%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG122+1 : 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 : n024.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 0.17s 0.40s % Output : Proof 0.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : RNG122+1 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 09:08:00 EDT 2026 % 0.07/0.25 % CPUTime : % 0.17/0.33 %----Proving TF0_NAR, FOF, or CNF % 0.17/0.40 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.17/0.40 % SZS status Theorem % 0.17/0.40 % SZS output start Proof % 0.17/0.40 ( % 0.17/0.40 (declare-sort $$unsorted 0) % 0.17/0.40 (declare-const tptp.xq $$unsorted) % 0.17/0.40 (declare-const tptp.xu $$unsorted) % 0.17/0.40 (declare-const tptp.xc $$unsorted) % 0.17/0.40 (declare-const tptp.xa $$unsorted) % 0.17/0.40 (declare-const tptp.xI $$unsorted) % 0.17/0.40 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 0.17/0.40 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.17/0.40 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.17/0.40 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.17/0.40 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.17/0.40 (declare-const tptp.sz00 $$unsorted) % 0.17/0.40 (declare-const tptp.sz10 $$unsorted) % 0.17/0.40 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.17/0.40 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.17/0.40 (declare-const tptp.xr $$unsorted) % 0.17/0.40 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.17/0.40 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.17/0.40 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.17/0.40 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 0.17/0.40 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.17/0.40 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.17/0.40 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.17/0.40 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.17/0.40 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.17/0.40 (declare-const tptp.xb $$unsorted) % 0.17/0.40 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.17/0.40 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.17/0.40 (define @t1 () (@var "W0" $$unsorted)) % 0.17/0.40 (define @t2 () (tptp.aElement0 @t1)) % 0.17/0.40 (define @t3 () (@list @t1)) % 0.17/0.40 (define @t4 () (tptp.smndt0 @t1)) % 0.17/0.40 (define @t5 () (@var "W1" $$unsorted)) % 0.17/0.40 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.17/0.40 (define @t7 () (tptp.aElement0 @t5)) % 0.17/0.40 (define @t8 () (and @t2 @t7)) % 0.17/0.40 (define @t9 () (@list @t1 @t5)) % 0.17/0.40 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.17/0.40 (define @t11 () (tptp.aElement0 @t10)) % 0.17/0.40 (define @t12 () (forall @t9 (=> @t8 @t11))) % 0.17/0.40 (define @t13 () (@var "W2" $$unsorted)) % 0.17/0.40 (define @t14 () (tptp.sdtpldt0 @t5 @t13)) % 0.17/0.40 (define @t15 () (= (tptp.sdtpldt0 @t6 @t13) (tptp.sdtpldt0 @t1 @t14))) % 0.17/0.40 (define @t16 () (tptp.aElement0 @t13)) % 0.17/0.40 (define @t17 () (and @t2 @t7 @t16)) % 0.17/0.40 (define @t18 () (@list @t1 @t5 @t13)) % 0.17/0.40 (define @t19 () (forall @t18 (=> @t17 @t15))) % 0.17/0.40 (define @t20 () (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1))) % 0.17/0.40 (define @t21 () (tptp.sdtpldt0 @t1 tptp.sz00)) % 0.17/0.40 (define @t22 () (and (= @t21 @t1) @t20)) % 0.17/0.40 (define @t23 () (=> @t2 @t22)) % 0.17/0.40 (define @t24 () (forall @t3 @t23)) % 