%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG122+4 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n002.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 33.96s 34.24s % Output : Proof 33.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG122+4 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n002.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 14:09:03 EDT 2026 % 0.15/0.34 % CPUTime : % 0.27/0.50 %----Proving TF0_NAR, FOF, or CNF % 33.96/34.24 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 33.96/34.24 --- Run --no-e-matching --full-saturate-quant at 6... % 33.96/34.24 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 33.96/34.24 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 33.96/34.24 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 33.96/34.24 % SZS status Theorem % 33.96/34.24 % SZS output start Proof % 33.96/34.24 ( % 33.96/34.24 (declare-sort $$unsorted 0) % 33.96/34.24 (declare-const tptp.xu $$unsorted) % 33.96/34.24 (declare-const tptp.xr $$unsorted) % 33.96/34.24 (declare-const tptp.xI $$unsorted) % 33.96/34.24 (declare-const tptp.xc $$unsorted) % 33.96/34.24 (declare-const tptp.xa $$unsorted) % 33.96/34.24 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 33.96/34.24 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 33.96/34.24 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 33.96/34.24 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 33.96/34.24 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 33.96/34.24 (declare-const tptp.sz00 $$unsorted) % 33.96/34.24 (declare-const tptp.xq $$unsorted) % 33.96/34.24 (declare-const tptp.sz10 $$unsorted) % 33.96/34.24 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 33.96/34.24 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 33.96/34.24 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 33.96/34.24 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 33.96/34.24 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 33.96/34.24 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 33.96/34.24 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 33.96/34.24 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 33.96/34.24 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 33.96/34.24 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 33.96/34.24 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 33.96/34.24 (declare-const tptp.xb $$unsorted) % 33.96/34.24 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 33.96/34.24 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 33.96/34.24 (define @t1 () (@var "W0" $$unsorted)) % 33.96/34.24 (define @t2 () (tptp.aElement0 @t1)) % 33.96/34.24 (define @t3 () (@list @t1)) % 33.96/34.24 (define @t4 () (tptp.smndt0 @t1)) % 33.96/34.24 (define @t5 () (@var "W1" $$unsorted)) % 33.96/34.24 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 33.96/34.24 (define @t7 () (tptp.aElement0 @t5)) % 33.96/34.24 (define @t8 () (and @t2 @t7)) % 33.96/34.24 (define @t9 () (@list @t1 @t5)) % 33.96/34.24 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 33.96/34.24 (define @t11 () (tptp.aElement0 @t10)) % 33.96/34.24 (define @t12 () (forall @t9 (=> @t8 @t11))) % 33.96/34.24 (define @t13 () (@var "W2" $$unsorted)) % 33.96/34.24 (define @t14 () (tptp.sdtpldt0 @t5 @t13)) % 33.96/34.24 (define @t15 () (= (tptp.sdtpldt0 @t6 @t13) (tptp.sdtpldt0 @t1 @t14))) % 33.96/34.24 (define @t16 () (tptp.aElement0 @t13)) % 33.96/34.24 (define @t17 () (and @t2 @t7 @t16)) % 33.96/34.24 (define @t18 () (@list @t1 @t5 @t13)) % 33.96/34.24 (define @t19 () (forall @t18 (=> @t17 @t15))) % 33.96/34.24 (define @t20 () (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1))) % 33.96/34.24 (define @t21 () (tptp.sdtpldt0 @t1 tptp.sz00)) % 33.96/34.24 (define @t22 () (and (= @t21 @t1) @t20)) % 33.96/34.24 (define @t23 () (=> @t2 @t22)) % 33.96/34.24 (define @t24 () (forall @t3 @t23)) % 33.96/34.24 (define @t25 () (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1))) % 33.96/34.24 (define @t26 () (tptp.sdtpldt0 @t1 @t4)) % 33.96/34.24 (define @t27 () (and (= @t26 tptp.sz00) @t25)) % 33.96/34.24 (define @t28 () (=> @t2 @t27)) % 33.96/34.24 (define @t29 () (forall @t3 @t28)) % 33.96/34.24 (define @t30 () (tptp.sdtasdt0 @t5 @t1)) % 33.96/34.24 (define @t31 () (tptp.sdtasdt0 @t1 @t13)) % 33.96/34.24 (define @t32 () (tptp.smndt0 tptp.sz10)) % 33.96/34.24 (define @t33 () (= @t5 tptp.sz00)) % 33.96/34.24 (define @t34 () (= @t1 tptp.sz00)) % 33.96/34.24 (define @t35 () (tptp.aSet0 @t1)) % 33.96/34.24 (define @t36 () (tptp.aElementOf0 @t5 @t1)) % 33.96/34.24 (define @t37 () (@list @t5)) % 33.96/34.24 (define @t38 () (forall @t37 (=> @t36 @t7))) % 33.96/34.24 (define @t39 () (=> @t35 @t38)) % 33.96/34.24 (define @t40 () (forall @t3 @t39)) % 33.96/34.24 (define @t41 () (tptp.aElementOf0 @t13 @t1)) % 33.96/34.24 (define @t42 () (tptp.aElementOf0 @t13 @t5)) % 33.96/34.24 (define @t43 () (@list @t13)) % 33.96/34.24 (define @t44 () (tptp.aSet0 @t5)) % 33.96/34.24 (define @t45 () (and @t35 @t44)) % 33.96/34.24 (define @t46 () (@var "W3" $$unsorted)) % 33.96/34.24 (define @t47 () (@var "W5" $$unsorted)) % 33.96/34.24 (define @t48 () (@var "W4" $$unsorted)) % 33.96/34.24 (define @t49 () (tptp.aElementOf0 @t46 @t13)) % 33.96/34.24 (define @t50 () (@list @t46)) % 33.96/34.24 (define @t51 () (tptp.aSet0 @t13)) % 33.96/34.24 (define @t52 () (tptp.sdtpldt1 @t1 @t5)) % 33.96/34.24 (define @t53 () (tptp.sdtasasdt0 @t1 @t5)) % 33.96/34.24 (define @t54 () (tptp.sdtasdt0 @t13 @t5)) % 33.96/34.24 (define @t55 () (tptp.aIdeal0 @t1)) % 33.96/34.24 (define @t56 () (and @t55 (tptp.aIdeal0 @t5))) % 33.96/34.24 (define @t57 () (tptp.aElement0 @t46)) % 33.96/34.24 (define @t58 () (@list @t13 @t46)) % 33.96/34.24 (define @t59 () (tptp.aNaturalNumber0 @t1)) % 33.96/34.24 (define @t60 () (tptp.sbrdtbr0 @t1)) % 33.96/34.24 (define @t61 () (not @t34)) % 33.96/34.24 (define @t62 () (tptp.slsdtgt0 @t1)) % 33.96/34.24 (define @t63 () (tptp.sdtasdt0 tptp.xc @t1)) % 33.96/34.24 (define @t64 () (tptp.aElement0 tptp.xc)) % 33.96/34.24 (define @t65 () (tptp.slsdtgt0 tptp.xb)) % 33.96/34.24 (define @t66 () (tptp.slsdtgt0 tptp.xa)) % 33.96/34.24 (define @t67 () (tptp.sdtpldt1 @t66 @t65)) % 33.96/34.24 (define @t68 () (tptp.aElementOf0 @t5 @t66)) % 33.96/34.24 (define @t69 () (exists (@list @t5 @t13) (and @t68 (tptp.aElementOf0 @t13 @t65) (= @t14 @t1)))) % 33.96/34.24 (define @t70 () (tptp.aElementOf0 @t1 tptp.xI)) % 33.96/34.24 (define @t71 () (tptp.sdtasdt0 tptp.xb @t5)) % 33.96/34.24 (define @t72 () (tptp.aElementOf0 @t1 @t66)) % 33.96/34.24 (define @t73 () (tptp.aSet0 tptp.xI)) % 33.96/34.24 (define @t74 () (tptp.sdtasdt0 tptp.xb @t1)) % 33.96/34.24 (define @t75 () (tptp.sdtasdt0 tptp.xa @t1)) % 33.96/34.24 (define @t76 () (tptp.aElementOf0 @t5 @t65)) % 33.96/34.24 (define @t77 () (tptp.sbrdtbr0 tptp.xu)) % 33.96/34.24 (define @t78 () (tptp.aElementOf0 tptp.xu tptp.xI)) % 33.96/34.24 (define @t79 () (tptp.doDivides0 tptp.xu tptp.xb)) % 33.96/34.24 (define @t80 () (tptp.sdtasdt0 tptp.xu @t1)) % 33.96/34.24 (define @t81 () (exists @t3 (and @t2 (= @t80 tptp.xb)))) % 33.96/34.24 (define @t82 () (tptp.doDivides0 tptp.xu tptp.xa)) % 33.96/34.24 (define @t83 () (exists @t3 (and @t2 (= @t80 tptp.xa)))) % 33.96/34.24 (define @t84 () (= tptp.xr tptp.sz00)) % 33.96/34.24 (define @t85 () (tptp.sdtasdt0 tptp.xq tptp.xu)) % 33.96/34.24 (define @t86 () (tptp.sdtpldt0 @t85 tptp.xr)) % 33.96/34.24 (define @t87 () (tptp.aElement0 tptp.xr)) % 33.96/34.24 (define @t88 () (tptp.aElement0 tptp.xq)) % 33.96/34.24 (define @t89 () (tptp.smndt0 @t85)) % 33.96/34.24 (define @t90 () (tptp.aElementOf0 @t89 tptp.xI)) % 33.96/34.24 (define @t91 () (exists @t9 (and @t72 @t76 (= @t6 tptp.xb)))) % 33.96/34.24 (define @t92 () (tptp.sdtpldt0 @t89 tptp.xb)) % 33.96/34.24 (define @t93 () (= tptp.xr @t92)) % 33.96/34.24 (define @t94 () (not @t93)) % 33.96/34.24 (define @t95 () (and (= @t1 @t21) @t20)) % 33.96/34.24 (define @t96 () (tptp.sdtpldt0 tptp.sz00 tptp.xr)) % 33.96/34.24 (define @t97 () (= tptp.xr @t96)) % 33.96/34.24 (define @t98 () (and (= tptp.xr (tptp.sdtpldt0 tptp.xr tptp.sz00)) @t97)) % 33.96/34.24 (define @t99 () (not @t87)) % 33.96/34.24 (define @t100 () (or @t99 @t98)) % 33.96/34.24 (define @t101 () (@list false false)) % 33.96/34.24 (define @t102 () (@list false)) % 33.96/34.24 (define @t103 () (not @t16)) % 33.96/34.25 (define @t104 () (not @t7)) % 33.96/34.25 (define @t105 () (not @t2)) % 33.96/34.25 (define @t106 () (or @t105 @t104 @t103 @t15)) % 33.96/34.25 (define @t107 () (or @t105 @t104 @t103)) % 33.96/34.25 (define @t108 () (tptp.sdtpldt0 @t89 @t85)) % 33.96/34.25 (define @t109 () (tptp.sdtpldt0 @t108 tptp.xr)) % 33.96/34.25 (define @t110 () (tptp.sdtpldt0 @t89 @t86)) % 33.96/34.25 (define @t111 () (tptp.aElement0 @t85)) % 33.96/34.25 (define @t112 () (not @t111)) % 33.96/34.25 (define @t113 () (tptp.aElement0 @t89)) % 33.96/34.25 (define @t114 () (not @t113)) % 33.96/34.25 (define @t115 () (or @t114 @t112 @t99 (= @t109 @t110))) % 33.96/34.25 (define @t116 () (forall @t18 @t106)) % 33.96/34.25 (define @t117 () (= @t110 @t109)) % 33.96/34.25 (define @t118 () (or @t114 @t112 @t99 @t117)) % 33.96/34.25 (define @t119 () (@var "BOUND_VARIABLE_8007" $$unsorted)) % 33.96/34.25 (define @t120 () (tptp.aElement0 @t119)) % 33.96/34.25 (define @t121 () (not (tptp.aElementOf0 @t119 @t1))) % 33.96/34.25 (define @t122 () (not @t35)) % 33.96/34.25 (define @t123 () (or @t121 @t120)) % 33.96/34.25 (define @t124 () (or @t122 @t123)) % 33.96/34.25 (define @t125 () (forall (@list @t1 @t119) @t124)) % 33.96/34.25 (define @t126 () (@list @t119)) % 33.96/34.25 (define @t127 () (forall @t126 @t124)) % 33.96/34.25 (define @t128 () (forall @t126 @t123)) % 33.96/34.25 (define @t129 () (or @t122 @t128)) % 33.96/34.25 (define @t130 () (forall @t37 (or (not @t36) @t7))) % 33.96/34.25 (define @t131 () (tptp.sdtpldt1 @t66 (tptp.slsdtgt0 @t86))) % 33.96/34.25 (define @t132 () (tptp.aElementOf0 @t89 @t131)) % 33.96/34.25 (define @t133 () (not @t132)) % 33.96/34.25 (define @t134 () (tptp.aSet0 @t131)) % 33.96/34.25 (define @t135 () (not @t134)) % 33.96/34.25 (define @t136 () (or @t135 @t133 @t113)) % 33.96/34.25 (define @t137 () (@list false false false)) % 33.96/34.25 (define @t138 () (tptp.aElement0 tptp.xu)) % 33.96/34.25 (define @t139 () (tptp.aElementOf0 tptp.xu @t131)) % 33.96/34.25 (define @t140 () (not @t139)) % 33.96/34.25 (define @t141 () (or @t135 @t140 @t138)) % 33.96/34.25 (define @t142 () (not @t138)) % 33.96/34.25 (define @t143 () (not @t88)) % 33.96/34.25 (define @t144 () (or @t143 @t142 @t111)) % 33.96/34.25 (define @t145 () (and (= tptp.sz00 @t26) @t25)) % 33.96/34.25 (define @t146 () (= tptp.sz00 @t108)) % 33.96/34.25 (define @t147 () (and (= tptp.sz00 (tptp.sdtpldt0 @t85 @t89)) @t146)) % 33.96/34.25 (define @t148 () (or @t112 @t147)) % 33.96/34.25 (define @t149 () (= tptp.xr @t110)) % 33.96/34.25 (define @t150 () (and @t117 @t97 @t146)) % 33.96/34.25 (assume @p1 (forall @t3 (=> @t2 true))) % 33.96/34.25 (assume @p2 (tptp.aElement0 tptp.sz00)) % 33.96/34.25 (assume @p3 (tptp.aElement0 tptp.sz10)) % 33.96/34.25 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 33.96/34.25 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 33.96/34.25 (assume @p6 @t12) % 33.96/34.25 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 33.96/34.25 (assume @p8 @t19) % 33.96/34.25 (assume @p9 @t24) % 33.96/34.25 (assume @p10 @t29) % 33.96/34.25 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t30)))) % 33.96/34.25 (assume @p12 (forall @t18 (=> @t17 (= (tptp.sdtasdt0 @t10 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t13)))))) % 33.96/34.25 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 33.96/34.25 (assume @p14 (forall @t18 (=> @t17 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t10 @t31)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t30 (tptp.sdtasdt0 @t13 @t1))))))) % 33.96/34.25 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t32 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t32)))))) % 33.96/34.25 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 33.96/34.25 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t34 @t33))))) % 33.96/34.25 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 33.96/34.25 (assume @p19 (forall @t3 (=> @t35 true))) % 33.96/34.25 (assume @p20 @t40) % 33.96/34.25 (assume @p21 (forall @t9 (=> @t45 (=> (and (forall @t43 (=> @t41 @t42)) (forall @t43 (=> @t42 @t41))) (= @t1 @t5))))) % 33.96/34.25 (assume @p22 (forall @t9 (=> @t45 (forall @t43 (= (= @t13 @t52) (and @t51 (forall @t50 (= @t49 (exists (@list @t48 @t47) (and (tptp.aElementOf0 @t48 @t1) (tptp.aElementOf0 @t47 @t5) (= (tptp.sdtpldt0 @t48 @t47) @t46))))))))))) % 33.96/34.25 (assume @p23 (forall @t9 (=> @t45 (forall @t43 (= (= @t13 @t53) (and @t51 (forall @t50 (= @t49 (and (tptp.aElementOf0 @t46 @t1) (tptp.aElementOf0 @t46 @t5)))))))))) % 33.96/34.25 (assume @p24 (forall @t3 (= @t55 (and @t35 (forall @t37 (=> @t36 (and (forall @t43 (=> @t41 (tptp.aElementOf0 @t14 @t1))) (forall @t43 (=> @t16 (tptp.aElementOf0 @t54 @t1)))))))))) % 33.96/34.25 (assume @p25 (forall @t9 (=> @t56 (tptp.aIdeal0 @t52)))) % 33.96/34.25 (assume @p26 (forall @t9 (=> @t56 (tptp.aIdeal0 @t53)))) % 33.96/34.25 (assume @p27 (forall @t18 (=> (and @t2 @t7 (tptp.aIdeal0 @t13)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t13) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t13))))) % 33.96/34.25 (assume @p28 (forall @t9 (=> @t56 (=> (forall @t43 (=> @t16 (tptp.aElementOf0 @t13 @t52))) (forall @t58 (=> (and @t16 @t57) (exists (@list @t48) (and (tptp.aElement0 @t48) (tptp.sdteqdtlpzmzozddtrp0 @t48 @t13 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t48 @t46 @t5))))))))) % 33.96/34.25 (assume @p29 (forall @t3 (=> @t59 true))) % 33.96/34.25 (assume @p30 (forall @t3 (=> (and @t2 @t61) (tptp.aNaturalNumber0 @t60)))) % 33.96/34.25 (assume @p31 (forall @t9 (=> (and @t59 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 33.96/34.25 (assume @p32 (forall @t9 (=> (and @t2 @t7 (not @t33)) (exists @t58 (and @t16 @t57 (= @t1 (tptp.sdtpldt0 @t54 @t46)) (=> (not (= @t46 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t46) (tptp.sbrdtbr0 @t5)))))))) % 33.96/34.25 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t43 (and @t16 (= @t31 @t5))))))) % 33.96/34.25 (assume @p34 (forall @t3 (=> @t2 (forall @t37 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 