%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG119+4 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n029.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 0.44s 0.65s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG119+4 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n029.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 14:08:32 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.65 % SZS status Theorem % 0.44/0.65 % SZS output start Proof % 0.44/0.65 ( % 0.44/0.65 (declare-sort $$unsorted 0) % 0.44/0.65 (declare-const tptp.xu $$unsorted) % 0.44/0.65 (declare-const tptp.xr $$unsorted) % 0.44/0.65 (declare-const tptp.xI $$unsorted) % 0.44/0.65 (declare-const tptp.xc $$unsorted) % 0.44/0.65 (declare-const tptp.xa $$unsorted) % 0.44/0.65 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.sz00 $$unsorted) % 0.44/0.65 (declare-const tptp.xq $$unsorted) % 0.44/0.65 (declare-const tptp.sz10 $$unsorted) % 0.44/0.65 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.xb $$unsorted) % 0.44/0.65 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.44/0.65 (define @t1 () (@var "W0" $$unsorted)) % 0.44/0.65 (define @t2 () (tptp.aElement0 @t1)) % 0.44/0.65 (define @t3 () (@list @t1)) % 0.44/0.65 (define @t4 () (tptp.smndt0 @t1)) % 0.44/0.65 (define @t5 () (@var "W1" $$unsorted)) % 0.44/0.65 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.44/0.65 (define @t7 () (tptp.aElement0 @t5)) % 0.44/0.65 (define @t8 () (and @t2 @t7)) % 0.44/0.65 (define @t9 () (@list @t1 @t5)) % 0.44/0.65 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.44/0.65 (define @t11 () (tptp.aElement0 @t10)) % 0.44/0.65 (define @t12 () (forall @t9 (=> @t8 @t11))) % 0.44/0.65 (define @t13 () (@var "W2" $$unsorted)) % 0.44/0.65 (define @t14 () (tptp.sdtpldt0 @t5 @t13)) % 0.44/0.65 (define @t15 () (tptp.aElement0 @t13)) % 0.44/0.65 (define @t16 () (and @t2 @t7 @t15)) % 0.44/0.65 (define @t17 () (@list @t1 @t5 @t13)) % 0.44/0.65 (define @t18 () (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1))) % 0.44/0.65 (define @t19 () (tptp.sdtpldt0 @t1 tptp.sz00)) % 0.44/0.65 (define @t20 () (and (= @t19 @t1) @t18)) % 0.44/0.65 (define @t21 () (=> @t2 @t20)) % 0.44/0.65 (define @t22 () (forall @t3 @t21)) % 0.44/0.65 (define @t23 () (tptp.sdtasdt0 @t5 @t1)) % 0.44/0.65 (define @t24 () (= @t10 @t23)) % 0.44/0.65 (define @t25 () (forall @t9 (=> @t8 @t24))) % 0.44/0.65 (define @t26 () (tptp.sdtasdt0 @t1 @t13)) % 0.44/0.65 (define @t27 () (tptp.smndt0 tptp.sz10)) % 0.44/0.65 (define @t28 () (= @t5 tptp.sz00)) % 0.44/0.65 (define @t29 () (= @t1 tptp.sz00)) % 0.44/0.65 (define @t30 () (tptp.aSet0 @t1)) % 0.44/0.65 (define @t31 () (tptp.aElementOf0 @t5 @t1)) % 0.44/0.65 (define @t32 () (@list @t5)) % 0.44/0.65 (define @t33 () (forall @t32 (=> @t31 @t7))) % 0.44/0.65 (define @t34 () (=> @t30 @t33)) % 0.44/0.65 (define @t35 () (forall @t3 @t34)) % 0.44/0.65 (define @t36 () (tptp.aElementOf0 @t13 @t1)) % 0.44/0.65 (define @t37 () (tptp.aElementOf0 @t13 @t5)) % 0.44/0.65 (define @t38 () (@list @t13)) % 0.44/0.65 (define @t39 () (tptp.aSet0 @t5)) % 0.44/0.65 (define @t40 () (and @t30 @t39)) % 0.44/0.65 (define @t41 () (@var "W3" $$unsorted)) % 