%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG111+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 08:45:43 AM UTC 2026 % Result : Theorem 0.37s 0.62s % Output : Proof 0.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG111+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 14:08:04 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.62 % SZS status Theorem % 0.37/0.62 % SZS output start Proof % 0.37/0.62 ( % 0.37/0.62 (declare-sort $$unsorted 0) % 0.37/0.62 (declare-const tptp.xc $$unsorted) % 0.37/0.62 (declare-const tptp.xa $$unsorted) % 0.37/0.62 (declare-const tptp.xI $$unsorted) % 0.37/0.62 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.sz00 $$unsorted) % 0.37/0.62 (declare-const tptp.sz10 $$unsorted) % 0.37/0.62 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.xb $$unsorted) % 0.37/0.62 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.37/0.62 (define @t1 () (@var "W0" $$unsorted)) % 0.37/0.62 (define @t2 () (tptp.aElement0 @t1)) % 0.37/0.62 (define @t3 () (@list @t1)) % 0.37/0.62 (define @t4 () (tptp.smndt0 @t1)) % 0.37/0.62 (define @t5 () (@var "W1" $$unsorted)) % 0.37/0.62 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.37/0.62 (define @t7 () (tptp.aElement0 @t5)) % 0.37/0.62 (define @t8 () (and @t2 @t7)) % 0.37/0.62 (define @t9 () (@list @t1 @t5)) % 0.37/0.62 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.37/0.62 (define @t11 () (@var "W2" $$unsorted)) % 0.37/0.62 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 0.37/0.62 (define @t13 () (tptp.aElement0 @t11)) % 0.37/0.62 (define @t14 () (and @t2 @t7 @t13)) % 0.37/0.62 (define @t15 () (@list @t1 @t5 @t11)) % 0.37/0.62 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 0.37/0.62 (define @t17 () (tptp.sdtasdt0 @t1 @t11)) % 0.37/0.62 (define @t18 () (tptp.smndt0 tptp.sz10)) % 0.37/0.62 (define @t19 () (= @t5 tptp.sz00)) % 0.37/0.62 (define @t20 () (= @t1 tptp.sz00)) % 0.37/0.62 (define @t21 () (tptp.aSet0 @t1)) % 0.37/0.62 (define @t22 () (tptp.aElementOf0 @t5 @t1)) % 0.37/0.62 (define @t23 () (@list @t5)) % 0.37/0.62 (define @t24 () (tptp.aElementOf0 @t11 @t1)) % 0.37/0.62 (define @t25 () (tptp.aElementOf0 @t11 @t5)) % 0.37/0.62 (define @t26 () (@list @t11)) % 0.37/0.62 (define @t27 () (tptp.aSet0 @t5)) % 0.37/0.62 (define @t28 () (and @t21 @t27)) % 0.37/0.62 (define @t29 () (@var "W3" $$unsorted)) % 0.37/0.62 (define @t30 () (@var "W5" $$unsorted)) % 0.37/0.62 (define @t31 () (@var "W4" $$unsorted)) % 0.37/0.62 (define @t32 () (tptp.aElementOf0 @t29 @t11)) % 0.37/0.62 (define @t33 () (@list @t29)) % 0.37/0.62 (define @t34 () (tptp.aSet0 @t11)) % 0.37/0.62 (define @t35 () (tptp.sdtpldt1 @t1 @t5)) % 0.37/0.62 (define @t36 () (tptp.sdtasasdt0 @t1 @t5)) % 0.37/0.62 (define @t37 () (tptp.sdtasdt0 @t11 @t5)) % 0.37/0.62 (define @t38 () (tptp.aIdeal0 @t1)) % 0.37/0.62 (define @t39 () (and @t38 (tptp.aIdeal0 @t5))) % 0.37/0.62 (define @t40 () (tptp.aElement0 @t29)) % 0.37/0.62 (define @t41 () (@list @t11 @t29)) % 0.37/0.62 (define @t42 () (tptp.aNaturalNumber0 @t1)) % 0.37/0.62 (define @t43 () (tptp.sbrdtbr0 @t1)) % 0.37/0.62 (define @t44 () (not @t20)) % 0.37/0.62 (define @t45 () (tptp.sbrdtbr0 @t5)) % 0.37/0.62 (define @t46 () (tptp.sbrdtbr0 @t29)) % 0.37/0.62 (define @t47 () (not (= @t29 tptp.sz00))) % 0.37/0.62 (define @t48 () (not @t19)) % 0.37/0.62 (define @t49 () (tptp.slsdtgt0 @t1)) % 0.37/0.62 (define @t50 () (tptp.slsdtgt0 tptp.xb)) % 0.37/0.62 (define @t51 () (tptp.slsdtgt0 tptp.xa)) % 0.37/0.62 (define @t52 () (tptp.sdtpldt1 @t51 @t50)) % 0.37/0.62 (define @t53 () (tptp.sbrdtbr0 @t11)) % 0.37/0.62 (define @t54 () (not (tptp.iLess0 @t53 @t45))) % 0.37/0.62 (define @t55 () (not (= @t11 tptp.sz00))) % 0.37/0.62 (define @t56 () (tptp.aElementOf0 @t11 tptp.xI)) % 0.37/0.62 (define @t57 () (and @t56 @t55)) % 0.37/0.62 (define @t58 () (=> @t57 @t54)) % 0.37/0.62 (define @t59 () (forall @t26 @t58)) % 0.37/0.62 (define @t60 () (tptp.aElementOf0 @t5 tptp.xI)) % 0.37/0.62 (define @t61 () (and @t60 @t48 @t59)) % 0.37/0.62 (define @t62 () (exists @t23 @t61)) % 0.37/0.62 (define @t63 () (not (tptp.iLess0 @t46 @t53))) % 0.37/0.62 (define @t64 () (tptp.aElementOf0 @t29 tptp.xI)) % 0.37/0.62 (define @t65 () (and @t64 @t47)) % 0.37/0.62 (define @t66 () (=> @t65 @t63)) % 0.37/0.62 (define @t67 () (forall @t33 @t66)) % 0.37/0.62 (define @t68 () (and @t56 @t55 @t67)) % 0.37/0.62 (define @t69 () (exists @t26 @t68)) % 0.37/0.62 (define @t70 () (tptp.iLess0 @t45 @t43)) % 0.37/0.62 (define @t71 () (=> @t70 @t69)) % 0.37/0.62 (define @t72 () (and @t60 @t48)) % 0.37/0.62 (define @t73 () (=> @t72 @t71)) % 0.37/0.62 (define @t74 () (forall @t23 @t73)) % 0.37/0.62 (define @t75 () (=> @t74 @t62)) % 0.37/0.62 (define @t76 () (tptp.aElementOf0 @t1 tptp.xI)) % 0.37/0.62 (define @t77 () (and @t76 @t44)) % 0.37/0.62 (define @t78 () (=> @t77 @t75)) % 0.37/0.62 (define @t79 () (forall @t3 @t78)) % 0.37/0.62 (define @t80 () (not @t79)) % 0.37/0.62 (define @t81 () (not @t70)) % 0.37/0.62 (define @t82 () (= tptp.sz00 @t5)) % 0.37/0.62 (define @t83 () (not @t60)) % 0.37/0.62 (define @t84 () (or @t83 @t82 @t81)) % 0.37/0.62 (define @t85 () (forall @t23 @t84)) % 0.37/0.62 (define @t86 () (not @t85)) % 0.37/0.62 (define @t87 () (@var "BOUND_VARIABLE_8272" $$unsorted)) % 0.37/0.62 (define @t88 () (= tptp.sz00 @t29)) % 0.37/0.62 (define @t89 () (not @t64)) % 0.37/0.62 (define @t90 () (or (not (tptp.aElementOf0 @t87 tptp.xI)) (= tptp.sz00 @t87) (not (forall @t33 (or @t89 @t88 (not (tptp.iLess0 @t46 (tptp.sbrdtbr0 @t87)))))))) % 0.37/0.62 (define @t91 () (and @t90 @t86)) % 0.37/0.62 (define @t92 () (not @t76)) % 0.37/0.62 (define @t93 () (or @t92 @t20 @t91)) % 0.37/0.62 (define @t94 () (forall (@list @t1 @t87) @t93)) % 0.37/0.62 (define @t95 () (@list @t87)) % 0.37/0.62 (define @t96 () (forall @t95 @t93)) % 0.37/0.62 (define @t97 () (forall @t95 @t86)) % 0.37/0.62 (define @t98 () (forall @t95 @t90)) % 0.37/0.62 (define @t99 () (@list @t11)) % 0.37/0.62 (define @t100 () (and @t98 @t97)) % 0.37/0.62 (define @t101 () (forall @t95 @t91)) % 0.37/0.62 (define @t102 () (or @t92 @t20 @t101)) % 0.37/0.62 (define @t103 () (or @t89 @t88 @t63)) % 0.37/0.62 (define @t104 () (forall @t33 @t103)) % 0.37/0.62 (define @t105 () (not @t104)) % 0.37/0.62 (define @t106 () (= tptp.sz00 @t11)) % 0.37/0.62 (define @t107 () (not @t56)) % 0.37/0.62 (define @t108 () (forall @t26 (or @t107 @t106 @t105))) % 0.37/0.62 (define @t109 () (and @t108 @t86)) % 0.37/0.62 (define @t110 () (or @t92 @t20 @t109)) % 0.37/0.62 (define @t111 () (forall @t3 @t110)) % 0.37/0.62 (define @t112 () (or @t107 @t106 @t54)) % 0.37/0.62 (define @t113 () (forall @t26 @t112)) % 0.37/0.62 (define @t114 () (not @t113)) % 0.37/0.62 (define @t115 () (not (forall @t23 (or @t83 @t82 @t114)))) % 0.37/0.62 (define @t116 () (or @t115 @t111)) % 0.37/0.62 (define @t117 () (or @t115 @t110)) % 0.37/0.62 (define @t118 () (or @t92 @t20 @t109 @t115)) % 0.37/0.62 (define @t119 () (not @t108)) % 0.37/0.62 (define @t120 () (or @t119 @t85)) % 0.37/0.62 (define @t121 () (=> @t120 @t115)) % 0.37/0.62 (define @t122 () (not @t82)) % 0.37/0.62 (define @t123 () (not @t122)) % 0.37/0.62 (define @t124 () (or @t83 @t123 @t114)) % 0.37/0.62 (define @t125 () (and @t60 @t122 @t113)) % 0.37/0.62 (define @t126 () (forall @t23 (not @t125))) % 0.37/0.62 (define @t127 () (not @t126)) % 0.37/0.62 (define @t128 () (not @t106)) % 0.37/0.62 (define @t129 () (not @t128)) % 0.37/0.62 (define @t130 () (and @t56 @t128)) % 0.37/0.62 (define @t131 () (or @t119 @t84)) % 0.37/0.62 (define @t132 () (or @t83 @t82 @t81 @t119)) % 0.37/0.62 (define @t133 () (=> @t70 @t119)) % 0.37/0.62 (define @t134 () (and @t60 @t122)) % 0.37/0.62 (define @t135 () (or @t107 @t129 @t105)) % 0.37/0.62 (define @t136 () (and @t56 @t128 @t104)) % 0.37/0.62 (define @t137 () (forall @t26 (not @t136))) % 0.37/0.62 (define @t138 () (not @t137)) % 0.37/0.62 (define @t139 () (not @t88)) % 0.37/0.62 (define @t140 () (and @t64 @t139)) % 0.37/0.62 (define @t141 () (@quantifiers_skolemize @t94 0)) % 0.37/0.62 (define @t142 () (tptp.sbrdtbr0 @t141)) % 0.37/0.62 (define @t143 () (forall @t23 (or @t83 @t82 (not (tptp.iLess0 @t45 @t142))))) % 0.37/0.62 (define @t144 () (not @t143)) % 0.37/0.62 (define @t145 () (@quantifiers_skolemize @t94 1)) % 0.37/0.62 (define @t146 () (tptp.sbrdtbr0 @t145)) % 0.37/0.62 (define @t147 () (forall @t33 (or @t89 @t88 (not (tptp.iLess0 @t46 @t146))))) % 0.37/0.62 (define @t148 () (not @t147)) % 0.37/0.62 (define @t149 () (= tptp.sz00 @t145)) % 0.37/0.62 (define @t150 () (tptp.aElementOf0 @t145 tptp.xI)) % 0.37/0.62 (define @t151 () (not @t150)) % 0.37/0.62 (define @t152 () (or @t151 @t149 @t148)) % 0.37/0.62 (define @t153 () (and @t152 @t144)) % 0.37/0.62 (define @t154 () (= tptp.sz00 @t141)) % 0.37/0.62 (define @t155 () (tptp.aElementOf0 @t141 tptp.xI)) % 0.37/0.62 (define @t156 () (not @t155)) % 0.37/0.62 (define @t157 () (or @t156 @t154 @t153)) % 0.37/0.62 (define @t158 () (not @t157)) % 0.37/0.62 (define @t159 () (not @t94)) % 0.37/0.62 (define @t160 () (or @t156 (= @t141 tptp.sz00) @t153)) % 0.37/0.62 (define @t161 () (not @t160)) % 0.37/0.62 (define @t162 () (@list true)) % 0.37/0.62 (define @t163 () (@list @t157)) % 0.37/0.62 (define @t164 () (forall @t26 (or @t107 @t106 (not (tptp.iLess0 @t53 @t142))))) % 0.37/0.62 (define @t165 () (not @t164)) % 0.37/0.62 (define @t166 () (or @t156 @t154 @t165)) % 0.37/0.62 (define @t167 () (@list false true false)) % 0.37/0.62 (define @t168 () (not @t152)) % 0.37/0.62 (define @t169 () (@list @t152)) % 0.37/0.62 (define @t170 () (forall @t26 (or @t107 @t106 (not (tptp.iLess0 @t53 @t146))))) % 0.37/0.62 (define @t171 () (not @t170)) % 0.37/0.62 (define @t172 () (or @t151 @t149 @t171)) % 0.37/0.62 (assume @p1 (forall @t3 (=> @t2 true))) % 0.37/0.62 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.37/0.62 (assume @p3 (tptp.aElement0 tptp.sz10)) % 0.37/0.62 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 0.37/0.62 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 0.37/0.62 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 0.37/0.62 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.37/0.62 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 0.37/0.62 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.37/0.62 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.37/0.62 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t16)))) % 0.37/0.62 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 0.37/0.62 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.37/0.62 (assume @p14 (forall @t15 (=> @t14 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t10 @t17)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t16 (tptp.sdtasdt0 @t11 @t1))))))) % 0.37/0.62 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t18)))))) % 0.37/0.62 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.37/0.62 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t20 @t19))))) % 0.37/0.62 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.37/0.62 (assume @p19 (forall @t3 (=> @t21 true))) % 0.37/0.62 (assume @p20 (forall @t3 (=> @t21 (forall @t23 (=> @t22 @t7))))) % 0.37/0.62 (assume @p21 (forall @t9 (=> @t28 (=> (and (forall @t26 (=> @t24 @t25)) (forall @t26 (=> @t25 @t24))) (= @t1 @t5))))) % 0.37/0.62 (assume @p22 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t35) (and @t34 (forall @t33 (= @t32 (exists (@list @t31 @t30) (and (tptp.aElementOf0 @t31 @t1) (tptp.aElementOf0 @t30 @t5) (= (tptp.sdtpldt0 @t31 @t30) @t29))))))))))) % 0.37/0.62 (assume @p23 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t36) (and @t34 (forall @t33 (= @t32 (and (tptp.aElementOf0 @t29 @t1) (tptp.aElementOf0 @t29 @t5)))))))))) % 0.37/0.62 (assume @p24 (forall @t3 (= @t38 (and @t21 (forall @t23 (=> @t22 (and (forall @t26 (=> @t24 (tptp.aElementOf0 @t12 @t1))) (forall @t26 (=> @t13 (tptp.aElementOf0 @t37 @t1)))))))))) % 0.37/0.62 (assume @p25 (forall @t9 (=> @t39 (tptp.aIdeal0 @t35)))) % 0.37/0.62 (assume @p26 (forall @t9 (=> @t39 (tptp.aIdeal0 @t36)))) % 0.37/0.62 (assume @p27 (forall @t15 (=> (and @t2 @t7 (tptp.aIdeal0 @t11)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t11))))) % 0.37/0.62 (assume @p28 (forall @t9 (=> @t39 (=> (forall @t26 (=> @t13 (tptp.aElementOf0 @t11 @t35))) (forall @t41 (=> (and @t13 @t40) (exists (@list @t31) (and (tptp.aElement0 @t31) (tptp.sdteqdtlpzmzozddtrp0 @t31 @t11 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t31 @t29 @t5))))))))) % 0.37/0.62 (assume @p29 (forall @t3 (=> @t42 true))) % 0.37/0.62 (assume @p30 (forall @t3 (=> (and @t2 @t44) (tptp.aNaturalNumber0 @t43)))) % 0.37/0.62 (assume @p31 (forall @t9 (=> (and @t42 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 0.37/0.62 (assume @p32 (forall @t9 (=> (and @t2 @t7 @t48) (exists @t41 (and @t13 @t40 (= @t1 (tptp.sdtpldt0 @t37 @t29)) (=> @t47 (tptp.iLess0 @t46 @t45))))))) % 0.37/0.62 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t26 (and @t13 (= @t17 @t5))))))) % 0.37/0.62 (assume @p34 (forall @t3 (=> @t2 (forall @t23 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 0.37/0.62 (assume @p35 (forall @t9 (=> @t8 (forall @t26 (= (tptp.aGcdOfAnd0 @t11 @t1 @t5) (and (tptp.aDivisorOf0 @t11 @t1) (tptp.aDivisorOf0 @t11 @t5) (forall @t33 (=> (and (tptp.aDivisorOf0 @t29 @t1) (tptp.aDivisorOf0 @t29 @t5)) (tptp.doDivides0 @t29 @t11))))))))) % 0.37/0.62 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 0.37/0.62 (assume @p37 (forall @t3 (=> @t2 (forall @t23 (= (= @t5 @t49) (and @t27 (forall @t26 (= @t25 (exists @t33 (and @t40 (= (tptp.sdtasdt0 @t1 @t29) @t11))))))))))) % 0.37/0.62 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t49)))) % 0.37/0.62 (assume @p39 (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb))) % 0.37/0.62 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 0.37/0.62 (assume @p41 (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb)) % 0.37/0.62 (assume @p42 (and (tptp.aIdeal0 tptp.xI) (= tptp.xI @t52))) % 0.37/0.62 (assume @p43 (and (tptp.aElementOf0 tptp.sz00 @t51) (tptp.aElementOf0 tptp.xa @t51) (tptp.aElementOf0 tptp.sz00 @t50) (tptp.aElementOf0 tptp.xb @t50))) % 0.37/0.62 (assume @p44 (exists @t3 (and (tptp.aElementOf0 @t1 @t52) @t44))) % 0.37/0.62 (assume @p45 @t80) % 0.37/0.62 (assume @p46 true) % 0.37/0.62 (step @p47 :rule quant-merge-prenex :args ((= (forall @t3 @t96) @t94))) % 0.37/0.62 (step @p48 :rule quant-unused-vars :args ((= @t97 @t86))) % 0.37/0.62 (step @p49 :rule alpha_equiv :args (@t98 (@list @t87) @t99)) % 0.37/0.62 (step @p50 :rule nary_cong :premises (@p49 @p48) :args (@t100)) % 0.37/0.62 (step @p51 :rule quant-miniscope-and :args ((= @t101 @t100))) % 0.37/0.62 (step @p52 :rule trans :premises (@p51 @p50)) % 0.37/0.62 (step @p53 :rule refl :args (@t20)) % 0.37/0.62 (step @p54 :rule refl :args (@t92)) % 0.37/0.62 (step @p55 :rule nary_cong :premises (@p54 @p53 @p52) :args (@t102)) % 