33.96/34.25 (assume @p35 (forall @t9 (=> @t8 (forall @t43 (= (tptp.aGcdOfAnd0 @t13 @t1 @t5) (and (tptp.aDivisorOf0 @t13 @t1) (tptp.aDivisorOf0 @t13 @t5) (forall @t50 (=> (and (tptp.aDivisorOf0 @t46 @t1) (tptp.aDivisorOf0 @t46 @t5)) (tptp.doDivides0 @t46 @t13))))))))) % 33.96/34.25 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 33.96/34.25 (assume @p37 (forall @t3 (=> @t2 (forall @t37 (= (= @t5 @t62) (and @t44 (forall @t43 (= @t42 (exists @t50 (and @t57 (= (tptp.sdtasdt0 @t1 @t46) @t13))))))))))) % 33.96/34.25 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t62)))) % 33.96/34.25 (assume @p39 (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb))) % 33.96/34.25 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 33.96/34.25 (assume @p41 (and @t64 (exists @t3 (and @t2 (= @t63 tptp.xa))) (tptp.doDivides0 tptp.xc tptp.xa) (tptp.aDivisorOf0 tptp.xc tptp.xa) @t64 (exists @t3 (and @t2 (= @t63 tptp.xb))) (tptp.doDivides0 tptp.xc tptp.xb) (tptp.aDivisorOf0 tptp.xc tptp.xb) (forall @t3 (=> (and (or (and @t2 (or (exists @t37 (and @t7 (= @t10 tptp.xa))) (tptp.doDivides0 @t1 tptp.xa))) (tptp.aDivisorOf0 @t1 tptp.xa)) (or (exists @t37 (and @t7 (= @t10 tptp.xb))) (tptp.doDivides0 @t1 tptp.xb) (tptp.aDivisorOf0 @t1 tptp.xb))) (and (exists @t37 (and @t7 (= @t10 tptp.xc))) (tptp.doDivides0 @t1 tptp.xc)))) (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb))) % 33.96/34.25 (assume @p42 (and @t73 (forall @t3 (=> @t70 (and (forall @t37 (=> (tptp.aElementOf0 @t5 tptp.xI) (tptp.aElementOf0 @t6 tptp.xI))) (forall @t37 (=> @t7 (tptp.aElementOf0 @t30 tptp.xI)))))) (tptp.aIdeal0 tptp.xI) (forall @t3 (= @t72 (exists @t37 (and @t7 (= (tptp.sdtasdt0 tptp.xa @t5) @t1))))) (forall @t3 (= (tptp.aElementOf0 @t1 @t65) (exists @t37 (and @t7 (= @t71 @t1))))) (forall @t3 (= @t70 @t69)) (= tptp.xI @t67))) % 33.96/34.25 (assume @p43 (and (exists @t3 (and @t2 (= @t75 tptp.sz00))) (tptp.aElementOf0 tptp.sz00 @t66) (exists @t3 (and @t2 (= @t75 tptp.xa))) (tptp.aElementOf0 tptp.xa @t66) (exists @t3 (and @t2 (= @t74 tptp.sz00))) (tptp.aElementOf0 tptp.sz00 @t65) (exists @t3 (and @t2 (= @t74 tptp.xb))) (tptp.aElementOf0 tptp.xb @t65))) % 33.96/34.25 (assume @p44 (exists @t3 (and (forall @t37 (= @t68 (exists @t43 (and @t16 (= (tptp.sdtasdt0 tptp.xa @t13) @t5))))) (forall @t37 (= @t76 (exists @t43 (and @t16 (= (tptp.sdtasdt0 tptp.xb @t13) @t5))))) @t69 (tptp.aElementOf0 @t1 @t67) @t61))) % 33.96/34.25 (assume @p45 (and (exists @t9 (and @t72 @t76 (= @t6 tptp.xu))) @t78 (not (= tptp.xu tptp.sz00)) (forall @t3 (=> (and (or @t69 @t70) @t61) (not (tptp.iLess0 @t60 @t77)))))) % 33.96/34.25 (assume @p46 (not (and (or @t83 @t82 (tptp.aDivisorOf0 tptp.xu tptp.xa)) (or @t81 @t79 (tptp.aDivisorOf0 tptp.xu tptp.xb))))) % 33.96/34.25 (assume @p47 (exists @t9 (and @t2 @t7 (= tptp.xu (tptp.sdtpldt0 @t75 @t71))))) % 33.96/34.25 (assume @p48 (not (not (and @t83 @t82)))) % 33.96/34.25 (assume @p49 (not (or @t81 @t79))) % 33.96/34.25 (assume @p50 (and @t88 @t87 (= tptp.xb @t86) (or @t84 (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) @t77)))) % 33.96/34.25 (assume @p51 (not @t84)) % 33.96/34.25 (assume @p52 (and (exists @t9 (and @t72 @t76 (= @t6 @t89))) @t90)) % 33.96/34.25 (assume @p53 (and @t91 @t91 (tptp.aElementOf0 tptp.xb tptp.xI))) % 33.96/34.25 (assume @p54 @t94) % 33.96/34.25 (assume @p55 true) % 33.96/34.25 (step @p56 :rule and_elim :premises (@p50) :args (2)) % 33.96/34.25 (step @p57 :rule refl :args (@t89)) % 33.96/34.25 (step @p58 :rule cong :premises (@p57 @p56) :args (@t92)) % 33.96/34.25 (step @p59 :rule refl :args (tptp.xr)) % 33.96/34.25 (step @p60 :rule cong :premises (@p59 @p58) :args (@t93)) % 33.96/34.25 (step @p61 :rule cong :premises (@p60) :args (@t94)) % 33.96/34.25 (step @p62 :rule eq_resolve :premises (@p54 @p61)) % 33.96/34.25 (step @p63 :rule bool-impl-elim :args (@t2 @t95)) % 33.96/34.25 (step @p64 :rule cong :premises (@p63) :args ((forall @t3 (=> @t2 @t95)))) % 33.96/34.25 (step @p65 :rule refl :args (@t20)) % 33.96/34.25 (step @p66 :rule eq-symm :args (@t21 @t1)) % 33.96/34.25 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t22)) % 33.96/34.25 (step @p68 :rule refl :args (@t2)) % 33.96/34.25 (step @p69 :rule cong :premises (@p68 @p67) :args (@t23)) % 33.96/34.25 (step @p70 :rule cong :premises (@p69) :args (@t24)) % 33.96/34.25 (step @p71 :rule trans :premises (@p70 @p64)) % 33.96/34.25 (step @p72 :rule eq_resolve :premises (@p9 @p71)) % 33.96/34.25 (step @p73 :rule instantiate :premises (@p72) :args ((@list tptp.xr))) % 33.96/34.25 (step @p74 :rule and_elim :premises (@p50) :args (1)) % 33.96/34.25 (step @p75 :rule cnf_or_pos :args (@t100)) % 33.96/34.25 (step @p76 :rule reordering :premises (@p75) :args ((or @t99 @t98 (not @t100)))) % 33.96/34.25 (step @p77 :rule chain_m_resolution :premises (@p76 @p74 @p73) :args (@t98 @t101 (@list @t87 @t100))) % 33.96/34.25 (step @p78 :rule cnf_and_pos :args (@t98 1)) % 33.96/34.25 (step @p79 :rule reordering :premises (@p78) :args ((or @t97 (not @t98)))) % 33.96/34.25 (step @p80 :rule chain_m_resolution :premises (@p79 @p77) :args (@t97 @t102 (@list @t98))) % 33.96/34.25 (step @p81 :rule aci_norm :args ((= (or @t107 @t15) @t106))) % 33.96/34.25 (step @p82 :rule refl :args (@t15)) % 33.96/34.25 (step @p83 :rule aci_norm :args ((= (or @t105 (or @t104 @t103)) @t107))) % 33.96/34.25 (step @p84 :rule bool-and-de-morgan :args (@t7 @t16 true)) % 33.96/34.25 (step @p85 :rule refl :args (@t105)) % 33.96/34.25 (step @p86 :rule nary_cong :premises (@p85 @p84) :args ((or @t105 (not (and @t7 @t16))))) % 33.96/34.25 (step @p87 :rule bool-and-de-morgan :args (@t2 @t7 (and @t16))) % 33.96/34.25 (step @p88 :rule trans :premises (@p87 @p86)) % 33.96/34.25 (step @p89 :rule trans :premises (@p88 @p83)) % 33.96/34.25 (step @p90 :rule nary_cong :premises (@p89 @p82) :args ((or (not @t17) @t15))) % 33.96/34.25 (step @p91 :rule trans :premises (@p90 @p81)) % 33.96/34.25 (step @p92 :rule bool-impl-elim :args (@t17 @t15)) % 33.96/34.25 (step @p93 :rule trans :premises (@p92 @p91)) % 33.96/34.25 (step @p94 :rule cong :premises (@p93) :args (@t19)) % 33.96/34.25 (step @p95 :rule eq_resolve :premises (@p8 @p94)) % 33.96/34.25 (step @p96 :rule eq-symm :args (@t109 @t110)) % 33.96/34.25 (step @p97 :rule refl :args (@t99)) % 33.96/34.25 (step @p98 :rule refl :args (@t112)) % 33.96/34.25 (step @p99 :rule refl :args (@t114)) % 33.96/34.25 (step @p100 :rule nary_cong :premises (@p99 @p98 @p97 @p96) :args (@t115)) % 33.96/34.25 (step @p101 :rule refl :args (@t116)) % 33.96/34.25 (step @p102 :rule cong :premises (@p101 @p100) :args ((=> @t116 @t115))) % 33.96/34.25 (assume-push @p203 @t116) % 33.96/34.25 (step @p104 :rule instantiate :premises (@p95) :args ((@list @t89 @t85 tptp.xr))) % 33.96/34.25 (step-pop @p204 :rule scope :premises (@p104)) % 33.96/34.25 (step @p105 :rule process_scope :premises (@p204) :args (@t115)) % 33.96/34.25 (step @p107 :rule eq_resolve :premises (@p105 @p102)) % 33.96/34.25 (step @p108 :rule implies_elim :premises (@p107)) % 33.96/34.25 (step @p109 :rule chain_m_resolution :premises (@p108 @p95) :args (@t118 @t102 (@list @t116))) % 33.96/34.25 (step @p110 :rule aci_norm :args ((= @t124 (or @t122 @t121 @t120)))) % 