0.44/0.65 (define @t42 () (@var "W5" $$unsorted)) % 0.44/0.65 (define @t43 () (@var "W4" $$unsorted)) % 0.44/0.65 (define @t44 () (tptp.aElementOf0 @t41 @t13)) % 0.44/0.65 (define @t45 () (@list @t41)) % 0.44/0.65 (define @t46 () (tptp.aSet0 @t13)) % 0.44/0.65 (define @t47 () (tptp.sdtpldt1 @t1 @t5)) % 0.44/0.65 (define @t48 () (tptp.sdtasasdt0 @t1 @t5)) % 0.44/0.65 (define @t49 () (tptp.sdtasdt0 @t13 @t5)) % 0.44/0.65 (define @t50 () (tptp.aIdeal0 @t1)) % 0.44/0.65 (define @t51 () (and @t50 (tptp.aIdeal0 @t5))) % 0.44/0.65 (define @t52 () (tptp.aElement0 @t41)) % 0.44/0.65 (define @t53 () (@list @t13 @t41)) % 0.44/0.65 (define @t54 () (tptp.aNaturalNumber0 @t1)) % 0.44/0.65 (define @t55 () (tptp.sbrdtbr0 @t1)) % 0.44/0.65 (define @t56 () (not @t29)) % 0.44/0.65 (define @t57 () (tptp.slsdtgt0 @t1)) % 0.44/0.65 (define @t58 () (tptp.sdtasdt0 tptp.xc @t1)) % 0.44/0.65 (define @t59 () (tptp.aElement0 tptp.xc)) % 0.44/0.65 (define @t60 () (tptp.slsdtgt0 tptp.xb)) % 0.44/0.65 (define @t61 () (tptp.slsdtgt0 tptp.xa)) % 0.44/0.65 (define @t62 () (tptp.sdtpldt1 @t61 @t60)) % 0.44/0.65 (define @t63 () (tptp.aElementOf0 @t5 @t61)) % 0.44/0.65 (define @t64 () (exists (@list @t5 @t13) (and @t63 (tptp.aElementOf0 @t13 @t60) (= @t14 @t1)))) % 0.44/0.65 (define @t65 () (tptp.aElementOf0 @t1 tptp.xI)) % 0.44/0.65 (define @t66 () (tptp.sdtasdt0 tptp.xb @t5)) % 0.44/0.65 (define @t67 () (tptp.aElementOf0 @t1 @t61)) % 0.44/0.65 (define @t68 () (tptp.aSet0 tptp.xI)) % 0.44/0.65 (define @t69 () (tptp.sdtasdt0 tptp.xb @t1)) % 0.44/0.65 (define @t70 () (tptp.sdtasdt0 tptp.xa @t1)) % 0.44/0.65 (define @t71 () (tptp.aElementOf0 @t5 @t60)) % 0.44/0.65 (define @t72 () (tptp.sbrdtbr0 tptp.xu)) % 0.44/0.65 (define @t73 () (tptp.aElementOf0 tptp.xu tptp.xI)) % 0.44/0.65 (define @t74 () (tptp.aDivisorOf0 tptp.xu tptp.xb)) % 0.44/0.65 (define @t75 () (tptp.doDivides0 tptp.xu tptp.xb)) % 0.44/0.65 (define @t76 () (tptp.sdtasdt0 tptp.xu @t1)) % 0.44/0.65 (define @t77 () (and @t2 (= @t76 tptp.xb))) % 0.44/0.65 (define @t78 () (exists @t3 @t77)) % 0.44/0.65 (define @t79 () (or @t78 @t75 @t74)) % 0.44/0.65 (define @t80 () (tptp.aDivisorOf0 tptp.xu tptp.xa)) % 0.44/0.65 (define @t81 () (tptp.doDivides0 tptp.xu tptp.xa)) % 0.44/0.65 (define @t82 () (and @t2 (= @t76 tptp.xa))) % 0.44/0.65 (define @t83 () (exists @t3 @t82)) % 0.44/0.65 (define @t84 () (or @t83 @t81 @t80)) % 0.44/0.65 (define @t85 () (and @t84 @t79)) % 0.44/0.65 (define @t86 () (not @t85)) % 0.44/0.65 (define @t87 () (and @t83 @t81)) % 0.44/0.65 (define @t88 () (= tptp.xr tptp.sz00)) % 0.44/0.65 (define @t89 () (tptp.sdtasdt0 tptp.xq tptp.xu)) % 0.44/0.65 (define @t90 () (tptp.sdtpldt0 @t89 tptp.xr)) % 0.44/0.65 (define @t91 () (= tptp.xb @t90)) % 0.44/0.65 (define @t92 () (tptp.aElement0 tptp.xq)) % 0.44/0.65 (define @t93 () (= tptp.xa @t76)) % 0.44/0.65 (define @t94 () (and @t2 @t93)) % 0.44/0.65 (define @t95 () (forall @t3 (not @t94))) % 0.44/0.65 (define @t96 () (not @t95)) % 0.44/0.65 (define @t97 () (not @t2)) % 0.44/0.65 (define @t98 () (forall @t3 (or @t97 (not @t93)))) % 0.44/0.65 (define @t99 () (not @t98)) % 0.44/0.65 (define @t100 () (or @t99 @t81 @t80)) % 0.44/0.65 (define @t101 () (@list true)) % 0.44/0.65 (define @t102 () (= tptp.xb @t76)) % 0.44/0.65 (define @t103 () (and @t2 @t102)) % 0.44/0.65 (define @t104 () (forall @t3 (not @t103))) % 0.44/0.65 (define @t105 () (not @t104)) % 0.44/0.65 (define @t106 () (forall @t3 (or @t97 (not @t102)))) % 0.44/0.65 (define @t107 () (not @t106)) % 0.44/0.65 (define @t108 () (or @t107 @t75 @t74)) % 0.44/0.65 (define @t109 () (@list false)) % 0.44/0.65 (define @t110 () (tptp.sdtasdt0 tptp.xu tptp.xq)) % 0.44/0.65 (define @t111 () (= tptp.xb @t110)) % 0.44/0.65 (define @t112 () (not @t111)) % 0.44/0.65 (define @t113 () (not @t92)) % 0.44/0.65 (define @t114 () (or @t113 @t112)) % 0.44/0.65 (define @t115 () (@list false false)) % 0.44/0.65 (define @t116 () (not @t7)) % 0.44/0.65 (define @t117 () (or @t97 @t116)) % 0.44/0.65 (define @t118 () (not @t8)) % 0.44/0.65 (define @t119 () (@list tptp.xq tptp.xu)) % 0.44/0.65 (define @t120 () (@var "BOUND_VARIABLE_7994" $$unsorted)) % 0.44/0.65 (define @t121 () (tptp.aElement0 @t120)) % 0.44/0.65 (define @t122 () (not (tptp.aElementOf0 @t120 @t1))) % 0.44/0.65 (define @t123 () (not @t30)) % 0.44/0.65 (define @t124 () (or @t122 @t121)) % 0.44/0.65 (define @t125 () (or @t123 @t124)) % 0.44/0.65 (define @t126 () (forall (@list @t1 @t120) @t125)) % 0.44/0.65 (define @t127 () (@list @t120)) % 0.44/0.65 (define @t128 () (forall @t127 @t125)) % 0.44/0.65 (define @t129 () (forall @t127 @t124)) % 0.44/0.65 (define @t130 () (or @t123 @t129)) % 0.44/0.65 (define @t131 () (forall @t32 (or (not @t31) @t7))) % 0.44/0.65 (define @t132 () (tptp.aElement0 tptp.xu)) % 0.44/0.65 (define @t133 () (not @t73)) % 0.44/0.65 (define @t134 () (not @t68)) % 0.44/0.65 (define @t135 () (or @t134 @t133 @t132)) % 0.44/0.65 (define @t136 () (@list false false false)) % 0.44/0.65 (define @t137 () (= @t89 @t110)) % 0.44/0.65 (define @t138 () (not @t132)) % 0.44/0.65 (define @t139 () (or @t113 @t138 @t137)) % 0.44/0.65 (define @t140 () (and (= @t1 @t19) @t18)) % 0.44/0.65 (define @t141 () (tptp.aElement0 @t89)) % 0.44/0.65 (define @t142 () (or @t113 @t138 @t141)) % 0.44/0.65 (define @t143 () (= @t89 (tptp.sdtpldt0 @t89 tptp.sz00))) % 0.44/0.65 (define @t144 () (and @t143 (= @t89 (tptp.sdtpldt0 tptp.sz00 @t89)))) % 0.44/0.65 (define @t145 () (not @t141)) % 0.44/0.65 (define @t146 () (or @t145 @t144)) % 0.44/0.65 (define @t147 () (= tptp.sz00 tptp.xr)) % 0.44/0.65 (define @t148 () (and @t91 @t147 @t143 @t137)) % 0.44/0.65 (assume @p1 (forall @t3 (=> @t2 true))) % 0.44/0.65 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.44/0.65 (assume @p3 (tptp.aElement0 tptp.sz10)) % 0.44/0.65 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 0.44/0.65 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 0.44/0.65 (assume @p6 @t12) % 0.44/0.65 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.44/0.65 (assume @p8 (forall @t17 (=> @t16 (= (tptp.sdtpldt0 @t6 @t13) (tptp.sdtpldt0 @t1 @t14))))) % 0.44/0.65 (assume @p9 @t22) % 0.44/0.65 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.44/0.65 (assume @p11 @t25) % 0.44/0.65 (assume @p12 (forall @t17 (=> @t16 (= (tptp.sdtasdt0 @t10 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t13)))))) % 