%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG121+1 : 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 : n019.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 08:45:45 AM UTC 2026 % Result : Theorem 149.19s 149.45s % Output : Proof 149.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG121+1 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n019.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 14:08:19 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.50 %----Proving TF0_NAR, FOF, or CNF % 149.19/149.45 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 149.19/149.45 --- Run --no-e-matching --full-saturate-quant at 6... % 149.19/149.45 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 149.19/149.45 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 149.19/149.45 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 149.19/149.45 --- Run --trigger-sel=max --full-saturate-quant at 15... % 149.19/149.45 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 149.19/149.45 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 149.19/149.45 --- Run --prenex-quant=none --full-saturate-quant at 30... % 149.19/149.45 % SZS status Theorem % 149.19/149.45 % SZS output start Proof % 149.19/149.45 ( % 149.19/149.45 (declare-sort $$unsorted 0) % 149.19/149.45 (declare-const tptp.xq $$unsorted) % 149.19/149.45 (declare-const tptp.xu $$unsorted) % 149.19/149.45 (declare-const tptp.xc $$unsorted) % 149.19/149.45 (declare-const tptp.xa $$unsorted) % 149.19/149.45 (declare-const tptp.xI $$unsorted) % 149.19/149.45 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 149.19/149.45 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 149.19/149.45 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 149.19/149.45 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 149.19/149.45 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 149.19/149.45 (declare-const tptp.sz00 $$unsorted) % 149.19/149.45 (declare-const tptp.sz10 $$unsorted) % 149.19/149.45 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 149.19/149.45 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 149.19/149.45 (declare-const tptp.xr $$unsorted) % 149.19/149.45 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 149.19/149.45 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 149.19/149.45 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 149.19/149.45 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 149.19/149.45 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 149.19/149.45 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 149.19/149.45 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 149.19/149.45 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 149.19/149.45 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 149.19/149.45 (declare-const tptp.xb $$unsorted) % 149.19/149.45 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 149.19/149.45 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 149.19/149.45 (define @t1 () (@var "W0" $$unsorted)) % 149.19/149.45 (define @t2 () (tptp.aElement0 @t1)) % 149.19/149.45 (define @t3 () (@list @t1)) % 149.19/149.45 (define @t4 () (tptp.smndt0 @t1)) % 149.19/149.45 (define @t5 () (@var "W1" $$unsorted)) % 149.19/149.45 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 149.19/149.45 (define @t7 () (tptp.aElement0 @t5)) % 149.19/149.45 (define @t8 () (and @t2 @t7)) % 149.19/149.45 (define @t9 () (@list @t1 @t5)) % 149.19/149.45 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 149.19/149.45 (define @t11 () (@var "W2" $$unsorted)) % 149.19/149.45 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 149.19/149.45 (define @t13 () (tptp.aElement0 @t11)) % 149.19/149.45 (define @t14 () (and @t2 @t7 @t13)) % 149.19/149.45 (define @t15 () (@list @t1 @t5 @t11)) % 149.19/149.45 (define @t16 () (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1))) % 