0.37/0.62 (step @p56 :rule quant-miniscope-or :args ((= @t96 @t102))) % 0.37/0.62 (step @p57 :rule trans :premises (@p56 @p55)) % 0.37/0.62 (step @p58 :rule symm :premises (@p57)) % 0.37/0.62 (step @p59 :rule cong :premises (@p58) :args (@t111)) % 0.37/0.62 (step @p60 :rule trans :premises (@p59 @p47)) % 0.37/0.62 (step @p61 :rule refl :args (@t115)) % 0.37/0.62 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t116)) % 0.37/0.62 (step @p63 :rule quant-miniscope-or :args ((= (forall @t3 @t117) @t116))) % 0.37/0.62 (step @p64 :rule aci_norm :args ((= @t118 @t117))) % 0.37/0.62 (step @p65 :rule cong :premises (@p64) :args ((forall @t3 @t118))) % 0.37/0.62 (step @p66 :rule trans :premises (@p65 @p63)) % 0.37/0.62 (step @p67 :rule trans :premises (@p66 @p62)) % 0.37/0.62 (step @p68 :rule aci_norm :args ((= (or (or @t92 @t20) (or @t109 @t115)) @t118))) % 0.37/0.62 (step @p69 :rule refl :args (@t115)) % 0.37/0.62 (step @p70 :rule refl :args (@t86)) % 0.37/0.62 (step @p71 :rule bool-double-not-elim :args (@t108)) % 0.37/0.62 (step @p72 :rule nary_cong :premises (@p71 @p70) :args ((and (not @t119) @t86))) % 0.37/0.62 (step @p73 :rule bool-or-de-morgan :args (@t119 @t85 false)) % 0.37/0.62 (step @p74 :rule trans :premises (@p73 @p72)) % 0.37/0.62 (step @p75 :rule nary_cong :premises (@p74 @p69) :args ((or (not @t120) @t115))) % 0.37/0.62 (step @p76 :rule bool-impl-elim :args (@t120 @t115)) % 0.37/0.62 (step @p77 :rule trans :premises (@p76 @p75)) % 0.37/0.62 (step @p78 :rule bool-double-not-elim :args (@t20)) % 0.37/0.62 (step @p79 :rule nary_cong :premises (@p54 @p78) :args ((or @t92 (not @t44)))) % 0.37/0.62 (step @p80 :rule bool-and-de-morgan :args (@t76 @t44 true)) % 0.37/0.62 (step @p81 :rule trans :premises (@p80 @p79)) % 0.37/0.62 (step @p82 :rule nary_cong :premises (@p81 @p77) :args ((or (not @t77) @t121))) % 0.37/0.62 (step @p83 :rule trans :premises (@p82 @p68)) % 0.37/0.62 (step @p84 :rule bool-impl-elim :args (@t77 @t121)) % 0.37/0.62 (step @p85 :rule trans :premises (@p84 @p83)) % 0.37/0.62 (step @p86 :rule cong :premises (@p85) :args ((forall @t3 (=> @t77 @t121)))) % 0.37/0.62 (step @p87 :rule trans :premises (@p86 @p67)) % 0.37/0.62 (step @p88 :rule refl :args (@t114)) % 0.37/0.62 (step @p89 :rule bool-double-not-elim :args (@t82)) % 0.37/0.62 (step @p90 :rule refl :args (@t83)) % 0.37/0.62 (step @p91 :rule nary_cong :premises (@p90 @p89 @p88) :args (@t124)) % 0.37/0.62 (step @p92 :rule aci_norm :args ((= (or @t83 (or @t123 @t114)) @t124))) % 0.37/0.62 (step @p93 :rule trans :premises (@p92 @p91)) % 0.37/0.62 (step @p94 :rule bool-and-de-morgan :args (@t122 @t113 true)) % 0.37/0.62 (step @p95 :rule nary_cong :premises (@p90 @p94) :args ((or @t83 (not (and @t122 @t113))))) % 0.37/0.62 (step @p96 :rule bool-and-de-morgan :args (@t60 @t122 (and @t113))) % 0.37/0.62 (step @p97 :rule trans :premises (@p96 @p95)) % 0.37/0.62 (step @p98 :rule trans :premises (@p97 @p93)) % 0.37/0.62 (step @p99 :rule cong :premises (@p98) :args (@t126)) % 0.37/0.62 (step @p100 :rule cong :premises (@p99) :args (@t127)) % 0.37/0.62 (step @p101 :rule exists-elim :args ((= (exists @t23 @t125) @t127))) % 0.37/0.62 (step @p102 :rule trans :premises (@p101 @p100)) % 0.37/0.62 (step @p103 :rule aci_norm :args ((= (or (or @t107 @t106) @t54) @t112))) % 0.37/0.62 (step @p104 :rule refl :args (@t54)) % 0.37/0.62 (step @p105 :rule bool-double-not-elim :args (@t106)) % 0.37/0.62 (step @p106 :rule refl :args (@t107)) % 0.37/0.62 (step @p107 :rule nary_cong :premises (@p106 @p105) :args ((or @t107 @t129))) % 0.37/0.62 (step @p108 :rule bool-and-de-morgan :args (@t56 @t128 true)) % 0.37/0.62 (step @p109 :rule trans :premises (@p108 @p107)) % 0.37/0.62 (step @p110 :rule