0.44/0.65 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.44/0.65 (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))))))) % 0.44/0.65 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t27 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t27)))))) % 0.44/0.65 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.44/0.65 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t29 @t28))))) % 0.44/0.65 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.44/0.65 (assume @p19 (forall @t3 (=> @t30 true))) % 0.44/0.65 (assume @p20 @t35) % 0.44/0.65 (assume @p21 (forall @t9 (=> @t40 (=> (and (forall @t38 (=> @t36 @t37)) (forall @t38 (=> @t37 @t36))) (= @t1 @t5))))) % 0.44/0.65 (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))))))))))) % 0.44/0.65 (assume @p23 (forall @t9 (=> @t40 (forall @t38 (= (= @t13 @t48) (and @t46 (forall @t45 (= @t44 (and (tptp.aElementOf0 @t41 @t1) (tptp.aElementOf0 @t41 @t5)))))))))) % 0.44/0.65 (assume @p24 (forall @t3 (= @t50 (and @t30 (forall @t32 (=> @t31 (and (forall @t38 (=> @t36 (tptp.aElementOf0 @t14 @t1))) (forall @t38 (=> @t15 (tptp.aElementOf0 @t49 @t1)))))))))) % 0.44/0.65 (assume @p25 (forall @t9 (=> @t51 (tptp.aIdeal0 @t47)))) % 0.44/0.65 (assume @p26 (forall @t9 (=> @t51 (tptp.aIdeal0 @t48)))) % 0.44/0.65 (assume @p27 (forall @t17 (=> (and @t2 @t7 (tptp.aIdeal0 @t13)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t13) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t13))))) % 0.44/0.65 (assume @p28 (forall @t9 (=> @t51 (=> (forall @t38 (=> @t15 (tptp.aElementOf0 @t13 @t47))) (forall @t53 (=> (and @t15 @t52) (exists (@list @t43) (and (tptp.aElement0 @t43) (tptp.sdteqdtlpzmzozddtrp0 @t43 @t13 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t43 @t41 @t5))))))))) % 0.44/0.65 (assume @p29 (forall @t3 (=> @t54 true))) % 0.44/0.65 (assume @p30 (forall @t3 (=> (and @t2 @t56) (tptp.aNaturalNumber0 @t55)))) % 0.44/0.65 (assume @p31 (forall @t9 (=> (and @t54 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 0.44/0.65 (assume @p32 (forall @t9 (=> (and @t2 @t7 (not @t28)) (exists @t53 (and @t15 @t52 (= @t1 (tptp.sdtpldt0 @t49 @t41)) (=> (not (= @t41 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t41) (tptp.sbrdtbr0 @t5)))))))) % 0.44/0.65 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t38 (and @t15 (= @t26 @t5))))))) % 0.44/0.65 (assume @p34 (forall @t3 (=> @t2 (forall @t32 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 0.44/0.65 (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))))))))) % 0.44/0.65 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 0.44/0.65 (assume @p37 (forall @t3 (=> @t2 (forall @t32 (= (= @t5 @t57) (and @t39 (forall @t38 (= @t37 (exists @t45 (and @t52 (= (tptp.sdtasdt0 @t1 @t41) @t13))))))))))) % 0.44/0.65 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t57)))) % 0.44/0.65 (assume @p39 (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb))) % 0.44/0.65 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 0.44/0.65 (assume @p41 (and @t59 (exists @t3 (and @t2 (= @t58 tptp.xa))) (tptp.doDivides0 tptp.xc tptp.xa) (tptp.aDivisorOf0 tptp.xc tptp.xa) @t59 (exists @t3 (and @t2 (= @t58 tptp.xb))) (tptp.doDivides0 