0.17/0.40 (define @t25 () (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1))) % 0.17/0.40 (define @t26 () (tptp.sdtpldt0 @t1 @t4)) % 0.17/0.40 (define @t27 () (and (= @t26 tptp.sz00) @t25)) % 0.17/0.40 (define @t28 () (=> @t2 @t27)) % 0.17/0.40 (define @t29 () (forall @t3 @t28)) % 0.17/0.40 (define @t30 () (tptp.sdtasdt0 @t5 @t1)) % 0.17/0.40 (define @t31 () (tptp.sdtasdt0 @t1 @t13)) % 0.17/0.40 (define @t32 () (tptp.smndt0 tptp.sz10)) % 0.17/0.40 (define @t33 () (= @t5 tptp.sz00)) % 0.17/0.40 (define @t34 () (= @t1 tptp.sz00)) % 0.17/0.40 (define @t35 () (tptp.aSet0 @t1)) % 0.17/0.40 (define @t36 () (tptp.aElementOf0 @t5 @t1)) % 0.17/0.40 (define @t37 () (@list @t5)) % 0.17/0.40 (define @t38 () (forall @t37 (=> @t36 @t7))) % 0.17/0.40 (define @t39 () (=> @t35 @t38)) % 0.17/0.40 (define @t40 () (forall @t3 @t39)) % 0.17/0.40 (define @t41 () (tptp.aElementOf0 @t13 @t1)) % 0.17/0.40 (define @t42 () (tptp.aElementOf0 @t13 @t5)) % 0.17/0.40 (define @t43 () (@list @t13)) % 0.17/0.40 (define @t44 () (tptp.aSet0 @t5)) % 0.17/0.40 (define @t45 () (and @t35 @t44)) % 0.17/0.40 (define @t46 () (@var "W3" $$unsorted)) % 0.17/0.40 (define @t47 () (@var "W5" $$unsorted)) % 0.17/0.40 (define @t48 () (@var "W4" $$unsorted)) % 0.17/0.40 (define @t49 () (tptp.aElementOf0 @t46 @t13)) % 0.17/0.40 (define @t50 () (@list @t46)) % 0.17/0.40 (define @t51 () (tptp.aSet0 @t13)) % 0.17/0.40 (define @t52 () (tptp.sdtpldt1 @t1 @t5)) % 0.17/0.40 (define @t53 () (tptp.sdtasasdt0 @t1 @t5)) % 0.17/0.40 (define @t54 () (tptp.sdtasdt0 @t13 @t5)) % 0.17/0.40 (define @t55 () (tptp.aElementOf0 @t54 @t1)) % 0.17/0.40 (define @t56 () (forall @t43 (=> @t16 @t55))) % 0.17/0.40 (define @t57 () (tptp.aElementOf0 @t14 @t1)) % 0.17/0.40 (define @t58 () (forall @t43 (=> @t41 @t57))) % 0.17/0.40 (define @t59 () (and @t58 @t56)) % 0.17/0.40 (define @t60 () (=> @t36 @t59)) % 0.17/0.40 (define @t61 () (forall @t37 @t60)) % 0.17/0.40 (define @t62 () (and @t35 @t61)) % 0.17/0.40 (define @t63 () (tptp.aIdeal0 @t1)) % 0.17/0.40 (define @t64 () (= @t63 @t62)) % 0.17/0.40 (define @t65 () (forall @t3 @t64)) % 0.17/0.40 (define @t66 () (and @t63 (tptp.aIdeal0 @t5))) % 0.17/0.40 (define @t67 () (tptp.aElement0 @t46)) % 0.17/0.40 (define @t68 () (@list @t13 @t46)) % 0.17/0.40 (define @t69 () (tptp.aNaturalNumber0 @t1)) % 0.17/0.40 (define @t70 () (tptp.sbrdtbr0 @t1)) % 0.17/0.40 (define @t71 () (not @t34)) % 0.17/0.40 (define @t72 () (tptp.slsdtgt0 @t1)) % 0.17/0.40 (define @t73 () (tptp.slsdtgt0 tptp.xb)) % 0.17/0.40 (define @t74 () (tptp.slsdtgt0 tptp.xa)) % 0.17/0.40 (define @t75 () (tptp.sdtpldt1 @t74 @t73)) % 0.17/0.40 (define @t76 () (tptp.aIdeal0 tptp.xI)) % 0.17/0.40 (define @t77 () (tptp.sbrdtbr0 tptp.xu)) % 0.17/0.40 (define @t78 () (tptp.aElementOf0 tptp.xu tptp.xI)) % 0.17/0.40 (define @t79 () (= tptp.xr tptp.sz00)) % 0.17/0.40 (define @t80 () (tptp.sdtasdt0 tptp.xq tptp.xu)) % 0.17/0.40 (define @t81 () (tptp.sdtpldt0 @t80 tptp.xr)) % 0.17/0.40 (define @t82 () (= tptp.xb @t81)) % 0.17/0.40 (define @t83 () (tptp.aElement0 tptp.xr)) % 0.17/0.40 (define @t84 () (tptp.aElement0 tptp.xq)) % 0.17/0.40 (define @t85 () (tptp.smndt0 @t80)) % 0.17/0.40 (define @t86 () (tptp.aElementOf0 @t85 tptp.xI)) % 0.17/0.40 (define @t87 () (= tptp.xr (tptp.sdtpldt0 @t85 tptp.xb))) % 0.17/0.40 (define @t88 () (and (= @t1 @t21) @t20)) % 0.17/0.40 (define @t89 () (tptp.sdtpldt0 tptp.sz00 tptp.xr)) % 0.17/0.40 (define @t90 () (= tptp.xr @t89)) % 0.17/0.40 (define @t91 () (and (= tptp.xr (tptp.sdtpldt0 tptp.xr tptp.sz00)) @t90)) % 0.17/0.40 (define @t92 () (not @t83)) % 0.17/0.40 (define @t93 () (or @t92 @t91)) % 0.17/0.40 (define @t94 () (@list false false)) % 0.17/0.40 (define @t95 () (@list false)) % 0.17/0.40 (define @t96 () (not @t16)) % 0.17/0.40 (define @t97 () (not @t7)) % 0.17/0.40 (define @t98 () (not @t2)) % 0.17/0.40 (define @t99 () (or @t98 @t97 @t96)) % 0.17/0.40 (define @t100 () (@var "BOUND_VARIABLE_7887" $$unsorted)) % 0.17/0.40 (define @t101 () (tptp.aElement0 @t100)) % 0.17/0.40 (define @t102 () (not (tptp.aElementOf0 @t100 @t1))) % 0.17/0.40 (define @t103 () (not @t35)) % 0.17/0.40 (define @t104 () (or @t102 @t101)) % 0.17/0.40 (define @t105 () (or @t103 @t104)) % 0.17/0.40 (define @t106 () (forall (@list @t1 @t100) @t105)) % 0.17/0.40 (define @t107 () (@list @t100)) % 0.17/0.40 (define @t108 () (forall @t107 @t105)) % 0.17/0.40 (define @t109 () (forall @t107 @t104)) % 0.17/0.40 (define @t110 () (or @t103 @t109)) % 0.17/0.40 (define @t111 () (not @t36)) % 0.17/0.40 (define @t112 () (forall @t37 (or @t111 @t7))) % 0.17/0.40 (define @t113 () (@var "BOUND_VARIABLE_7999" $$unsorted)) % 0.17/0.40 (define @t114 () (tptp.sdtasdt0 @t113 @t5)) % 0.17/0.40 (define @t115 () (not (tptp.aElement0 @t113))) % 0.17/0.40 (define @t116 () (or @t115 (tptp.aElementOf0 @t114 @t1))) % 0.17/0.40 (define @t117 () (@var "BOUND_VARIABLE_7992" $$unsorted)) % 0.17/0.40 (define @t118 () (tptp.sdtpldt0 @t5 @t117)) % 0.17/0.40 (define @t119 () (or (not (tptp.aElementOf0 @t117 @t1)) (tptp.aElementOf0 @t118 @t1))) % 0.17/0.40 (define @t120 () (and @t119 @t116)) % 0.17/0.40 (define @t121 () (or @t111 @t120)) % 0.17/0.40 (define @t122 () (@list @t5 @t117 @t113)) % 0.17/0.40 (define @t123 () (@list @t117 @t113)) % 0.17/0.40 (define @t124 () (forall @t123 @t121)) % 0.17/0.40 (define @t125 () (forall (@list @t113) @t116)) % 0.17/0.40 (define @t126 () (@list @t13)) % 0.17/0.40 (define @t127 () (forall @t123 @t116)) % 0.17/0.40 (define @t128 () (forall (@list @t117) @t119)) % 0.17/0.40 (define @t129 () (forall @t123 @t119)) % 0.17/0.40 (define @t130 () (and @t129 @t127)) % 0.17/0.40 (define @t131 () (forall @t123 @t120)) % 0.17/0.40 (define @t132 () (or @t111 @t131)) % 0.17/0.40 (define @t133 () (and (forall @t43 (or (not @t41) @t57)) (forall @t43 (or @t96 @t55)))) % 0.17/0.40 (define @t134 () (tptp.aSet0 tptp.xI)) % 0.17/0.40 (define @t135 () (and @t134 (forall @t122 (or (not (tptp.aElementOf0 @t5 tptp.xI)) (and (or (not (tptp.aElementOf0 @t117 tptp.xI)) (tptp.aElementOf0 @t118 tptp.xI)) (or @t115 (tptp.aElementOf0 @t114 tptp.xI))))))) % 0.17/0.40 (define @t136 () (= @t76 @t135)) % 0.17/0.40 (define @t137 () (tptp.aElement0 @t85)) % 0.17/0.40 (define @t138 () (not @t86)) % 0.17/0.40 (define @t139 () (not @t134)) % 0.17/0.40 (define @t140 () (or @t139 @t138 @t137)) % 0.17/0.40 (define @t141 () (@list false false false)) % 0.17/0.40 (define @t142 () (tptp.aElement0 tptp.xu)) % 0.17/0.40 (define @t143 () (not @t78)) % 0.17/0.40 (define @t144 () (or @t139 @t143 @t142)) % 0.17/0.40 (define @t145 () (tptp.aElement0 @t80)) % 0.17/0.40 (define @t146 () (not @t142)) % 0.17/0.40 (define @t147 () (not @t84)) % 0.17/0.40 (define @t148 () (or @t147 @t146 @t145)) % 0.17/0.40 (define @t149 () (tptp.sdtpldt0 @t85 @t81)) % 0.17/0.40 (define @t150 () (tptp.sdtpldt0 @t85 @t80)) % 0.17/0.40 (define @t151 () (= (tptp.sdtpldt0 @t150 