149.19/149.45 (define @t17 () (tptp.sdtpldt0 @t1 tptp.sz00)) % 149.19/149.45 (define @t18 () (and (= @t17 @t1) @t16)) % 149.19/149.45 (define @t19 () (=> @t2 @t18)) % 149.19/149.45 (define @t20 () (forall @t3 @t19)) % 149.19/149.45 (define @t21 () (tptp.sdtasdt0 @t5 @t1)) % 149.19/149.45 (define @t22 () (tptp.sdtasdt0 @t1 @t11)) % 149.19/149.45 (define @t23 () (tptp.smndt0 tptp.sz10)) % 149.19/149.45 (define @t24 () (= @t5 tptp.sz00)) % 149.19/149.45 (define @t25 () (= @t1 tptp.sz00)) % 149.19/149.45 (define @t26 () (tptp.aSet0 @t1)) % 149.19/149.45 (define @t27 () (tptp.aElementOf0 @t5 @t1)) % 149.19/149.45 (define @t28 () (@list @t5)) % 149.19/149.45 (define @t29 () (tptp.aElementOf0 @t11 @t1)) % 149.19/149.45 (define @t30 () (tptp.aElementOf0 @t11 @t5)) % 149.19/149.45 (define @t31 () (@list @t11)) % 149.19/149.45 (define @t32 () (tptp.aSet0 @t5)) % 149.19/149.45 (define @t33 () (and @t26 @t32)) % 149.19/149.45 (define @t34 () (@var "W3" $$unsorted)) % 149.19/149.45 (define @t35 () (@var "W5" $$unsorted)) % 149.19/149.45 (define @t36 () (@var "W4" $$unsorted)) % 149.19/149.45 (define @t37 () (tptp.sdtpldt0 @t36 @t35)) % 149.19/149.45 (define @t38 () (tptp.aElementOf0 @t35 @t5)) % 149.19/149.45 (define @t39 () (tptp.aElementOf0 @t36 @t1)) % 149.19/149.45 (define @t40 () (and @t39 @t38 (= @t37 @t34))) % 149.19/149.45 (define @t41 () (@list @t36 @t35)) % 149.19/149.45 (define @t42 () (exists @t41 @t40)) % 149.19/149.45 (define @t43 () (tptp.aElementOf0 @t34 @t11)) % 149.19/149.45 (define @t44 () (= @t43 @t42)) % 149.19/149.45 (define @t45 () (@list @t34)) % 149.19/149.45 (define @t46 () (forall @t45 @t44)) % 149.19/149.45 (define @t47 () (tptp.aSet0 @t11)) % 149.19/149.45 (define @t48 () (and @t47 @t46)) % 149.19/149.45 (define @t49 () (tptp.sdtpldt1 @t1 @t5)) % 149.19/149.45 (define @t50 () (= @t11 @t49)) % 149.19/149.45 (define @t51 () (= @t50 @t48)) % 149.19/149.45 (define @t52 () (forall @t31 @t51)) % 149.19/149.45 (define @t53 () (=> @t33 @t52)) % 149.19/149.45 (define @t54 () (forall @t9 @t53)) % 149.19/149.45 (define @t55 () (tptp.sdtasasdt0 @t1 @t5)) % 149.19/149.45 (define @t56 () (tptp.sdtasdt0 @t11 @t5)) % 149.19/149.45 (define @t57 () (tptp.aElementOf0 @t56 @t1)) % 149.19/149.45 (define @t58 () (forall @t31 (=> @t13 @t57))) % 149.19/149.45 (define @t59 () (tptp.aElementOf0 @t12 @t1)) % 149.19/149.45 (define @t60 () (forall @t31 (=> @t29 @t59))) % 149.19/149.45 (define @t61 () (and @t60 @t58)) % 149.19/149.45 (define @t62 () (=> @t27 @t61)) % 149.19/149.45 (define @t63 () (forall @t28 @t62)) % 149.19/149.45 (define @t64 () (and @t26 @t63)) % 149.19/149.45 (define @t65 () (tptp.aIdeal0 @t1)) % 149.19/149.45 (define @t66 () (= @t65 @t64)) % 149.19/149.45 (define @t67 () (forall @t3 @t66)) % 149.19/149.45 (define @t68 () (and @t65 (tptp.aIdeal0 @t5))) % 149.19/149.45 (define @t69 () (tptp.aElement0 @t34)) % 149.19/149.45 (define @t70 () (@list @t11 @t34)) % 149.19/149.45 (define @t71 () (tptp.aNaturalNumber0 @t1)) % 149.19/149.45 (define @t72 () (tptp.sbrdtbr0 @t1)) % 149.19/149.45 (define @t73 () (not @t25)) % 149.19/149.45 (define @t74 () (tptp.slsdtgt0 @t1)) % 149.19/149.45 (define @t75 () (tptp.aIdeal0 @t74)) % 149.19/149.45 (define @t76 () (forall @t3 (=> @t2 @t75))) % 149.19/149.45 (define @t77 () (tptp.aElement0 tptp.xb)) % 149.19/149.45 (define @t78 () (tptp.aElement0 tptp.xa)) % 149.19/149.46 (define @t79 () (tptp.slsdtgt0 tptp.xb)) % 149.19/149.46 (define @t80 () (tptp.slsdtgt0 tptp.xa)) % 149.19/149.46 (define @t81 () (tptp.sdtpldt1 @t80 @t79)) % 149.19/149.46 (define @t82 () (tptp.aElementOf0 tptp.xb @t79)) % 149.19/149.46 (define @t83 () (tptp.aElementOf0 tptp.sz00 @t80)) % 149.19/149.46 (define @t84 () (tptp.sbrdtbr0 tptp.xu)) % 149.19/149.46 (define @t85 () (= tptp.xr tptp.sz00)) % 149.19/149.46 (define @t86 () (tptp.sdtasdt0 tptp.xq tptp.xu)) % 