tptp.xc tptp.xb) (tptp.aDivisorOf0 tptp.xc tptp.xb) (forall @t3 (=> (and (or (and @t2 (or (exists @t32 (and @t7 (= @t10 tptp.xa))) (tptp.doDivides0 @t1 tptp.xa))) (tptp.aDivisorOf0 @t1 tptp.xa)) (or (exists @t32 (and @t7 (= @t10 tptp.xb))) (tptp.doDivides0 @t1 tptp.xb) (tptp.aDivisorOf0 @t1 tptp.xb))) (and (exists @t32 (and @t7 (= @t10 tptp.xc))) (tptp.doDivides0 @t1 tptp.xc)))) (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb))) % 0.44/0.65 (assume @p42 (and @t68 (forall @t3 (=> @t65 (and (forall @t32 (=> (tptp.aElementOf0 @t5 tptp.xI) (tptp.aElementOf0 @t6 tptp.xI))) (forall @t32 (=> @t7 (tptp.aElementOf0 @t23 tptp.xI)))))) (tptp.aIdeal0 tptp.xI) (forall @t3 (= @t67 (exists @t32 (and @t7 (= (tptp.sdtasdt0 tptp.xa @t5) @t1))))) (forall @t3 (= (tptp.aElementOf0 @t1 @t60) (exists @t32 (and @t7 (= @t66 @t1))))) (forall @t3 (= @t65 @t64)) (= tptp.xI @t62))) % 0.44/0.65 (assume @p43 (and (exists @t3 (and @t2 (= @t70 tptp.sz00))) (tptp.aElementOf0 tptp.sz00 @t61) (exists @t3 (and @t2 (= @t70 tptp.xa))) (tptp.aElementOf0 tptp.xa @t61) (exists @t3 (and @t2 (= @t69 tptp.sz00))) (tptp.aElementOf0 tptp.sz00 @t60) (exists @t3 (and @t2 (= @t69 tptp.xb))) (tptp.aElementOf0 tptp.xb @t60))) % 0.44/0.65 (assume @p44 (exists @t3 (and (forall @t32 (= @t63 (exists @t38 (and @t15 (= (tptp.sdtasdt0 tptp.xa @t13) @t5))))) (forall @t32 (= @t71 (exists @t38 (and @t15 (= (tptp.sdtasdt0 tptp.xb @t13) @t5))))) @t64 (tptp.aElementOf0 @t1 @t62) @t56))) % 0.44/0.65 (assume @p45 (and (exists @t9 (and @t67 @t71 (= @t6 tptp.xu))) @t73 (not (= tptp.xu tptp.sz00)) (forall @t3 (=> (and (or @t64 @t65) @t56) (not (tptp.iLess0 @t55 @t72)))))) % 0.44/0.65 (assume @p46 @t86) % 0.44/0.65 (assume @p47 (exists @t9 (and @t2 @t7 (= tptp.xu (tptp.sdtpldt0 @t70 @t66))))) % 0.44/0.65 (assume @p48 (not (not @t87))) % 0.44/0.65 (assume @p49 (not (or @t78 @t75))) % 0.44/0.65 (assume @p50 (and @t92 (tptp.aElement0 tptp.xr) @t91 (or @t88 (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) @t72)))) % 0.44/0.65 (assume @p51 (not (not @t88))) % 0.44/0.65 (assume @p52 true) % 0.44/0.65 (step @p53 :rule and_elim :premises (@p50) :args (2)) % 0.44/0.65 (step @p54 :rule eq-symm :args (tptp.xr tptp.sz00)) % 0.44/0.65 (step @p55 :rule bool-double-not-elim :args (@t88)) % 0.44/0.65 (step @p56 :rule trans :premises (@p55 @p54)) % 0.44/0.65 (step @p57 :rule eq_resolve :premises (@p51 @p56)) % 0.44/0.65 (step @p58 :rule refl :args (@t81)) % 0.44/0.65 (step @p59 :rule bool-and-de-morgan :args (@t2 @t93 true)) % 0.44/0.65 (step @p60 :rule cong :premises (@p59) :args (@t95)) % 0.44/0.65 (step @p61 :rule cong :premises (@p60) :args (@t96)) % 0.44/0.65 (step @p62 :rule exists-elim :args ((= (exists @t3 @t94) @t96))) % 0.44/0.65 (step @p63 :rule trans :premises (@p62 @p61)) % 0.44/0.65 (step @p64 :rule eq-symm :args (@t76 tptp.xa)) % 0.44/0.65 (step @p65 :rule refl :args (@t2)) % 0.44/0.65 (step @p66 :rule nary_cong :premises (@p65 @p64) :args (@t82)) % 0.44/0.65 (step @p67 :rule cong :premises (@p66) :args (@t83)) % 0.44/0.65 (step @p68 :rule trans :premises (@p67 @p63)) % 0.44/0.65 (step @p69 :rule nary_cong :premises (@p68 @p58) :args (@t87)) % 0.44/0.65 (step @p70 :rule