturalNumber0 @t5)) % 1.42/1.64 (define @t7 () (tptp.aNaturalNumber0 @t4)) % 1.42/1.64 (define @t8 () (and @t2 @t7)) % 1.42/1.64 (define @t9 () (@list @t1 @t4)) % 1.42/1.64 (define @t10 () (forall @t9 (=> @t8 @t6))) % 1.42/1.64 (define @t11 () (tptp.sdtasdt0 @t1 @t4)) % 1.42/1.64 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 1.42/1.64 (define @t13 () (@var "W2" $$unsorted)) % 1.42/1.64 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 1.42/1.64 (define @t15 () (tptp.sdtpldt0 @t5 @t13)) % 1.42/1.64 (define @t16 () (tptp.aNaturalNumber0 @t13)) % 1.42/1.64 (define @t17 () (and @t2 @t7 @t16)) % 1.42/1.64 (define @t18 () (@list @t1 @t4 @t13)) % 1.42/1.64 (define @t19 () (tptp.sdtasdt0 @t4 @t1)) % 1.42/1.64 (define @t20 () (tptp.sdtasdt0 @t13 @t1)) % 1.42/1.64 (define @t21 () (tptp.sdtasdt0 @t1 @t13)) % 1.42/1.64 (define @t22 () (= @t4 @t13)) % 1.42/1.64 (define @t23 () (tptp.sdtpldt0 @t13 @t1)) % 1.42/1.64 (define @t24 () (tptp.sdtpldt0 @t1 @t13)) % 1.42/1.64 (define @t25 () (= @t19 @t20)) % 1.42/1.64 (define @t26 () (= @t11 @t21)) % 1.42/1.64 (define @t27 () (= @t1 tptp.sz00)) % 1.42/1.64 (define @t28 () (not @t27)) % 1.42/1.64 (define @t29 () (= @t4 tptp.sz00)) % 1.42/1.64 (define @t30 () (and @t16 (= @t24 @t4))) % 1.42/1.64 (define @t31 () (@list @t13)) % 1.42/1.64 (define @t32 () (tptp.sdtlseqdt0 @t1 @t4)) % 1.42/1.64 (define @t33 () (= @t1 @t4)) % 1.42/1.64 (define @t34 () (tptp.sdtlseqdt0 @t4 @t1)) % 1.42/1.64 (define @t35 () (tptp.sdtlseqdt0 @t4 @t13)) % 1.42/1.64 (define @t36 () (= @t4 @t1)) % 1.42/1.64 (define @t37 () (tptp.sdtlseqdt0 @t24 @t14)) % 1.42/1.64 (define @t38 () (not (= @t24 @t14))) % 1.42/1.64 (define @t39 () (tptp.sdtpldt0 @t13 @t4)) % 1.42/1.64 (define @t40 () (tptp.sdtlseqdt0 @t23 @t39)) % 1.42/1.64 (define @t41 () (not (= @t23 @t39))) % 1.42/1.64 (define @t42 () (and @t41 @t40 @t38 @t37)) % 1.42/1.64 (define @t43 () (=> @t16 @t42)) % 1.42/1.64 (define @t44 () (forall @t31 @t43)) % 1.42/1.64 (define @t45 () (not @t33)) % 1.42/1.64 (define @t46 () (and @t45 @t32)) % 1.42/1.64 (define @t47 () (=> @t46 @t44)) % 1.42/1.64 (define @t48 () (=> @t8 @t47)) % 1.42/1.64 (define @t49 () (forall @t9 @t48)) % 1.42/1.64 (define @t50 () (= @t1 tptp.sz10)) % 1.42/1.64 (define @t51 () (tptp.iLess0 @t1 @t4)) % 1.42/1.64 (define @t52 () (and @t16 (= @t4 @t21))) % 1.42/1.64 (define @t53 () (tptp.doDivides0 @t1 @t4)) % 1.42/1.64 (define @t54 () (tptp.sdtsldt0 @t4 @t1)) % 1.42/1.64 (define @t55 () (and @t28 @t53)) % 1.42/1.64 (define @t56 () (tptp.doDivides0 @t1 @t13)) % 1.42/1.64 (define @t57 () (tptp.doDivides0 @t1 @t14)) % 1.42/1.64 (define @t58 () (tptp.doDivides0 @t4 @t1)) % 1.42/1.64 (define @t59 () (@list @t4)) % 1.42/1.64 (define @t60 () (not @t50)) % 1.42/1.64 (define @t61 () (tptp.aNaturalNumber0 tptp.xp)) % 1.42/1.64 (define @t62 () (tptp.aNaturalNumber0 tptp.xm)) % 1.42/1.64 (define @t63 () (tptp.aNaturalNumber0 tptp.xn)) % 1.42/1.64 (define @t64 () (@var "W3" $$unsorted)) % 1.42/1.64 (define @t65 () (tptp.sdtasdt0 @t13 @t64)) % 1.42/1.64 (define @t66 () (tptp.aNaturalNumber0 @t64)) % 1.42/1.64 (define @t67 () (@list @t64)) % 1.42/1.64 (define @t68 () (tptp.sdtpldt0 tptp.xn tptp.xm)) % 1.42/1.64 (define @t69 () (tptp.sdtpldt0 @t68 tptp.xp)) % 1.42/1.64 (define @t70 () (@var "W4" $$unsorted)) % 1.42/1.64 (define @t71 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 1.42/1.64 (define @t72 () (tptp.sdtasdt0 tptp.xp @t1)) % 1.42/1.64 (define @t73 () (tptp.sdtpldt0 tptp.xp @t1)) % 1.42/1.64 (define @t74 () (= tptp.xk tptp.sz10)) % 1.42/1.64 (define @t75 () (= tptp.xk tptp.sz00)) % 1.42/1.64 (define @t76 () (tptp.sdtasdt0 tptp.xr @t1)) % 1.42/1.64 (define @t77 () (and (exists @t3 (and @t2 (= tptp.xn @t76))) (tptp.doDivides0 tptp.xr tptp.xn))) % 1.42/1.64 (define @t78 () (tptp.sdtsldt0 tptp.xn tptp.xr)) % 1.42/1.64 (define @t79 () (tptp.sdtlseqdt0 @t78 tptp.xn)) % 1.42/1.64 (define @t80 () (= tptp.xn (tptp.sdtasdt0 tptp.xr @t78))) % 1.42/1.64 (define @t81 () (tptp.aNaturalNumber0 @t78)) % 1.42/1.64 (define @t82 () (= @t78 tptp.xn)) % 1.42/1.64 (define @t83 () (and @t81 @t80)) % 1.42/1.64 (define @t84 () (=> @t83 @t82)) % 1.42/1.64 (define @t85 () (not @t84)) % 1.42/1.64 (define @t86 () (tptp.sdtasdt0 @t78 tptp.xm)) % 1.42/1.64 (define @t87 () (tptp.sdtpldt0 @t78 tptp.xm)) % 1.42/1.64 (define @t88 () (tptp.sdtpldt0 @t87 tptp.xp)) % 1.42/1.64 (define @t89 () (tptp.sdtlseqdt0 @t88 @t69)) % 1.42/1.64 (define @t90 () (tptp.sdtpldt0 @t88 @t1)) % 1.42/1.64 (define @t91 () (and @t2 (= @t90 @t69))) % 1.42/1.64 (define @t92 () (exists @t3 @t91)) % 1.42/1.64 (define @t93 () (or @t92 @t89)) % 1.42/1.64 (define @t94 () (=> @t83 @t93)) % 1.42/1.64 (define @t95 () (and @t81 @t80 (= @t88 @t69))) % 1.42/1.64 (define @t96 () (not @t95)) % 1.42/1.64 (define @t97 () (and @t96 @t94)) % 1.42/1.64 (define @t98 () (not @t97)) % 1.42/1.64 (define @t99 () (@var "BOUND_VARIABLE_8109" $$unsorted)) % 1.42/1.64 (define @t100 () (tptp.sdtpldt0 @t4 @t99)) % 1.42/1.64 (define @t101 () (tptp.sdtpldt0 @t1 @t99)) % 1.42/1.64 (define @t102 () (tptp.sdtpldt0 @t99 @t4)) % 1.42/1.64 (define @t103 () (tptp.sdtpldt0 @t99 @t1)) % 1.42/1.64 (define @t104 () (and (not (= @t103 @t102)) (tptp.sdtlseqdt0 @t103 @t102) (not (= @t100 @t101)) (tptp.sdtlseqdt0 @t101 @t100))) % 1.42/1.64 (define @t105 () (not (tptp.aNaturalNumber0 @t99))) % 1.42/1.64 (define @t106 () (not @t32)) % 1.42/1.64 (define @t107 () (not @t7)) % 1.42/1.64 (define @t108 () (not @t2)) % 1.42/1.64 (define @t109 () (or @t108 @t107 @t33 @t106 @t105 @t104)) % 1.42/1.64 (define @t110 () (or @t105 @t104)) % 1.42/1.64 (define @t111 () (or @t108 @t107 @t33 @t106 @t110)) % 1.42/1.64 (define @t112 () (@list @t1 @t4 @t99)) % 1.42/1.64 (define @t113 () (forall @t112 @t111)) % 1.42/1.64 (define @t114 () (@list @t99)) % 1.42/1.64 (define @t115 () (forall @t114 @t111)) % 1.42/1.64 (define @t116 () (forall @t114 @t110)) % 1.42/1.64 (define @t117 () (or @t108 @t107 @t33 @t106 @t116)) % 1.42/1.64 (define @t118 () (and @t41 @t40 (not (= @t14 @t24)) @t37)) % 1.42/1.64 (define @t119 () (forall @t31 (or (not @t16) @t118))) % 1.42/1.64 (define @t120 () (or @t108 @t107 @t33 @t106 @t119)) % 1.42/1.64 (define @t121 () (or @t33 @t106 @t119)) % 1.42/1.64 (define @t122 () (or @t108 @t107)) % 1.42/1.64 (define @t123 () (=> @t46 @t119)) % 1.42/1.64 (define @t124 () (not @t8)) % 1.42/1.64 (define @t125 () (= @t69 @t88)) % 1.42/1.64 (define @t126 () (not @t125)) % 1.42/1.64 (define @t127 () (tptp.sdtpldt0 tptp.xp @t68)) % 1.42/1.64 (define @t128 () (tptp.sdtpldt0 tptp.xp @t87)) % 1.42/1.64 (define @t129 () (tptp.sdtlseqdt0 @t128 @t127)) % 1.42/1.64 (define @t130 () (not (= @t128 @t127))) % 1.42/1.64 (define @t131 () (and @t130 @t129 @t126 @t89)) % 1.42/1.64 (define @t132 () (not @t61)) % 1.42/1.64 (define @t133 () (tptp.sdtlseqdt0 @t87 @t68)) % 1.42/1.64 (define @t134 () (not @t133)) % 1.42/1.64 (define @t135 () (tptp.aNaturalNumber0 @t68)) % 