nary_cong :premises (@p109 @p104) :args ((or (not @t130) @t54))) % 0.37/0.62 (step @p111 :rule trans :premises (@p110 @p103)) % 0.37/0.62 (step @p112 :rule bool-impl-elim :args (@t130 @t54)) % 0.37/0.62 (step @p113 :rule trans :premises (@p112 @p111)) % 0.37/0.62 (step @p114 :rule cong :premises (@p113) :args ((forall @t26 (=> @t130 @t54)))) % 0.37/0.62 (step @p115 :rule refl :args (@t54)) % 0.37/0.62 (step @p116 :rule eq-symm :args (@t11 tptp.sz00)) % 0.37/0.62 (step @p117 :rule cong :premises (@p116) :args (@t55)) % 0.37/0.62 (step @p118 :rule refl :args (@t56)) % 0.37/0.62 (step @p119 :rule nary_cong :premises (@p118 @p117) :args (@t57)) % 0.37/0.62 (step @p120 :rule cong :premises (@p119 @p115) :args (@t58)) % 0.37/0.62 (step @p121 :rule cong :premises (@p120) :args (@t59)) % 0.37/0.62 (step @p122 :rule trans :premises (@p121 @p114)) % 0.37/0.62 (step @p123 :rule eq-symm :args (@t5 tptp.sz00)) % 0.37/0.62 (step @p124 :rule cong :premises (@p123) :args (@t48)) % 0.37/0.62 (step @p125 :rule refl :args (@t60)) % 0.37/0.62 (step @p126 :rule nary_cong :premises (@p125 @p124 @p122) :args (@t61)) % 0.37/0.62 (step @p127 :rule cong :premises (@p126) :args (@t62)) % 0.37/0.62 (step @p128 :rule trans :premises (@p127 @p102)) % 0.37/0.62 (step @p129 :rule quant-miniscope-or :args ((= (forall @t23 @t131) @t120))) % 0.37/0.62 (step @p130 :rule aci_norm :args ((= @t132 @t131))) % 0.37/0.62 (step @p131 :rule cong :premises (@p130) :args ((forall @t23 @t132))) % 0.37/0.62 (step @p132 :rule trans :premises (@p131 @p129)) % 0.37/0.62 (step @p133 :rule aci_norm :args ((= (or (or @t83 @t82) (or @t81 @t119)) @t132))) % 0.37/0.62 (step @p134 :rule bool-impl-elim :args (@t70 @t119)) % 0.37/0.62 (step @p135 :rule nary_cong :premises (@p90 @p89) :args ((or @t83 @t123))) % 0.37/0.62 (step @p136 :rule bool-and-de-morgan :args (@t60 @t122 true)) % 0.37/0.62 (step @p137 :rule trans :premises (@p136 @p135)) % 0.37/0.62 (step @p138 :rule nary_cong :premises (@p137 @p134) :args ((or (not @t134) @t133))) % 0.37/0.62 (step @p139 :rule trans :premises (@p138 @p133)) % 0.37/0.62 (step @p140 :rule bool-impl-elim :args (@t134 @t133)) % 0.37/0.62 (step @p141 :rule trans :premises (@p140 @p139)) % 0.37/0.62 (step @p142 :rule cong :premises (@p141) :args ((forall @t23 (=> @t134 @t133)))) % 0.37/0.62 (step @p143 :rule trans :premises (@p142 @p132)) % 0.37/0.62 (step @p144 :rule refl :args (@t105)) % 0.37/0.62 (step @p145 :rule nary_cong :premises (@p106 @p105 @p144) :args (@t135)) % 0.37/0.62 (step @p146 :rule aci_norm :args ((= (or @t107 (or @t129 @t105)) @t135))) % 0.37/0.62 (step @p147 :rule trans :premises (@p146 @p145)) % 0.37/0.62 (step @p148 :rule bool-and-de-morgan :args (@t128 @t104 true)) % 0.37/0.62 (step @p149 :rule nary_cong :premises (@p106 @p148) :args ((or @t107 (not (and @t128 @t104))))) % 0.37/0.62 (step @p150 :rule bool-and-de-morgan :args (@t56 @t128 (and @t104))) % 0.37/0.62 (step @p151 :rule trans :premises (@p150 @p149)) % 0.37/0.62 (step @p152 :rule trans :premises (@p151 @p147)) % 0.37/0.62 (step @p153 :rule cong :premises (@p152) :args (@t137)) % 0.37/0.62 (step @p154 :rule cong :premises (@p153) :args (@t138)) % 0.37/0.62 (step @p155 :rule exists-elim :args ((= (exists @t26 @t136) @t138))) % 0.37/0.62 (step @p156 :rule trans :premises (@p155 @p154)) % 0.37/0.62 (step @p157 :rule aci_norm :args ((= (or (or @t89 @t88) @t63) @t103))) % 0.37/0.62 (step @p158 :rule refl :args (@t63)) % 0.37/0.62 (step @p159 :rule bool-double-not-elim :args (@t88)) % 0.37/0.62 (step @p160 :rule refl :args (@t89)) % 0.37/0.62 (step @p161 :rule nary_cong :premises (@p160 @p159) :args ((or @t89 (not @t139)))) % 0.37/0.62 (step @p162 :rule bool-and-de-morgan :args (@t64 @t139 