bool-double-not-elim :args (@t87)) % 0.44/0.65 (step @p71 :rule trans :premises (@p70 @p69)) % 0.44/0.65 (step @p72 :rule eq_resolve :premises (@p48 @p71)) % 0.44/0.65 (step @p73 :rule and_elim :premises (@p72) :args (0)) % 0.44/0.65 (step @p74 :rule bool-double-not-elim :args (@t98)) % 0.44/0.65 (step @p75 :rule refl :args (@t100)) % 0.44/0.65 (step @p76 :rule nary_cong :premises (@p75 @p74) :args ((or @t100 (not @t99)))) % 0.44/0.65 (step @p77 :rule cnf_or_neg :args (@t100 0)) % 0.44/0.65 (step @p78 :rule eq_resolve :premises (@p77 @p76)) % 0.44/0.65 (step @p79 :rule reordering :premises (@p78) :args ((or @t98 @t100))) % 0.44/0.65 (step @p80 :rule chain_m_resolution :premises (@p79 @p73) :args (@t100 @t101 (@list @t98))) % 0.44/0.65 (step @p81 :rule refl :args (@t74)) % 0.44/0.65 (step @p82 :rule refl :args (@t75)) % 0.44/0.65 (step @p83 :rule bool-and-de-morgan :args (@t2 @t102 true)) % 0.44/0.65 (step @p84 :rule cong :premises (@p83) :args (@t104)) % 0.44/0.65 (step @p85 :rule cong :premises (@p84) :args (@t105)) % 0.44/0.65 (step @p86 :rule exists-elim :args ((= (exists @t3 @t103) @t105))) % 0.44/0.65 (step @p87 :rule trans :premises (@p86 @p85)) % 0.44/0.65 (step @p88 :rule eq-symm :args (@t76 tptp.xb)) % 0.44/0.65 (step @p89 :rule nary_cong :premises (@p65 @p88) :args (@t77)) % 0.44/0.65 (step @p90 :rule cong :premises (@p89) :args (@t78)) % 0.44/0.65 (step @p91 :rule trans :premises (@p90 @p87)) % 0.44/0.65 (step @p92 :rule nary_cong :premises (@p91 @p82 @p81) :args (@t79)) % 0.44/0.65 (step @p93 :rule refl :args (@t80)) % 0.44/0.65 (step @p94 :rule nary_cong :premises (@p68 @p58 @p93) :args (@t84)) % 0.44/0.65 (step @p95 :rule nary_cong :premises (@p94 @p92) :args (@t85)) % 0.44/0.65 (step @p96 :rule cong :premises (@p95) :args (@t86)) % 0.44/0.65 (step @p97 :rule eq_resolve :premises (@p46 @p96)) % 0.44/0.65 (step @p98 :rule not_and :premises (@p97)) % 0.44/0.65 (step @p99 :rule chain_m_resolution :premises (@p98 @p80) :args ((not @t108) @t109 (@list @t100))) % 0.44/0.65 (step @p100 :rule bool-double-not-elim :args (@t106)) % 0.44/0.65 (step @p101 :rule refl :args (@t108)) % 0.44/0.65 (step @p102 :rule nary_cong :premises (@p101 @p100) :args ((or @t108 (not @t107)))) % 0.44/0.65 (step @p103 :rule cnf_or_neg :args (@t108 0)) % 0.44/0.65 (step @p104 :rule eq_resolve :premises (@p103 @p102)) % 0.44/0.65 (step @p105 :rule reordering :premises (@p104) :args ((or @t106 @t108))) % 0.44/0.65 (step @p106 :rule chain_m_resolution :premises (@p105 @p99) :args (@t106 @t101 (@list @t108))) % 0.44/0.65 (step @p107 :rule instantiate :premises (@p106) :args ((@list tptp.xq))) % 0.44/0.65 (step @p108 :rule and_elim :premises (@p50) :args (0)) % 0.44/0.65 (step @p109 :rule cnf_or_pos :args (@t114)) % 0.44/0.65 (step @p110 :rule reordering :premises (@p109) :args ((or @t113 @t112 (not @t114)))) % 0.44/0.65 (step @p111 :rule chain_m_resolution :premises (@p110 @p108 @p107) :args (@t112 @t115 (@list @t92 @t114))) % 0.44/0.65 (step @p112 :rule aci_norm :args ((= (or @t117 @t24) (or @t97 @t116 @t24)))) % 0.44/0.65 (step @p113 :rule refl :args (@t24)) % 0.44/0.65 (step @p114 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 