1.42/1.64 (define @t136 () (not @t135)) % 1.42/1.64 (define @t137 () (tptp.aNaturalNumber0 @t87)) % 1.42/1.64 (define @t138 () (not @t137)) % 1.42/1.64 (define @t139 () (or @t138 @t136 (= @t87 @t68) @t134 @t132 @t131)) % 1.42/1.64 (define @t140 () (forall @t112 @t109)) % 1.42/1.64 (define @t141 () (and (not (= @t127 @t128)) @t129 @t126 @t89)) % 1.42/1.64 (define @t142 () (= @t68 @t87)) % 1.42/1.64 (define @t143 () (or @t138 @t136 @t142 @t134 @t132 @t141)) % 1.42/1.64 (define @t144 () (@list false)) % 1.42/1.64 (define @t145 () (@list @t140)) % 1.42/1.64 (define @t146 () (not @t142)) % 1.42/1.64 (define @t147 () (tptp.sdtpldt0 tptp.xm tptp.xn)) % 1.42/1.64 (define @t148 () (tptp.sdtpldt0 tptp.xm @t78)) % 1.42/1.64 (define @t149 () (tptp.sdtlseqdt0 @t148 @t147)) % 1.42/1.64 (define @t150 () (not (= @t148 @t147))) % 1.42/1.64 (define @t151 () (and @t150 @t149 @t146 @t133)) % 1.42/1.64 (define @t152 () (not @t62)) % 1.42/1.64 (define @t153 () (not @t79)) % 1.42/1.64 (define @t154 () (not @t63)) % 1.42/1.64 (define @t155 () (not @t81)) % 1.42/1.64 (define @t156 () (or @t155 @t154 @t82 @t153 @t152 @t151)) % 1.42/1.64 (define @t157 () (and (not (= @t147 @t148)) @t149 @t146 @t133)) % 1.42/1.64 (define @t158 () (= tptp.xn @t78)) % 1.42/1.64 (define @t159 () (or @t155 @t154 @t158 @t153 @t152 @t157)) % 1.42/1.64 (define @t160 () (not @t157)) % 1.42/1.64 (define @t161 () (@list @t157)) % 1.42/1.64 (define @t162 () (or @t155 @t152 @t137)) % 1.42/1.64 (define @t163 () (@list false false false)) % 1.42/1.64 (define @t164 () (or @t154 @t152 @t135)) % 1.42/1.64 (define @t165 () (not @t141)) % 1.42/1.64 (define @t166 () (@list @t141)) % 1.42/1.64 (define @t167 () (= @t69 @t90)) % 1.42/1.64 (define @t168 () (or (not (forall @t3 (or @t108 (not @t167)))) @t89)) % 1.42/1.64 (define @t169 () (and @t81 @t80 @t125)) % 1.42/1.64 (define @t170 () (not @t169)) % 1.42/1.64 (define @t171 () (@list true)) % 1.42/1.64 (define @t172 () (=> @t83 @t168)) % 1.42/1.64 (define @t173 () (not @t172)) % 1.42/1.64 (define @t174 () (and @t2 @t167)) % 1.42/1.64 (define @t175 () (forall @t3 (not @t174))) % 1.42/1.64 (define @t176 () (not @t175)) % 1.42/1.64 (assume @p1 (forall @t3 (=> @t2 true))) % 1.42/1.64 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 1.42/1.64 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 1.42/1.64 (assume @p4 @t10) % 1.42/1.64 (assume @p5 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t11)))) % 1.42/1.64 (assume @p6 (forall @t9 (=> @t8 (= @t5 @t12)))) % 1.42/1.64 (assume @p7 (forall @t18 (=> @t17 (= @t15 (tptp.sdtpldt0 @t1 @t14))))) % 1.42/1.64 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 1.42/1.64 (assume @p9 (forall @t9 (=> @t8 (= @t11 @t19)))) % 1.42/1.64 (assume @p10 (forall @t18 (=> @t17 (= (tptp.sdtasdt0 @t11 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 1.42/1.64 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 1.42/1.64 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 1.42/1.64 (assume @p13 (forall @t18 (=> @t17 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t11 @t21)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t19 @t20)))))) % 1.42/1.64 (assume @p14 (forall @t18 (=> @t17 (=> (or (= @t5 @t24) (= @t12 @t23)) @t22)))) % 1.42/1.64 (assume @p15 (forall @t3 (=> @t2 (=> @t28 (forall (@list @t4 @t13) (=> (and @t7 @t16) (=> (or @t26 @t25) @t22))))))) % 1.42/1.64 (assume @p16 (forall @t9 (=> @t8 (=> (= @t5 tptp.sz00) (and @t27 @t29))))) % 