149.19/149.46 (define @t87 () (tptp.sdtpldt0 @t86 tptp.xr)) % 149.19/149.46 (define @t88 () (tptp.aElementOf0 tptp.xb tptp.xI)) % 149.19/149.46 (define @t89 () (not @t88)) % 149.19/149.46 (define @t90 () (= @t34 @t37)) % 149.19/149.46 (define @t91 () (not @t90)) % 149.19/149.46 (define @t92 () (not @t38)) % 149.19/149.46 (define @t93 () (not @t39)) % 149.19/149.46 (define @t94 () (or @t93 @t92 @t91)) % 149.19/149.46 (define @t95 () (forall @t31 (= @t50 (and @t47 (forall @t45 (= @t43 (not (forall @t41 @t94)))))))) % 149.19/149.46 (define @t96 () (not @t32)) % 149.19/149.46 (define @t97 () (not @t26)) % 149.19/149.46 (define @t98 () (and @t39 @t38 @t90)) % 149.19/149.46 (define @t99 () (forall @t41 (not @t98))) % 149.19/149.46 (define @t100 () (not @t99)) % 149.19/149.46 (define @t101 () (tptp.slsdtgt0 @t87)) % 149.19/149.46 (define @t102 () (not @t13)) % 149.19/149.46 (define @t103 () (and (forall @t31 (or (not @t29) @t59)) (forall @t31 (or @t102 @t57)))) % 149.19/149.46 (define @t104 () (@list @t87)) % 149.19/149.46 (define @t105 () (tptp.aIdeal0 @t101)) % 149.19/149.46 (define @t106 () (tptp.aElement0 @t87)) % 149.19/149.46 (define @t107 () (not @t106)) % 149.19/149.46 (define @t108 () (or @t107 @t105)) % 149.19/149.46 (define @t109 () (@list false false)) % 149.19/149.46 (define @t110 () (tptp.aSet0 @t101)) % 149.19/149.46 (define @t111 () (and @t110 (forall @t28 (or (not (tptp.aElementOf0 @t5 @t101)) (and (forall @t31 (or (not (tptp.aElementOf0 @t11 @t101)) (tptp.aElementOf0 @t12 @t101))) (forall @t31 (or @t102 (tptp.aElementOf0 @t56 @t101)))))))) % 149.19/149.46 (define @t112 () (= @t105 @t111)) % 149.19/149.46 (define @t113 () (@list false)) % 149.19/149.46 (define @t114 () (tptp.aIdeal0 @t80)) % 149.19/149.46 (define @t115 () (not @t78)) % 149.19/149.46 (define @t116 () (or @t115 @t114)) % 149.19/149.46 (define @t117 () (tptp.aSet0 @t80)) % 149.19/149.46 (define @t118 () (and @t117 (forall @t28 (or (not (tptp.aElementOf0 @t5 @t80)) (and (forall @t31 (or (not (tptp.aElementOf0 @t11 @t80)) (tptp.aElementOf0 @t12 @t80))) (forall @t31 (or @t102 (tptp.aElementOf0 @t56 @t80)))))))) % 149.19/149.46 (define @t119 () (= @t114 @t118)) % 149.19/149.46 (define @t120 () (not (tptp.aElementOf0 @t35 @t101))) % 149.19/149.46 (define @t121 () (not (tptp.aElementOf0 @t36 @t80))) % 149.19/149.46 (define @t122 () (not (forall @t41 (or @t121 @t120 @t91)))) % 149.19/149.46 (define @t123 () (tptp.sdtpldt1 @t80 @t101)) % 149.19/149.46 (define @t124 () (forall @t31 (= (= @t11 @t123) (and @t47 (forall @t45 (= @t43 @t122)))))) % 149.19/149.46 (define @t125 () (not @t110)) % 149.19/149.46 (define @t126 () (not @t117)) % 149.19/149.46 (define @t127 () (or @t126 @t125 @t124)) % 149.19/149.46 (define @t128 () (@list false false false)) % 149.19/149.46 (define @t129 () (forall @t45 (= (tptp.aElementOf0 @t34 @t123) @t122))) % 149.19/149.46 (define @t130 () (and (tptp.aSet0 @t123) @t129)) % 149.19/149.46 (define @t131 () (= (= @t123 @t123) @t130)) % 149.19/149.46 (define @t132 () (not (= @t87 @t37))) % 149.19/149.46 (define @t133 () (or @t121 @t120 @t132)) % 149.19/149.46 (define @t134 () (forall @t41 @t133)) % 149.19/149.46 (define @t135 () (not @t134)) % 149.19/149.46 (define @t136 () (tptp.aElementOf0 @t87 @t123)) % 149.19/149.46 (define @t137 () (= @t136 @t135)) % 149.19/149.46 (define @t138 () (forall @t41 (or @t121 @t120 (not (= @t37 @t87))))) % 149.19/149.46 (define @t139 () (not @t138)) % 149.19/149.46 (define @t140 () (= @t136 @t139)) % 149.19/149.46 (define @t141 () (not @t140)) % 149.19/149.46 (define @t142 () (@list true false)) % 149.19/149.46 (define @t143 () (and (= @t1 @t17) @t16)) % 149.19/149.46 (define @t144 () (tptp.sdtpldt0 tptp.sz00 @t87)) % 149.19/149.46 (define @t145 () (= @t87 @t144)) % 149.19/149.46 (define @t146 () (and (= @t87 (tptp.sdtpldt0 @t87 tptp.sz00)) @t145)) % 149.19/149.46 (define @t147 () (or @t107 @t146)) % 149.19/149.46 (define @t148 () (not @t145)) % 149.19/149.46 (define @t149 () (tptp.aElementOf0 @t87 @t101)) % 149.19/149.46 (define @t150 () (not @t149)) % 149.19/149.46 (define @t151 () (not @t83)) % 149.19/149.46 (define @t152 () (or @t151 @t150 @t148)) % 149.19/149.46 (define @t153 () (not @t152)) % 149.19/149.46 (define @t154 () (not (= @t144 @t87))) % 149.19/149.46 (define @t155 () (or @t151 @t150 @t154)) % 149.19/149.46 (assume @p1 (forall @t3 (=> @t2 true))) % 149.19/149.46 (assume @p2 (tptp.aElement0 tptp.sz00)) % 149.19/149.46 (assume @p3 (tptp.aElement0 tptp.sz10)) % 149.19/149.46 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 149.19/149.46 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 149.19/149.46 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 149.19/149.46 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 149.19/149.46 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 149.19/149.46 (assume @p9 @t20) % 149.19/149.46 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 149.19/149.46 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t21)))) % 149.19/149.46 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 149.19/149.46 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 149.19/149.46 (assume @p14 (forall @t15 (=> @t14 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t10 @t22)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t21 (tptp.sdtasdt0 @t11 @t1))))))) % 149.19/149.46 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t23 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t23)))))) % 149.19/149.46 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 149.19/149.46 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t25 @t24))))) % 149.19/149.46 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 149.19/149.46 (assume @p19 (forall @t3 (=> @t26 true))) % 149.19/149.46 (assume @p20 (forall @t3 (=> @t26 (forall @t28 (=> @t27 @t7))))) % 149.19/149.46 (assume @p21 (forall @t9 (=> @t33 (=> (and (forall @t31 (=> @t29 @t30)) (forall @t31 (=> @t30 @t29))) (= @t1 @t5))))) % 149.19/149.46 (assume @p22 @t54) % 149.19/149.46 (assume @p23 (forall @t9 (=> @t33 (forall @t31 (= (= @t11 @t55) (and @t47 (forall @t45 (= @t43 (and (tptp.aElementOf0 @t34 @t1) (tptp.aElementOf0 @t34 @t5)))))))))) % 149.19/149.46 (assume @p24 @t67) % 149.19/149.46 (assume @p25 (forall @t9 (=> @t68 (tptp.aIdeal0 @t49)))) % 149.19/149.46 (assume @p26 (forall @t9 (=> @t68 (tptp.aIdeal0 @t55)))) % 149.19/149.46 (assume @p27 (forall @t15 (=> (and @t2 @t7 (tptp.aIdeal0 @t11)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t11))))) % 149.19/149.46 (assume @p28 (forall @t9 (=> @t68 (=> (forall @t31 (=> @t13 (tptp.aElementOf0 @t11 @t49))) (forall @t70 (=> (and @t13 @t69) (exists (@list @t36) (and (tptp.aElement0 @t36) (tptp.sdteqdtlpzmzozddtrp0 @t36 @t11 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t36 @t34 @t5))))))))) % 149.19/149.46 (assume @p29 (forall @t3 (=> @t71 true))) % 149.19/149.46 (assume @p30 (forall @t3 (=> (and @t2 @t73) (tptp.aNaturalNumber0 @t72)))) % 149.19/149.46 (assume @p31 (forall @t9 (=> (and @t71 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 149.19/149.46 (assume @p32 (forall @t9 (=> (and @t2 @t7 (not @t24)) (exists @t70 (and @t13 @t69 (= @t1 (tptp.sdtpldt0 @t56 @t34)) (=> (not (= @t34 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t34) (tptp.sbrdtbr0 @t5)))))))) % 149.19/149.46 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t31 (and @t13 (= @t22 @t5))))))) % 149.19/149.46 (assume @p34 (forall @t3 (=> @t2 (forall @t28 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 149.19/149.46 (assume @p35 (forall @t9 (=> @t8 (forall @t31 (= (tptp.aGcdOfAnd0 @t11 @t1 @t5) (and (tptp.aDivisorOf0 @t11 @t1) (tptp.aDivisorOf0 @t11 @t5) (forall @t45 (=> (and (tptp.aDivisorOf0 @t34 @t1) (tptp.aDivisorOf0 @t34 @t5)) (tptp.doDivides0 @t34 @t11))))))))) % 149.19/149.46 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 149.19/149.46 (assume @p37 (forall @t3 (=> @t2 (forall @t28 (= (= @t5 @t74) (and @t32 (forall @t31 (= @t30 (exists @t45 (and @t69 (= (tptp.sdtasdt0 @t1 @t34) @t11))))))))))) % 149.19/149.46 (assume @p38 @t76) % 149.19/149.46 (assume @p39 (and @t78 @t77)) % 149.19/149.46 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 149.19/149.46 (assume @p41 (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb)) % 149.19/149.46 (assume @p42 (and (tptp.aIdeal0 tptp.xI) (= tptp.xI @t81))) % 149.19/149.46 (assume @p43 (and @t83 (tptp.aElementOf0 tptp.xa @t80) (tptp.aElementOf0 tptp.sz00 @t79) @t82)) % 149.19/149.46 (assume @p44 (exists @t3 (and (tptp.aElementOf0 @t1 @t81) @t73))) % 149.19/149.46 (assume @p45 (and (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.xu tptp.sz00)) (forall @t3 (=> (and (tptp.aElementOf0 @t1 tptp.xI) @t73) (not (tptp.iLess0 @t72 @t84)))))) % 149.19/149.46 (assume @p46 (not (and (tptp.aDivisorOf0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xb)))) % 149.19/149.46 (assume @p47 (exists @t9 (and @t2 @t7 (= tptp.xu (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xa @t1) (tptp.sdtasdt0 tptp.xb @t5)))))) % 149.19/149.46 (assume @p48 (not (not (tptp.doDivides0 tptp.xu tptp.xa)))) % 149.19/149.46 (assume @p49 (not (tptp.doDivides0 tptp.xu tptp.xb))) % 149.19/149.46 (assume @p50 (and (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xr) (= tptp.xb @t87) (or @t85 (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) @t84)))) % 149.19/149.46 (assume @p51 (not @t85)) % 149.19/149.46 (assume @p52 (tptp.aElementOf0 (tptp.smndt0 @t86) tptp.xI)) % 149.19/149.46 (assume @p53 @t89) % 149.19/149.46 (assume @p54 true) % 149.19/149.46 (step @p55 :rule aci_norm :args ((= (or (or @t97 @t96) @t95) (or @t97 @t96 @t95)))) % 149.19/149.46 (step @p56 :rule refl :args (@t95)) % 149.19/149.46 (step @p57 :rule bool-and-de-morgan :args (@t26 @t32 true)) % 149.19/149.46 (step @p58 :rule nary_cong :premises (@p57 @p56) :args ((or (not @t33) @t95))) % 149.19/149.46 (step @p59 :rule trans :premises (@p58 @p55)) % 149.19/149.46 (step @p60 :rule bool-impl-elim :args (@t33 @t95)) % 149.19/149.46 (step @p61 :rule trans :premises (@p60 @p59)) % 149.19/149.46 (step @p62 :rule cong :premises (@p61) :args ((forall @t9 (=> @t33 @t95)))) % 149.19/149.46 (step @p63 :rule aci_norm :args ((= (or @t93 (or @t92 @t91)) @t94))) % 149.19/149.46 (step @p64 :rule bool-and-de-morgan :args (@t38 @t90 true)) % 149.19/149.46 (step @p65 :rule refl :args (@t93)) % 149.19/149.46 (step @p66 :rule nary_cong :premises (@p65 @p64) :args ((or @t93 (not (and @t38 @t90))))) % 149.19/149.46 (step @p67 :rule bool-and-de-morgan :args (@t39 @t38 (and @t90))) % 149.19/149.46 (step @p68 :rule trans :premises (@p67 @p66)) % 149.19/149.46 (step @p69 :rule trans :premises (@p68 @p63)) % 149.19/149.46 (step @p70 :rule cong :premises (@p69) :args (@t99)) % 149.19/149.46 (step @p71 :rule cong :premises (@p70) :args (@t100)) % 149.19/149.46 (step @p72 :rule exists-elim :args ((= (exists @t41 @t98) @t100))) % 149.19/149.46 (step @p73 :rule trans :premises (@p72 @p71)) % 149.19/149.46 (step @p74 :rule eq-symm :args (@t37 @t34)) % 149.19/149.46 (step @p75 :rule refl :args (@t38)) % 149.19/149.46 (step @p76 :rule refl :args (@t39)) % 149.19/149.46 (step @p77 :rule nary_cong :premises (@p76 @p75 @p74) :args (@t40)) % 149.19/149.46 (step @p78 :rule cong :premises (@p77) :args (@t42)) % 149.19/149.46 (step @p79 :rule trans :premises (@p78 @p73)) % 149.19/149.46 (step @p80 :rule refl :args (@t43)) % 149.19/149.46 (step @p81 :rule cong :premises (@p80 @p79) :args (@t44)) % 149.19/149.46 (step @p82 :rule cong :premises (@p81) :args (@t46)) % 149.19/149.46 (step @p83 :rule refl :args (@t47)) % 149.19/149.46 (step @p84 :rule nary_cong :premises (@p83 @p82) :args (@t48)) % 149.19/149.46 (step @p85 :rule refl :args (@t50)) % 149.19/149.46 (step @p86 :rule cong :premises (@p85 @p84) :args (@t51)) % 149.19/149.46 (step @p87 :rule cong :premises (@p86) :args (@t52)) % 149.19/149.46 (step @p88 :rule refl :args (@t33)) % 149.19/149.46 (step @p89 :rule cong :premises (@p88 @p87) :args (@t53)) % 149.19/149.46 (step @p90 :rule cong :premises (@p89) :args (@t54)) % 149.19/149.46 (step @p91 :rule trans :premises (@p90 @p62)) % 149.19/149.46 (step @p92 :rule eq_resolve :premises (@p22 @p91)) % 149.19/149.46 (step @p93 :rule instantiate :premises (@p92) :args ((@list @t80 @t101))) % 149.19/149.46 (step @p94 :rule bool-impl-elim :args (@t27 @t103)) % 149.19/149.46 (step @p95 :rule cong :premises (@p94) :args ((forall @t28 (=> @t27 @t103)))) % 149.19/149.46 (step @p96 :rule bool-impl-elim :args (@t13 @t57)) % 149.19/149.46 (step @p97 :rule cong :premises (@p96) :args (@t58)) % 149.19/149.46 (step @p98 :rule bool-impl-elim :args (@t29 @t59)) % 149.19/149.46 (step @p99 :rule cong :premises (@p98) :args (@t60)) % 149.19/149.46 (step @p100 :rule nary_cong :premises (@p99 @p97) :args (@t61)) % 149.19/149.46 (step @p101 :rule refl :args (@t27)) % 149.19/149.46 (step @p102 :rule cong :premises (@p101 @p100) :args (@t62)) % 149.19/149.46 (step @p103 :rule cong :premises (@p102) :args (@t63)) % 149.19/149.46 (step @p104 :rule trans :premises (@p103 @p95)) % 149.19/149.46 (step @p105 :rule refl :args (@t26)) % 149.19/149.46 (step @p106 :rule nary_cong :premises (@p105 @p104) :args (@t64)) % 149.19/149.46 (step @p107 :rule refl :args (@t65)) % 149.19/149.46 (step @p108 :rule cong :premises (@p107 @p106) :args (@t66)) % 149.19/149.46 (step @p109 :rule cong :premises (@p108) :args (@t67)) % 149.19/149.46 (step @p110 :rule eq_resolve :premises (@p24 @p109)) % 149.19/149.46 (step @p111 :rule instantiate :premises (@p110) :args ((@list @t101))) % 149.19/149.46 (step @p112 :rule bool-impl-elim :args (@t2 @t75)) % 149.19/149.46 (step @p113 :rule cong :premises (@p112) :args (@t76)) % 149.19/149.46 (step @p114 :rule eq_resolve :premises (@p38 @p113)) % 149.19/149.46 (step @p115 :rule instantiate :premises (@p114) :args (@t104)) % 149.19/149.46 (step @p116 :rule and_elim :premises (@p50) :args (2)) % 149.19/149.46 (step @p117 :rule cong :premises (@p116) :args (@t77)) % 149.19/149.46 (step @p118 :rule and_elim :premises (@p39) :args (1)) % 149.19/149.46 (step @p119 :rule eq_resolve :premises (@p118 @p117)) % 149.19/149.46 (step @p120 :rule cnf_or_pos :args (@t108)) % 149.19/149.46 (step @p121 :rule reordering :premises (@p120) :args ((or @t107 @t105 (not @t108)))) % 149.19/149.46 (step @p122 :rule chain_m_resolution :premises (@p121 @p119 @p115) :args (@t105 @t109 (@list @t106 @t108))) % 149.19/149.46 (step @p123 :rule cnf_equiv_pos1 :args (@t112)) % 149.19/149.46 (step @p124 :rule reordering :premises (@p123) :args ((or (not @t105) @t111 (not @t112)))) % 149.19/149.46 (step @p125 :rule chain_m_resolution :premises (@p124 @p122 @p111) :args (@t111 @t109 (@list @t105 @t112))) % 149.19/149.46 (step @p126 :rule cnf_and_pos :args (@t111 0)) % 149.19/149.46 (step @p127 :rule reordering :premises (@p126) :args ((or @t110 (not @t111)))) % 149.19/149.46 (step @p128 :rule chain_m_resolution :premises (@p127 @p125) :args (@t110 @t113 (@list @t111))) % 149.19/149.46 (step @p129 :rule instantiate :premises (@p110) :args ((@list @t80))) % 149.19/149.46 (step @p130 :rule instantiate :premises (@p114) :args ((@list tptp.xa))) % 149.19/149.46 (step @p131 :rule and_elim :premises (@p39) :args (0)) % 149.19/149.46 (step @p132 :rule cnf_or_pos :args (@t116)) % 149.19/149.46 (step @p133 :rule reordering :premises (@p132) :args ((or @t115 @t114 (not @t116)))) % 149.19/149.46 (step @p134 :rule chain_m_resolution :premises (@p133 @p131 @p130) :args (@t114 @t109 (@list @t78 @t116))) % 149.19/149.46 (step @p135 :rule cnf_equiv_pos1 :args (@t119)) % 149.19/149.46 (step @p136 :rule reordering :premises (@p135) :args ((or (not @t114) @t118 (not @t119)))) % 149.19/149.46 (step @p137 :rule chain_m_resolution :premises (@p136 @p134 @p129) :args (@t118 @t109 (@list @t114 @t119))) % 149.19/149.46 (step @p138 :rule cnf_and_pos :args (@t118 0)) % 149.19/149.46 (step @p139 :rule reordering :premises (@p138) :args ((or @t117 (not @t118)))) % 149.19/149.46 (step @p140 :rule chain_m_resolution :premises (@p139 @p137) :args (@t117 @t113 (@list @t118))) % 149.19/149.46 (step @p141 :rule cnf_or_pos :args (@t127)) % 149.19/149.46 (step @p142 :rule reordering :premises (@p141) :args ((or @t126 @t125 @t124 (not @t127)))) % 149.19/149.46 (step @p143 :rule chain_m_resolution :premises (@p142 @p140 @p128 @p93) :args (@t124 @t128 (@list @t117 @t110 @t127))) % 149.19/149.46 (step @p144 :rule bool-eq-true :args (@t130)) % 149.19/149.46 (step @p145 :rule eq-symm :args (true @t130)) % 149.19/149.46 (step @p146 :rule trans :premises (@p145 @p144)) % 149.19/149.46 (step @p147 :rule refl :args (@t130)) % 149.19/149.46 (step @p148 :rule eq-refl :args (@t123)) % 149.19/149.46 (step @p149 :rule cong :premises (@p148 @p147) :args (@t131)) % 149.19/149.46 (step @p150 :rule trans :premises (@p149 @p146)) % 149.19/149.46 (step @p151 :rule refl :args (@t124)) % 149.19/149.46 (step @p152 :rule cong :premises (@p151 @p150) :args ((=> @t124 @t131))) % 149.19/149.46 (assume-push @p234 @t124) % 149.19/149.46 (step @p154 :rule instantiate :premises (@p143) :args ((@list @t123))) % 149.19/149.46 (step-pop @p235 :rule scope :premises (@p154)) % 149.19/149.46 (step @p155 :rule process_scope :premises (@p235) :args (@t131)) % 149.19/149.46 (step @p157 :rule eq_resolve :premises (@p155 @p152)) % 149.19/149.46 (step @p158 :rule implies_elim :premises (@p157)) % 149.19/149.46 (step @p159 :rule chain_m_resolution :premises (@p158 @p143) :args (@t130 @t113 (@list @t124))) % 149.19/149.46 (step @p160 :rule cnf_and_pos :args (@t130 1)) % 149.19/149.46 (step @p161 :rule reordering :premises (@p160) :args ((or @t129 (not @t130)))) % 149.19/149.46 (step @p162 :rule chain_m_resolution :premises (@p161 @p159) :args (@t129 @t113 (@list @t130))) % 149.19/149.46 (step @p163 :rule eq-symm :args (@t87 @t37)) % 149.19/149.46 (step @p164 :rule cong :premises (@p163) :args (@t132)) % 149.19/149.46 (step @p165 :rule refl :args (@t120)) % 149.19/149.46 (step @p166 :rule refl :args (@t121)) % 149.19/149.46 (step @p167 :rule nary_cong :premises (@p166 @p165 @p164) :args (@t133)) % 149.19/149.46 (step @p168 :rule cong :premises (@p167) :args (@t134)) % 149.19/149.46 (step @p169 :rule cong :premises (@p168) :args (@t135)) % 149.19/149.46 (step @p170 :rule refl :args (@t136)) % 149.19/149.46 (step @p171 :rule cong :premises (@p170 @p169) :args (@t137)) % 149.19/149.46 (step @p172 :rule refl :args (@t129)) % 149.19/149.46 (step @p173 :rule cong :premises (@p172 @p171) :args ((=> @t129 @t137))) % 149.19/149.46 (assume-push @p236 @t129) % 149.19/149.46 (step @p175 :rule instantiate :premises (@p162) :args (@t104)) % 149.19/149.47 (step-pop @p237 :rule scope :premises (@p175)) % 149.19/149.47 (step @p176 :rule process_scope :premises (@p237) :args (@t137)) % 149.19/149.47 (step @p178 :rule eq_resolve :premises (@p176 @p173)) % 149.19/149.47 (step @p179 :rule implies_elim :premises (@p178)) % 149.19/149.47 (step @p180 :rule chain_m_resolution :premises (@p179 @p162) :args (@t140 @t113 (@list @t129))) % 149.19/149.47 (step @p181 :rule cong :premises (@p116) :args (@t79)) % 149.19/149.47 (step @p182 :rule refl :args (@t80)) % 149.19/149.47 (step @p183 :rule cong :premises (@p182 @p181) :args (@t81)) % 149.19/149.47 (step @p184 :rule and_elim :premises (@p42) :args (1)) % 149.19/149.47 (step @p185 :rule trans :premises (@p184 @p183)) % 149.19/149.47 (step @p186 :rule