33.96/34.25 (step @p111 :rule cong :premises (@p110) :args (@t125)) % 33.96/34.25 (step @p112 :rule quant-merge-prenex :args ((= (forall @t3 @t127) @t125))) % 33.96/34.25 (step @p113 :rule alpha_equiv :args (@t128 (@list @t119) (@list @t5))) % 33.96/34.25 (step @p114 :rule refl :args (@t122)) % 33.96/34.25 (step @p115 :rule nary_cong :premises (@p114 @p113) :args (@t129)) % 33.96/34.25 (step @p116 :rule quant-miniscope-or :args ((= @t127 @t129))) % 33.96/34.25 (step @p117 :rule trans :premises (@p116 @p115)) % 33.96/34.25 (step @p118 :rule symm :premises (@p117)) % 33.96/34.25 (step @p119 :rule cong :premises (@p118) :args ((forall @t3 (or @t122 @t130)))) % 33.96/34.25 (step @p120 :rule trans :premises (@p119 @p112)) % 33.96/34.25 (step @p121 :rule trans :premises (@p120 @p111)) % 33.96/34.25 (step @p122 :rule bool-impl-elim :args (@t35 @t130)) % 33.96/34.25 (step @p123 :rule cong :premises (@p122) :args ((forall @t3 (=> @t35 @t130)))) % 33.96/34.25 (step @p124 :rule trans :premises (@p123 @p121)) % 33.96/34.25 (step @p125 :rule bool-impl-elim :args (@t36 @t7)) % 33.96/34.25 (step @p126 :rule cong :premises (@p125) :args (@t38)) % 33.96/34.25 (step @p127 :rule refl :args (@t35)) % 33.96/34.25 (step @p128 :rule cong :premises (@p127 @p126) :args (@t39)) % 33.96/34.25 (step @p129 :rule cong :premises (@p128) :args (@t40)) % 33.96/34.25 (step @p130 :rule trans :premises (@p129 @p124)) % 33.96/34.25 (step @p131 :rule eq_resolve :premises (@p20 @p130)) % 33.96/34.25 (step @p132 :rule instantiate :premises (@p131) :args ((@list @t131 @t89))) % 33.96/34.25 (step @p133 :rule cong :premises (@p56) :args (@t65)) % 33.96/34.25 (step @p134 :rule refl :args (@t66)) % 33.96/34.25 (step @p135 :rule cong :premises (@p134 @p133) :args (@t67)) % 33.96/34.25 (step @p136 :rule and_elim :premises (@p42) :args (6)) % 33.96/34.25 (step @p137 :rule trans :premises (@p136 @p135)) % 33.96/34.25 (step @p138 :rule cong :premises (@p57 @p137) :args (@t90)) % 33.96/34.25 (step @p139 :rule and_elim :premises (@p52) :args (1)) % 33.96/34.25 (step @p140 :rule eq_resolve :premises (@p139 @p138)) % 33.96/34.25 (step @p141 :rule cong :premises (@p137) :args (@t73)) % 33.96/34.25 (step @p142 :rule and_elim :premises (@p42) :args (0)) % 33.96/34.25 (step @p143 :rule eq_resolve :premises (@p142 @p141)) % 33.96/34.25 (step @p144 :rule cnf_or_pos :args (@t136)) % 33.96/34.25 (step @p145 :rule reordering :premises (@p144) :args ((or @t135 @t133 @t113 (not @t136)))) % 33.96/34.25 (step @p146 :rule chain_m_resolution :premises (@p145 @p143 @p140 @p132) :args (@t113 @t137 (@list @t134 @t132 @t136))) % 33.96/34.25 (step @p147 :rule aci_norm :args ((= (or (or @t105 @t104) @t11) (or @t105 @t104 @t11)))) % 33.96/34.25 (step @p148 :rule refl :args (@t11)) % 33.96/34.25 (step @p149 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 33.96/34.25 (step @p150 :rule nary_cong :premises (@p149 @p148) :args ((or (not @t8) @t11))) % 33.96/34.25 (step @p151 :rule trans :premises (@p150 @p147)) % 33.96/34.25 (step @p152 :rule bool-impl-elim :args (@t8 @t11)) % 33.96/34.25 (step @p153 :rule trans :premises (@p152 @p151)) % 33.96/34.25 (step @p154 :rule cong :premises (@p153) :args (@t12)) % 33.96/34.25 (step @p155 :rule eq_resolve :premises (@p6 @p154)) % 33.96/34.25 (step @p156 :rule instantiate :premises (@p155) :args ((@list tptp.xq tptp.xu))) % 33.96/34.25 (step @p157 :rule instantiate :premises (@p131) :args ((@list @t131 tptp.xu))) % 33.96/34.25 (step @p158 :rule refl :args (tptp.xu)) % 33.96/34.25 (step @p159 :rule cong :premises (@p158 @p137) :args (@t78)) % 33.96/34.25 (step @p160 :rule