0.44/0.65 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((or @t118 @t24))) % 0.44/0.65 (step @p116 :rule trans :premises (@p115 @p112)) % 0.44/0.65 (step @p117 :rule bool-impl-elim :args (@t8 @t24)) % 0.44/0.65 (step @p118 :rule trans :premises (@p117 @p116)) % 0.44/0.65 (step @p119 :rule cong :premises (@p118) :args (@t25)) % 0.44/0.65 (step @p120 :rule eq_resolve :premises (@p11 @p119)) % 0.44/0.65 (step @p121 :rule instantiate :premises (@p120) :args (@t119)) % 0.44/0.65 (step @p122 :rule aci_norm :args ((= @t125 (or @t123 @t122 @t121)))) % 0.44/0.65 (step @p123 :rule cong :premises (@p122) :args (@t126)) % 0.44/0.65 (step @p124 :rule quant-merge-prenex :args ((= (forall @t3 @t128) @t126))) % 0.44/0.65 (step @p125 :rule alpha_equiv :args (@t129 (@list @t120) (@list @t5))) % 0.44/0.65 (step @p126 :rule refl :args (@t123)) % 0.44/0.65 (step @p127 :rule nary_cong :premises (@p126 @p125) :args (@t130)) % 0.44/0.65 (step @p128 :rule quant-miniscope-or :args ((= @t128 @t130))) % 0.44/0.65 (step @p129 :rule trans :premises (@p128 @p127)) % 0.44/0.65 (step @p130 :rule symm :premises (@p129)) % 0.44/0.65 (step @p131 :rule cong :premises (@p130) :args ((forall @t3 (or @t123 @t131)))) % 0.44/0.65 (step @p132 :rule trans :premises (@p131 @p124)) % 0.44/0.65 (step @p133 :rule trans :premises (@p132 @p123)) % 0.44/0.65 (step @p134 :rule bool-impl-elim :args (@t30 @t131)) % 0.44/0.65 (step @p135 :rule cong :premises (@p134) :args ((forall @t3 (=> @t30 @t131)))) % 0.44/0.65 (step @p136 :rule trans :premises (@p135 @p133)) % 0.44/0.65 (step @p137 :rule bool-impl-elim :args (@t31 @t7)) % 0.44/0.65 (step @p138 :rule cong :premises (@p137) :args (@t33)) % 0.44/0.65 (step @p139 :rule refl :args (@t30)) % 0.44/0.65 (step @p140 :rule cong :premises (@p139 @p138) :args (@t34)) % 0.44/0.65 (step @p141 :rule cong :premises (@p140) :args (@t35)) % 0.44/0.65 (step @p142 :rule trans :premises (@p141 @p136)) % 0.44/0.65 (step @p143 :rule eq_resolve :premises (@p20 @p142)) % 0.44/0.65 (step @p144 :rule instantiate :premises (@p143) :args ((@list tptp.xI tptp.xu))) % 0.44/0.65 (step @p145 :rule and_elim :premises (@p45) :args (1)) % 0.44/0.65 (step @p146 :rule and_elim :premises (@p42) :args (0)) % 0.44/0.65 (step @p147 :rule cnf_or_pos :args (@t135)) % 0.44/0.65 (step @p148 :rule reordering :premises (@p147) :args ((or @t134 @t133 @t132 (not @t135)))) % 0.44/0.65 (step @p149 :rule chain_m_resolution :premises (@p148 @p146 @p145 @p144) :args (@t132 @t136 (@list @t68 @t73 @t135))) % 0.44/0.65 (step @p150 :rule cnf_or_pos :args (@t139)) % 0.44/0.65 (step @p151 :rule reordering :premises (@p150) :args ((or @t113 @t138 @t137 (not @t139)))) % 0.44/0.65 (step @p152 :rule chain_m_resolution :premises (@p151 @p108 @p149 @p121) :args (@t137 @t136 (@list @t92 @t132 @t139))) % 0.44/0.65 (step @p153 :rule bool-impl-elim :args (@t2 @t140)) % 0.44/0.65 (step @p154 :rule cong :premises (@p153) :args ((forall @t3 (=> @t2 @t140)))) % 0.44/0.65 (step @p155 :rule refl :args (@t18)) % 0.44/0.65 (step @p156 :rule eq-symm :args (@t19 @t1)) % 0.44/0.65 (step @p157 :rule nary_cong :premises (@p156 @p155) :args (@t20)) % 0.44/0.65 (step @p158 :rule cong :premises (@p65 @p157) :args (@t21)) % 0.44/0.65 (step @p159 :rule cong :premises (@p158) :args (@t22)) % 0.44/0.65 (step @p160 :rule trans :premises (@p159 @p154)) % 0.44/0.65 (step @p161 :rule eq_resolve :premises (@p9 @p160)) % 0.44/0.65 (step @p162 :rule instantiate :premises (@p161) :args ((@list @t89))) % 0.44/0.65 (step @p163 :rule aci_norm :args ((= (or @t117 @t11) (or @t97 @t116 @t11)))) % 0.44/0.65 (step @p164 :rule refl :args (@t11)) % 0.44/0.65 (step @p165 :rule nary_cong :premises (@p114 @p164) :args ((or @t118 @t11))) % 0.44/0.65 (step @p166 :rule trans :premises (@p165 @p163)) % 0.44/0.65 (step @p167 :rule bool-impl-elim :args (@t8 @t11)) % 0.44/0.65 (step @p168 :rule trans :premises (@p167 @p166)) % 0.44/0.65 (step @p169 :rule cong :premises (@p168) :args (@t12)) % 0.44/0.65 (step @p170 :rule eq_resolve :premises (@p6 @p169)) % 0.44/0.66 (step @p171 :rule instantiate :premises (@p170) :args (@t119)) % 0.44/0.66 (step @p172 :rule cnf_or_pos :args (@t142)) % 0.44/0.66 (step @p173 :rule reordering :premises (@p172) :args ((or @t113 @t138 @t141 (not @t142)))) % 0.44/0.66 (step @p174 :rule chain_m_resolution :premises (@p173 @p108 @p149 @p171) :args (@t141 @t136 (@list @t92 @t132 @t142))) % 0.44/0.66 (step @p175 :rule cnf_or_pos :args (@t146)) % 0.44/0.66 (step @p176 :rule reordering :premises (@p175) :args ((or @t145 @t144 (not @t146)))) % 0.44/0.66 (step @p177 :rule chain_m_resolution :premises (@p176 @p174 @p162) :args (@t144 @t115 (@list @t141 @t146))) % 0.44/0.66 (step @p178 :rule cnf_and_pos :args (@t144 0)) % 0.44/0.66 (step @p179 :rule reordering :premises (@p178) :args ((or @t143 (not @t144)))) % 0.44/0.66 (step @p180 :rule chain_m_resolution :premises (@p179 @p177) :args (@t143 @t109 (@list @t144))) % 0.44/0.66 (assume-push @p200 @t91) % 0.44/0.66 (assume-push @p201 @t147) % 0.44/0.66 (assume-push @p202 @t143) % 0.44/0.66 (assume-push @p203 @t137) % 0.44/0.66 (step @p185 :rule symm :premises (@p180)) % 0.44/0.66 (step @p186 :rule symm :premises (@p57)) % 0.44/0.66 (step @p187 :rule refl :args (@t89)) % 0.44/0.66 (step @p188 :rule cong :premises (@p187 @p186) :args (@t90)) % 0.44/0.66 (step @p189 :rule trans :premises (@p53 @p188 @p185 @p152)) % 0.44/0.66 (step-pop @p204 :rule scope :premises (@p189)) % 0.44/0.66 (step-pop @p205 :rule scope :premises (@p204)) % 0.44/0.66 (step-pop @p206 :rule scope :premises (@p205)) % 0.44/0.66 (step-pop @p207 :rule scope :premises (@p206)) % 0.44/0.66 (step @p190 :rule process_scope :premises (@p207) :args (@t111)) % 0.44/0.66 (step @p195 :rule implies_elim :premises (@p190)) % 0.44/0.66 (step @p196 :rule cnf_and_neg :args (@t148)) % 0.44/0.66 (step @p197 :rule resolution :premises (@p196 @p195) :args (true @t148)) % 0.44/0.66 (step @p198 :rule reordering :premises (@p197) :args ((or (not @t91) (not @t147) @t111 (not @t143) (not @t137)))) % 0.44/0.66 (step @p199 false :rule chain_m_resolution :premises (@p198 @p180 @p152 @p111 @p57 @p53) :args (false (@list false false true false false) (@list @t143 @t137 @t111 @t147 @t91))) % 0.44/0.66 ) % 0.44/0.66 % SZS output end Proof % 0.44/0.66 % cvc5 exiting %------------------------------------------------------------------------------