%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG108+4 : 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 : n004.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 08:45:42 AM UTC 2026 % Result : Theorem 0.37s 0.59s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG108+4 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n004.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 14:07:37 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.59 % SZS status Theorem % 0.37/0.59 % SZS output start Proof % 0.37/0.59 ( % 0.37/0.59 (declare-sort $$unsorted 0) % 0.37/0.59 (declare-const tptp.xI $$unsorted) % 0.37/0.59 (declare-const tptp.xc $$unsorted) % 0.37/0.59 (declare-const tptp.xa $$unsorted) % 0.37/0.59 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.sz00 $$unsorted) % 0.37/0.59 (declare-const tptp.sz10 $$unsorted) % 0.37/0.59 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.xb $$unsorted) % 0.37/0.59 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.37/0.59 (define @t1 () (@var "W0" $$unsorted)) % 0.37/0.59 (define @t2 () (tptp.aElement0 @t1)) % 0.37/0.59 (define @t3 () (@list @t1)) % 0.37/0.59 (define @t4 () (tptp.aElement0 tptp.sz00)) % 0.37/0.59 (define @t5 () (tptp.aElement0 tptp.sz10)) % 0.37/0.59 (define @t6 () (tptp.smndt0 @t1)) % 0.37/0.59 (define @t7 () (@var "W1" $$unsorted)) % 0.37/0.59 (define @t8 () (tptp.sdtpldt0 @t1 @t7)) % 0.37/0.59 (define @t9 () (tptp.aElement0 @t7)) % 0.37/0.59 (define @t10 () (and @t2 @t9)) % 0.37/0.59 (define @t11 () (@list @t1 @t7)) % 0.37/0.59 (define @t12 () (tptp.sdtasdt0 @t1 @t7)) % 0.37/0.59 (define @t13 () (@var "W2" $$unsorted)) % 0.37/0.59 (define @t14 () (tptp.sdtpldt0 @t7 @t13)) % 0.37/0.59 (define @t15 () (tptp.aElement0 @t13)) % 0.37/0.59 (define @t16 () (and @t2 @t9 @t15)) % 0.37/0.59 (define @t17 () (@list @t1 @t7 @t13)) % 0.37/0.59 (define @t18 () (tptp.sdtasdt0 @t7 @t1)) % 0.37/0.59 (define @t19 () (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1))) % 0.37/0.59 (define @t20 () (tptp.sdtasdt0 @t1 tptp.sz10)) % 0.37/0.59 (define @t21 () (and (= @t20 @t1) @t19)) % 0.37/0.59 (define @t22 () (=> @t2 @t21)) % 0.37/0.59 (define @t23 () (forall @t3 @t22)) % 0.37/0.59 (define @t24 () (tptp.sdtasdt0 @t1 @t13)) % 0.37/0.59 (define @t25 () (tptp.smndt0 tptp.sz10)) % 0.37/0.59 (define @t26 () (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1))) % 0.37/0.59 (define @t27 () (tptp.sdtasdt0 @t1 tptp.sz00)) % 0.37/0.59 (define @t28 () (and (= @t27 tptp.sz00) @t26)) % 0.37/0.59 (define @t29 () (=> @t2 @t28)) % 0.37/0.59 (define @t30 () (forall @t3 @t29)) % 0.37/0.59 (define @t31 () (= @t7 tptp.sz00)) % 0.37/0.59 (define @t32 () (= @t1 tptp.sz00)) % 0.37/0.59 (define @t33 () (tptp.aSet0 @t1)) % 0.37/0.59 (define @t34 () (tptp.aElementOf0 @t7 @t1)) % 0.37/0.59 (define @t35 () (@list @t7)) % 0.37/0.59 (define @t36 () (tptp.aElementOf0 @t13 @t1)) % 0.37/0.59 (define @t37 () (tptp.aElementOf0 @t13 @t7)) % 0.37/0.59 (define @t38 () (@list @t13)) % 0.37/0.59 (define @t39 () (tptp.aSet0 @t7)) % 0.37/0.59 (define @t40 () (and @t33 @t39)) % 0.37/0.59 (define @t41 () (@var "W3" $$unsorted)) % 0.37/0.59 (define @t42 () (@var "W5" $$unsorted)) % 0.37/0.59 (define @t43 () (@var "W4" $$unsorted)) % 0.37/0.59 (define @t44 () (tptp.aElementOf0 @t41 @t13)) % 0.37/0.59 (define @t45 () (@list @t41)) % 0.37/0.59 (define @t46 () (tptp.aSet0 @t13)) % 0.37/0.59 (define @t47 () (tptp.sdtpldt1 @t1 @t7)) % 0.37/0.59 (define @t48 () (tptp.sdtasasdt0 @t1 @t7)) % 0.37/0.59 (define @t49 () (tptp.sdtasdt0 @t13 @t7)) % 0.37/0.59 (define @t50 () (tptp.aIdeal0 @t1)) % 0.37/0.59 (define @t51 () (and @t50 (tptp.aIdeal0 @t7))) % 0.37/0.59 (define @t52 () (tptp.aElement0 @t41)) % 0.37/0.59 (define @t53 () (@list @t13 @t41)) % 0.37/0.59 (define @t54 () (tptp.aNaturalNumber0 @t1)) % 0.37/0.59 (define @t55 () (tptp.slsdtgt0 @t1)) % 0.37/0.59 (define @t56 () (tptp.aElement0 tptp.xb)) % 0.37/0.59 (define @t57 () (tptp.aElement0 tptp.xa)) % 0.37/0.59 (define @t58 () (tptp.sdtasdt0 tptp.xc @t1)) % 0.37/0.59 (define @t59 () (tptp.aElement0 tptp.xc)) % 0.37/0.59 (define @t60 () (tptp.slsdtgt0 tptp.xb)) % 0.37/0.59 (define @t61 () (tptp.slsdtgt0 tptp.xa)) % 0.37/0.59 (define @t62 () (tptp.aElementOf0 @t1 tptp.xI)) % 0.37/0.59 (define @t63 () (tptp.aElementOf0 tptp.xb @t60)) % 0.37/0.59 (define @t64 () (tptp.sdtasdt0 tptp.xb @t1)) % 0.37/0.59 (define @t65 () (and @t2 (= @t64 tptp.xb))) % 0.37/0.59 (define @t66 () (exists @t3 @t65)) % 0.37/0.59 (define @t67 () (or @t66 @t63)) % 0.37/0.59 (define @t68 () (tptp.aElementOf0 tptp.sz00 @t60)) % 0.37/0.59 (define @t69 () (and @t2 (= @t64 tptp.sz00))) % 0.37/0.59 (define @t70 () (exists @t3 @t69)) % 0.37/0.59 (define @t71 () (or @t70 @t68)) % 0.37/0.59 (define @t72 () (tptp.aElementOf0 tptp.xa @t61)) % 0.37/0.59 (define @t73 () (tptp.sdtasdt0 tptp.xa @t1)) % 0.37/0.59 (define @t74 () (and @t2 (= @t73 tptp.xa))) % 0.37/0.59 (define @t75 () (exists @t3 @t74)) % 0.37/0.59 (define @t76 () (or @t75 @t72)) % 0.37/0.59 (define @t77 () (tptp.aElementOf0 tptp.sz00 @t61)) % 0.37/0.59 (define @t78 () (and @t2 (= @t73 tptp.sz00))) % 0.37/0.59 (define @t79 () (exists @t3 @t78)) % 0.37/0.59 (define @t80 () (or @t79 @t77)) % 0.37/0.59 (define @t81 () (and @t80 @t76 @t71 @t67)) % 0.37/0.59 (define @t82 () (not @t81)) % 0.37/0.59 (define @t83 () (and (= @t1 @t20) @t19)) % 0.37/0.59 (define @t84 () (@list tptp.xb)) % 0.37/0.59 (define @t85 () (= tptp.xb (tptp.sdtasdt0 tptp.xb tptp.sz10))) % 0.37/0.59 (define @t86 () (and @t85 (= tptp.xb (tptp.sdtasdt0 tptp.sz10 tptp.xb)))) % 0.37/0.59 (define @t87 () (not @t56)) % 0.37/0.59 (define @t88 () (or @t87 @t86)) % 0.37/0.59 (define @t89 () (@list false false)) % 0.37/0.59 (define @t90 () (@list false)) % 0.37/0.60 (define @t91 () (not @t85)) % 0.37/0.60 (define @t92 () (not @t5)) % 0.37/0.60 (define @t93 () (or @t92 @t91)) % 0.37/0.60 (define @t94 () (not @t93)) % 0.37/0.60 (define @t95 () (= tptp.xb @t64)) % 0.37/0.60 (define @t96 () (not @t2)) % 0.37/0.60 (define @t97 () (forall @t3 (or @t96 (not @t95)))) % 0.37/0.60 (define @t98 () (@list tptp.sz10)) % 0.37/0.60 (define @t99 () (not @t97)) % 0.37/0.60 (define @t100 () (@list true)) % 0.37/0.60 (define @t101 () (or @t99 @t63)) % 0.37/0.60 (define @t102 () (and (= tptp.sz00 @t27) @t26)) % 0.37/0.60 (define @t103 () (= tptp.sz00 (tptp.sdtasdt0 tptp.xb tptp.sz00))) % 0.37/0.60 (define @t104 () (and @t103 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xb)))) % 0.37/0.60 (define @t105 () (or @t87 @t104)) % 0.37/0.60 (define @t106 () (not @t103)) % 