and_elim :premises (@p45) :args (1)) % 33.96/34.25 (step @p161 :rule eq_resolve :premises (@p160 @p159)) % 33.96/34.25 (step @p162 :rule cnf_or_pos :args (@t141)) % 33.96/34.25 (step @p163 :rule reordering :premises (@p162) :args ((or @t135 @t140 @t138 (not @t141)))) % 33.96/34.25 (step @p164 :rule chain_m_resolution :premises (@p163 @p143 @p161 @p157) :args (@t138 @t137 (@list @t134 @t139 @t141))) % 33.96/34.25 (step @p165 :rule and_elim :premises (@p50) :args (0)) % 33.96/34.25 (step @p166 :rule cnf_or_pos :args (@t144)) % 33.96/34.25 (step @p167 :rule reordering :premises (@p166) :args ((or @t143 @t142 @t111 (not @t144)))) % 33.96/34.25 (step @p168 :rule chain_m_resolution :premises (@p167 @p165 @p164 @p156) :args (@t111 @t137 (@list @t88 @t138 @t144))) % 33.96/34.25 (step @p169 :rule cnf_or_pos :args (@t118)) % 33.96/34.25 (step @p170 :rule reordering :premises (@p169) :args ((or @t99 @t112 @t114 @t117 (not @t118)))) % 33.96/34.25 (step @p171 :rule chain_m_resolution :premises (@p170 @p74 @p168 @p146 @p109) :args (@t117 (@list false false false false) (@list @t87 @t111 @t113 @t118))) % 33.96/34.25 (step @p172 :rule bool-impl-elim :args (@t2 @t145)) % 33.96/34.25 (step @p173 :rule cong :premises (@p172) :args ((forall @t3 (=> @t2 @t145)))) % 33.96/34.25 (step @p174 :rule refl :args (@t25)) % 33.96/34.25 (step @p175 :rule eq-symm :args (@t26 tptp.sz00)) % 33.96/34.25 (step @p176 :rule nary_cong :premises (@p175 @p174) :args (@t27)) % 33.96/34.25 (step @p177 :rule cong :premises (@p68 @p176) :args (@t28)) % 33.96/34.25 (step @p178 :rule cong :premises (@p177) :args (@t29)) % 33.96/34.25 (step @p179 :rule trans :premises (@p178 @p173)) % 33.96/34.25 (step @p180 :rule eq_resolve :premises (@p10 @p179)) % 33.96/34.25 (step @p181 :rule instantiate :premises (@p180) :args ((@list @t85))) % 33.96/34.25 (step @p182 :rule cnf_or_pos :args (@t148)) % 33.96/34.25 (step @p183 :rule reordering :premises (@p182) :args ((or @t112 @t147 (not @t148)))) % 33.96/34.25 (step @p184 :rule chain_m_resolution :premises (@p183 @p168 @p181) :args (@t147 @t101 (@list @t111 @t148))) % 33.96/34.25 (step @p185 :rule cnf_and_pos :args (@t147 1)) % 33.96/34.25 (step @p186 :rule reordering :premises (@p185) :args ((or @t146 (not @t147)))) % 33.96/34.25 (step @p187 :rule chain_m_resolution :premises (@p186 @p184) :args (@t146 @t102 (@list @t147))) % 33.96/34.25 (assume-push @p205 @t117) % 33.96/34.25 (assume-push @p206 @t97) % 33.96/34.25 (assume-push @p207 @t146) % 33.96/34.25 (step @p191 :rule symm :premises (@p171)) % 33.96/34.25 (step @p192 :rule cong :premises (@p187 @p59) :args (@t96)) % 33.96/34.25 (step @p193 :rule trans :premises (@p80 @p192 @p191)) % 33.96/34.25 (step-pop @p208 :rule scope :premises (@p193)) % 33.96/34.25 (step-pop @p209 :rule scope :premises (@p208)) % 33.96/34.25 (step-pop @p210 :rule scope :premises (@p209)) % 33.96/34.25 (step @p194 :rule process_scope :premises (@p210) :args (@t149)) % 33.96/34.25 (step @p198 :rule implies_elim :premises (@p194)) % 33.96/34.25 (step @p199 :rule cnf_and_neg :args (@t150)) % 33.96/34.25 (step @p200 :rule resolution :premises (@p199 @p198) :args (true @t150)) % 33.96/34.25 (step @p201 :rule reordering :premises (@p200) :args ((or @t149 (not @t117) (not @t97) (not @t146)))) % 33.96/34.25 (step @p202 false :rule chain_m_resolution :premises (@p201 @p187 @p171 @p80 @p62) :args (false (@list false false false true) (@list @t146 @t117 @t97 @t149))) % 33.96/34.25 ) % 33.96/34.25 % SZS output end Proof % 33.96/34.25 % cvc5 exiting %------------------------------------------------------------------------------