%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG119+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 : n027.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 08:45:44 AM UTC 2026 % Result : Theorem 0.53s 0.70s % Output : Proof 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG119+1 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n027.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 14:08:36 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.53/0.70 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.53/0.70 % SZS status Theorem % 0.53/0.70 % SZS output start Proof % 0.53/0.70 ( % 0.53/0.70 (declare-sort $$unsorted 0) % 0.53/0.70 (declare-const tptp.xq $$unsorted) % 0.53/0.70 (declare-const tptp.xu $$unsorted) % 0.53/0.70 (declare-const tptp.xc $$unsorted) % 0.53/0.70 (declare-const tptp.xa $$unsorted) % 0.53/0.70 (declare-const tptp.xI $$unsorted) % 0.53/0.70 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 0.53/0.70 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.53/0.70 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.53/0.70 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.53/0.70 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.53/0.70 (declare-const tptp.sz00 $$unsorted) % 0.53/0.70 (declare-const tptp.sz10 $$unsorted) % 0.53/0.70 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.53/0.70 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.53/0.70 (declare-const tptp.xr $$unsorted) % 0.53/0.70 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.70 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.70 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.53/0.70 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 0.53/0.70 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.70 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.53/0.70 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.53/0.70 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.53/0.70 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.53/0.70 (declare-const tptp.xb $$unsorted) % 0.53/0.70 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.70 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.53/0.70 (define @t1 () (@var "W0" $$unsorted)) % 0.53/0.70 (define @t2 () (tptp.aElement0 @t1)) % 0.53/0.70 (define @t3 () (@list @t1)) % 0.53/0.70 (define @t4 () (tptp.smndt0 @t1)) % 0.53/0.70 (define @t5 () (@var "W1" $$unsorted)) % 0.53/0.70 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.53/0.70 (define @t7 () (tptp.aElement0 @t5)) % 0.53/0.70 (define @t8 () (and @t2 @t7)) % 0.53/0.70 (define @t9 () (@list @t1 @t5)) % 0.53/0.70 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.53/0.70 (define @t11 () (tptp.aElement0 @t10)) % 0.53/0.70 (define @t12 () (forall @t9 (=> @t8 @t11))) % 0.53/0.71 (define @t13 () (@var "W2" $$unsorted)) % 0.53/0.71 (define @t14 () (tptp.sdtpldt0 @t5 @t13)) % 0.53/0.71 (define @t15 () (tptp.aElement0 @t13)) % 0.53/0.71 (define @t16 () (and @t2 @t7 @t15)) % 0.53/0.71 (define @t17 () (@list @t1 @t5 @t13)) % 0.53/0.71 (define @t18 () (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1))) % 0.53/0.71 (define @t19 () (tptp.sdtpldt0 @t1 tptp.sz00)) % 0.53/0.71 (define @t20 () (and (= @t19 @t1) @t18)) % 0.53/0.71 (define @t21 () (=> @t2 @t20)) % 0.53/0.71 (define @t22 () (forall @t3 @t21)) % 0.53/0.71 (define @t23 () (tptp.sdtasdt0 @t5 @t1)) % 0.53/0.71 (define @t24 () (= @t10 @t23)) % 0.53/0.71 (define @t25 () (forall @t9 (=> @t8 @t24))) % 0.53/0.71 (define @t26 () (tptp.sdtasdt0 @t1 @t13)) % 0.53/0.71 (define @t27 () (tptp.smndt0 tptp.sz10)) % 0.53/0.71 (define @t28 () (= @t5 tptp.sz00)) % 0.53/0.71 (define @t29 () (= @t1 tptp.sz00)) % 0.53/0.71 (define @t30 () (tptp.aSet0 @t1)) % 0.53/0.71 (define @t31 () (tptp.aElementOf0 @t5 @t1)) % 0.53/0.71 (define @t32 () (@list @t5)) % 