1.42/1.64 (assume @p17 (forall @t9 (=> @t8 (=> (= @t11 tptp.sz00) (or @t27 @t29))))) % 1.42/1.64 (assume @p18 (forall @t9 (=> @t8 (= @t32 (exists @t31 @t30))))) % 1.42/1.64 (assume @p19 (forall @t9 (=> @t8 (=> @t32 (forall @t31 (= (= @t13 (tptp.sdtmndt0 @t4 @t1)) @t30)))))) % 1.42/1.64 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 1.42/1.64 (assume @p21 (forall @t9 (=> @t8 (=> (and @t32 @t34) @t33)))) % 1.42/1.64 (assume @p22 (forall @t18 (=> @t17 (=> (and @t32 @t35) (tptp.sdtlseqdt0 @t1 @t13))))) % 1.42/1.64 (assume @p23 (forall @t9 (=> @t8 (or @t32 (and (not @t36) @t34))))) % 1.42/1.64 (assume @p24 @t49) % 1.42/1.64 (assume @p25 (forall @t18 (=> @t17 (=> (and @t28 (not @t22) @t35) (and (not @t26) (tptp.sdtlseqdt0 @t11 @t21) (not @t25) (tptp.sdtlseqdt0 @t19 @t20)))))) % 1.42/1.64 (assume @p26 (forall @t3 (=> @t2 (or @t27 @t50 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 1.42/1.64 (assume @p27 (forall @t9 (=> @t8 (=> @t28 (tptp.sdtlseqdt0 @t4 @t19))))) % 1.42/1.64 (assume @p28 (forall @t9 (=> @t8 (=> @t51 true)))) % 1.42/1.64 (assume @p29 (forall @t9 (=> @t8 (=> @t46 @t51)))) % 1.42/1.64 (assume @p30 (forall @t9 (=> @t8 (= @t53 (exists @t31 @t52))))) % 1.42/1.64 (assume @p31 (forall @t9 (=> @t8 (=> @t55 (forall @t31 (= (= @t13 @t54) @t52)))))) % 1.42/1.64 (assume @p32 (forall @t18 (=> @t17 (=> (and @t53 (tptp.doDivides0 @t4 @t13)) @t56)))) % 1.42/1.64 (assume @p33 (forall @t18 (=> @t17 (=> (and @t53 @t56) @t57)))) % 1.42/1.64 (assume @p34 (forall @t18 (=> @t17 (=> (and @t53 @t57) @t56)))) % 1.42/1.64 (assume @p35 (forall @t9 (=> @t8 (=> (and @t53 (not @t29)) @t32)))) % 1.42/1.64 (assume @p36 (forall @t9 (=> @t8 (=> @t55 (forall @t31 (=> @t16 (= (tptp.sdtasdt0 @t13 @t54) (tptp.sdtsldt0 (tptp.sdtasdt0 @t13 @t4) @t1)))))))) % 1.42/1.64 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t28 @t60 (forall @t59 (=> (and @t7 @t58) (or (= @t4 tptp.sz10) @t36)))))))) % 1.42/1.64 (assume @p38 (forall @t3 (=> (and @t2 @t28 @t60) (exists @t59 (and @t7 @t58 (tptp.isPrime0 @t4)))))) % 1.42/1.64 (assume @p39 (and @t63 @t62 @t61)) % 1.42/1.64 (assume @p40 (forall @t18 (=> @t17 (=> (and (or (and (not (= @t13 tptp.sz00)) (not (= @t13 tptp.sz10)) (forall @t67 (=> (and @t66 (exists (@list @t70) (and (tptp.aNaturalNumber0 @t70) (= @t13 (tptp.sdtasdt0 @t64 @t70)))) (tptp.doDivides0 @t64 @t13)) (or (= @t64 tptp.sz10) (= @t64 @t13))))) (tptp.isPrime0 @t13)) (or (exists @t67 (and @t66 (= @t11 @t65))) (tptp.doDivides0 @t13 @t11))) (=> (tptp.iLess0 @t15 @t69) (or (and (exists @t67 (and @t66 (= @t1 @t65))) (tptp.doDivides0 @t13 @t1)) (and (exists @t67 (and @t66 (= @t4 @t65))) (tptp.doDivides0 @t13 @t4)))))))) % 1.42/1.64 (assume @p41 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t59 (and @t7 (= tptp.xp @t11))) (tptp.doDivides0 @t1 tptp.xp))) (or @t50 (= @t1 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists @t3 (and @t2 (= @t71 @t72))) (tptp.doDivides0 tptp.xp @t71))) % 1.42/1.64 (assume @p42 (not (or (exists @t3 (and @t2 (= @t73 tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn)))) % 1.42/1.64 (assume @p43 (not (or (exists @t3 (and @t2 (= @t73 tptp.xm))) (tptp.sdtlseqdt0 tptp.xp tptp.xm)))) % 1.42/1.64 (assume @p44 (and (not (= tptp.xn tptp.xp)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xn @t1) tptp.xp))) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xm @t1) tptp.xp))) (tptp.sdtlseqdt0 tptp.xm tptp.xp))) % 1.42/1.64 (assume @p45 (and (tptp.aNaturalNumber0 