tptp.xr) @t149)) % 0.17/0.40 (define @t152 () (not @t145)) % 0.17/0.40 (define @t153 () (not @t137)) % 0.17/0.40 (define @t154 () (or @t153 @t152 @t92 @t151)) % 0.17/0.40 (define @t155 () (and (= tptp.sz00 @t26) @t25)) % 0.17/0.40 (define @t156 () (= tptp.sz00 @t150)) % 0.17/0.40 (define @t157 () (and (= tptp.sz00 (tptp.sdtpldt0 @t80 @t85)) @t156)) % 0.17/0.40 (define @t158 () (or @t152 @t157)) % 0.17/0.40 (define @t159 () (and @t82 @t151 @t90 @t156)) % 0.17/0.40 (assume @p1 (forall @t3 (=> @t2 true))) % 0.17/0.40 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.17/0.40 (assume @p3 (tptp.aElement0 tptp.sz10)) % 0.17/0.40 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 0.17/0.40 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 0.17/0.40 (assume @p6 @t12) % 0.17/0.40 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.17/0.40 (assume @p8 @t19) % 0.17/0.40 (assume @p9 @t24) % 0.17/0.40 (assume @p10 @t29) % 0.17/0.40 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t30)))) % 0.17/0.40 (assume @p12 (forall @t18 (=> @t17 (= (tptp.sdtasdt0 @t10 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t13)))))) % 0.17/0.40 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.17/0.40 (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))))))) % 0.17/0.40 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t32 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t32)))))) % 0.17/0.40 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.17/0.40 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t34 @t33))))) % 0.17/0.40 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.17/0.40 (assume @p19 (forall @t3 (=> @t35 true))) % 0.17/0.40 (assume @p20 @t40) % 0.17/0.40 (assume @p21 (forall @t9 (=> @t45 (=> (and (forall @t43 (=> @t41 @t42)) (forall @t43 (=> @t42 @t41))) (= @t1 @t5))))) % 0.17/0.40 (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))))))))))) % 0.17/0.40 (assume @p23 (forall @t9 (=> @t45 (forall @t43 (= (= @t13 @t53) (and @t51 (forall @t50 (= @t49 (and (tptp.aElementOf0 @t46 @t1) (tptp.aElementOf0 @t46 @t5)))))))))) % 0.17/0.40 (assume @p24 @t65) % 0.17/0.40 (assume @p25 (forall @t9 (=> @t66 (tptp.aIdeal0 @t52)))) % 0.17/0.40 (assume @p26 (forall @t9 (=> @t66 (tptp.aIdeal0 @t53)))) % 0.17/0.40 (assume @p27 (forall @t18 (=> (and @t2 @t7 (tptp.aIdeal0 @t13)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t13) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t13))))) % 0.17/0.40 (assume @p28 (forall @t9 (=> @t66 (=> (forall @t43 (=> @t16 (tptp.aElementOf0 @t13 @t52))) (forall @t68 (=> (and @t16 @t67) (exists (@list @t48) (and (tptp.aElement0 @t48) (tptp.sdteqdtlpzmzozddtrp0 @t48 @t13 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t48 @t46 @t5))))))))) % 0.17/0.40 (assume @p29 (forall @t3 (=> @t69 true))) % 0.17/0.40 (assume @p30 (forall @t3 (=> (and @t2 @t71) (tptp.aNaturalNumber0 @t70)))) % 0.17/0.40 (assume @p31 (forall @t9 (=> (and @t69 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 0.17/0.40 (assume @p32 (forall @t9 (=> (and @t2 @t7 (not @t33)) (exists @t68 (and @t16 @t67 (= @t1 (tptp.sdtpldt0 @t54 @t46)) (=> (not (= @t46 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t46) (tptp.sbrdtbr0 @t5)))))))) % 0.17/0.40 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t43 (and @t16 (= @t31 @t5))))))) % 0.17/0.40 (assume @p34 (forall @t3 (=> @t2 (forall @t37 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 0.17/0.40 (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))))))))) % 0.17/0.40 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 0.17/0.40 (assume @p37 (forall @t3 (=> @t2 (forall @t37 (= (= @t5 @t72) (and @t44 (forall @t43 (= @t42 (exists @t50 (and @t67 (= (tptp.sdtasdt0 @t1 @t46) @t13))))))))))) % 0.17/0.40 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t72)))) % 0.17/0.40 (assume @p39 (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb))) % 0.17/0.40 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 0.17/0.40 (assume @p41 (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb)) % 0.17/0.40 (assume @p42 (and @t76 (= tptp.xI @t75))) % 0.17/0.40 (assume @p43 (and (tptp.aElementOf0 tptp.sz00 @t74) (tptp.aElementOf0 tptp.xa @t74) (tptp.aElementOf0 tptp.sz00 @t73) (tptp.aElementOf0 tptp.xb @t73))) % 0.17/0.40 (assume @p44 (exists @t3 (and (tptp.aElementOf0 @t1 @t75) @t71))) % 0.17/0.40 (assume @p45 (and @t78 (not (= tptp.xu tptp.sz00)) (forall @t3 (=> (and (tptp.aElementOf0 @t1 tptp.xI) @t71) (not (tptp.iLess0 @t70 @t77)))))) % 0.17/0.40 (assume @p46 (not (and (tptp.aDivisorOf0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xb)))) % 0.17/0.40 (assume @p47 (exists @t9 (and @t2 @t7 (= tptp.xu (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xa @t1) (tptp.sdtasdt0 tptp.xb @t5)))))) % 0.17/0.40 (assume @p48 (not (not (tptp.doDivides0 tptp.xu tptp.xa)))) % 0.17/0.40 (assume @p49 (not (tptp.doDivides0 tptp.xu tptp.xb))) % 0.17/0.40 (assume @p50 (and @t84 @t83 @t82 (or @t79 (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) @t77)))) % 0.17/0.40 (assume @p51 (not @t79)) % 0.17/0.40 (assume @p52 @t86) % 0.17/0.40 (assume @p53 (tptp.aElementOf0 tptp.xb tptp.xI)) % 0.17/0.40 (assume @p54 (not @t87)) % 0.17/0.40 (assume @p55 true) % 0.17/0.40 (step @p56 :rule and_elim :premises (@p50) :args (2)) % 0.17/0.40 (step @p57 :rule bool-impl-elim :args (@t2 @t88)) % 0.17/0.40 (step @p58 :rule cong :premises (@p57) :args ((forall @t3 (=> @t2 @t88)))) % 0.17/0.40 (step @p59 :rule refl :args (@t20)) % 0.17/0.40 (step @p60 :rule eq-symm :args (@t21 @t1)) % 0.17/0.40 (step @p61 :rule nary_cong :premises (@p60 @p59) :args (@t22)) % 0.17/0.40 (step @p62 :rule refl :args (@t2)) % 0.17/0.40 (step @p63 :rule cong :premises (@p62 @p61) :args (@t23)) % 0.17/0.40 (step @p64 :rule cong :premises (@p63) :args (@t24)) % 0.17/0.40 (step @p65 :rule trans :premises (@p64 @p58)) % 0.17/0.40 (step @p66 :rule eq_resolve :premises (@p9 @p65)) % 0.17/0.40 (step @p67 :rule instantiate :premises (@p66) :args ((@list tptp.xr))) % 0.17/0.40 (step @p68 :rule and_elim :premises (@p50) :args (1)) % 0.17/0.40 (step @p69 :rule cnf_or_pos :args (@t93)) % 0.17/0.40 (step @p70 :rule reordering :premises (@p69) :args ((or @t92 @t91 (not @t93)))) % 0.17/0.40 (step @p71 :rule chain_m_resolution :premises (@p70 @p68 @p67) :args (@t91 @t94 (@list @t83 @t93))) % 0.17/0.40 (step @p72 :rule cnf_and_pos :args (@t91 1)) % 0.17/0.40 (step @p73 :rule reordering :premises (@p72) :args ((or @t90 (not @t91)))) % 0.17/0.40 (step @p74 :rule chain_m_resolution :premises (@p73 @p71) :args (@t90 @t95 (@list @t91))) % 0.17/0.40 (step @p75 :rule aci_norm :args ((= (or @t99 @t15) (or @t98 @t97 @t96 @t15)))) % 0.17/0.40 (step @p76 :rule refl :args (@t15)) % 0.17/0.40 (step @p77 :rule aci_norm :args ((= (or @t98 (or @t97 @t96)) @t99))) % 0.17/0.40 (step @p78 :rule bool-and-de-morgan :args (@t7 @t16 true)) % 0.17/0.40 (step @p79 :rule