0.53/0.71 (define @t33 () (forall @t32 (=> @t31 @t7))) % 0.53/0.71 (define @t34 () (=> @t30 @t33)) % 0.53/0.71 (define @t35 () (forall @t3 @t34)) % 0.53/0.71 (define @t36 () (tptp.aElementOf0 @t13 @t1)) % 0.53/0.71 (define @t37 () (tptp.aElementOf0 @t13 @t5)) % 0.53/0.71 (define @t38 () (@list @t13)) % 0.53/0.71 (define @t39 () (tptp.aSet0 @t5)) % 0.53/0.71 (define @t40 () (and @t30 @t39)) % 0.53/0.71 (define @t41 () (@var "W3" $$unsorted)) % 0.53/0.71 (define @t42 () (@var "W5" $$unsorted)) % 0.53/0.71 (define @t43 () (@var "W4" $$unsorted)) % 0.53/0.71 (define @t44 () (tptp.aElementOf0 @t41 @t13)) % 0.53/0.71 (define @t45 () (@list @t41)) % 0.53/0.71 (define @t46 () (tptp.aSet0 @t13)) % 0.53/0.71 (define @t47 () (tptp.sdtpldt1 @t1 @t5)) % 0.53/0.71 (define @t48 () (tptp.sdtasasdt0 @t1 @t5)) % 0.53/0.71 (define @t49 () (tptp.sdtasdt0 @t13 @t5)) % 0.53/0.71 (define @t50 () (tptp.aElementOf0 @t49 @t1)) % 0.53/0.71 (define @t51 () (forall @t38 (=> @t15 @t50))) % 0.53/0.71 (define @t52 () (tptp.aElementOf0 @t14 @t1)) % 0.53/0.71 (define @t53 () (forall @t38 (=> @t36 @t52))) % 0.53/0.71 (define @t54 () (and @t53 @t51)) % 0.53/0.71 (define @t55 () (=> @t31 @t54)) % 0.53/0.71 (define @t56 () (forall @t32 @t55)) % 0.53/0.71 (define @t57 () (and @t30 @t56)) % 0.53/0.71 (define @t58 () (tptp.aIdeal0 @t1)) % 0.53/0.71 (define @t59 () (= @t58 @t57)) % 0.53/0.71 (define @t60 () (forall @t3 @t59)) % 0.53/0.71 (define @t61 () (and @t58 (tptp.aIdeal0 @t5))) % 0.53/0.71 (define @t62 () (tptp.aElement0 @t41)) % 0.53/0.71 (define @t63 () (@list @t13 @t41)) % 0.53/0.71 (define @t64 () (tptp.aNaturalNumber0 @t1)) % 0.53/0.71 (define @t65 () (tptp.sbrdtbr0 @t1)) % 0.53/0.71 (define @t66 () (not @t29)) % 0.53/0.71 (define @t67 () (and @t15 (= @t26 @t5))) % 0.53/0.71 (define @t68 () (exists @t38 @t67)) % 0.53/0.71 (define @t69 () (tptp.doDivides0 @t1 @t5)) % 0.53/0.71 (define @t70 () (= @t69 @t68)) % 0.53/0.71 (define @t71 () (=> @t8 @t70)) % 0.53/0.71 (define @t72 () (forall @t9 @t71)) % 0.53/0.71 (define @t73 () (tptp.slsdtgt0 @t1)) % 0.53/0.71 (define @t74 () (tptp.aElement0 tptp.xb)) % 0.53/0.71 (define @t75 () (tptp.slsdtgt0 tptp.xb)) % 0.53/0.71 (define @t76 () (tptp.slsdtgt0 tptp.xa)) % 0.53/0.71 (define @t77 () (tptp.sdtpldt1 @t76 @t75)) % 0.53/0.71 (define @t78 () (tptp.aIdeal0 tptp.xI)) % 0.53/0.71 (define @t79 () (tptp.sbrdtbr0 tptp.xu)) % 0.53/0.71 (define @t80 () (tptp.aElementOf0 tptp.xu tptp.xI)) % 0.53/0.71 (define @t81 () (tptp.doDivides0 tptp.xu tptp.xb)) % 0.53/0.71 (define @t82 () (= tptp.xr tptp.sz00)) % 0.53/0.71 (define @t83 () (tptp.sdtasdt0 tptp.xq tptp.xu)) % 0.53/0.71 (define @t84 () (tptp.sdtpldt0 @t83 tptp.xr)) % 0.53/0.71 (define @t85 () (= tptp.xb @t84)) % 0.53/0.71 (define @t86 () (tptp.aElement0 tptp.xq)) % 0.53/0.71 (define @t87 () (not @t7)) % 0.53/0.71 (define @t88 () (not @t2)) % 0.53/0.71 (define @t89 () (or @t88 @t87)) % 0.53/0.71 (define @t90 () (not @t8)) % 0.53/0.71 (define @t91 () (@list tptp.xq tptp.xu)) % 0.53/0.71 (define @t92 () (@var "BOUND_VARIABLE_7882" $$unsorted)) % 0.53/0.71 (define @t93 () (tptp.aElement0 @t92)) % 0.53/0.71 (define @t94 () (not (tptp.aElementOf0 @t92 @t1))) % 0.53/0.71 (define @t95 () (not @t30)) % 0.53/0.71 (define @t96 () (or @t94 @t93)) % 0.53/0.71 (define @t97 () (or @t95 @t96)) % 0.53/0.71 (define @t98 () (forall (@list @t1 @t92) @t97)) % 0.53/0.71 (define @t99 () (@list @t92)) % 0.53/0.71 (define @t100 () (forall @t99 @t97)) % 0.53/0.71 (define @t101 () (forall @t99 @t96)) % 0.53/0.71 (define @t102 () (or @t95 @t101)) % 0.53/0.71 (define @t103 () (not @t31)) % 0.53/0.71 (define @t104 () (forall @t32 (or @t103 @t7))) % 0.53/0.71 (define @t105 () (@var "BOUND_VARIABLE_7994" $$unsorted)) % 0.53/0.71 (define @t106 () (tptp.sdtasdt0 @t105 @t5)) % 0.53/0.71 (define @t107 () (not (tptp.aElement0 @t105))) % 0.53/0.71 (define @t108 () (or @t107 (tptp.aElementOf0 @t106 @t1))) % 0.53/0.71 (define @t109 () (@var "BOUND_VARIABLE_7987" $$unsorted)) % 0.53/0.71 (define @t110 () (tptp.sdtpldt0 @t5 @t109)) % 0.53/0.71 (define @t111 () (or (not (tptp.aElementOf0 @t109 @t1)) (tptp.aElementOf0 @t110 @t1))) % 0.53/0.71 (define @t112 () (and @t111 @t108)) % 0.53/0.71 (define @t113 () (or @t103 @t112)) % 0.53/0.71 (define @t114 () (@list @t5 @t109 @t105)) % 0.53/0.71 (define @t115 () (@list @t109 @t105)) % 0.53/0.71 (define @t116 () (forall @t115 @t113)) % 0.53/0.71 (define @t117 () (forall (@list @t105) @t108)) % 0.53/0.71 (define @t118 () (@list @t13)) % 0.53/0.71 (define @t119 () (forall @t115 @t108)) % 0.53/0.71 (define @t120 () (forall (@list @t109) @t111)) % 0.53/0.71 (define @t121 () (forall @t115 @t111)) % 0.53/0.71 (define @t122 () (and @t121 @t119)) % 0.53/0.71 (define @t123 () (forall @t115 @t112)) % 0.53/0.71 (define @t124 () (or @t103 @t123)) % 0.53/0.71 (define @t125 () (not @t15)) % 0.53/0.71 (define @t126 () (and (forall @t38 (or (not @t36) @t52)) (forall @t38 (or @t125 @t50)))) % 0.53/0.71 (define @t127 () (tptp.aSet0 tptp.xI)) % 0.53/0.71 (define @t128 () (and @t127 (forall @t114 (or (not (tptp.aElementOf0 @t5 tptp.xI)) (and (or (not (tptp.aElementOf0 @t109 tptp.xI)) (tptp.aElementOf0 @t110 tptp.xI)) (or @t107 (tptp.aElementOf0 @t106 tptp.xI))))))) % 0.53/0.71 (define @t129 () (= @t78 @t128)) % 0.53/0.71 (define @t130 () (@list false false)) % 0.53/0.71 (define @t131 () (@list false)) % 0.53/0.71 (define @t132 () (tptp.aElement0 tptp.xu)) % 0.53/0.71 (define @t133 () (not @t80)) % 0.53/0.71 (define @t134 () (not @t127)) % 0.53/0.71 (define @t135 () (or @t134 @t133 @t132)) % 0.53/0.71 (define @t136 () (@list false false false)) % 0.53/0.71 (define @t137 () (tptp.sdtasdt0 tptp.xu tptp.xq)) % 0.53/0.71 (define @t138 () (= @t83 @t137)) % 0.53/0.71 (define @t139 () (not @t132)) % 0.53/0.71 (define @t140 () (not @t86)) % 0.53/0.71 (define @t141 () (or @t140 @t139 @t138)) % 0.53/0.71 (define @t142 () (@list @t86 @t132 @t141)) % 0.53/0.71 (define @t143 () (and (= @t1 @t19) @t18)) % 0.53/0.71 (define @t144 () (tptp.aElement0 @t83)) % 0.53/0.71 (define @t145 () (or @t140 @t139 @t144)) % 0.53/0.71 (define @t146 () (= @t83 (tptp.sdtpldt0 @t83 tptp.sz00))) % 0.53/0.71 (define @t147 () (and @t146 (= @t83 (tptp.sdtpldt0 tptp.sz00 @t83)))) % 0.53/0.71 (define @t148 () (not @t144)) % 0.53/0.71 (define @t149 () (or @t148 @t147)) % 0.53/0.71 (define @t150 () (= @t5 @t26)) % 0.53/0.71 (define @t151 () (= @t69 (not (forall @t38 (or @t125 (not @t150)))))) % 0.53/0.71 (define @t152 () (and @t15 @t150)) % 0.53/0.71 (define @t153 () (forall @t38 (not @t152))) % 0.53/0.71 (define @t154 () (not @t153)) % 0.53/0.71 (define @t155 () (forall @t38 (or @t125 (not (= tptp.xb (tptp.sdtasdt0 tptp.xu @t13)))))) % 0.53/0.71 (define @t156 () (not @t155)) % 0.53/0.71 (define @t157 () (= @t81 @t156)) % 0.53/0.71 (define @t158 () (not @t74)) % 0.53/0.71 (define @t159 () (or @t139 @t158 @t157)) % 0.53/0.71 (define @t160 () (not @t157)) % 0.53/0.71 (define @t161 () (= tptp.xb @t137)) % 0.53/0.71 (define @t162 () (not @t161)) % 0.53/0.71 (define @t163 () (or @t140 @t162)) % 0.53/0.71 (define @t164 () (not @t138)) % 0.53/0.71 (define @t165 () (not @t146)) % 0.53/0.71 (define @t166 () (= tptp.sz00 tptp.xr)) % 0.53/0.71 (define @t167 () (not @t166)) % 0.53/0.71 (define @t168 () (not @t85)) % 0.53/0.71 (define @t169 () (and @t161 @t162)) % 0.53/0.71 (assume @p1 (forall @t3 (=> @t2 true))) % 0.53/0.71 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.53/0.71 (assume @p3 (tptp.aElement0 tptp.sz10)) % 0.53/0.71 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 0.53/0.71 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 0.53/0.71 (assume @p6 @t12) % 0.53/0.71 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.53/0.71 (assume @p8 (forall @t17 (=> @t16 (= (tptp.sdtpldt0 @t6 @t13) (tptp.sdtpldt0 @t1 @t14))))) % 0.53/0.71 (assume @p9 @t22) % 0.53/0.71 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.53/0.71 (assume @p11 @t25) % 0.53/0.71 (assume @p12 (forall @t17 (=> @t16 (= (tptp.sdtasdt0 @t10 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t13)))))) % 0.53/0.71 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.53/0.71 (assume @p14 (forall @t17 (=> @t16 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t10 @t26)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t23 (tptp.sdtasdt0 @t13 @t1))))))) % 0.53/0.71 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t27 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t27)))))) % 0.53/0.71 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.53/0.71 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t29 @t28))))) % 0.53/0.71 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.53/0.71 (assume @p19 (forall @t3 (=> @t30 true))) % 0.53/0.71 (assume @p20 @t35) % 0.53/0.71 (assume @p21 (forall @t9 (=> @t40 (=> (and (forall @t38 (=> @t36 @t37)) (forall @t38 (=> @t37 @t36))) (= @t1 @t5))))) % 0.53/0.71 (assume @p22 (forall @t9 (=> @t40 (forall @t38 (= (= @t13 @t47) (and @t46 (forall @t45 (= @t44 (exists (@list @t43 @t42) (and (tptp.aElementOf0 @t43 @t1) (tptp.aElementOf0 @t42 @t5) (= (tptp.sdtpldt0 @t43 @t42) @t41))))))))))) % 0.53/0.71 (assume @p23 (forall @t9 (=> @t40 (forall @t38 (= (= @t13 @t48) (and @t46 (forall @t45 (= @t44 (and (tptp.aElementOf0 @t41 @t1) (tptp.aElementOf0 @t41 @t5)))))))))) % 0.53/0.71 (assume @p24 @t60) % 0.53/0.71 (assume @p25 (forall @t9 (=> @t61 (tptp.aIdeal0 @t47)))) % 0.53/0.71 (assume @p26 (forall @t9 (=> @t61 (tptp.aIdeal0 @t48)))) % 0.53/0.71 (assume @p27 (forall @t17 (=> (and @t2 @t7 (tptp.aIdeal0 @t13)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t13) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t13))))) % 0.53/0.71 (assume @p28 (forall @t9 (=> @t61 (=> (forall @t38 (=> @t15 (tptp.aElementOf0 @t13 @t47))) (forall @t63 (=> (and @t15 @t62) (exists (@list @t43) (and (tptp.aElement0 @t43) (tptp.sdteqdtlpzmzozddtrp0 @t43 @t13 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t43 @t41 @t5))))))))) % 0.53/0.71 (assume @p29 (forall @t3 (=> @t64 true))) % 0.53/0.71 (assume @p30 (forall @t3 (=> (and @t2 @t66) (tptp.aNaturalNumber0 @t65)))) % 0.53/0.71 (assume @p31 (forall @t9 (=> (and @t64 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 0.53/0.71 (assume @p32 (forall @t9 (=> (and @t2 @t7 (not @t28)) (exists @t63 (and @t15 @t62 (= @t1 (tptp.sdtpldt0 @t49 @t41)) (=> (not (= @t41 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t41) (tptp.sbrdtbr0 @t5)))))))) % 0.53/0.71 (assume @p33 @t72) % 0.53/0.71 (assume @p34 (forall @t3 (=> @t2 (forall @t32 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 0.53/0.71 (assume @p35 (forall @t9 (=> @t8 (forall @t38 (= (tptp.aGcdOfAnd0 @t13 @t1 @t5) (and (tptp.aDivisorOf0 @t13 @t1) (tptp.aDivisorOf0 @t13 @t5) (forall @t45 (=> (and (tptp.aDivisorOf0 @t41 @t1) (tptp.aDivisorOf0 @t41 @t5)) (tptp.doDivides0 @t41 @t13))))))))) % 0.53/0.71 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 0.53/0.71 (assume @p37 (forall @t3 (=> @t2 (forall @t32 (= (= @t5 @t73) (and @t39 (forall @t38 (= @t37 (exists @t45 (and @t62 (= (tptp.sdtasdt0 @t1 @t41) @t13))))))))))) % 0.53/0.71 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t73)))) % 0.53/0.71 (assume @p39 (and (tptp.aElement0 tptp.xa) @t74)) % 0.53/0.71 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 0.53/0.71 (assume @p41 (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb)) % 0.53/0.71 (assume @p42 (and @t78 (= tptp.xI @t77))) % 0.53/0.71 (assume @p43 (and (tptp.aElementOf0 tptp.sz00 @t76) (tptp.aElementOf0 tptp.xa @t76) (tptp.aElementOf0 tptp.sz00 @t75) (tptp.aElementOf0 