tptp.xk) (= @t71 (tptp.sdtasdt0 tptp.xp tptp.xk)) (= tptp.xk (tptp.sdtsldt0 @t71 tptp.xp)))) % 1.42/1.64 (assume @p46 (not (or @t75 @t74))) % 1.42/1.64 (assume @p47 (and (not @t75) (not @t74))) % 1.42/1.64 (assume @p48 (and (tptp.aNaturalNumber0 tptp.xr) (exists @t3 (and @t2 (= tptp.xk @t76))) (tptp.doDivides0 tptp.xr tptp.xk) (not (= tptp.xr tptp.sz00)) (not (= tptp.xr tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t59 (and @t7 (= tptp.xr @t11))) (tptp.doDivides0 @t1 tptp.xr))) (or @t50 (= @t1 tptp.xr)))) (tptp.isPrime0 tptp.xr))) % 1.42/1.64 (assume @p49 (and (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xr @t1) tptp.xk))) (exists @t3 (and @t2 (= @t71 @t76))) (tptp.doDivides0 tptp.xr @t71))) % 1.42/1.64 (assume @p50 (and (not (= tptp.xk tptp.xp)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xk @t1) tptp.xp))) (tptp.sdtlseqdt0 tptp.xk tptp.xp))) % 1.42/1.64 (assume @p51 (or @t77 (and (exists @t3 (and @t2 (= tptp.xm @t76))) (tptp.doDivides0 tptp.xr tptp.xm)))) % 1.42/1.64 (assume @p52 @t77) % 1.42/1.64 (assume @p53 (and @t85 @t81 @t80 (exists @t3 (and @t2 (= (tptp.sdtpldt0 @t78 @t1) tptp.xn))) @t79)) % 1.42/1.64 (assume @p54 (and @t81 @t80 (exists @t3 (and @t2 (= @t86 @t72))) (tptp.doDivides0 tptp.xp @t86))) % 1.42/1.64 (assume @p55 @t98) % 1.42/1.64 (assume @p56 true) % 1.42/1.64 (step @p57 :rule aci_norm :args ((= @t111 @t109))) % 1.42/1.64 (step @p58 :rule cong :premises (@p57) :args (@t113)) % 1.42/1.64 (step @p59 :rule quant-merge-prenex :args ((= (forall @t9 @t115) @t113))) % 1.42/1.64 (step @p60 :rule alpha_equiv :args (@t116 (@list @t99) (@list @t13))) % 1.42/1.64 (step @p61 :rule refl :args (@t106)) % 1.42/1.64 (step @p62 :rule refl :args (@t33)) % 1.42/1.64 (step @p63 :rule refl :args (@t107)) % 1.42/1.64 (step @p64 :rule refl :args (@t108)) % 1.42/1.64 (step @p65 :rule nary_cong :premises (@p64 @p63 @p62 @p61 @p60) :args (@t117)) % 1.42/1.64 (step @p66 :rule quant-miniscope-or :args ((= @t115 @t117))) % 1.42/1.64 (step @p67 :rule trans :premises (@p66 @p65)) % 1.42/1.64 (step @p68 :rule symm :premises (@p67)) % 1.42/1.64 (step @p69 :rule cong :premises (@p68) :args ((forall @t9 @t120))) % 1.42/1.64 (step @p70 :rule trans :premises (@p69 @p59)) % 1.42/1.64 (step @p71 :rule trans :premises (@p70 @p58)) % 1.42/1.64 (step @p72 :rule aci_norm :args ((= (or @t122 @t121) @t120))) % 1.42/1.64 (step @p73 :rule aci_norm :args ((= (or (or @t33 @t106) @t119) @t121))) % 1.42/1.64 (step @p74 :rule refl :args (@t119)) % 1.42/1.64 (step @p75 :rule bool-double-not-elim :args (@t33)) % 1.42/1.64 (step @p76 :rule nary_cong :premises (@p75 @p61) :args ((or (not @t45) @t106))) % 1.42/1.64 (step @p77 :rule bool-and-de-morgan :args (@t45 @t32 true)) % 1.42/1.64 (step @p78 :rule trans :premises (@p77 @p76)) % 1.42/1.64 (step @p79 :rule nary_cong :premises (@p78 @p74) :args ((or (not @t46) @t119))) % 1.42/1.64 (step @p80 :rule trans :premises (@p79 @p73)) % 1.42/1.64 (step @p81 :rule bool-impl-elim :args (@t46 @t119)) % 1.42/1.64 (step @p82 :rule trans :premises (@p81 @p80)) % 1.42/1.64 (step @p83 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 1.42/1.64 (step @p84 :rule nary_cong :premises (@p83 @p82) :args ((or @t124 @t123))) % 1.42/1.64 (step @p85 :rule trans :premises (@p84 @p72)) % 1.42/1.64 (step @p86 :rule bool-impl-elim :args (@t8 @t123)) % 1.42/1.64 (step @p87 :rule trans :premises (@p86 @p85)) % 1.42/1.64 (step @p88 :rule cong :premises (@p87) :args ((forall @t9 (=> @t8 @t123)))) % 1.42/1.64 (step @p89 :rule trans :premises (@p88 @p71)) % 1.42/1.64 (step @p90 :rule bool-impl-elim :args (@t16 @t118)) % 1.42/1.64 (step @p91 :rule cong :premises (@p90) :args ((forall @t31 (=> @t16 @t118)))) % 1.42/1.64 (step @p92 :rule refl :args (@t37)) % 1.42/1.64 (step @p93 :rule eq-symm :args (@t24 @t14)) % 1.42/1.64 (step @p94 :rule cong :premises (@p93) :args (@t38)) % 1.42/1.64 (step @p95 :rule refl :args (@t40)) % 1.42/1.64 (step @p96 :rule refl :args (@t41)) % 1.42/1.64 (step @p97 :rule nary_cong :premises (@p96 @p95 @p94 @p92) :args (@t42)) % 1.42/1.64 (step @p98 :rule refl :args (@t16)) % 1.42/1.64 (step @p99 :rule cong :premises (@p98 @p97) :args (@t43)) % 1.42/1.64 (step @p100 :rule cong :premises (@p99) :args (@t44)) % 1.42/1.64 (step @p101 :rule trans :premises (@p100 @p91)) % 1.42/1.64 (step @p102 :rule refl :args (@t46)) % 1.42/1.64 (step @p103 :rule cong :premises (@p102 @p101) :args (@t47)) % 1.42/1.64 (step @p104 :rule refl :args (@t8)) % 1.42/1.64 (step @p105 :rule cong :premises (@p104 @p103) :args (@t48)) % 1.42/1.64 (step @p106 :rule cong :premises (@p105) :args (@t49)) % 1.42/1.64 (step @p107 :rule trans :premises (@p106 @p89)) % 1.42/1.64 (step @p108 :rule eq_resolve :premises (@p24 @p107)) % 1.42/1.64 (step @p109 :rule refl :args (@t89)) % 1.42/1.64 (step @p110 :rule refl :args (@t126)) % 1.42/1.64 (step @p111 :rule refl :args (@t129)) % 1.42/1.64 (step @p112 :rule eq-symm :args (@t128 @t127)) % 1.42/1.64 (step @p113 :rule cong :premises (@p112) :args (@t130)) % 1.42/1.64 (step @p114 :rule nary_cong :premises (@p113 @p111 @p110 @p109) :args (@t131)) % 1.42/1.64 (step @p115 :rule refl :args (@t132)) % 1.42/1.64 (step @p116 :rule refl :args (@t134)) % 1.42/1.64 (step @p117 :rule eq-symm :args (@t87 @t68)) % 1.42/1.64 (step @p118 :rule refl :args (@t136)) % 1.42/1.64 (step @p119 :rule refl :args (@t138)) % 1.42/1.64 (step @p120 :rule nary_cong :premises (@p119 @p118 @p117 @p116 @p115 @p114) :args (@t139)) % 1.42/1.64 (step @p121 :rule refl :args (@t140)) % 1.42/1.64 (step @p122 :rule cong :premises (@p121 @p120) :args ((=> @t140 @t139))) % 1.42/1.64 (assume-push @p229 @t140) % 1.42/1.64 (step @p124 :rule instantiate :premises (@p108) :args ((@list @t87 @t68 tptp.xp))) % 1.42/1.64 (step-pop @p230 :rule scope :premises (@p124)) % 1.42/1.64 (step @p125 :rule process_scope :premises (@p230) :args (@t139)) % 1.42/1.64 (step @p127 :rule eq_resolve :premises (@p125 @p122)) % 1.42/1.64 (step @p128 :rule implies_elim :premises (@p127)) % 1.42/1.64 (step @p129 :rule chain_m_resolution :premises (@p128 @p108) :args (@t143 @t144 @t145)) % 1.42/1.64 (step @p130 :rule refl :args (@t133)) % 1.42/1.64 (step @p131 :rule refl :args (@t146)) % 1.42/1.64 (step @p132 :rule refl :args (@t149)) % 1.42/1.64 (step @p133 :rule eq-symm :args (@t148 @t147)) % 1.42/1.64 (step @p134 :rule cong :premises (@p133) :args (@t150)) % 1.42/1.64 (step @p135 :rule nary_cong :premises (@p134 @p132 @p131 @p130) :args (@t151)) % 1.42/1.64 (step @p136 :rule refl :args (@t152)) % 1.42/1.64 (step @p137 :rule refl :args (@t153)) % 1.42/1.64 (step @p138 :rule eq-symm :args (@t78 tptp.xn)) % 1.42/1.64 (step @p139 :rule refl :args (@t154)) % 1.42/1.64 (step @p140 :rule refl :args (@t155)) % 1.42/1.64 (step @p141 :rule nary_cong :premises (@p140 @p139 @p138 @p137 @p136 @p135) :args (@t156)) % 1.42/1.64 (step @p142 :rule cong :premises (@p121 @p141) :args ((=> @t140 @t156))) % 1.42/1.64 (assume-push @p231 @t140) % 1.42/1.64 (step @p144 :rule instantiate :premises (@p108) :args ((@list @t78 tptp.xn tptp.xm))) % 1.42/1.64 (step-pop @p232 :rule scope :premises (@p144)) % 1.42/1.64 (step @p145 :rule process_scope :premises (@p232) :args (@t156)) % 1.42/1.64 (step @p147 :rule eq_resolve :premises (@p145 @p142)) % 1.42/1.64 (step @p148 :rule implies_elim :premises (@p147)) % 1.42/1.64 (step @p149 :rule chain_m_resolution :premises (@p148 @p108) :args (@t159 @t144 @t145)) % 1.42/1.64 (step @p150 :rule and_elim :premises (@p53) :args (4)) % 1.42/1.64 (step @p151 :rule refl :args (@t83)) % 1.42/1.64 (step @p152 :rule cong :premises (@p151 @p138) :args (@t84)) % 1.42/1.64 (step @p153 :rule cong :premises (@p152) :args (@t85)) % 1.42/1.64 (step @p154 :rule and_elim :premises (@p53) :args (0)) % 1.42/1.64 (step @p155 :rule eq_resolve :premises (@p154 @p153)) % 1.42/1.64 (step @p156 :rule not_implies_elim1 :premises (@p155)) % 1.42/1.64 (step @p157 :rule and_elim :premises (@p156) :args (0)) % 1.42/1.64 (step @p158 :rule and_elim :premises (@p39) :args (1)) % 1.42/1.64 (step @p159 :rule and_elim :premises (@p39) :args (0)) % 1.42/1.64 (step @p160 :rule not_implies_elim2 :premises (@p155)) % 1.42/1.64 (step @p161 :rule cnf_or_pos :args (@t159)) % 1.42/1.64 (step @p162 :rule reordering :premises (@p161) :args ((or @t158 @t154 @t152 @t155 @t153 @t157 (not @t159)))) % 1.42/1.64 (step @p163 :rule chain_m_resolution :premises (@p162 @p160 @p159 @p158 @p157 @p150 @p149) :args (@t157 (@list true false false false false false) (@list @t158 @t63 @t62 @t81 @t79 @t159))) % 1.42/1.64 (step @p164 :rule cnf_and_pos :args (@t157 2)) % 1.42/1.64 (step @p165 :rule reordering :premises (@p164) :args ((or @t146 @t160))) % 1.42/1.64 (step @p166 :rule chain_m_resolution :premises (@p165 @p163) :args (@t146 @t144 @t161)) % 1.42/1.64 (step @p167 :rule cnf_and_pos :args (@t157 3)) % 1.42/1.64 (step @p168 :rule reordering :premises (@p167) :args ((or @t133 @t160))) % 1.42/1.64 (step @p169 :rule chain_m_resolution :premises (@p168 @p163) :args (@t133 @t144 @t161)) % 1.42/1.64 (step @p170 :rule aci_norm :args ((= (or @t122 @t6) (or @t108 @t107 @t6)))) % 1.42/1.64 (step @p171 :rule refl :args (@t6)) % 1.42/1.64 (step @p172 :rule nary_cong :premises (@p83 @p171) :args ((or @t124 @t6))) % 1.42/1.64 (step @p173 :rule trans :premises (@p172 @p170)) % 1.42/1.64 (step @p174 :rule bool-impl-elim :args (@t8 @t6)) % 1.42/1.64 (step @p175 :rule trans :premises (@p174 @p173)) % 1.42/1.64 (step @p176 :rule cong :premises (@p175) :args (@t10)) % 1.42/1.65 (step @p177 :rule eq_resolve :premises (@p4 @p176)) % 1.42/1.65 (step @p178 :rule instantiate :premises (@p177) :args ((@list @t78 tptp.xm))) % 1.42/1.65 (step @p179 :rule cnf_or_pos :args (@t162)) % 1.42/1.65 (step @p180 :rule reordering :premises (@p179) :args ((or @t152 @t155 @t137 (not @t162)))) % 1.42/1.65 (step @p181 :rule chain_m_resolution :premises (@p180 @p158 @p157 @p178) :args (@t137 @t163 (@list @t62 @t81 @t162))) % 1.42/1.65 (step @p182 :rule instantiate :premises (@p177) :args ((@list tptp.xn tptp.xm))) % 1.42/1.65 (step @p183 :rule cnf_or_pos :args (@t164)) % 1.42/1.65 (step @p184 :rule reordering :premises (@p183) :args ((or @t154 @t152 @t135 (not @t164)))) % 1.42/1.65 (step @p185 :rule chain_m_resolution :premises (@p184 @p159 @p158 @p182) :args (@t135 @t163 (@list @t63 @t62 @t164))) % 1.42/1.65 (step @p186 :rule and_elim :premises (@p39) :args (2)) % 1.42/1.65 (step @p187 :rule cnf_or_pos :args (@t143)) % 1.42/1.65 (step @p188 :rule reordering :premises (@p187) :args ((or @t132 @t136 @t138 @t134 @t142 @t141 (not @t143)))) % 1.42/1.65 (step @p189 :rule chain_m_resolution :premises (@p188 @p186 @p185 @p181 @p169 @p166 @p129) :args (@t141 (@list false false false false true false) (@list @t61 @t135 @t137 @t133 @t142 @t143))) % 1.42/1.65 (step @p190 :rule cnf_and_pos :args (@t141 3)) % 1.42/1.65 (step @p191 :rule reordering :premises (@p190) :args ((or @t89 @t165))) % 1.42/1.65 (step @p192 :rule chain_m_resolution :premises (@p191 @p189) :args (@t89 @t144 @t166)) % 1.42/1.65 (step @p193 :rule cnf_or_neg :args (@t168 1)) % 1.42/1.65 (step @p194 :rule chain_m_resolution :premises (@p193 @p192) :args (@t168 @t144 (@list @t89))) % 1.42/1.65 (step @p195 :rule cnf_and_pos :args (@t141 2)) % 1.42/1.65 (step @p196 :rule reordering :premises (@p195) :args ((or @t126 @t165))) % 1.42/1.65 (step @p197 :rule chain_m_resolution :premises (@p196 @p189) :args (@t126 @t144 @t166)) % 1.42/1.65 (step @p198 :rule cnf_and_pos :args (@t169 2)) % 1.42/1.65 (step @p199 :rule reordering :premises (@p198) :args ((or @t125 @t170))) % 1.42/1.65 (step @p200 :rule chain_m_resolution :premises (@p199 @p197) :args (@t170 @t171 (@list @t125))) % 1.42/1.65 (step @p201 :rule refl :args (@t173)) % 1.42/1.65 (step @p202 :rule bool-double-not-elim :args (@t169)) % 1.42/1.65 (step @p203 :rule nary_cong :premises (@p202 @p201) :args ((or (not @t170) @t173))) % 1.42/1.65 (step @p204 :rule bool-and-de-morgan :args (@t2 @t167 true)) % 1.42/1.65 (step @p205 :rule cong :premises (@p204) :args (@t175)) % 1.42/1.65 (step @p206 :rule cong :premises (@p205) :args (@t176)) % 1.42/1.65 (step @p207 :rule exists-elim :args ((= (exists @t3 @t174) @t176))) % 1.42/1.65 (step @p208 :rule trans :premises (@p207 @p206)) % 1.42/1.65 (step @p209 :rule eq-symm :args (@t90 @t69)) % 1.42/1.65 (step @p210 :rule refl :args (@t2)) % 1.42/1.65 (step @p211 :rule nary_cong :premises (@p210 @p209) :args (@t91)) % 1.42/1.65 (step @p212 :rule cong :premises (@p211) :args (@t92)) % 1.42/1.65 (step @p213 :rule trans :premises (@p212 @p208)) % 1.42/1.65 (step @p214 :rule nary_cong :premises (@p213 @p109) :args (@t93)) % 1.42/1.65 (step @p215 :rule cong :premises (@p151 @p214) :args (@t94)) % 1.42/1.65 (step @p216 :rule eq-symm :args (@t88 @t69)) % 1.42/1.65 (step @p217 :rule refl :args (@t80)) % 1.42/1.65 (step @p218 :rule refl :args (@t81)) % 1.42/1.65 (step @p219 :rule nary_cong :premises (@p218 @p217 @p216) :args (@t95)) % 1.42/1.65 (step @p220 :rule cong :premises (@p219) :args (@t96)) % 1.42/1.65 (step @p221 :rule nary_cong :premises (@p220 @p215) :args (@t97)) % 1.42/1.65 (step @p222 :rule cong :premises (@p221) :args (@t98)) % 1.42/1.65 (step @p223 :rule eq_resolve :premises (@p55 @p222)) % 1.42/1.65 (step @p224 :rule not_and :premises (@p223)) % 1.42/1.65 (step @p225 :rule eq_resolve :premises (@p224 @p203)) % 1.42/1.65 (step @p226 :rule chain_m_resolution :premises (@p225 @p200) :args (@t173 @t171 (@list @t169))) % 1.42/1.65 (step @p227 :rule cnf_implies_neg2 :args (@t172)) % 1.42/1.65 (step @p228 false :rule chain_m_resolution :premises (@p227 @p226 @p194) :args (false (@list true false) (@list @t172 @t168))) % 1.42/1.65 ) % 1.42/1.65 % SZS output end Proof % 1.42/1.65 % cvc5 exiting %------------------------------------------------------------------------------