refl :args (@t98)) % 0.17/0.40 (step @p80 :rule nary_cong :premises (@p79 @p78) :args ((or @t98 (not (and @t7 @t16))))) % 0.17/0.40 (step @p81 :rule bool-and-de-morgan :args (@t2 @t7 (and @t16))) % 0.17/0.40 (step @p82 :rule trans :premises (@p81 @p80)) % 0.17/0.40 (step @p83 :rule trans :premises (@p82 @p77)) % 0.17/0.40 (step @p84 :rule nary_cong :premises (@p83 @p76) :args ((or (not @t17) @t15))) % 0.17/0.40 (step @p85 :rule trans :premises (@p84 @p75)) % 0.17/0.40 (step @p86 :rule bool-impl-elim :args (@t17 @t15)) % 0.17/0.40 (step @p87 :rule trans :premises (@p86 @p85)) % 0.17/0.40 (step @p88 :rule cong :premises (@p87) :args (@t19)) % 0.17/0.40 (step @p89 :rule eq_resolve :premises (@p8 @p88)) % 0.17/0.40 (step @p90 :rule instantiate :premises (@p89) :args ((@list @t85 @t80 tptp.xr))) % 0.17/0.40 (step @p91 :rule aci_norm :args ((= @t105 (or @t103 @t102 @t101)))) % 0.17/0.40 (step @p92 :rule cong :premises (@p91) :args (@t106)) % 0.17/0.40 (step @p93 :rule quant-merge-prenex :args ((= (forall @t3 @t108) @t106))) % 0.17/0.40 (step @p94 :rule alpha_equiv :args (@t109 (@list @t100) (@list @t5))) % 0.17/0.40 (step @p95 :rule refl :args (@t103)) % 0.17/0.40 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t110)) % 0.17/0.40 (step @p97 :rule quant-miniscope-or :args ((= @t108 @t110))) % 0.17/0.40 (step @p98 :rule trans :premises (@p97 @p96)) % 0.17/0.40 (step @p99 :rule symm :premises (@p98)) % 0.17/0.40 (step @p100 :rule cong :premises (@p99) :args ((forall @t3 (or @t103 @t112)))) % 0.17/0.40 (step @p101 :rule trans :premises (@p100 @p93)) % 0.17/0.40 (step @p102 :rule trans :premises (@p101 @p92)) % 0.17/0.40 (step @p103 :rule bool-impl-elim :args (@t35 @t112)) % 0.17/0.40 (step @p104 :rule cong :premises (@p103) :args ((forall @t3 (=> @t35 @t112)))) % 0.17/0.40 (step @p105 :rule trans :premises (@p104 @p102)) % 0.17/0.40 (step @p106 :rule bool-impl-elim :args (@t36 @t7)) % 0.17/0.40 (step @p107 :rule cong :premises (@p106) :args (@t38)) % 0.17/0.40 (step @p108 :rule refl :args (@t35)) % 0.17/0.40 (step @p109 :rule cong :premises (@p108 @p107) :args (@t39)) % 0.17/0.40 (step @p110 :rule cong :premises (@p109) :args (@t40)) % 0.17/0.40 (step @p111 :rule trans :premises (@p110 @p105)) % 0.17/0.40 (step @p112 :rule eq_resolve :premises (@p20 @p111)) % 0.17/0.40 (step @p113 :rule instantiate :premises (@p112) :args ((@list tptp.xI @t85))) % 0.17/0.40 (step @p114 :rule quant-merge-prenex :args ((= (forall @t37 @t124) (forall @t122 @t121)))) % 0.17/0.40 (step @p115 :rule alpha_equiv :args (@t125 (@list @t113) @t126)) % 0.17/0.40 (step @p116 :rule quant-unused-vars :args ((= @t127 @t125))) % 0.17/0.40 (step @p117 :rule trans :premises (@p116 @p115)) % 0.17/0.40 (step @p118 :rule alpha_equiv :args (@t128 (@list @t117) @t126)) % 0.17/0.40 (step @p119 :rule quant-unused-vars :args ((= @t129 @t128))) % 0.17/0.40 (step @p120 :rule trans :premises (@p119 @p118)) % 0.17/0.40 (step @p121 :rule nary_cong :premises (@p120 @p117) :args (@t130)) % 0.17/0.40 (step @p122 :rule quant-miniscope-and :args ((= @t131 @t130))) % 0.17/0.40 (step @p123 :rule trans :premises (@p122 @p121)) % 0.17/0.40 (step @p124 :rule refl :args (@t111)) % 0.17/0.40 (step @p125 :rule nary_cong :premises (@p124 @p123) :args (@t132)) % 0.17/0.40 (step @p126 :rule quant-miniscope-or :args ((= @t124 @t132))) % 0.17/0.40 (step @p127 :rule trans :premises (@p126 @p125)) % 0.17/0.40 (step @p128 :rule symm :premises (@p127)) % 0.17/0.40 (step @p129 :rule cong :premises (@p128) :args ((forall @t37 (or @t111 @t133)))) % 0.17/0.40 (step @p130 :rule trans :premises (@p129 @p114)) % 0.17/0.40 (step @p131 :rule bool-impl-elim :args (@t36 @t133)) % 0.17/0.40 (step @p132 :rule cong :premises (@p131) :args ((forall @t37 (=> @t36 @t133)))) % 0.17/0.40 (step @p133 :rule trans :premises (@p132 @p130)) % 0.17/0.40 (step @p134 :rule bool-impl-elim :args (@t16 @t55)) % 0.17/0.40 (step @p135 :rule cong :premises (@p134) :args (@t56)) % 0.17/0.40 (step @p136 :rule bool-impl-elim :args (@t41 @t57)) % 0.17/0.40 (step @p137 :rule cong :premises (@p136) :args (@t58)) % 0.17/0.40 (step @p138 :rule nary_cong :premises (@p137 @p135) :args (@t59)) % 0.17/0.40 (step @p139 :rule refl :args (@t36)) % 0.17/0.40 (step @p140 :rule cong :premises (@p139 @p138) :args (@t60)) % 0.17/0.40 (step @p141 :rule cong :premises (@p140) :args (@t61)) % 0.17/0.40 (step @p142 :rule trans :premises (@p141 @p133)) % 0.17/0.40 (step @p143 :rule nary_cong :premises (@p108 @p142) :args (@t62)) % 0.17/0.40 (step @p144 :rule refl :args (@t63)) % 0.17/0.40 (step @p145 :rule cong :premises (@p144 @p143) :args (@t64)) % 0.17/0.40 (step @p146 :rule cong :premises (@p145) :args (@t65)) % 0.17/0.40 (step @p147 :rule eq_resolve :premises (@p24 @p146)) % 0.17/0.40 (step @p148 :rule instantiate :premises (@p147) :args ((@list tptp.xI))) % 0.17/0.40 (step @p149 :rule and_elim :premises (@p42) :args (0)) % 0.17/0.40 (step @p150 :rule cnf_equiv_pos1 :args (@t136)) % 0.17/0.40 (step @p151 :rule reordering :premises (@p150) :args ((or (not @t76) @t135 (not @t136)))) % 0.17/0.40 (step @p152 :rule chain_m_resolution :premises (@p151 @p149 @p148) :args (@t135 @t94 (@list @t76 @t136))) % 0.17/0.40 (step @p153 :rule cnf_and_pos :args (@t135 0)) % 0.17/0.40 (step @p154 :rule reordering :premises (@p153) :args ((or @t134 (not @t135)))) % 0.17/0.40 (step @p155 :rule chain_m_resolution :premises (@p154 @p152) :args (@t134 @t95 (@list @t135))) % 0.17/0.40 (step @p156 :rule cnf_or_pos :args (@t140)) % 0.17/0.40 (step @p157 :rule reordering :premises (@p156) :args ((or @t138 @t137 @t139 (not @t140)))) % 0.17/0.40 (step @p158 :rule chain_m_resolution :premises (@p157 @p52 @p155 @p113) :args (@t137 @t141 (@list @t86 @t134 @t140))) % 0.17/0.40 (step @p159 :rule aci_norm :args ((= (or (or @t98 @t97) @t11) (or @t98 @t97 @t11)))) % 0.17/0.40 (step @p160 :rule refl :args (@t11)) % 0.17/0.40 (step @p161 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 0.17/0.40 (step @p162 :rule nary_cong :premises (@p161 @p160) :args ((or (not @t8) @t11))) % 0.17/0.40 (step @p163 :rule trans :premises (@p162 @p159)) % 0.17/0.40 (step @p164 :rule bool-impl-elim :args (@t8 @t11)) % 0.17/0.40 (step @p165 :rule trans :premises (@p164 @p163)) % 0.17/0.40 (step @p166 :rule cong :premises (@p165) :args (@t12)) % 0.17/0.40 (step @p167 :rule eq_resolve :premises (@p6 @p166)) % 0.17/0.40 (step @p168 :rule instantiate :premises (@p167) :args ((@list tptp.xq tptp.xu))) % 0.17/0.40 (step @p169 :rule instantiate :premises (@p112) :args ((@list tptp.xI tptp.xu))) % 0.17/0.40 (step @p170 :rule and_elim :premises (@p45) :args (0)) % 0.17/0.40 (step @p171 :rule cnf_or_pos :args (@t144)) % 0.17/0.40 (step @p172 :rule reordering :premises (@p171) :args ((or @t143 @t142 @t139 (not @t144)))) % 0.17/0.40 (step @p173 :rule chain_m_resolution :premises (@p172 @p170 @p155 @p169) :args (@t142 @t141 (@list @t78 @t134 @t144))) % 0.17/0.40 (step @p174 :rule and_elim :premises (@p50) :args (0)) % 0.17/0.40 (step @p175 :rule cnf_or_pos :args (@t148)) % 0.17/0.40 (step @p176 :rule reordering :premises (@p175) :args ((or @t147 @t145 @t146 (not @t148)))) % 0.17/0.40 (step @p177 :rule chain_m_resolution :premises (@p176 @p174 @p173 @p168) :args (@t145 @t141 (@list @t84 @t142 @t148))) % 0.17/0.40 (step @p178 :rule cnf_or_pos :args (@t154)) % 0.17/0.40 (step @p179 :rule reordering :premises (@p178) :args ((or @t92 @t152 @t153 @t151 (not @t154)))) % 0.17/0.40 (step @p180 :rule chain_m_resolution :premises (@p179 @p68 @p177 @p158 @p90) :args (@t151 (@list false false false false) (@list @t83 @t145 @t137 @t154))) % 0.17/0.40 (step @p181 :rule bool-impl-elim :args (@t2 @t155)) % 0.17/0.40 (step @p182 :rule cong :premises (@p181) :args ((forall @t3 (=> @t2 @t155)))) % 0.17/0.40 (step @p183 :rule refl :args (@t25)) % 0.17/0.40 (step @p184 :rule eq-symm :args (@t26 tptp.sz00)) % 0.17/0.40 (step @p185 :rule nary_cong :premises (@p184 @p183) :args (@t27)) % 0.17/0.40 (step @p186 :rule cong :premises (@p62 @p185) :args (@t28)) % 0.17/0.40 (step @p187 :rule cong :premises (@p186) :args (@t29)) % 0.17/0.40 (step @p188 :rule trans :premises (@p187 @p182)) % 0.17/0.40 (step @p189 :rule eq_resolve :premises (@p10 @p188)) % 0.17/0.40 (step @p190 :rule instantiate :premises (@p189) :args ((@list @t80))) % 0.17/0.40 (step @p191 :rule cnf_or_pos :args (@t158)) % 0.17/0.40 (step @p192 :rule reordering :premises (@p191) :args ((or @t152 @t157 (not @t158)))) % 0.17/0.40 (step @p193 :rule chain_m_resolution :premises (@p192 @p177 @p190) :args (@t157 @t94 (@list @t145 @t158))) % 0.17/0.40 (step @p194 :rule cnf_and_pos :args (@t157 1)) % 0.17/0.40 (step @p195 :rule reordering :premises (@p194) :args ((or @t156 (not @t157)))) % 0.17/0.40 (step @p196 :rule chain_m_resolution :premises (@p195 @p193) :args (@t156 @t95 (@list @t157))) % 0.17/0.40 (assume-push @p217 @t82) % 0.17/0.40 (assume-push @p218 @t151) % 0.17/0.40 (assume-push @p219 @t90) % 0.17/0.40 (assume-push @p220 @t156) % 0.17/0.40 (step @p201 :rule symm :premises (@p56)) % 0.17/0.40 (step @p202 :rule refl :args (@t85)) % 0.17/0.40 (step @p203 :rule cong :premises (@p202 @p201) :args (@t149)) % 0.17/0.40 (step @p204 :rule refl :args (tptp.xr)) % 0.17/0.40 (step @p205 :rule cong :premises (@p196 @p204) :args (@t89)) % 0.17/0.40 (step @p206 :rule trans :premises (@p74 @p205 @p180 @p203)) % 0.17/0.40 (step-pop @p221 :rule scope :premises (@p206)) % 0.17/0.40 (step-pop @p222 :rule scope :premises (@p221)) % 0.17/0.40 (step-pop @p223 :rule scope :premises (@p222)) % 0.17/0.40 (step-pop @p224 :rule scope :premises (@p223)) % 0.17/0.40 (step @p207 :rule process_scope :premises (@p224) :args (@t87)) % 0.17/0.40 (step @p212 :rule implies_elim :premises (@p207)) % 0.17/0.40 (step @p213 :rule cnf_and_neg :args (@t159)) % 0.17/0.40 (step @p214 :rule resolution :premises (@p213 @p212) :args (true @t159)) % 0.17/0.40 (step @p215 :rule reordering :premises (@p214) :args ((or @t87 (not @t82) (not @t151) (not @t90) (not @t156)))) % 0.17/0.40 (step @p216 false :rule chain_m_resolution :premises (@p215 @p196 @p180 @p74 @p54 @p56) :args (false (@list false false false true false) (@list @t156 @t151 @t90 @t87 @t82))) % 0.17/0.40 ) % 0.17/0.40 % SZS output end Proof % 0.17/0.40 % cvc5 exiting %------------------------------------------------------------------------------