tptp.xb @t75))) % 0.53/0.71 (assume @p44 (exists @t3 (and (tptp.aElementOf0 @t1 @t77) @t66))) % 0.53/0.71 (assume @p45 (and @t80 (not (= tptp.xu tptp.sz00)) (forall @t3 (=> (and (tptp.aElementOf0 @t1 tptp.xI) @t66) (not (tptp.iLess0 @t65 @t79)))))) % 0.53/0.71 (assume @p46 (not (and (tptp.aDivisorOf0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xb)))) % 0.53/0.71 (assume @p47 (exists @t9 (and @t2 @t7 (= tptp.xu (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xa @t1) (tptp.sdtasdt0 tptp.xb @t5)))))) % 0.53/0.71 (assume @p48 (not (not (tptp.doDivides0 tptp.xu tptp.xa)))) % 0.53/0.71 (assume @p49 (not @t81)) % 0.53/0.71 (assume @p50 (and @t86 (tptp.aElement0 tptp.xr) @t85 (or @t82 (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) @t79)))) % 0.53/0.71 (assume @p51 (not (not @t82))) % 0.53/0.71 (assume @p52 true) % 0.53/0.71 (step @p53 :rule and_elim :premises (@p50) :args (2)) % 0.53/0.71 (step @p54 :rule eq-symm :args (tptp.xr tptp.sz00)) % 0.53/0.71 (step @p55 :rule bool-double-not-elim :args (@t82)) % 0.53/0.71 (step @p56 :rule trans :premises (@p55 @p54)) % 0.53/0.71 (step @p57 :rule eq_resolve :premises (@p51 @p56)) % 0.53/0.71 (step @p58 :rule aci_norm :args ((= (or @t89 @t24) (or @t88 @t87 @t24)))) % 0.53/0.71 (step @p59 :rule refl :args (@t24)) % 0.53/0.71 (step @p60 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 0.53/0.71 (step @p61 :rule nary_cong :premises (@p60 @p59) :args ((or @t90 @t24))) % 0.53/0.71 (step @p62 :rule trans :premises (@p61 @p58)) % 0.53/0.71 (step @p63 :rule bool-impl-elim :args (@t8 @t24)) % 0.53/0.71 (step @p64 :rule trans :premises (@p63 @p62)) % 0.53/0.71 (step @p65 :rule cong :premises (@p64) :args (@t25)) % 0.53/0.71 (step @p66 :rule eq_resolve :premises (@p11 @p65)) % 0.53/0.71 (step @p67 :rule instantiate :premises (@p66) :args (@t91)) % 0.53/0.71 (step @p68 :rule aci_norm :args ((= @t97 (or @t95 @t94 @t93)))) % 0.53/0.71 (step @p69 :rule cong :premises (@p68) :args (@t98)) % 0.53/0.71 (step @p70 :rule quant-merge-prenex :args ((= (forall @t3 @t100) @t98))) % 0.53/0.71 (step @p71 :rule alpha_equiv :args (@t101 (@list @t92) (@list @t5))) % 0.53/0.71 (step @p72 :rule refl :args (@t95)) % 0.53/0.71 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t102)) % 0.53/0.71 (step @p74 :rule quant-miniscope-or :args ((= @t100 @t102))) % 0.53/0.71 (step @p75 :rule trans :premises (@p74 @p73)) % 0.53/0.71 (step @p76 :rule symm :premises (@p75)) % 0.53/0.71 (step @p77 :rule cong :premises (@p76) :args ((forall @t3 (or @t95 @t104)))) % 0.53/0.71 (step @p78 :rule trans :premises (@p77 @p70)) % 0.53/0.71 (step @p79 :rule trans :premises (@p78 @p69)) % 0.53/0.71 (step @p80 :rule bool-impl-elim :args (@t30 @t104)) % 0.53/0.71 (step @p81 :rule cong :premises (@p80) :args ((forall @t3 (=> @t30 @t104)))) % 0.53/0.71 (step @p82 :rule trans :premises (@p81 @p79)) % 0.53/0.71 (step @p83 :rule bool-impl-elim :args (@t31 @t7)) % 0.53/0.71 (step @p84 :rule cong :premises (@p83) :args (@t33)) % 0.53/0.71 (step @p85 :rule refl :args (@t30)) % 0.53/0.71 (step @p86 :rule cong :premises (@p85 @p84) :args (@t34)) % 0.53/0.71 (step @p87 :rule cong :premises (@p86) :args (@t35)) % 0.53/0.71 (step @p88 :rule trans :premises (@p87 @p82)) % 0.53/0.71 (step @p89 :rule eq_resolve :premises (@p20 @p88)) % 0.53/0.71 (step @p90 :rule instantiate :premises (@p89) :args ((@list tptp.xI tptp.xu))) % 0.53/0.71 (step @p91 :rule quant-merge-prenex :args ((= (forall @t32 @t116) (forall @t114 @t113)))) % 0.53/0.71 (step @p92 :rule alpha_equiv :args (@t117 (@list @t105) @t118)) % 0.53/0.71 (step @p93 :rule quant-unused-vars :args ((= @t119 @t117))) % 0.53/0.71 (step @p94 :rule trans :premises (@p93 @p92)) % 0.53/0.71 (step @p95 :rule alpha_equiv :args (@t120 (@list @t109) @t118)) % 0.53/0.71 (step @p96 :rule quant-unused-vars :args ((= @t121 @t120))) % 0.53/0.71 (step @p97 :rule trans :premises (@p96 @p95)) % 0.53/0.71 (step @p98 :rule nary_cong :premises (@p97 @p94) :args (@t122)) % 0.53/0.71 (step @p99 :rule quant-miniscope-and :args ((= @t123 @t122))) % 0.53/0.71 (step @p100 :rule trans :premises (@p99 @p98)) % 0.53/0.71 (step @p101 :rule refl :args (@t103)) % 0.53/0.71 (step @p102 :rule nary_cong :premises (@p101 @p100) :args (@t124)) % 0.53/0.71 (step @p103 :rule quant-miniscope-or :args ((= @t116 @t124))) % 0.53/0.71 (step @p104 :rule trans :premises (@p103 @p102)) % 0.53/0.71 (step @p105 :rule symm :premises (@p104)) % 0.53/0.71 (step @p106 :rule cong :premises (@p105) :args ((forall @t32 (or @t103 @t126)))) % 0.53/0.71 (step @p107 :rule trans :premises (@p106 @p91)) % 0.53/0.71 (step @p108 :rule bool-impl-elim :args (@t31 @t126)) % 0.53/0.71 (step @p109 :rule cong :premises (@p108) :args ((forall @t32 (=> @t31 @t126)))) % 0.53/0.71 (step @p110 :rule trans :premises (@p109 @p107)) % 0.53/0.71 (step @p111 :rule bool-impl-elim :args (@t15 @t50)) % 0.53/0.71 (step @p112 :rule cong :premises (@p111) :args (@t51)) % 0.53/0.71 (step @p113 :rule bool-impl-elim :args (@t36 @t52)) % 0.53/0.71 (step @p114 :rule cong :premises (@p113) :args (@t53)) % 0.53/0.71 (step @p115 :rule nary_cong :premises (@p114 @p112) :args (@t54)) % 0.53/0.71 (step @p116 :rule refl :args (@t31)) % 0.53/0.71 (step @p117 :rule cong :premises (@p116 @p115) :args (@t55)) % 0.53/0.71 (step @p118 :rule cong :premises (@p117) :args (@t56)) % 0.53/0.71 (step @p119 :rule trans :premises (@p118 @p110)) % 0.53/0.71 (step @p120 :rule nary_cong :premises (@p85 @p119) :args (@t57)) % 0.53/0.71 (step @p121 :rule refl :args (@t58)) % 0.53/0.71 (step @p122 :rule cong :premises (@p121 @p120) :args (@t59)) % 0.53/0.71 (step @p123 :rule cong :premises (@p122) :args (@t60)) % 0.53/0.71 (step @p124 :rule eq_resolve :premises (@p24 @p123)) % 0.53/0.71 (step @p125 :rule instantiate :premises (@p124) :args ((@list tptp.xI))) % 0.53/0.71 (step @p126 :rule and_elim :premises (@p42) :args (0)) % 0.53/0.71 (step @p127 :rule cnf_equiv_pos1 :args (@t129)) % 0.53/0.71 (step @p128 :rule reordering :premises (@p127) :args ((or (not @t78) @t128 (not @t129)))) % 0.53/0.71 (step @p129 :rule chain_m_resolution :premises (@p128 @p126 @p125) :args (@t128 @t130 (@list @t78 @t129))) % 0.53/0.71 (step @p130 :rule cnf_and_pos :args (@t128 0)) % 0.53/0.71 (step @p131 :rule reordering :premises (@p130) :args ((or @t127 (not @t128)))) % 0.53/0.71 (step @p132 :rule chain_m_resolution :premises (@p131 @p129) :args (@t127 @t131 (@list @t128))) % 0.53/0.71 (step @p133 :rule and_elim :premises (@p45) :args (0)) % 0.53/0.71 (step @p134 :rule cnf_or_pos :args (@t135)) % 0.53/0.71 (step @p135 :rule reordering :premises (@p134) :args ((or @t133 @t132 @t134 (not @t135)))) % 0.53/0.71 (step @p136 :rule chain_m_resolution :premises (@p135 @p133 @p132 @p90) :args (@t132 @t136 (@list @t80 @t127 @t135))) % 0.53/0.71 (step @p137 :rule and_elim :premises (@p50) :args (0)) % 0.53/0.71 (step @p138 :rule cnf_or_pos :args (@t141)) % 0.53/0.71 (step @p139 :rule reordering :premises (@p138) :args ((or @t140 @t139 @t138 (not @t141)))) % 0.53/0.71 (step @p140 :rule chain_m_resolution :premises (@p139 @p137 @p136 @p67) :args (@t138 @t136 @t142)) % 0.53/0.71 (step @p141 :rule bool-impl-elim :args (@t2 @t143)) % 0.53/0.71 (step @p142 :rule cong :premises (@p141) :args ((forall @t3 (=> @t2 @t143)))) % 0.53/0.71 (step @p143 :rule refl :args (@t18)) % 0.53/0.71 (step @p144 :rule eq-symm :args (@t19 @t1)) % 0.53/0.71 (step @p145 :rule nary_cong :premises (@p144 @p143) :args (@t20)) % 0.53/0.71 (step @p146 :rule refl :args (@t2)) % 0.53/0.71 (step @p147 :rule cong :premises (@p146 @p145) :args (@t21)) % 0.53/0.71 (step @p148 :rule cong :premises (@p147) :args (@t22)) % 0.53/0.71 (step @p149 :rule trans :premises (@p148 @p142)) % 