true)) % 0.37/0.62 (step @p163 :rule trans :premises (@p162 @p161)) % 0.37/0.62 (step @p164 :rule nary_cong :premises (@p163 @p158) :args ((or (not @t140) @t63))) % 0.37/0.62 (step @p165 :rule trans :premises (@p164 @p157)) % 0.37/0.62 (step @p166 :rule bool-impl-elim :args (@t140 @t63)) % 0.37/0.62 (step @p167 :rule trans :premises (@p166 @p165)) % 0.37/0.62 (step @p168 :rule cong :premises (@p167) :args ((forall @t33 (=> @t140 @t63)))) % 0.37/0.62 (step @p169 :rule refl :args (@t63)) % 0.37/0.62 (step @p170 :rule eq-symm :args (@t29 tptp.sz00)) % 0.37/0.62 (step @p171 :rule cong :premises (@p170) :args (@t47)) % 0.37/0.62 (step @p172 :rule refl :args (@t64)) % 0.37/0.62 (step @p173 :rule nary_cong :premises (@p172 @p171) :args (@t65)) % 0.37/0.62 (step @p174 :rule cong :premises (@p173 @p169) :args (@t66)) % 0.37/0.62 (step @p175 :rule cong :premises (@p174) :args (@t67)) % 0.37/0.62 (step @p176 :rule trans :premises (@p175 @p168)) % 0.37/0.62 (step @p177 :rule nary_cong :premises (@p118 @p117 @p176) :args (@t68)) % 0.37/0.62 (step @p178 :rule cong :premises (@p177) :args (@t69)) % 0.37/0.62 (step @p179 :rule trans :premises (@p178 @p156)) % 0.37/0.62 (step @p180 :rule refl :args (@t70)) % 0.37/0.62 (step @p181 :rule cong :premises (@p180 @p179) :args (@t71)) % 0.37/0.62 (step @p182 :rule nary_cong :premises (@p125 @p124) :args (@t72)) % 0.37/0.62 (step @p183 :rule cong :premises (@p182 @p181) :args (@t73)) % 0.37/0.62 (step @p184 :rule cong :premises (@p183) :args (@t74)) % 0.37/0.62 (step @p185 :rule trans :premises (@p184 @p143)) % 0.37/0.62 (step @p186 :rule cong :premises (@p185 @p128) :args (@t75)) % 0.37/0.62 (step @p187 :rule refl :args (@t77)) % 0.37/0.62 (step @p188 :rule cong :premises (@p187 @p186) :args (@t78)) % 0.37/0.62 (step @p189 :rule cong :premises (@p188) :args (@t79)) % 0.37/0.62 (step @p190 :rule trans :premises (@p189 @p87)) % 0.37/0.62 (step @p191 :rule cong :premises (@p190) :args (@t80)) % 0.37/0.62 (step @p192 :rule eq_resolve :premises (@p45 @p191)) % 0.37/0.62 (step @p193 :rule not_or_elim :premises (@p192) :args (1)) % 0.37/0.62 (step @p194 :rule refl :args (@t158)) % 0.37/0.62 (step @p195 :rule bool-double-not-elim :args (@t94)) % 0.37/0.62 (step @p196 :rule nary_cong :premises (@p195 @p194) :args ((or (not @t159) @t158))) % 0.37/0.62 (step @p197 :rule refl :args (@t153)) % 0.37/0.62 (step @p198 :rule eq-symm :args (@t141 tptp.sz00)) % 0.37/0.62 (step @p199 :rule refl :args (@t156)) % 0.37/0.62 (step @p200 :rule nary_cong :premises (@p199 @p198 @p197) :args (@t160)) % 0.37/0.62 (step @p201 :rule cong :premises (@p200) :args (@t161)) % 0.37/0.62 (step @p202 :rule refl :args (@t159)) % 0.37/0.62 (step @p203 :rule cong :premises (@p202 @p201) :args ((=> @t159 @t161))) % 0.37/0.62 (assume-push @p261 @t159) % 0.37/0.62 (step @p205 :rule skolemize :premises (@p193)) % 0.37/0.62 (step-pop @p262 :rule scope :premises (@p205)) % 0.37/0.62 (step @p206 :rule process_scope :premises (@p262) :args (@t161)) % 0.37/0.62 (step @p208 :rule eq_resolve :premises (@p206 @p203)) % 0.37/0.62 (step @p209 :rule implies_elim :premises (@p208)) % 0.37/0.62 (step @p210 :rule eq_resolve :premises (@p209 @p196)) % 0.37/0.62 (step @p211 :rule chain_m_resolution :premises (@p210 @p193) :args (@t158 @t162 (@list @t94))) % 0.37/0.62 (step @p212 :rule cnf_or_neg :args (@t157 2)) % 0.37/0.62 (step @p213 :rule chain_m_resolution :premises (@p212 @p211) :args ((not @t153) @t162 @t163)) % 0.37/0.62 (step @p214 :rule not_or_elim :premises (@p192) :args (0)) % 0.37/0.62 (step @p215 :rule not_not_elim :premises (@p214)) % 0.37/0.62 (step @p216 :rule instantiate :premises (@p215) :args ((@list @t141))) % 0.37/0.62 (step @p217 :rule cnf_or_neg :args (@t157 1)) % 0.37/0.62 (step @p218 :rule chain_m_resolution :premises (@p217 @p211) :args ((not @t154) @t162 @t163)) % 0.37/0.62 (step @p219 :rule bool-double-not-elim :args (@t155)) % 0.37/0.62 (step @p220 :rule refl :args (@t157)) % 0.37/0.62 (step @p221 :rule nary_cong :premises (@p220 @p219) :args ((or @t157 (not @t156)))) % 0.37/0.62 (step @p222 :rule cnf_or_neg :args (@t157 0)) % 0.37/0.62 (step @p223 :rule eq_resolve :premises (@p222 @p221)) % 0.37/0.62 (step @p224 :rule reordering :premises (@p223) :args ((or @t155 @t157))) % 0.37/0.62 (step @p225 :rule chain_m_resolution :premises (@p224 @p211) :args (@t155 @t162 @t163)) % 0.37/0.62 (step @p226 :rule cnf_or_pos :args (@t166)) % 0.37/0.62 (step @p227 :rule reordering :premises (@p226) :args ((or @t156 @t154 @t165 (not @t166)))) % 0.37/0.62 (step @p228 :rule chain_m_resolution :premises (@p227 @p225 @p218 @p216) :args (@t165 @t167 (@list @t155 @t154 @t166))) % 0.37/0.62 (step @p229 :rule alpha_equiv :args (@t143 (@list @t5) @t99)) % 0.37/0.62 (step @p230 :rule equiv_elim1 :premises (@p229)) % 0.37/0.62 (step @p231 :rule chain_m_resolution :premises (@p230 @p228) :args (@t144 @t162 (@list @t164))) % 0.37/0.62 (step @p232 :rule bool-double-not-elim :args (@t143)) % 0.37/0.62 (step @p233 :rule refl :args (@t168)) % 0.37/0.62 (step @p234 :rule nary_cong :premises (@p197 @p233 @p232) :args ((or @t153 @t168 (not @t144)))) % 0.37/0.62 (step @p235 :rule cnf_and_neg :args (@t153)) % 0.37/0.62 (step @p236 :rule eq_resolve :premises (@p235 @p234)) % 0.37/0.62 (step @p237 :rule reordering :premises (@p236) :args ((or @t143 @t153 @t168))) % 0.37/0.62 (step @p238 :rule chain_m_resolution :premises (@p237 @p231 @p213) :args (@t168 (@list true true) (@list @t143 @t153))) % 0.37/0.62 (step @p239 :rule bool-double-not-elim :args (@t147)) % 0.37/0.62 (step @p240 :rule refl :args (@t152)) % 0.37/0.62 (step @p241 :rule nary_cong :premises (@p240 @p239) :args ((or @t152 (not @t148)))) % 0.37/0.62 (step @p242 :rule cnf_or_neg :args (@t152 2)) % 0.37/0.62 (step @p243 :rule eq_resolve :premises (@p242 @p241)) % 0.37/0.62 (step @p244 :rule reordering :premises (@p243) :args ((or @t147 @t152))) % 0.37/0.62 (step @p245 :rule chain_m_resolution :premises (@p244 @p238) :args (@t147 @t162 @t169)) % 0.37/0.62 (step @p246 :rule instantiate :premises (@p215) :args ((@list @t145))) % 0.37/0.62 (step @p247 :rule cnf_or_neg :args (@t152 1)) % 0.37/0.62 (step @p248 :rule chain_m_resolution :premises (@p247 @p238) :args ((not @t149) @t162 @t169)) % 0.47/0.63 (step @p249 :rule bool-double-not-elim :args (@t150)) % 0.47/0.63 (step @p250 :rule nary_cong :premises (@p240 @p249) :args ((or @t152 (not @t151)))) % 0.47/0.63 (step @p251 :rule cnf_or_neg :args (@t152 0)) % 0.47/0.63 (step @p252 :rule eq_resolve :premises (@p251 @p250)) % 0.47/0.63 (step @p253 :rule reordering :premises (@p252) :args ((or @t150 @t152))) % 0.47/0.63 (step @p254 :rule chain_m_resolution :premises (@p253 @p238) :args (@t150 @t162 @t169)) % 0.47/0.63 (step @p255 :rule cnf_or_pos :args (@t172)) % 0.47/0.63 (step @p256 :rule reordering :premises (@p255) :args ((or @t151 @t149 @t171 (not @t172)))) % 0.47/0.63 (step @p257 :rule chain_m_resolution :premises (@p256 @p254 @p248 @p246) :args (@t171 @t167 (@list @t150 @t149 @t172))) % 0.47/0.63 (step @p258 :rule alpha_equiv :args (@t147 (@list @t29) @t99)) % 0.47/0.63 (step @p259 :rule equiv_elim1 :premises (@p258)) % 0.47/0.63 (step @p260 false :rule chain_m_resolution :premises (@p259 @p257 @p245) :args (false (@list true false) (@list @t170 @t147))) % 0.47/0.63 ) % 0.47/0.63 % SZS output end Proof % 0.47/0.63 % cvc5 exiting %------------------------------------------------------------------------------