cong :premises (@p116 @p185) :args (@t88)) % 149.19/149.47 (step @p187 :rule cong :premises (@p186) :args (@t89)) % 149.19/149.47 (step @p188 :rule eq_resolve :premises (@p53 @p187)) % 149.19/149.47 (step @p189 :rule bool-double-not-elim :args (@t138)) % 149.19/149.47 (step @p190 :rule refl :args (@t141)) % 149.19/149.47 (step @p191 :rule nary_cong :premises (@p190 @p170 @p189) :args ((or @t141 @t136 (not @t139)))) % 149.19/149.47 (step @p192 :rule cnf_equiv_pos2 :args (@t140)) % 149.19/149.47 (step @p193 :rule eq_resolve :premises (@p192 @p191)) % 149.19/149.47 (step @p194 :rule reordering :premises (@p193) :args ((or @t136 @t138 @t141))) % 149.19/149.47 (step @p195 :rule chain_m_resolution :premises (@p194 @p188 @p180) :args (@t138 @t142 (@list @t136 @t140))) % 149.19/149.47 (step @p196 :rule bool-impl-elim :args (@t2 @t143)) % 149.19/149.47 (step @p197 :rule cong :premises (@p196) :args ((forall @t3 (=> @t2 @t143)))) % 149.19/149.47 (step @p198 :rule refl :args (@t16)) % 149.19/149.47 (step @p199 :rule eq-symm :args (@t17 @t1)) % 149.19/149.47 (step @p200 :rule nary_cong :premises (@p199 @p198) :args (@t18)) % 149.19/149.47 (step @p201 :rule refl :args (@t2)) % 149.19/149.47 (step @p202 :rule cong :premises (@p201 @p200) :args (@t19)) % 149.19/149.47 (step @p203 :rule cong :premises (@p202) :args (@t20)) % 149.19/149.47 (step @p204 :rule trans :premises (@p203 @p197)) % 149.19/149.47 (step @p205 :rule eq_resolve :premises (@p9 @p204)) % 149.19/149.47 (step @p206 :rule instantiate :premises (@p205) :args (@t104)) % 149.19/149.47 (step @p207 :rule cnf_or_pos :args (@t147)) % 149.19/149.47 (step @p208 :rule reordering :premises (@p207) :args ((or @t107 @t146 (not @t147)))) % 149.19/149.47 (step @p209 :rule chain_m_resolution :premises (@p208 @p119 @p206) :args (@t146 @t109 (@list @t106 @t147))) % 149.19/149.47 (step @p210 :rule cnf_and_pos :args (@t146 1)) % 149.19/149.47 (step @p211 :rule reordering :premises (@p210) :args ((or @t145 (not @t146)))) % 149.19/149.47 (step @p212 :rule chain_m_resolution :premises (@p211 @p209) :args (@t145 @t113 (@list @t146))) % 149.19/149.47 (step @p213 :rule cong :premises (@p116 @p181) :args (@t82)) % 149.19/149.47 (step @p214 :rule and_elim :premises (@p43) :args (3)) % 149.19/149.47 (step @p215 :rule eq_resolve :premises (@p214 @p213)) % 149.19/149.47 (step @p216 :rule and_elim :premises (@p43) :args (0)) % 149.19/149.47 (step @p217 :rule cnf_or_pos :args (@t152)) % 149.19/149.47 (step @p218 :rule reordering :premises (@p217) :args ((or @t151 @t150 @t148 @t153))) % 149.19/149.47 (step @p219 :rule chain_m_resolution :premises (@p218 @p216 @p215 @p212) :args (@t153 @t128 (@list @t83 @t149 @t145))) % 149.19/149.47 (step @p220 :rule eq-symm :args (@t144 @t87)) % 149.19/149.47 (step @p221 :rule cong :premises (@p220) :args (@t154)) % 149.19/149.47 (step @p222 :rule refl :args (@t150)) % 149.19/149.47 (step @p223 :rule refl :args (@t151)) % 149.19/149.47 (step @p224 :rule nary_cong :premises (@p223 @p222 @p221) :args (@t155)) % 149.19/149.47 (step @p225 :rule refl :args (@t138)) % 149.19/149.47 (step @p226 :rule cong :premises (@p225 @p224) :args ((=> @t138 @t155))) % 149.19/149.47 (assume-push @p238 @t138) % 149.19/149.47 (step @p228 :rule instantiate :premises (@p195) :args ((@list tptp.sz00 @t87))) % 149.19/149.47 (step-pop @p239 :rule scope :premises (@p228)) % 149.19/149.47 (step @p229 :rule process_scope :premises (@p239) :args (@t155)) % 149.19/149.47 (step @p231 :rule eq_resolve :premises (@p229 @p226)) % 149.19/149.47 (step @p232 :rule implies_elim :premises (@p231)) % 149.19/149.47 (step @p233 false :rule chain_m_resolution :premises (@p232 @p219 @p195) :args (false @t142 (@list @t152 @t138))) % 149.19/149.47 ) % 149.19/149.47 % SZS output end Proof % 149.19/149.47 % cvc5 exiting %------------------------------------------------------------------------------