0.53/0.71 (step @p150 :rule eq_resolve :premises (@p9 @p149)) % 0.53/0.71 (step @p151 :rule instantiate :premises (@p150) :args ((@list @t83))) % 0.53/0.71 (step @p152 :rule aci_norm :args ((= (or @t89 @t11) (or @t88 @t87 @t11)))) % 0.53/0.71 (step @p153 :rule refl :args (@t11)) % 0.53/0.71 (step @p154 :rule nary_cong :premises (@p60 @p153) :args ((or @t90 @t11))) % 0.53/0.71 (step @p155 :rule trans :premises (@p154 @p152)) % 0.53/0.71 (step @p156 :rule bool-impl-elim :args (@t8 @t11)) % 0.53/0.71 (step @p157 :rule trans :premises (@p156 @p155)) % 0.53/0.71 (step @p158 :rule cong :premises (@p157) :args (@t12)) % 0.53/0.71 (step @p159 :rule eq_resolve :premises (@p6 @p158)) % 0.53/0.71 (step @p160 :rule instantiate :premises (@p159) :args (@t91)) % 0.53/0.71 (step @p161 :rule cnf_or_pos :args (@t145)) % 0.53/0.71 (step @p162 :rule reordering :premises (@p161) :args ((or @t140 @t139 @t144 (not @t145)))) % 0.53/0.71 (step @p163 :rule chain_m_resolution :premises (@p162 @p137 @p136 @p160) :args (@t144 @t136 (@list @t86 @t132 @t145))) % 0.53/0.71 (step @p164 :rule cnf_or_pos :args (@t149)) % 0.53/0.71 (step @p165 :rule reordering :premises (@p164) :args ((or @t148 @t147 (not @t149)))) % 0.53/0.71 (step @p166 :rule chain_m_resolution :premises (@p165 @p163 @p151) :args (@t147 @t130 (@list @t144 @t149))) % 0.53/0.71 (step @p167 :rule cnf_and_pos :args (@t147 0)) % 0.53/0.71 (step @p168 :rule reordering :premises (@p167) :args ((or @t146 (not @t147)))) % 0.53/0.71 (step @p169 :rule chain_m_resolution :premises (@p168 @p166) :args (@t146 @t131 (@list @t147))) % 0.53/0.71 (step @p170 :rule aci_norm :args ((= (or @t89 @t151) (or @t88 @t87 @t151)))) % 0.53/0.71 (step @p171 :rule refl :args (@t151)) % 0.53/0.71 (step @p172 :rule nary_cong :premises (@p60 @p171) :args ((or @t90 @t151))) % 0.53/0.71 (step @p173 :rule trans :premises (@p172 @p170)) % 0.53/0.71 (step @p174 :rule bool-impl-elim :args (@t8 @t151)) % 0.53/0.71 (step @p175 :rule trans :premises (@p174 @p173)) % 0.53/0.71 (step @p176 :rule cong :premises (@p175) :args ((forall @t9 (=> @t8 @t151)))) % 0.53/0.71 (step @p177 :rule bool-and-de-morgan :args (@t15 @t150 true)) % 0.53/0.71 (step @p178 :rule cong :premises (@p177) :args (@t153)) % 0.53/0.71 (step @p179 :rule cong :premises (@p178) :args (@t154)) % 0.53/0.71 (step @p180 :rule exists-elim :args ((= (exists @t38 @t152) @t154))) % 0.53/0.71 (step @p181 :rule trans :premises (@p180 @p179)) % 0.53/0.71 (step @p182 :rule eq-symm :args (@t26 @t5)) % 0.53/0.71 (step @p183 :rule refl :args (@t15)) % 0.53/0.71 (step @p184 :rule nary_cong :premises (@p183 @p182) :args (@t67)) % 0.53/0.71 (step @p185 :rule cong :premises (@p184) :args (@t68)) % 0.53/0.71 (step @p186 :rule trans :premises (@p185 @p181)) % 0.53/0.71 (step @p187 :rule refl :args (@t69)) % 0.53/0.71 (step @p188 :rule cong :premises (@p187 @p186) :args (@t70)) % 0.53/0.71 (step @p189 :rule refl :args (@t8)) % 0.53/0.71 (step @p190 :rule cong :premises (@p189 @p188) :args (@t71)) % 0.53/0.71 (step @p191 :rule cong :premises (@p190) :args (@t72)) % 0.53/0.71 (step @p192 :rule trans :premises (@p191 @p176)) % 0.53/0.71 (step @p193 :rule eq_resolve :premises (@p33 @p192)) % 0.53/0.71 (step @p194 :rule instantiate :premises (@p193) :args ((@list tptp.xu tptp.xb))) % 0.53/0.71 (step @p195 :rule and_elim :premises (@p39) :args (1)) % 0.53/0.71 (step @p196 :rule cnf_or_pos :args (@t159)) % 0.53/0.71 (step @p197 :rule reordering :premises (@p196) :args ((or @t158 @t139 @t157 (not @t159)))) % 0.53/0.71 (step @p198 :rule chain_m_resolution :premises (@p197 @p195 @p136 @p194) :args (@t157 @t136 (@list @t74 @t132 @t159))) % 0.53/0.71 (step @p199 :rule bool-double-not-elim :args (@t155)) % 0.53/0.71 (step @p200 :rule refl :args (@t81)) % 0.53/0.71 (step @p201 :rule refl :args (@t160)) % 0.53/0.71 (step @p202 :rule nary_cong :premises (@p201 @p200 @p199) :args ((or @t160 @t81 (not @t156)))) % 0.53/0.71 (step @p203 :rule cnf_equiv_pos2 :args (@t157)) % 0.53/0.71 (step @p204 :rule eq_resolve :premises (@p203 @p202)) % 0.53/0.71 (step @p205 :rule reordering :premises (@p204) :args ((or @t81 @t155 @t160))) % 0.53/0.71 (step @p206 :rule chain_m_resolution :premises (@p205 @p49 @p198) :args (@t155 (@list true false) (@list @t81 @t157))) % 0.53/0.71 (step @p207 :rule instantiate :premises (@p206) :args ((@list tptp.xq))) % 0.53/0.71 (step @p208 :rule cnf_or_pos :args (@t163)) % 0.53/0.71 (step @p209 :rule reordering :premises (@p208) :args ((or @t140 @t162 (not @t163)))) % 0.53/0.71 (step @p210 :rule chain_m_resolution :premises (@p209 @p137 @p207) :args (@t162 @t130 (@list @t86 @t163))) % 0.53/0.71 (step @p211 :rule bool-double-not-elim :args (@t161)) % 0.53/0.71 (step @p212 :rule refl :args (@t164)) % 0.53/0.71 (step @p213 :rule refl :args (@t165)) % 0.53/0.71 (step @p214 :rule refl :args (@t167)) % 0.53/0.71 (step @p215 :rule refl :args (@t168)) % 0.53/0.71 (step @p216 :rule nary_cong :premises (@p215 @p214 @p213 @p212 @p211) :args ((or @t168 @t167 @t165 @t164 (not @t162)))) % 0.53/0.71 (assume-push @p253 @t161) % 0.53/0.71 (assume-push @p254 @t162) % 0.53/0.71 (step @p219 :rule evaluate :args ((= true false))) % 0.53/0.71 (step @p220 :rule false_intro :premises (@p210)) % 0.53/0.71 (step @p221 :rule chain_m_resolution :premises (@p139 @p137 @p136 @p67) :args (@t138 @t136 @t142)) % 0.53/0.71 (step @p222 :rule symm :premises (@p169)) % 0.53/0.71 (step @p223 :rule symm :premises (@p57)) % 0.53/0.71 (step @p224 :rule refl :args (@t83)) % 0.53/0.71 (step @p225 :rule cong :premises (@p224 @p223) :args (@t84)) % 0.53/0.71 (step @p226 :rule and_elim :premises (@p50) :args (2)) % 0.53/0.71 (step @p227 :rule trans :premises (@p226 @p225 @p222 @p221)) % 0.53/0.71 (step @p228 :rule true_intro :premises (@p227)) % 0.53/0.71 (step @p229 :rule symm :premises (@p228)) % 0.53/0.71 (step @p230 :rule trans :premises (@p229 @p220)) % 0.53/0.71 (step @p231 false :rule eq_resolve :premises (@p230 @p219)) % 0.53/0.71 (step-pop @p255 :rule scope :premises (@p231)) % 0.53/0.71 (step-pop @p256 :rule scope :premises (@p255)) % 0.53/0.71 (step @p232 :rule process_scope :premises (@p256) :args (false)) % 0.53/0.71 (assume-push @p257 @t85) % 0.53/0.71 (assume-push @p258 @t166) % 0.53/0.71 (assume-push @p259 @t146) % 0.53/0.71 (assume-push @p260 @t138) % 0.53/0.71 (assume-push @p261 @t162) % 0.53/0.71 (step @p222 :rule symm :premises (@p169)) % 0.53/0.71 (step @p223 :rule symm :premises (@p57)) % 0.53/0.71 (step @p224 :rule refl :args (@t83)) % 0.53/0.71 (step @p225 :rule cong :premises (@p224 @p223) :args (@t84)) % 0.53/0.71 (step @p240 :rule trans :premises (@p53 @p225 @p222 @p140)) % 0.53/0.71 (step @p241 :rule and_intro :premises (@p240 @p210)) % 0.53/0.71 (step-pop @p262 :rule scope :premises (@p241)) % 0.53/0.71 (step-pop @p263 :rule scope :premises (@p262)) % 0.53/0.71 (step-pop @p264 :rule scope :premises (@p263)) % 0.53/0.71 (step-pop @p265 :rule scope :premises (@p264)) % 0.53/0.71 (step-pop @p266 :rule scope :premises (@p265)) % 0.53/0.71 (step @p242 :rule process_scope :premises (@p266) :args (@t169)) % 0.53/0.71 (step @p248 :rule implies_elim :premises (@p242)) % 0.53/0.71 (step @p249 :rule resolution :premises (@p248 @p232) :args (true @t169)) % 0.53/0.71 (step @p250 :rule not_and :premises (@p249)) % 0.53/0.71 (step @p251 :rule eq_resolve :premises (@p250 @p216)) % 0.53/0.71 (step @p252 false :rule chain_m_resolution :premises (@p251 @p210 @p169 @p140 @p57 @p53) :args (false (@list true false false false false) (@list @t161 @t146 @t138 @t166 @t85))) % 0.53/0.71 ) % 0.53/0.71 % SZS output end Proof % 0.53/0.71 % cvc5 exiting %------------------------------------------------------------------------------