0.37/0.60 (define @t107 () (not @t4)) % 0.37/0.60 (define @t108 () (or @t107 @t106)) % 0.37/0.60 (define @t109 () (not @t108)) % 0.37/0.60 (define @t110 () (= tptp.sz00 @t64)) % 0.37/0.60 (define @t111 () (forall @t3 (or @t96 (not @t110)))) % 0.37/0.60 (define @t112 () (@list tptp.sz00)) % 0.37/0.60 (define @t113 () (not @t111)) % 0.37/0.60 (define @t114 () (or @t113 @t68)) % 0.37/0.60 (define @t115 () (@list tptp.xa)) % 0.37/0.60 (define @t116 () (= tptp.xa (tptp.sdtasdt0 tptp.xa tptp.sz10))) % 0.37/0.60 (define @t117 () (and @t116 (= tptp.xa (tptp.sdtasdt0 tptp.sz10 tptp.xa)))) % 0.37/0.60 (define @t118 () (not @t57)) % 0.37/0.60 (define @t119 () (or @t118 @t117)) % 0.37/0.60 (define @t120 () (not @t116)) % 0.37/0.60 (define @t121 () (or @t92 @t120)) % 0.37/0.60 (define @t122 () (not @t121)) % 0.37/0.60 (define @t123 () (= tptp.xa @t73)) % 0.37/0.60 (define @t124 () (forall @t3 (or @t96 (not @t123)))) % 0.37/0.60 (define @t125 () (not @t124)) % 0.37/0.60 (define @t126 () (or @t125 @t72)) % 0.37/0.60 (define @t127 () (= tptp.sz00 (tptp.sdtasdt0 tptp.xa tptp.sz00))) % 0.37/0.60 (define @t128 () (and @t127 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xa)))) % 0.37/0.60 (define @t129 () (or @t118 @t128)) % 0.37/0.60 (define @t130 () (not @t127)) % 0.37/0.60 (define @t131 () (or @t107 @t130)) % 0.37/0.60 (define @t132 () (not @t131)) % 0.37/0.60 (define @t133 () (= tptp.sz00 @t73)) % 0.37/0.60 (define @t134 () (forall @t3 (or @t96 (not @t133)))) % 0.37/0.60 (define @t135 () (not @t134)) % 0.37/0.60 (define @t136 () (or @t135 @t77)) % 0.37/0.60 (define @t137 () (and @t2 @t95)) % 0.37/0.60 (define @t138 () (forall @t3 (not @t137))) % 0.37/0.60 (define @t139 () (not @t138)) % 0.37/0.60 (define @t140 () (and @t2 @t110)) % 0.37/0.60 (define @t141 () (forall @t3 (not @t140))) % 0.37/0.60 (define @t142 () (not @t141)) % 0.37/0.60 (define @t143 () (and @t2 @t123)) % 0.37/0.60 (define @t144 () (forall @t3 (not @t143))) % 0.37/0.60 (define @t145 () (not @t144)) % 0.37/0.60 (define @t146 () (and @t2 @t133)) % 0.37/0.60 (define @t147 () (forall @t3 (not @t146))) % 0.37/0.60 (define @t148 () (not @t147)) % 0.37/0.60 (assume @p1 (forall @t3 (=> @t2 true))) % 0.37/0.60 (assume @p2 @t4) % 0.37/0.60 (assume @p3 @t5) % 0.37/0.60 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t6)))) % 0.37/0.60 (assume @p5 (forall @t11 (=> @t10 (tptp.aElement0 @t8)))) % 0.37/0.60 (assume @p6 (forall @t11 (=> @t10 (tptp.aElement0 @t12)))) % 0.37/0.60 (assume @p7 (forall @t11 (=> @t10 (= @t8 (tptp.sdtpldt0 @t7 @t1))))) % 0.37/0.60 (assume @p8 (forall @t17 (=> @t16 (= (tptp.sdtpldt0 @t8 @t13) (tptp.sdtpldt0 @t1 @t14))))) % 0.37/0.60 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.37/0.60 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t6) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t6 @t1)))))) % 0.37/0.60 (assume @p11 (forall @t11 (=> @t10 (= @t12 @t18)))) % 0.37/0.60 (assume @p12 (forall @t17 (=> @t16 (= (tptp.sdtasdt0 @t12 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t7 @t13)))))) % 0.37/0.60 (assume @p13 @t23) % 0.37/0.60 (assume @p14 (forall @t17 (=> @t16 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t12 @t24)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t18 (tptp.sdtasdt0 @t13 @t1))))))) % 