%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG105+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 : n025.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 08:45:41 AM UTC 2026 % Result : Theorem 25.85s 26.12s % Output : Proof 25.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG105+1 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.33 % Computer : n025.cluster.edu % 0.17/0.33 % Model : x86_64 x86_64 % 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.33 % Memory : 8042.1875MB % 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.33 % CPULimit : 300 % 0.17/0.33 % WCLimit : 300 % 0.17/0.33 % DateTime : Tue Jun 2 14:07:31 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 25.85/26.12 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 25.85/26.12 --- Run --no-e-matching --full-saturate-quant at 6... % 25.85/26.12 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 25.85/26.12 % SZS status Theorem % 25.85/26.12 % SZS output start Proof % 25.85/26.12 ( % 25.85/26.12 (declare-sort $$unsorted 0) % 25.85/26.12 (declare-const tptp.xu $$unsorted) % 25.85/26.12 (declare-const tptp.xx $$unsorted) % 25.85/26.12 (declare-const tptp.xy $$unsorted) % 25.85/26.12 (declare-const tptp.xv $$unsorted) % 25.85/26.12 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 25.85/26.12 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 25.85/26.12 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 25.85/26.12 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 25.85/26.12 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 25.85/26.12 (declare-const tptp.sz00 $$unsorted) % 25.85/26.12 (declare-const tptp.sz10 $$unsorted) % 25.85/26.12 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 25.85/26.12 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 25.85/26.12 (declare-const tptp.xc $$unsorted) % 25.85/26.12 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 25.85/26.12 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 25.85/26.12 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 25.85/26.12 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 25.85/26.12 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 25.85/26.12 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 25.85/26.12 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 25.85/26.12 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 25.85/26.12 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 25.85/26.12 (declare-const tptp.xz $$unsorted) % 25.85/26.12 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 25.85/26.12 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 25.85/26.12 (define @t1 () (@var "W0" $$unsorted)) % 25.85/26.12 (define @t2 () (tptp.aElement0 @t1)) % 25.85/26.12 (define @t3 () (@list @t1)) % 25.85/26.12 (define @t4 () (tptp.smndt0 @t1)) % 25.85/26.12 (define @t5 () (@var "W1" $$unsorted)) % 25.85/26.12 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 25.85/26.12 (define @t7 () (tptp.aElement0 @t6)) % 25.85/26.12 (define @t8 () (tptp.aElement0 @t5)) % 25.85/26.12 (define @t9 () (and @t2 @t8)) % 25.85/26.12 (define @t10 () (@list @t1 @t5)) % 25.85/26.12 (define @t11 () (forall @t10 (=> @t9 @t7))) % 25.85/26.12 (define @t12 () (tptp.sdtasdt0 @t1 @t5)) % 25.85/26.12 (define @t13 () (tptp.aElement0 @t12)) % 25.85/26.12 (define @t14 () (forall @t10 (=> @t9 @t13))) % 25.85/26.12 (define @t15 () (@var "W2" $$unsorted)) % 25.85/26.12 (define @t16 () (tptp.sdtpldt0 @t5 @t15)) % 25.85/26.12 (define @t17 () (tptp.aElement0 @t15)) % 25.85/26.12 (define @t18 () (and @t2 @t8 @t17)) % 25.85/26.12 (define @t19 () (@list @t1 @t5 @t15)) % 25.85/26.12 (define @t20 () (tptp.sdtasdt0 @t5 @t1)) % 25.85/26.12 (define @t21 () (= @t12 @t20)) % 25.85/26.12 (define @t22 () (forall @t10 (=> @t9 @t21))) % 25.85/26.12 (define @t23 () (tptp.sdtasdt0 @t1 @t15)) % 25.85/26.12 (define @t24 () (tptp.smndt0 tptp.sz10)) % 25.85/26.12 (define @t25 () (= @t5 tptp.sz00)) % 25.85/26.12 (define @t26 () (= @t1 tptp.sz00)) % 25.85/26.12 (define @t27 () (tptp.aSet0 @t1)) % 25.85/26.12 (define @t28 () (tptp.aElementOf0 @t5 @t1)) % 25.85/26.12 (define @t29 () (@list @t5)) % 25.85/26.12 (define @t30 () (tptp.aElementOf0 @t15 @t1)) % 25.85/26.12 (define @t31 () (tptp.aElementOf0 @t15 @t5)) % 25.85/26.12 (define @t32 () (@list @t15)) % 25.85/26.12 (define @t33 () (tptp.aSet0 @t5)) % 25.85/26.12 (define @t34 () (and @t27 @t33)) % 25.85/26.12 (define @t35 () (@var "W3" $$unsorted)) % 25.85/26.12 (define @t36 () (@var "W5" $$unsorted)) % 25.85/26.12 (define @t37 () (@var "W4" $$unsorted)) % 25.85/26.12 (define @t38 () (tptp.aElementOf0 @t35 @t15)) % 25.85/26.12 (define @t39 () (@list @t35)) % 25.85/26.12 (define @t40 () (tptp.aSet0 @t15)) % 25.85/26.12 (define @t41 () (tptp.sdtpldt1 @t1 @t5)) % 25.85/26.12 (define @t42 () (tptp.sdtasasdt0 @t1 @t5)) % 25.85/26.12 (define @t43 () (tptp.sdtasdt0 @t15 @t5)) % 25.85/26.12 (define @t44 () (tptp.aIdeal0 @t1)) % 25.85/26.12 (define @t45 () (and @t44 (tptp.aIdeal0 @t5))) % 25.85/26.12 (define @t46 () (tptp.aElement0 @t35)) % 25.85/26.12 (define @t47 () (@list @t15 @t35)) % 25.85/26.12 (define @t48 () (tptp.aNaturalNumber0 @t1)) % 25.85/26.12 (define @t49 () (tptp.sdtasdt0 @t1 @t35)) % 25.85/26.12 (define @t50 () (and @t46 (= @t49 @t15))) % 25.85/26.12 (define @t51 () (exists @t39 @t50)) % 25.85/26.12 (define @t52 () (= @t31 @t51)) % 25.85/26.12 (define @t53 () (forall @t32 @t52)) % 25.85/26.12 (define @t54 () (and @t33 @t53)) % 25.85/26.12 (define @t55 () (tptp.slsdtgt0 @t1)) % 25.85/26.12 (define @t56 () (= @t5 @t55)) % 25.85/26.12 (define @t57 () (= @t56 @t54)) % 25.85/26.12 (define @t58 () (forall @t29 @t57)) % 25.85/26.12 (define @t59 () (=> @t2 @t58)) % 25.85/26.12 (define @t60 () (forall @t3 @t59)) % 25.85/26.12 (define @t61 () (tptp.aElement0 tptp.xc)) % 25.85/26.12 (define @t62 () (tptp.aElement0 tptp.xz)) % 25.85/26.12 (define @t63 () (tptp.slsdtgt0 tptp.xc)) % 25.85/26.12 (define @t64 () (tptp.sdtasdt0 tptp.xc tptp.xu)) % 25.85/26.12 (define @t65 () (tptp.aElement0 tptp.xu)) % 25.85/26.12 (define @t66 () (tptp.sdtasdt0 tptp.xc tptp.xv)) % 25.85/26.12 (define @t67 () (tptp.aElement0 tptp.xv)) % 25.85/26.12 (define @t68 () (tptp.sdtpldt0 tptp.xu tptp.xv)) % 25.85/26.12 (define @t69 () (tptp.sdtasdt0 tptp.xc @t68)) % 25.85/26.12 (define @t70 () (tptp.sdtpldt0 tptp.xx tptp.xy)) % 25.85/26.12 (define @t71 () (= @t70 @t69)) % 25.85/26.12 (define @t72 () (tptp.sdtasdt0 tptp.xu tptp.xz)) % 25.85/26.12 (define @t73 () (tptp.sdtasdt0 tptp.xc @t72)) % 25.85/26.12 (define @t74 () (tptp.sdtasdt0 tptp.xz tptp.xx)) % 25.85/26.12 (define @t75 () (= @t74 @t73)) % 25.85/26.12 (define @t76 () (tptp.aElementOf0 @t74 @t63)) % 25.85/26.12 (define @t77 () (tptp.aElementOf0 @t70 @t63)) % 25.85/26.12 (define @t78 () (and @t77 @t76)) % 25.85/26.12 (define @t79 () (not @t78)) % 25.85/26.12 (define @t80 () (not @t8)) % 25.85/26.12 (define @t81 () (not @t2)) % 25.85/26.12 (define @t82 () (or @t81 @t80 @t21)) % 25.85/26.12 (define @t83 () (or @t81 @t80)) % 25.85/26.12 (define @t84 () (not @t9)) % 25.85/26.12 (define @t85 () (tptp.sdtasdt0 tptp.xz tptp.xu)) % 25.85/26.12 (define @t86 () (not @t65)) % 25.85/26.12 (define @t87 () (not @t62)) % 25.85/26.12 (define @t88 () (or @t87 @t86 (= @t85 @t72))) % 25.85/26.12 (define @t89 () (forall @t10 @t82)) % 25.85/26.12 (define @t90 () (@list tptp.xz tptp.xu)) % 25.85/26.12 (define @t91 () (= @t72 @t85)) % 25.85/26.12 (define @t92 () (or @t87 @t86 @t91)) % 25.85/26.12 (define @t93 () (@list false)) % 25.85/26.12 (define @t94 () (@list false false false)) % 25.85/26.12 (define @t95 () (@var "BOUND_VARIABLE_8141" $$unsorted)) % 25.85/26.12 (define @t96 () (tptp.aElementOf0 @t15 @t95)) % 25.85/26.12 (define @t97 () (= @t15 @t49)) % 25.85/26.12 (define @t98 () (not @t46)) % 25.85/26.12 (define @t99 () (not (forall @t39 (or @t98 (not @t97))))) % 25.85/26.12 (define @t100 () (forall @t32 (= @t96 @t99))) % 25.85/26.12 (define @t101 () (tptp.aSet0 @t95)) % 25.85/26.12 (define @t102 () (and @t101 @t100)) % 25.85/26.12 (define @t103 () (= (= @t95 @t55) @t102)) % 25.85/26.12 (define @t104 () (or @t81 @t103)) % 25.85/26.12 (define @t105 () (@list @t1 @t95)) % 25.85/26.12 (define @t106 () (forall @t105 @t104)) % 25.85/26.12 (define @t107 () (@list @t95)) % 25.85/26.12 (define @t108 () (forall @t107 @t104)) % 25.85/26.12 (define @t109 () (forall @t107 @t103)) % 25.85/26.12 (define @t110 () (or @t81 @t109)) % 25.85/26.12 (define @t111 () (forall @t29 (= @t56 (and @t33 (forall @t32 (= @t31 @t99)))))) % 25.85/26.12 (define @t112 () (and @t46 @t97)) % 25.85/26.12 (define @t113 () (forall @t39 (not @t112))) % 25.85/26.12 (define @t114 () (not @t113)) % 25.85/26.12 (define @t115 () (tptp.sdtasdt0 tptp.xc @t35)) % 25.85/26.12 (define @t116 () (not (forall @t39 (or @t98 (not (= @t15 @t115)))))) % 25.85/26.12 (define @t117 () (tptp.aElementOf0 @t15 @t63)) % 25.85/26.12 (define @t118 () (forall @t32 (= @t117 @t116))) % 25.85/26.12 (define @t119 () (tptp.aSet0 @t63)) % 25.85/26.12 (define @t120 () (and @t119 @t118)) % 25.85/26.12 (define @t121 () (forall @t32 (= @t116 @t117))) % 25.85/26.12 (define @t122 () (and @t119 @t121)) % 25.85/26.12 (define @t123 () (= (= @t63 @t63) @t122)) % 25.85/26.12 (define @t124 () (not @t61)) % 25.85/26.12 (define @t125 () (or @t124 @t123)) % 25.85/26.12 (define @t126 () (forall @t105 (or @t81 (= (= @t55 @t95) (and @t101 (forall @t32 (= @t99 @t96))))))) % 25.85/26.12 (define @t127 () (or @t124 @t120)) % 25.85/26.12 (define @t128 () (@list false false)) % 25.85/26.12 (define @t129 () (tptp.sdtasdt0 tptp.xz @t64)) % 25.85/26.12 (define @t130 () (tptp.sdtpldt0 @t64 @t66)) % 25.85/26.12 (define @t131 () (tptp.aElement0 @t68)) % 25.85/26.12 (define @t132 () (not @t67)) % 25.85/26.12 (define @t133 () (or @t86 @t132 @t131)) % 25.85/26.12 (define @t134 () (= @t69 @t130)) % 25.85/26.12 (define @t135 () (not @t134)) % 25.85/26.12 (define @t136 () (not @t131)) % 25.85/26.12 (define @t137 () (or @t136 @t135)) % 25.85/26.12 (define @t138 () (not @t137)) % 25.85/26.12 (define @t139 () (not (= @t130 @t69))) % 25.85/26.12 (define @t140 () (or @t136 @t139)) % 25.85/26.12 (define @t141 () (forall @t39 (or @t98 (not (= @t130 @t115))))) % 25.85/26.12 (define @t142 () (not @t141)) % 25.85/26.12 (define @t143 () (tptp.aElementOf0 @t130 @t63)) % 25.85/26.12 (define @t144 () (= @t143 @t142)) % 25.85/26.12 (define @t145 () (not @t144)) % 25.85/26.12 (define @t146 () (@list true false)) % 25.85/26.12 (define @t147 () (tptp.aElementOf0 @t129 @t63)) % 25.85/26.12 (define @t148 () (forall @t39 (or @t98 (not (= @t129 @t115))))) % 25.85/26.12 (define @t149 () (not @t148)) % 25.85/26.12 (define @t150 () (= @t147 @t149)) % 25.85/26.12 (define @t151 () (not @t150)) % 25.85/26.12 (define @t152 () (not (= @t129 @t73))) % 25.85/26.12 (define @t153 () (tptp.aElement0 @t72)) % 25.85/26.12 (define @t154 () (not @t153)) % 25.85/26.12 (define @t155 () (or @t154 @t152)) % 25.85/26.12 (define @t156 () (= @t73 @t129)) % 25.85/26.12 (define @t157 () (not @t156)) % 25.85/26.12 (define @t158 () (or @t154 @t157)) % 25.85/26.12 (define @t159 () (tptp.aElement0 @t85)) % 25.85/26.12 (define @t160 () (or @t87 @t86 @t159)) % 25.85/26.12 (define @t161 () (not @t159)) % 25.85/26.12 (define @t162 () (not @t91)) % 25.85/26.12 (define @t163 () (and @t159 @t91 @t154)) % 25.85/26.12 (assume @p1 (forall @t3 (=> @t2 true))) % 25.85/26.12 (assume @p2 (tptp.aElement0 tptp.sz00)) % 25.85/26.12 (assume @p3 (tptp.aElement0 tptp.sz10)) % 25.85/26.12 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 25.85/26.12 (assume @p5 @t11) % 25.85/26.12 (assume @p6 @t14) % 25.85/26.12 (assume @p7 (forall @t10 (=> @t9 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 25.85/26.12 (assume @p8 (forall @t19 (=> @t18 (= (tptp.sdtpldt0 @t6 @t15) (tptp.sdtpldt0 @t1 @t16))))) % 25.85/26.12 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 25.85/26.12 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 25.85/26.12 (assume @p11 @t22) % 25.85/26.12 (assume @p12 (forall @t19 (=> @t18 (= (tptp.sdtasdt0 @t12 @t15) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t15)))))) % 25.85/26.12 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 25.85/26.12 (assume @p14 (forall @t19 (=> @t18 (and (= (tptp.sdtasdt0 @t1 @t16) (tptp.sdtpldt0 @t12 @t23)) (= (tptp.sdtasdt0 @t16 @t1) (tptp.sdtpldt0 @t20 (tptp.sdtasdt0 @t15 @t1))))))) % 25.85/26.12 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t24 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t24)))))) % 25.85/26.12 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 25.85/26.12 (assume @p17 (forall @t10 (=> @t9 (=> (= @t12 tptp.sz00) (or @t26 @t25))))) % 25.85/26.12 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 25.85/26.12 (assume @p19 (forall @t3 (=> @t27 true))) % 25.85/26.12 (assume @p20 (forall @t3 (=> @t27 (forall @t29 (=> @t28 @t8))))) % 25.85/26.12 (assume @p21 (forall @t10 (=> @t34 (=> (and (forall @t32 (=> @t30 @t31)) (forall @t32 (=> @t31 @t30))) (= @t1 @t5))))) % 25.85/26.12 (assume @p22 (forall @t10 (=> @t34 (forall @t32 (= (= @t15 @t41) (and @t40 (forall @t39 (= @t38 (exists (@list @t37 @t36) (and (tptp.aElementOf0 @t37 @t1) (tptp.aElementOf0 @t36 @t5) (= (tptp.sdtpldt0 @t37 @t36) @t35))))))))))) % 25.85/26.12 (assume @p23 (forall @t10 (=> @t34 (forall @t32 (= (= @t15 @t42) (and @t40 (forall @t39 (= @t38 (and (tptp.aElementOf0 @t35 @t1) (tptp.aElementOf0 @t35 @t5)))))))))) % 25.85/26.12 (assume @p24 (forall @t3 (= @t44 (and @t27 (forall @t29 (=> @t28 (and (forall @t32 (=> @t30 (tptp.aElementOf0 @t16 @t1))) (forall @t32 (=> @t17 (tptp.aElementOf0 @t43 @t1)))))))))) % 25.85/26.12 (assume @p25 (forall @t10 (=> @t45 (tptp.aIdeal0 @t41)))) % 25.85/26.12 (assume @p26 (forall @t10 (=> @t45 (tptp.aIdeal0 @t42)))) % 25.85/26.12 (assume @p27 (forall @t19 (=> (and @t2 @t8 (tptp.aIdeal0 @t15)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t15) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t15))))) % 25.85/26.12 (assume @p28 (forall @t10 (=> @t45 (=> (forall @t32 (=> @t17 (tptp.aElementOf0 @t15 @t41))) (forall @t47 (=> (and @t17 @t46) (exists (@list @t37) (and (tptp.aElement0 @t37) (tptp.sdteqdtlpzmzozddtrp0 @t37 @t15 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t37 @t35 @t5))))))))) % 25.85/26.12 (assume @p29 (forall @t3 (=> @t48 true))) % 25.85/26.12 (assume @p30 (forall @t3 (=> (and @t2 (not @t26)) (tptp.aNaturalNumber0 (tptp.sbrdtbr0 @t1))))) % 25.85/26.12 (assume @p31 (forall @t10 (=> (and @t48 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 25.85/26.12 (assume @p32 (forall @t10 (=> (and @t2 @t8 (not @t25)) (exists @t47 (and @t17 @t46 (= @t1 (tptp.sdtpldt0 @t43 @t35)) (=> (not (= @t35 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t35) (tptp.sbrdtbr0 @t5)))))))) % 25.85/26.12 (assume @p33 (forall @t10 (=> @t9 (= (tptp.doDivides0 @t1 @t5) (exists @t32 (and @t17 (= @t23 @t5))))))) % 25.85/26.12 (assume @p34 (forall @t3 (=> @t2 (forall @t29 (= (tptp.aDivisorOf0 @t5 @t1) (and @t8 (tptp.doDivides0 @t5 @t1))))))) % 25.85/26.12 (assume @p35 (forall @t10 (=> @t9 (forall @t32 (= (tptp.aGcdOfAnd0 @t15 @t1 @t5) (and (tptp.aDivisorOf0 @t15 @t1) (tptp.aDivisorOf0 @t15 @t5) (forall @t39 (=> (and (tptp.aDivisorOf0 @t35 @t1) (tptp.aDivisorOf0 @t35 @t5)) (tptp.doDivides0 @t35 @t15))))))))) % 25.85/26.12 (assume @p36 (forall @t10 (=> @t9 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 25.85/26.12 (assume @p37 @t60) % 25.85/26.12 (assume @p38 @t61) % 25.85/26.12 (assume @p39 (and (tptp.aElementOf0 tptp.xx @t63) (tptp.aElementOf0 tptp.xy @t63) @t62)) % 25.85/26.12 (assume @p40 (and @t65 (= @t64 tptp.xx))) % 25.85/26.12 (assume @p41 (and @t67 (= @t66 tptp.xy))) % 25.85/26.12 (assume @p42 @t71) % 25.85/26.12 (assume @p43 @t75) % 25.85/26.12 (assume @p44 @t79) % 25.85/26.12 (assume @p45 true) % 25.85/26.12 (step @p46 :rule aci_norm :args ((= (or @t83 @t21) @t82))) % 25.85/26.12 (step @p47 :rule refl :args (@t21)) % 25.85/26.12 (step @p48 :rule bool-and-de-morgan :args (@t2 @t8 true)) % 25.85/26.12 (step @p49 :rule nary_cong :premises (@p48 @p47) :args ((or @t84 @t21))) % 25.85/26.12 (step @p50 :rule trans :premises (@p49 @p46)) % 25.85/26.12 (step @p51 :rule bool-impl-elim :args (@t9 @t21)) % 25.85/26.12 (step @p52 :rule trans :premises (@p51 @p50)) % 25.85/26.12 (step @p53 :rule cong :premises (@p52) :args (@t22)) % 25.85/26.12 (step @p54 :rule eq_resolve :premises (@p11 @p53)) % 25.85/26.12 (step @p55 :rule eq-symm :args (@t85 @t72)) % 25.85/26.12 (step @p56 :rule refl :args (@t86)) % 25.85/26.12 (step @p57 :rule refl :args (@t87)) % 25.85/26.12 (step @p58 :rule nary_cong :premises (@p57 @p56 @p55) :args (@t88)) % 25.85/26.12 (step @p59 :rule refl :args (@t89)) % 25.85/26.12 (step @p60 :rule cong :premises (@p59 @p58) :args ((=> @t89 @t88))) % 25.85/26.12 (assume-push @p274 @t89) % 25.85/26.12 (step @p62 :rule instantiate :premises (@p54) :args (@t90)) % 25.85/26.12 (step-pop @p275 :rule scope :premises (@p62)) % 25.85/26.12 (step @p63 :rule process_scope :premises (@p275) :args (@t88)) % 25.85/26.12 (step @p65 :rule eq_resolve :premises (@p63 @p60)) % 25.85/26.12 (step @p66 :rule implies_elim :premises (@p65)) % 25.85/26.12 (step @p67 :rule chain_m_resolution :premises (@p66 @p54) :args (@t92 @t93 (@list @t89))) % 25.85/26.12 (step @p68 :rule and_elim :premises (@p40) :args (0)) % 25.85/26.12 (step @p69 :rule and_elim :premises (@p39) :args (2)) % 25.85/26.12 (step @p70 :rule cnf_or_pos :args (@t92)) % 25.85/26.12 (step @p71 :rule reordering :premises (@p70) :args ((or @t87 @t86 @t91 (not @t92)))) % 25.85/26.12 (step @p72 :rule chain_m_resolution :premises (@p71 @p69 @p68 @p67) :args (@t91 @t94 (@list @t62 @t65 @t92))) % 25.85/26.12 (step @p73 :rule eq-symm :args (@t96 @t99)) % 25.85/26.12 (step @p74 :rule cong :premises (@p73) :args (@t100)) % 25.85/26.12 (step @p75 :rule refl :args (@t101)) % 25.85/26.12 (step @p76 :rule nary_cong :premises (@p75 @p74) :args (@t102)) % 25.85/26.12 (step @p77 :rule eq-symm :args (@t95 @t55)) % 25.85/26.12 (step @p78 :rule cong :premises (@p77 @p76) :args (@t103)) % 25.85/26.12 (step @p79 :rule refl :args (@t81)) % 25.85/26.12 (step @p80 :rule nary_cong :premises (@p79 @p78) :args (@t104)) % 25.85/26.12 (step @p81 :rule cong :premises (@p80) :args (@t106)) % 25.85/26.12 (step @p82 :rule quant-merge-prenex :args ((= (forall @t3 @t108) @t106))) % 25.85/26.12 (step @p83 :rule alpha_equiv :args (@t109 (@list @t95) (@list @t5))) % 25.85/26.12 (step @p84 :rule refl :args (@t81)) % 25.85/26.12 (step @p85 :rule nary_cong :premises (@p84 @p83) :args (@t110)) % 25.85/26.12 (step @p86 :rule quant-miniscope-or :args ((= @t108 @t110))) % 25.85/26.12 (step @p87 :rule trans :premises (@p86 @p85)) % 25.85/26.12 (step @p88 :rule symm :premises (@p87)) % 25.85/26.12 (step @p89 :rule cong :premises (@p88) :args ((forall @t3 (or @t81 @t111)))) % 25.85/26.12 (step @p90 :rule trans :premises (@p89 @p82)) % 25.85/26.12 (step @p91 :rule trans :premises (@p90 @p81)) % 25.85/26.12 (step @p92 :rule bool-impl-elim :args (@t2 @t111)) % 25.85/26.12 (step @p93 :rule cong :premises (@p92) :args ((forall @t3 (=> @t2 @t111)))) % 25.85/26.12 (step @p94 :rule trans :premises (@p93 @p91)) % 25.85/26.12 (step @p95 :rule bool-and-de-morgan :args (@t46 @t97 true)) % 25.85/26.12 (step @p96 :rule cong :premises (@p95) :args (@t113)) % 25.85/26.12 (step @p97 :rule cong :premises (@p96) :args (@t114)) % 25.85/26.12 (step @p98 :rule exists-elim :args ((= (exists @t39 @t112) @t114))) % 25.85/26.12 (step @p99 :rule trans :premises (@p98 @p97)) % 25.85/26.12 (step @p100 :rule eq-symm :args (@t49 @t15)) % 25.85/26.12 (step @p101 :rule refl :args (@t46)) % 25.85/26.12 (step @p102 :rule nary_cong :premises (@p101 @p100) :args (@t50)) % 25.85/26.12 (step @p103 :rule cong :premises (@p102) :args (@t51)) % 25.85/26.12 (step @p104 :rule trans :premises (@p103 @p99)) % 25.85/26.12 (step @p105 :rule refl :args (@t31)) % 25.85/26.12 (step @p106 :rule cong :premises (@p105 @p104) :args (@t52)) % 25.85/26.12 (step @p107 :rule cong :premises (@p106) :args (@t53)) % 25.85/26.12 (step @p108 :rule refl :args (@t33)) % 25.85/26.12 (step @p109 :rule nary_cong :premises (@p108 @p107) :args (@t54)) % 25.85/26.12 (step @p110 :rule refl :args (@t56)) % 25.85/26.12 (step @p111 :rule cong :premises (@p110 @p109) :args (@t57)) % 25.85/26.12 (step @p112 :rule cong :premises (@p111) :args (@t58)) % 25.85/26.12 (step @p113 :rule refl :args (@t2)) % 25.85/26.12 (step @p114 :rule cong :premises (@p113 @p112) :args (@t59)) % 25.85/26.12 (step @p115 :rule cong :premises (@p114) :args (@t60)) % 25.85/26.12 (step @p116 :rule trans :premises (@p115 @p94)) % 25.85/26.12 (step @p117 :rule eq_resolve :premises (@p37 @p116)) % 25.85/26.12 (step @p118 :rule bool-eq-true :args (@t120)) % 25.85/26.12 (step @p119 :rule eq-symm :args (true @t120)) % 25.85/26.12 (step @p120 :rule trans :premises (@p119 @p118)) % 25.85/26.12 (step @p121 :rule eq-symm :args (@t116 @t117)) % 25.85/26.12 (step @p122 :rule cong :premises (@p121) :args (@t121)) % 25.85/26.12 (step @p123 :rule refl :args (@t119)) % 25.85/26.12 (step @p124 :rule nary_cong :premises (@p123 @p122) :args (@t122)) % 25.85/26.12 (step @p125 :rule eq-refl :args (@t63)) % 25.85/26.12 (step @p126 :rule cong :premises (@p125 @p124) :args (@t123)) % 25.85/26.12 (step @p127 :rule trans :premises (@p126 @p120)) % 25.85/26.12 (step @p128 :rule refl :args (@t124)) % 25.85/26.12 (step @p129 :rule nary_cong :premises (@p128 @p127) :args (@t125)) % 25.85/26.12 (step @p130 :rule refl :args (@t126)) % 25.85/26.12 (step @p131 :rule cong :premises (@p130 @p129) :args ((=> @t126 @t125))) % 25.85/26.12 (assume-push @p276 @t126) % 25.85/26.12 (step @p133 :rule instantiate :premises (@p117) :args ((@list tptp.xc @t63))) % 25.85/26.12 (step-pop @p277 :rule scope :premises (@p133)) % 25.85/26.12 (step @p134 :rule process_scope :premises (@p277) :args (@t125)) % 25.85/26.12 (step @p136 :rule eq_resolve :premises (@p134 @p131)) % 25.85/26.12 (step @p137 :rule implies_elim :premises (@p136)) % 25.85/26.12 (step @p138 :rule chain_m_resolution :premises (@p137 @p117) :args (@t127 @t93 (@list @t126))) % 25.85/26.12 (step @p139 :rule cnf_or_pos :args (@t127)) % 25.85/26.12 (step @p140 :rule reordering :premises (@p139) :args ((or @t124 @t120 (not @t127)))) % 25.85/26.12 (step @p141 :rule chain_m_resolution :premises (@p140 @p38 @p138) :args (@t120 @t128 (@list @t61 @t127))) % 25.85/26.12 (step @p142 :rule cnf_and_pos :args (@t120 1)) % 25.85/26.12 (step @p143 :rule reordering :premises (@p142) :args ((or @t118 (not @t120)))) % 25.85/26.12 (step @p144 :rule chain_m_resolution :premises (@p143 @p141) :args (@t118 @t93 (@list @t120))) % 25.85/26.12 (step @p145 :rule instantiate :premises (@p144) :args ((@list @t129))) % 25.85/26.12 (step @p146 :rule instantiate :premises (@p144) :args ((@list @t130))) % 25.85/26.12 (step @p147 :rule aci_norm :args ((= (or @t83 @t7) (or @t81 @t80 @t7)))) % 25.85/26.12 (step @p148 :rule refl :args (@t7)) % 25.85/26.12 (step @p149 :rule nary_cong :premises (@p48 @p148) :args ((or @t84 @t7))) % 25.85/26.12 (step @p150 :rule trans :premises (@p149 @p147)) % 25.85/26.12 (step @p151 :rule bool-impl-elim :args (@t9 @t7)) % 25.85/26.12 (step @p152 :rule trans :premises (@p151 @p150)) % 25.85/26.12 (step @p153 :rule cong :premises (@p152) :args (@t11)) % 25.85/26.12 (step @p154 :rule eq_resolve :premises (@p5 @p153)) % 25.85/26.12 (step @p155 :rule instantiate :premises (@p154) :args ((@list tptp.xu tptp.xv))) % 25.85/26.12 (step @p156 :rule and_elim :premises (@p41) :args (0)) % 25.85/26.12 (step @p157 :rule cnf_or_pos :args (@t133)) % 25.85/26.12 (step @p158 :rule reordering :premises (@p157) :args ((or @t86 @t132 @t131 (not @t133)))) % 25.85/26.12 (step @p159 :rule chain_m_resolution :premises (@p158 @p68 @p156 @p155) :args (@t131 @t94 (@list @t65 @t67 @t133))) % 25.85/26.12 (step @p160 :rule eq-symm :args (@t130 @t69)) % 25.85/26.12 (step @p161 :rule refl :args (@t69)) % 25.85/26.12 (step @p162 :rule and_elim :premises (@p41) :args (1)) % 25.85/26.12 (step @p163 :rule symm :premises (@p162)) % 25.85/26.12 (step @p164 :rule and_elim :premises (@p40) :args (1)) % 25.85/26.12 (step @p165 :rule symm :premises (@p164)) % 25.85/26.12 (step @p166 :rule cong :premises (@p165 @p163) :args (@t70)) % 25.85/26.12 (step @p167 :rule cong :premises (@p166 @p161) :args (@t71)) % 25.85/26.12 (step @p168 :rule trans :premises (@p167 @p160)) % 25.85/26.12 (step @p169 :rule eq_resolve :premises (@p42 @p168)) % 25.85/26.12 (step @p170 :rule cnf_or_pos :args (@t137)) % 25.85/26.12 (step @p171 :rule reordering :premises (@p170) :args ((or @t135 @t136 @t138))) % 25.85/26.12 (step @p172 :rule chain_m_resolution :premises (@p171 @p169 @p159) :args (@t138 @t128 (@list @t134 @t131))) % 25.85/26.12 (step @p173 :rule cong :premises (@p160) :args (@t139)) % 25.85/26.12 (step @p174 :rule refl :args (@t136)) % 25.85/26.12 (step @p175 :rule nary_cong :premises (@p174 @p173) :args (@t140)) % 25.85/26.12 (step @p176 :rule refl :args (@t141)) % 25.85/26.12 (step @p177 :rule cong :premises (@p176 @p175) :args ((=> @t141 @t140))) % 25.85/26.12 (assume-push @p278 @t141) % 25.85/26.12 (step @p179 :rule instantiate :premises (@p278) :args ((@list @t68))) % 25.85/26.12 (step-pop @p279 :rule scope :premises (@p179)) % 25.85/26.12 (step @p180 :rule process_scope :premises (@p279) :args (@t140)) % 25.85/26.12 (step @p182 :rule eq_resolve :premises (@p180 @p177)) % 25.85/26.12 (step @p183 :rule implies_elim :premises (@p182)) % 25.85/26.12 (step @p184 :rule chain_m_resolution :premises (@p183 @p172) :args (@t142 (@list true) (@list @t137))) % 25.85/26.12 (step @p185 :rule bool-double-not-elim :args (@t141)) % 25.85/26.12 (step @p186 :rule refl :args (@t143)) % 25.85/26.12 (step @p187 :rule refl :args (@t145)) % 25.85/26.12 (step @p188 :rule nary_cong :premises (@p187 @p186 @p185) :args ((or @t145 @t143 (not @t142)))) % 25.85/26.12 (step @p189 :rule cnf_equiv_pos2 :args (@t144)) % 25.85/26.12 (step @p190 :rule eq_resolve :premises (@p189 @p188)) % 25.85/26.12 (step @p191 :rule reordering :premises (@p190) :args ((or @t143 @t141 @t145))) % 25.85/26.12 (step @p192 :rule chain_m_resolution :premises (@p191 @p184 @p146) :args (@t143 @t146 (@list @t141 @t144))) % 25.85/26.12 (step @p193 :rule refl :args (@t63)) % 25.85/26.12 (step @p194 :rule refl :args (tptp.xz)) % 25.85/26.12 (step @p195 :rule cong :premises (@p194 @p165) :args (@t74)) % 25.85/26.12 (step @p196 :rule cong :premises (@p195 @p193) :args (@t76)) % 25.85/26.12 (step @p197 :rule cong :premises (@p166 @p193) :args (@t77)) % 25.85/26.12 (step @p198 :rule nary_cong :premises (@p197 @p196) :args (@t78)) % 25.85/26.12 (step @p199 :rule cong :premises (@p198) :args (@t79)) % 25.85/26.12 (step @p200 :rule eq_resolve :premises (@p44 @p199)) % 25.85/26.12 (step @p201 :rule not_and :premises (@p200)) % 25.85/26.12 (step @p202 :rule chain_m_resolution :premises (@p201 @p192) :args ((not @t147) @t93 (@list @t143))) % 25.85/26.12 (step @p203 :rule bool-double-not-elim :args (@t148)) % 25.85/26.12 (step @p204 :rule refl :args (@t147)) % 25.85/26.12 (step @p205 :rule refl :args (@t151)) % 25.85/26.12 (step @p206 :rule nary_cong :premises (@p205 @p204 @p203) :args ((or @t151 @t147 (not @t149)))) % 25.85/26.12 (step @p207 :rule cnf_equiv_pos2 :args (@t150)) % 25.85/26.12 (step @p208 :rule eq_resolve :premises (@p207 @p206)) % 25.85/26.12 (step @p209 :rule reordering :premises (@p208) :args ((or @t147 @t148 @t151))) % 25.85/26.12 (step @p210 :rule chain_m_resolution :premises (@p209 @p202 @p145) :args (@t148 @t146 (@list @t147 @t150))) % 25.85/26.12 (step @p211 :rule eq-symm :args (@t129 @t73)) % 25.85/26.12 (step @p212 :rule cong :premises (@p211) :args (@t152)) % 25.85/26.12 (step @p213 :rule refl :args (@t154)) % 25.85/26.12 (step @p214 :rule nary_cong :premises (@p213 @p212) :args (@t155)) % 25.85/26.12 (step @p215 :rule refl :args (@t148)) % 25.85/26.12 (step @p216 :rule cong :premises (@p215 @p214) :args ((=> @t148 @t155))) % 25.85/26.12 (assume-push @p280 @t148) % 25.85/26.12 (step @p218 :rule instantiate :premises (@p280) :args ((@list @t72))) % 25.85/26.12 (step-pop @p281 :rule scope :premises (@p218)) % 25.85/26.12 (step @p219 :rule process_scope :premises (@p281) :args (@t155)) % 25.85/26.12 (step @p221 :rule eq_resolve :premises (@p219 @p216)) % 25.85/26.12 (step @p222 :rule implies_elim :premises (@p221)) % 25.85/26.12 (step @p223 :rule chain_m_resolution :premises (@p222 @p210) :args (@t158 @t93 (@list @t148))) % 25.85/26.12 (step @p224 :rule refl :args (@t73)) % 25.85/26.12 (step @p225 :rule cong :premises (@p195 @p224) :args (@t75)) % 25.85/26.12 (step @p226 :rule trans :premises (@p225 @p211)) % 25.85/26.12 (step @p227 :rule eq_resolve :premises (@p43 @p226)) % 25.85/26.12 (step @p228 :rule cnf_or_pos :args (@t158)) % 25.85/26.12 (step @p229 :rule reordering :premises (@p228) :args ((or @t157 @t154 (not @t158)))) % 25.85/26.12 (step @p230 :rule chain_m_resolution :premises (@p229 @p227 @p223) :args (@t154 @t128 (@list @t156 @t158))) % 25.85/26.12 (step @p231 :rule aci_norm :args ((= (or @t83 @t13) (or @t81 @t80 @t13)))) % 25.85/26.12 (step @p232 :rule refl :args (@t13)) % 25.85/26.12 (step @p233 :rule nary_cong :premises (@p48 @p232) :args ((or @t84 @t13))) % 25.85/26.12 (step @p234 :rule trans :premises (@p233 @p231)) % 25.85/26.12 (step @p235 :rule bool-impl-elim :args (@t9 @t13)) % 25.85/26.12 (step @p236 :rule trans :premises (@p235 @p234)) % 25.85/26.12 (step @p237 :rule cong :premises (@p236) :args (@t14)) % 25.85/26.12 (step @p238 :rule eq_resolve :premises (@p6 @p237)) % 25.85/26.12 (step @p239 :rule instantiate :premises (@p238) :args (@t90)) % 25.85/26.12 (step @p240 :rule cnf_or_pos :args (@t160)) % 25.85/26.12 (step @p241 :rule reordering :premises (@p240) :args ((or @t87 @t86 @t159 (not @t160)))) % 25.85/26.12 (step @p242 :rule chain_m_resolution :premises (@p241 @p69 @p68 @p239) :args (@t159 @t94 (@list @t62 @t65 @t160))) % 25.85/26.12 (step @p243 :rule refl :args (@t161)) % 25.85/26.12 (step @p244 :rule bool-double-not-elim :args (@t153)) % 25.85/26.12 (step @p245 :rule refl :args (@t162)) % 25.85/26.12 (step @p246 :rule nary_cong :premises (@p245 @p244 @p243) :args ((or @t162 (not @t154) @t161))) % 25.85/26.12 (assume-push @p282 @t159) % 25.85/26.12 (assume-push @p283 @t91) % 25.85/26.12 (assume-push @p284 @t154) % 25.85/26.12 (step @p250 :rule evaluate :args ((= false true))) % 25.85/26.12 (step @p251 :rule true_intro :premises (@p242)) % 25.85/26.12 (step @p252 :rule cong :premises (@p72) :args (@t153)) % 25.85/26.12 (step @p253 :rule false_intro :premises (@p284)) % 25.85/26.12 (step @p254 :rule symm :premises (@p253)) % 25.85/26.12 (step @p255 :rule trans :premises (@p254 @p252 @p251)) % 25.85/26.12 (step @p256 false :rule eq_resolve :premises (@p255 @p250)) % 25.85/26.12 (step-pop @p285 :rule scope :premises (@p256)) % 25.85/26.12 (step-pop @p286 :rule scope :premises (@p285)) % 25.85/26.12 (step-pop @p287 :rule scope :premises (@p286)) % 25.85/26.12 (step @p257 :rule process_scope :premises (@p287) :args (false)) % 25.85/26.12 (assume-push @p288 @t91) % 25.85/26.12 (assume-push @p289 @t154) % 25.85/26.12 (assume-push @p290 @t159) % 25.85/26.12 (step @p264 :rule and_intro :premises (@p242 @p72 @p289)) % 25.85/26.12 (step-pop @p291 :rule scope :premises (@p264)) % 25.85/26.12 (step-pop @p292 :rule scope :premises (@p291)) % 25.85/26.12 (step-pop @p293 :rule scope :premises (@p292)) % 25.85/26.12 (step @p265 :rule process_scope :premises (@p293) :args (@t163)) % 25.85/26.12 (step @p269 :rule implies_elim :premises (@p265)) % 25.85/26.12 (step @p270 :rule resolution :premises (@p269 @p257) :args (true @t163)) % 25.85/26.12 (step @p271 :rule not_and :premises (@p270)) % 25.85/26.12 (step @p272 :rule eq_resolve :premises (@p271 @p246)) % 25.85/26.12 (step @p273 false :rule chain_m_resolution :premises (@p272 @p242 @p230 @p72) :args (false (@list false true false) (@list @t159 @t153 @t91))) % 25.85/26.12 ) % 25.85/26.12 % SZS output end Proof % 25.85/26.13 % cvc5 exiting %------------------------------------------------------------------------------