0.37/0.60 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t25 @t1) @t6) (= @t6 (tptp.sdtasdt0 @t1 @t25)))))) % 0.37/0.60 (assume @p16 @t30) % 0.37/0.60 (assume @p17 (forall @t11 (=> @t10 (=> (= @t12 tptp.sz00) (or @t32 @t31))))) % 0.37/0.60 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.37/0.60 (assume @p19 (forall @t3 (=> @t33 true))) % 0.37/0.60 (assume @p20 (forall @t3 (=> @t33 (forall @t35 (=> @t34 @t9))))) % 0.37/0.60 (assume @p21 (forall @t11 (=> @t40 (=> (and (forall @t38 (=> @t36 @t37)) (forall @t38 (=> @t37 @t36))) (= @t1 @t7))))) % 0.37/0.60 (assume @p22 (forall @t11 (=> @t40 (forall @t38 (= (= @t13 @t47) (and @t46 (forall @t45 (= @t44 (exists (@list @t43 @t42) (and (tptp.aElementOf0 @t43 @t1) (tptp.aElementOf0 @t42 @t7) (= (tptp.sdtpldt0 @t43 @t42) @t41))))))))))) % 0.37/0.60 (assume @p23 (forall @t11 (=> @t40 (forall @t38 (= (= @t13 @t48) (and @t46 (forall @t45 (= @t44 (and (tptp.aElementOf0 @t41 @t1) (tptp.aElementOf0 @t41 @t7)))))))))) % 0.37/0.60 (assume @p24 (forall @t3 (= @t50 (and @t33 (forall @t35 (=> @t34 (and (forall @t38 (=> @t36 (tptp.aElementOf0 @t14 @t1))) (forall @t38 (=> @t15 (tptp.aElementOf0 @t49 @t1)))))))))) % 0.37/0.60 (assume @p25 (forall @t11 (=> @t51 (tptp.aIdeal0 @t47)))) % 0.37/0.60 (assume @p26 (forall @t11 (=> @t51 (tptp.aIdeal0 @t48)))) % 0.37/0.60 (assume @p27 (forall @t17 (=> (and @t2 @t9 (tptp.aIdeal0 @t13)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t7 @t13) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t7)) @t13))))) % 0.37/0.60 (assume @p28 (forall @t11 (=> @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 @t7))))))))) % 0.37/0.60 (assume @p29 (forall @t3 (=> @t54 true))) % 0.37/0.60 (assume @p30 (forall @t3 (=> (and @t2 (not @t32)) (tptp.aNaturalNumber0 (tptp.sbrdtbr0 @t1))))) % 0.37/0.60 (assume @p31 (forall @t11 (=> (and @t54 (tptp.aNaturalNumber0 @t7)) (=> (tptp.iLess0 @t1 @t7) true)))) % 0.37/0.60 (assume @p32 (forall @t11 (=> (and @t2 @t9 (not @t31)) (exists @t53 (and @t15 @t52 (= @t1 (tptp.sdtpldt0 @t49 @t41)) (=> (not (= @t41 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t41) (tptp.sbrdtbr0 @t7)))))))) % 0.37/0.60 (assume @p33 (forall @t11 (=> @t10 (= (tptp.doDivides0 @t1 @t7) (exists @t38 (and @t15 (= @t24 @t7))))))) % 0.37/0.60 (assume @p34 (forall @t3 (=> @t2 (forall @t35 (= (tptp.aDivisorOf0 @t7 @t1) (and @t9 (tptp.doDivides0 @t7 @t1))))))) % 0.37/0.60 (assume @p35 (forall @t11 (=> @t10 (forall @t38 (= (tptp.aGcdOfAnd0 @t13 @t1 @t7) (and (tptp.aDivisorOf0 @t13 @t1) (tptp.aDivisorOf0 @t13 @t7) (forall @t45 (=> (and (tptp.aDivisorOf0 @t41 @t1) (tptp.aDivisorOf0 @t41 @t7)) (tptp.doDivides0 @t41 @t13))))))))) % 0.37/0.60 (assume @p36 (forall @t11 (=> @t10 (= (tptp.misRelativelyPrime0 @t1 @t7) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t7))))) % 0.37/0.60 (assume @p37 (forall @t3 (=> @t2 (forall @t35 (= (= @t7 @t55) (and @t39 (forall @t38 (= @t37 (exists @t45 (and @t52 (= (tptp.sdtasdt0 @t1 @t41) @t13))))))))))) % 0.37/0.60 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t55)))) % 0.37/0.60 (assume @p39 (and @t57 @t56)) % 0.37/0.60 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 0.37/0.60 (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 @t35 (and @t9 (= @t12 tptp.xa))) (tptp.doDivides0 @t1 tptp.xa))) (tptp.aDivisorOf0 @t1 tptp.xa)) (or (exists @t35 (and @t9 (= @t12 tptp.xb))) (tptp.doDivides0 @t1 tptp.xb) (tptp.aDivisorOf0 @t1 tptp.xb))) (and (exists @t35 (and @t9 (= @t12 tptp.xc))) (tptp.doDivides0 @t1 tptp.xc)))) (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb))) % 0.37/0.60 (assume @p42 (and (tptp.aSet0 tptp.xI) (forall @t3 (=> @t62 (and (forall @t35 (=> (tptp.aElementOf0 @t7 tptp.xI) (tptp.aElementOf0 @t8 tptp.xI))) (forall @t35 (=> @t9 (tptp.aElementOf0 @t18 tptp.xI)))))) (tptp.aIdeal0 tptp.xI) (forall @t3 (= (tptp.aElementOf0 @t1 @t61) (exists @t35 (and @t9 (= (tptp.sdtasdt0 tptp.xa @t7) @t1))))) (forall @t3 (= (tptp.aElementOf0 @t1 @t60) (exists @t35 (and @t9 (= (tptp.sdtasdt0 tptp.xb @t7) @t1))))) (forall @t3 (= @t62 (exists (@list @t7 @t13) (and (tptp.aElementOf0 @t7 @t61) (tptp.aElementOf0 @t13 @t60) (= @t14 @t1))))) (= tptp.xI (tptp.sdtpldt1 @t61 @t60)))) % 0.37/0.60 (assume @p43 @t82) % 0.37/0.60 (assume @p44 true) % 0.37/0.60 (step @p45 :rule bool-impl-elim :args (@t2 @t83)) % 0.37/0.60 (step @p46 :rule cong :premises (@p45) :args ((forall @t3 (=> @t2 @t83)))) % 0.37/0.60 (step @p47 :rule refl :args (@t19)) % 0.37/0.60 (step @p48 :rule eq-symm :args (@t20 @t1)) % 0.37/0.60 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t21)) % 0.37/0.60 (step @p50 :rule refl :args (@t2)) % 0.37/0.60 (step @p51 :rule cong :premises (@p50 @p49) :args (@t22)) % 0.37/0.60 (step @p52 :rule cong :premises (@p51) :args (@t23)) % 0.37/0.60 (step @p53 :rule trans :premises (@p52 @p46)) % 0.37/0.60 (step @p54 :rule eq_resolve :premises (@p13 @p53)) % 0.37/0.60 (step @p55 :rule instantiate :premises (@p54) :args (@t84)) % 0.37/0.60 (step @p56 :rule and_elim :premises (@p39) :args (1)) % 0.37/0.60 (step @p57 :rule cnf_or_pos :args (@t88)) % 0.37/0.60 (step @p58 :rule reordering :premises (@p57) :args ((or @t87 @t86 (not @t88)))) % 0.37/0.60 (step @p59 :rule chain_m_resolution :premises (@p58 @p56 @p55) :args (@t86 @t89 (@list @t56 @t88))) % 0.37/0.60 (step @p60 :rule cnf_and_pos :args (@t86 0)) % 0.37/0.60 (step @p61 :rule reordering :premises (@p60) :args ((or @t85 (not @t86)))) % 0.37/0.60 (step @p62 :rule chain_m_resolution :premises (@p61 @p59) :args (@t85 @t90 (@list @t86))) % 0.37/0.60 (step @p63 :rule cnf_or_pos :args (@t93)) % 0.37/0.60 (step @p64 :rule reordering :premises (@p63) :args ((or @t92 @t91 @t94))) % 0.37/0.60 (step @p65 :rule chain_m_resolution :premises (@p64 @p3 @p62) :args (@t94 @t89 (@list @t5 @t85))) % 0.37/0.60 (assume-push @p207 @t97) % 0.37/0.60 (step @p67 :rule instantiate :premises (@p207) :args (@t98)) % 0.37/0.60 (step-pop @p208 :rule scope :premises (@p67)) % 0.37/0.60 (step @p68 :rule process_scope :premises (@p208) :args (@t93)) % 0.37/0.60 (step @p70 :rule implies_elim :premises (@p68)) % 0.37/0.60 (step @p71 :rule chain_m_resolution :premises (@p70 @p65) :args (@t99 @t100 (@list @t93))) % 0.37/0.60 (step @p72 :rule bool-double-not-elim :args (@t97)) % 0.37/0.60 (step @p73 :rule refl :args (@t101)) % 0.37/0.60 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or @t101 (not @t99)))) % 0.37/0.60 (step @p75 :rule cnf_or_neg :args (@t101 0)) % 0.37/0.60 (step @p76 :rule eq_resolve :premises (@p75 @p74)) % 0.37/0.60 (step @p77 :rule reordering :premises (@p76) :args ((or @t97 @t101))) % 0.37/0.60 (step @p78 :rule chain_m_resolution :premises (@p77 @p71) :args (@t101 @t100 (@list @t97))) % 0.37/0.60 (step @p79 :rule bool-impl-elim :args (@t2 @t102)) % 0.37/0.60 (step @p80 :rule cong :premises (@p79) :args ((forall @t3 (=> @t2 @t102)))) % 0.37/0.60 (step @p81 :rule refl :args (@t26)) % 0.37/0.60 (step @p82 :rule eq-symm :args (@t27 tptp.sz00)) % 0.37/0.60 (step @p83 :rule nary_cong :premises (@p82 @p81) :args (@t28)) % 0.37/0.60 (step @p84 :rule cong :premises (@p50 @p83) :args (@t29)) % 0.37/0.60 (step @p85 :rule cong :premises (@p84) :args (@t30)) % 0.37/0.60 (step @p86 :rule trans :premises (@p85 @p80)) % 0.37/0.60 (step @p87 :rule eq_resolve :premises (@p16 @p86)) % 0.37/0.60 (step @p88 :rule instantiate :premises (@p87) :args (@t84)) % 0.37/0.60 (step @p89 :rule cnf_or_pos :args (@t105)) % 0.37/0.60 (step @p90 :rule reordering :premises (@p89) :args ((or @t87 @t104 (not @t105)))) % 0.37/0.60 (step @p91 :rule chain_m_resolution :premises (@p90 @p56 @p88) :args (@t104 @t89 (@list @t56 @t105))) % 0.37/0.60 (step @p92 :rule cnf_and_pos :args (@t104 0)) % 0.37/0.60 (step @p93 :rule reordering :premises (@p92) :args ((or @t103 (not @t104)))) % 0.37/0.60 (step @p94 :rule chain_m_resolution :premises (@p93 @p91) :args (@t103 @t90 (@list @t104))) % 0.37/0.60 (step @p95 :rule cnf_or_pos :args (@t108)) % 0.37/0.60 (step @p96 :rule reordering :premises (@p95) :args ((or @t107 @t106 @t109))) % 0.37/0.60 (step @p97 :rule chain_m_resolution :premises (@p96 @p2 @p94) :args (@t109 @t89 (@list @t4 @t103))) % 0.37/0.60 (assume-push @p209 @t111) % 0.37/0.60 (step @p99 :rule instantiate :premises (@p209) :args (@t112)) % 0.37/0.60 (step-pop @p210 :rule scope :premises (@p99)) % 0.37/0.60 (step @p100 :rule process_scope :premises (@p210) :args (@t108)) % 0.37/0.60 (step @p102 :rule implies_elim :premises (@p100)) % 0.37/0.60 (step @p103 :rule chain_m_resolution :premises (@p102 @p97) :args (@t113 @t100 (@list @t108))) % 0.37/0.60 (step @p104 :rule bool-double-not-elim :args (@t111)) % 0.37/0.60 (step @p105 :rule refl :args (@t114)) % 0.37/0.60 (step @p106 :rule nary_cong :premises (@p105 @p104) :args ((or @t114 (not @t113)))) % 0.37/0.60 (step @p107 :rule cnf_or_neg :args (@t114 0)) % 0.37/0.60 (step @p108 :rule eq_resolve :premises (@p107 @p106)) % 0.37/0.60 (step @p109 :rule reordering :premises (@p108) :args ((or @t111 @t114))) % 0.37/0.60 (step @p110 :rule chain_m_resolution :premises (@p109 @p103) :args (@t114 @t100 (@list @t111))) % 0.37/0.60 (step @p111 :rule instantiate :premises (@p54) :args (@t115)) % 0.37/0.60 (step @p112 :rule and_elim :premises (@p39) :args (0)) % 0.37/0.60 (step @p113 :rule cnf_or_pos :args (@t119)) % 0.37/0.60 (step @p114 :rule reordering :premises (@p113) :args ((or @t118 @t117 (not @t119)))) % 0.37/0.60 (step @p115 :rule chain_m_resolution :premises (@p114 @p112 @p111) :args (@t117 @t89 (@list @t57 @t119))) % 0.37/0.60 (step @p116 :rule cnf_and_pos :args (@t117 0)) % 0.37/0.60 (step @p117 :rule reordering :premises (@p116) :args ((or @t116 (not @t117)))) % 0.37/0.60 (step @p118 :rule chain_m_resolution :premises (@p117 @p115) :args (@t116 @t90 (@list @t117))) % 0.37/0.60 (step @p119 :rule cnf_or_pos :args (@t121)) % 0.37/0.60 (step @p120 :rule reordering :premises (@p119) :args ((or @t92 @t120 @t122))) % 0.37/0.60 (step @p121 :rule chain_m_resolution :premises (@p120 @p3 @p118) :args (@t122 @t89 (@list @t5 @t116))) % 0.37/0.60 (assume-push @p211 @t124) % 0.37/0.60 (step @p123 :rule instantiate :premises (@p211) :args (@t98)) % 0.37/0.60 (step-pop @p212 :rule scope :premises (@p123)) % 0.37/0.60 (step @p124 :rule process_scope :premises (@p212) :args (@t121)) % 0.37/0.60 (step @p126 :rule implies_elim :premises (@p124)) % 0.37/0.60 (step @p127 :rule chain_m_resolution :premises (@p126 @p121) :args (@t125 @t100 (@list @t121))) % 0.37/0.60 (step @p128 :rule bool-double-not-elim :args (@t124)) % 0.37/0.60 (step @p129 :rule refl :args (@t126)) % 0.37/0.60 (step @p130 :rule nary_cong :premises (@p129 @p128) :args ((or @t126 (not @t125)))) % 0.37/0.60 (step @p131 :rule cnf_or_neg :args (@t126 0)) % 0.37/0.60 (step @p132 :rule eq_resolve :premises (@p131 @p130)) % 0.37/0.60 (step @p133 :rule reordering :premises (@p132) :args ((or @t124 @t126))) % 0.37/0.60 (step @p134 :rule chain_m_resolution :premises (@p133 @p127) :args (@t126 @t100 (@list @t124))) % 0.37/0.60 (step @p135 :rule instantiate :premises (@p87) :args (@t115)) % 0.37/0.60 (step @p136 :rule cnf_or_pos :args (@t129)) % 0.37/0.60 (step @p137 :rule reordering :premises (@p136) :args ((or @t118 @t128 (not @t129)))) % 0.37/0.60 (step @p138 :rule chain_m_resolution :premises (@p137 @p112 @p135) :args (@t128 @t89 (@list @t57 @t129))) % 0.37/0.60 (step @p139 :rule cnf_and_pos :args (@t128 0)) % 0.37/0.60 (step @p140 :rule reordering :premises (@p139) :args ((or @t127 (not @t128)))) % 0.37/0.60 (step @p141 :rule chain_m_resolution :premises (@p140 @p138) :args (@t127 @t90 (@list @t128))) % 0.37/0.60 (step @p142 :rule cnf_or_pos :args (@t131)) % 0.37/0.60 (step @p143 :rule reordering :premises (@p142) :args ((or @t107 @t130 @t132))) % 0.37/0.60 (step @p144 :rule chain_m_resolution :premises (@p143 @p2 @p141) :args (@t132 @t89 (@list @t4 @t127))) % 0.37/0.60 (assume-push @p213 @t134) % 0.37/0.60 (step @p146 :rule instantiate :premises (@p213) :args (@t112)) % 0.37/0.60 (step-pop @p214 :rule scope :premises (@p146)) % 0.37/0.60 (step @p147 :rule process_scope :premises (@p214) :args (@t131)) % 0.37/0.60 (step @p149 :rule implies_elim :premises (@p147)) % 0.37/0.60 (step @p150 :rule chain_m_resolution :premises (@p149 @p144) :args (@t135 @t100 (@list @t131))) % 0.37/0.60 (step @p151 :rule bool-double-not-elim :args (@t134)) % 0.37/0.60 (step @p152 :rule refl :args (@t136)) % 0.37/0.60 (step @p153 :rule nary_cong :premises (@p152 @p151) :args ((or @t136 (not @t135)))) % 0.37/0.60 (step @p154 :rule cnf_or_neg :args (@t136 0)) % 0.37/0.60 (step @p155 :rule eq_resolve :premises (@p154 @p153)) % 0.37/0.60 (step @p156 :rule reordering :premises (@p155) :args ((or @t134 @t136))) % 0.37/0.60 (step @p157 :rule chain_m_resolution :premises (@p156 @p150) :args (@t136 @t100 (@list @t134))) % 0.37/0.60 (step @p158 :rule refl :args (@t63)) % 0.37/0.60 (step @p159 :rule bool-and-de-morgan :args (@t2 @t95 true)) % 0.37/0.60 (step @p160 :rule cong :premises (@p159) :args (@t138)) % 0.37/0.60 (step @p161 :rule cong :premises (@p160) :args (@t139)) % 0.37/0.60 (step @p162 :rule exists-elim :args ((= (exists @t3 @t137) @t139))) % 0.37/0.60 (step @p163 :rule trans :premises (@p162 @p161)) % 0.37/0.60 (step @p164 :rule eq-symm :args (@t64 tptp.xb)) % 0.37/0.60 (step @p165 :rule nary_cong :premises (@p50 @p164) :args (@t65)) % 0.37/0.60 (step @p166 :rule cong :premises (@p165) :args (@t66)) % 0.37/0.60 (step @p167 :rule trans :premises (@p166 @p163)) % 0.37/0.60 (step @p168 :rule nary_cong :premises (@p167 @p158) :args (@t67)) % 0.37/0.60 (step @p169 :rule refl :args (@t68)) % 0.37/0.60 (step @p170 :rule bool-and-de-morgan :args (@t2 @t110 true)) % 0.37/0.60 (step @p171 :rule cong :premises (@p170) :args (@t141)) % 0.37/0.60 (step @p172 :rule cong :premises (@p171) :args (@t142)) % 0.37/0.60 (step @p173 :rule exists-elim :args ((= (exists @t3 @t140) @t142))) % 0.37/0.60 (step @p174 :rule trans :premises (@p173 @p172)) % 0.37/0.60 (step @p175 :rule eq-symm :args (@t64 tptp.sz00)) % 0.37/0.60 (step @p176 :rule nary_cong :premises (@p50 @p175) :args (@t69)) % 0.37/0.60 (step @p177 :rule cong :premises (@p176) :args (@t70)) % 0.37/0.60 (step @p178 :rule trans :premises (@p177 @p174)) % 0.37/0.60 (step @p179 :rule nary_cong :premises (@p178 @p169) :args (@t71)) % 0.37/0.60 (step @p180 :rule refl :args (@t72)) % 0.37/0.60 (step @p181 :rule bool-and-de-morgan :args (@t2 @t123 true)) % 0.37/0.60 (step @p182 :rule cong :premises (@p181) :args (@t144)) % 0.37/0.60 (step @p183 :rule cong :premises (@p182) :args (@t145)) % 0.37/0.60 (step @p184 :rule exists-elim :args ((= (exists @t3 @t143) @t145))) % 0.37/0.60 (step @p185 :rule trans :premises (@p184 @p183)) % 0.37/0.60 (step @p186 :rule eq-symm :args (@t73 tptp.xa)) % 0.37/0.60 (step @p187 :rule nary_cong :premises (@p50 @p186) :args (@t74)) % 0.37/0.60 (step @p188 :rule cong :premises (@p187) :args (@t75)) % 0.37/0.60 (step @p189 :rule trans :premises (@p188 @p185)) % 0.37/0.60 (step @p190 :rule nary_cong :premises (@p189 @p180) :args (@t76)) % 0.37/0.60 (step @p191 :rule refl :args (@t77)) % 0.37/0.60 (step @p192 :rule bool-and-de-morgan :args (@t2 @t133 true)) % 0.37/0.60 (step @p193 :rule cong :premises (@p192) :args (@t147)) % 0.37/0.60 (step @p194 :rule cong :premises (@p193) :args (@t148)) % 0.37/0.60 (step @p195 :rule exists-elim :args ((= (exists @t3 @t146) @t148))) % 0.37/0.60 (step @p196 :rule trans :premises (@p195 @p194)) % 0.37/0.60 (step @p197 :rule eq-symm :args (@t73 tptp.sz00)) % 0.37/0.60 (step @p198 :rule nary_cong :premises (@p50 @p197) :args (@t78)) % 0.37/0.60 (step @p199 :rule cong :premises (@p198) :args (@t79)) % 0.37/0.60 (step @p200 :rule trans :premises (@p199 @p196)) % 0.37/0.60 (step @p201 :rule nary_cong :premises (@p200 @p191) :args (@t80)) % 0.37/0.60 (step @p202 :rule nary_cong :premises (@p201 @p190 @p179 @p168) :args (@t81)) % 0.37/0.60 (step @p203 :rule cong :premises (@p202) :args (@t82)) % 0.37/0.60 (step @p204 :rule eq_resolve :premises (@p43 @p203)) % 0.37/0.60 (step @p205 :rule not_and :premises (@p204)) % 0.37/0.60 (step @p206 false :rule chain_m_resolution :premises (@p205 @p157 @p134 @p110 @p78) :args (false (@list false false false false) (@list @t136 @t126 @t114 @t101))) % 0.37/0.60 ) % 0.37/0.60 % SZS output end Proof % 0.37/0.60 % cvc5 exiting %------------------------------------------------------------------------------