%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM494+3 : 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 08:39:36 AM UTC 2026 % Result : Theorem 0.73s 0.92s % Output : Proof 0.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM494+3 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.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 11:24:07 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.73/0.92 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.73/0.92 % SZS status Theorem % 0.73/0.92 % SZS output start Proof % 0.73/0.92 ( % 0.73/0.92 (declare-sort $$unsorted 0) % 0.73/0.92 (declare-const tptp.xr $$unsorted) % 0.73/0.92 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.73/0.92 (declare-const tptp.xm $$unsorted) % 0.73/0.92 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.73/0.92 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.73/0.92 (declare-const tptp.xn $$unsorted) % 0.73/0.92 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.73/0.92 (declare-const tptp.sz00 $$unsorted) % 0.73/0.92 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.73/0.92 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.73/0.92 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.73/0.92 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.73/0.92 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 0.73/0.92 (declare-const tptp.sz10 $$unsorted) % 0.73/0.92 (declare-const tptp.xp $$unsorted) % 0.73/0.92 (define @t1 () (@var "W0" $$unsorted)) % 0.73/0.92 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 0.73/0.92 (define @t3 () (@list @t1)) % 0.73/0.92 (define @t4 () (@var "W1" $$unsorted)) % 0.73/0.92 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 0.73/0.92 (define @t6 () (tptp.aNaturalNumber0 @t5)) % 0.73/0.92 (define @t7 () (tptp.aNaturalNumber0 @t4)) % 0.73/0.92 (define @t8 () (and @t2 @t7)) % 0.73/0.92 (define @t9 () (@list @t1 @t4)) % 0.73/0.92 (define @t10 () (forall @t9 (=> @t8 @t6))) % 0.73/0.92 (define @t11 () (tptp.sdtasdt0 @t1 @t4)) % 0.73/0.92 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 0.73/0.92 (define @t13 () (@var "W2" $$unsorted)) % 0.73/0.92 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 0.73/0.92 (define @t15 () (tptp.sdtpldt0 @t5 @t13)) % 0.73/0.92 (define @t16 () (tptp.aNaturalNumber0 @t13)) % 0.73/0.92 (define @t17 () (and @t2 @t7 @t16)) % 0.73/0.92 (define @t18 () (@list @t1 @t4 @t13)) % 0.73/0.92 (define @t19 () (tptp.sdtasdt0 @t4 @t1)) % 0.73/0.92 (define @t20 () (tptp.sdtasdt0 @t13 @t1)) % 0.73/0.92 (define @t21 () (tptp.sdtasdt0 @t1 @t13)) % 0.73/0.92 (define @t22 () (= @t4 @t13)) % 0.73/0.92 (define @t23 () (tptp.sdtpldt0 @t13 @t1)) % 0.73/0.92 (define @t24 () (tptp.sdtpldt0 @t1 @t13)) % 0.73/0.92 (define @t25 () (= @t19 @t20)) % 0.73/0.92 (define @t26 () (= @t11 @t21)) % 0.73/0.92 (define @t27 () (= @t1 tptp.sz00)) % 0.73/0.92 (define @t28 () (not @t27)) % 0.73/0.92 (define @t29 () (= @t4 tptp.sz00)) % 0.73/0.92 (define @t30 () (and @t16 (= @t24 @t4))) % 0.73/0.92 (define @t31 () (@list @t13)) % 0.73/0.92 (define @t32 () (tptp.sdtlseqdt0 @t1 @t4)) % 0.73/0.92 (define @t33 () (= @t1 @t4)) % 0.73/0.92 (define @t34 () (tptp.sdtlseqdt0 @t4 @t1)) % 0.73/0.92 (define @t35 () (tptp.sdtlseqdt0 @t4 @t13)) % 0.73/0.92 (define @t36 () (= @t4 @t1)) % 0.73/0.92 (define @t37 () (tptp.sdtlseqdt0 @t24 @t14)) % 0.73/0.92 (define @t38 () (not (= @t24 @t14))) % 0.73/0.92 (define @t39 () (tptp.sdtpldt0 @t13 @t4)) % 0.73/0.92 (define @t40 () (tptp.sdtlseqdt0 @t23 @t39)) % 0.73/0.92 (define @t41 () (not (= @t23 @t39))) % 0.73/0.92 (define @t42 () (and @t41 @t40 @t38 @t37)) % 0.73/0.92 (define @t43 () (=> @t16 @t42)) % 0.73/0.92 (define @t44 () (forall @t31 @t43)) % 0.73/0.92 (define @t45 () (not @t33)) % 0.73/0.92 (define @t46 () (and @t45 @t32)) % 0.73/0.92 (define @t47 () (=> @t46 @t44)) % 0.73/0.92 (define @t48 () (=> @t8 @t47)) % 0.73/0.92 (define @t49 () (forall @t9 @t48)) % 0.73/0.92 (define @t50 () (= @t1 tptp.sz10)) % 0.73/0.92 (define @t51 () (tptp.iLess0 @t1 @t4)) % 0.73/0.92 (define @t52 () (and @t16 (= @t4 @t21))) % 0.73/0.92 (define @t53 () (tptp.doDivides0 @t1 @t4)) % 0.73/0.92 (define @t54 () (tptp.sdtsldt0 @t4 @t1)) % 0.73/0.92 (define @t55 () (and @t28 @t53)) % 0.73/0.92 (define @t56 () (tptp.doDivides0 @t1 @t13)) % 0.73/0.92 (define @t57 () (tptp.doDivides0 @t1 @t14)) % 0.73/0.92 (define @t58 () (tptp.doDivides0 @t4 @t1)) % 0.73/0.92 (define @t59 () (@list @t4)) % 0.73/0.92 (define @t60 () (not @t50)) % 0.73/0.92 (define @t61 () (tptp.aNaturalNumber0 tptp.xp)) % 0.73/0.92 (define @t62 () (tptp.aNaturalNumber0 tptp.xm)) % 0.73/0.92 (define @t63 () (tptp.aNaturalNumber0 tptp.xn)) % 0.73/0.92 (define @t64 () (@var "W3" $$unsorted)) % 0.73/0.92 (define @t65 () (tptp.sdtasdt0 @t13 @t64)) % 0.73/0.92 (define @t66 () (tptp.aNaturalNumber0 @t64)) % 0.73/0.92 (define @t67 () (@list @t64)) % 0.73/0.92 (define @t68 () (tptp.sdtpldt0 tptp.xn tptp.xm)) % 0.73/0.92 (define @t69 () (tptp.sdtpldt0 @t68 tptp.xp)) % 0.73/0.92 (define @t70 () (@var "W4" $$unsorted)) % 0.73/0.92 (define @t71 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 0.73/0.92 (define @t72 () (tptp.sdtasdt0 tptp.xp @t1)) % 0.73/0.92 (define @t73 () (tptp.aNaturalNumber0 tptp.xr)) % 0.73/0.92 (define @t74 () (tptp.sdtlseqdt0 tptp.xr tptp.xn)) % 0.73/0.92 (define @t75 () (= tptp.xr tptp.xn)) % 0.73/0.92 (define @t76 () (tptp.sdtasdt0 tptp.xr tptp.xm)) % 0.73/0.92 (define @t77 () (tptp.sdtpldt0 tptp.xr tptp.xm)) % 0.73/0.92 (define @t78 () (tptp.sdtpldt0 @t77 tptp.xp)) % 0.73/0.92 (define @t79 () (tptp.sdtlseqdt0 @t78 @t69)) % 0.73/0.92 (define @t80 () (tptp.sdtpldt0 @t78 @t1)) % 0.73/0.92 (define @t81 () (and @t2 (= @t80 @t69))) % 0.73/0.92 (define @t82 () (exists @t3 @t81)) % 0.73/0.92 (define @t83 () (or @t82 @t79)) % 0.73/0.92 (define @t84 () (not (= @t78 @t69))) % 0.73/0.92 (define @t85 () (and @t84 @t83)) % 0.73/0.92 (define @t86 () (not @t85)) % 0.73/0.92 (define @t87 () (@var "BOUND_VARIABLE_8007" $$unsorted)) % 0.73/0.92 (define @t88 () (tptp.sdtpldt0 @t4 @t87)) % 0.73/0.92 (define @t89 () (tptp.sdtpldt0 @t1 @t87)) % 0.73/0.92 (define @t90 () (tptp.sdtpldt0 @t87 @t4)) % 0.73/0.92 (define @t91 () (tptp.sdtpldt0 @t87 @t1)) % 0.73/0.92 (define @t92 () (and (not (= @t91 @t90)) (tptp.sdtlseqdt0 @t91 @t90) (not (= @t88 @t89)) (tptp.sdtlseqdt0 @t89 @t88))) % 0.73/0.92 (define @t93 () (not (tptp.aNaturalNumber0 @t87))) % 0.73/0.92 (define @t94 () (not @t32)) % 0.73/0.92 (define @t95 () (not @t7)) % 0.73/0.92 (define @t96 () (not @t2)) % 0.73/0.92 (define @t97 () (or @t96 @t95 @t33 @t94 @t93 @t92)) % 0.73/0.92 (define @t98 () (or @t93 @t92)) % 0.73/0.92 (define @t99 () (or @t96 @t95 @t33 @t94 @t98)) % 0.73/0.92 (define @t100 () (@list @t1 @t4 @t87)) % 0.73/0.92 (define @t101 () (forall @t100 @t99)) % 0.73/0.92 (define @t102 () (@list @t87)) % 0.73/0.92 (define @t103 () (forall @t102 @t99)) % 0.73/0.92 (define @t104 () (forall @t102 @t98)) % 0.73/0.92 (define @t105 () (or @t96 @t95 @t33 @t94 @t104)) % 0.73/0.92 (define @t106 () (and @t41 @t40 (not (= @t14 @t24)) @t37)) % 0.73/0.92 (define @t107 () (forall @t31 (or (not @t16) @t106))) % 0.73/0.92 (define @t108 () (or @t96 @t95 @t33 @t94 @t107)) % 0.73/0.92 (define @t109 () (or @t33 @t94 @t107)) % 0.73/0.92 (define @t110 () (or @t96 @t95)) % 0.73/0.92 (define @t111 () (=> @t46 @t107)) % 0.73/0.92 (define @t112 () (not @t8)) % 0.73/0.92 (define @t113 () (= @t69 @t78)) % 0.73/0.92 (define @t114 () (not @t113)) % 0.73/0.92 (define @t115 () (tptp.sdtpldt0 tptp.xp @t68)) % 0.73/0.92 (define @t116 () (tptp.sdtpldt0 tptp.xp @t77)) % 0.73/0.92 (define @t117 () (tptp.sdtlseqdt0 @t116 @t115)) % 0.73/0.92 (define @t118 () (not (= @t116 @t115))) % 0.73/0.92 (define @t119 () (and @t118 @t117 @t114 @t79)) % 0.73/0.92 (define @t120 () (not @t61)) % 0.73/0.92 (define @t121 () (tptp.sdtlseqdt0 @t77 @t68)) % 0.73/0.92 (define @t122 () (not @t121)) % 0.73/0.92 (define @t123 () (tptp.aNaturalNumber0 @t68)) % 0.73/0.92 (define @t124 () (not @t123)) % 0.73/0.92 (define @t125 () (tptp.aNaturalNumber0 @t77)) % 0.73/0.92 (define @t126 () (not @t125)) % 0.73/0.92 (define @t127 () (or @t126 @t124 (= @t77 @t68) @t122 @t120 @t119)) % 0.73/0.92 (define @t128 () (forall @t100 @t97)) % 0.73/0.92 (define @t129 () (and (not (= @t115 @t116)) @t117 @t114 @t79)) % 0.73/0.92 (define @t130 () (= @t68 @t77)) % 0.73/0.92 (define @t131 () (or @t126 @t124 @t130 @t122 @t120 @t129)) % 0.73/0.92 (define @t132 () (@list false)) % 0.73/0.92 (define @t133 () (@list @t128)) % 0.73/0.92 (define @t134 () (not @t130)) % 0.73/0.92 (define @t135 () (tptp.sdtpldt0 tptp.xm tptp.xn)) % 0.73/0.92 (define @t136 () (tptp.sdtpldt0 tptp.xm tptp.xr)) % 0.73/0.92 (define @t137 () (tptp.sdtlseqdt0 @t136 @t135)) % 0.73/0.92 (define @t138 () (not (= @t136 @t135))) % 0.73/0.92 (define @t139 () (and @t138 @t137 @t134 @t121)) % 0.73/0.92 (define @t140 () (not @t62)) % 0.73/0.92 (define @t141 () (not @t74)) % 0.73/0.92 (define @t142 () (not @t63)) % 0.73/0.92 (define @t143 () (not @t73)) % 0.73/0.92 (define @t144 () (or @t143 @t142 @t75 @t141 @t140 @t139)) % 0.73/0.92 (define @t145 () (and (not (= @t135 @t136)) @t137 @t134 @t121)) % 0.73/0.92 (define @t146 () (= tptp.xn tptp.xr)) % 0.73/0.92 (define @t147 () (or @t143 @t142 @t146 @t141 @t140 @t145)) % 0.73/0.92 (define @t148 () (not @t145)) % 0.73/0.92 (define @t149 () (@list @t145)) % 0.73/0.92 (define @t150 () (or @t143 @t140 @t125)) % 0.73/0.92 (define @t151 () (@list false false false)) % 0.73/0.92 (define @t152 () (or @t142 @t140 @t123)) % 0.73/0.92 (define @t153 () (not @t129)) % 0.73/0.92 (define @t154 () (@list @t129)) % 0.73/0.92 (define @t155 () (= @t69 @t80)) % 0.73/0.92 (define @t156 () (or (not (forall @t3 (or @t96 (not @t155)))) @t79)) % 0.73/0.92 (define @t157 () (not @t156)) % 0.73/0.92 (define @t158 () (and @t2 @t155)) % 0.73/0.92 (define @t159 () (forall @t3 (not @t158))) % 0.73/0.92 (define @t160 () (not @t159)) % 0.73/0.92 (assume @p1 (forall @t3 (=> @t2 true))) % 0.73/0.92 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 0.73/0.92 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 0.73/0.92 (assume @p4 @t10) % 0.73/0.92 (assume @p5 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t11)))) % 0.73/0.92 (assume @p6 (forall @t9 (=> @t8 (= @t5 @t12)))) % 0.73/0.92 (assume @p7 (forall @t18 (=> @t17 (= @t15 (tptp.sdtpldt0 @t1 @t14))))) % 0.73/0.92 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.73/0.92 (assume @p9 (forall @t9 (=> @t8 (= @t11 @t19)))) % 0.73/0.92 (assume @p10 (forall @t18 (=> @t17 (= (tptp.sdtasdt0 @t11 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 0.73/0.92 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.73/0.92 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.73/0.92 (assume @p13 (forall @t18 (=> @t17 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t11 @t21)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t19 @t20)))))) % 0.73/0.92 (assume @p14 (forall @t18 (=> @t17 (=> (or (= @t5 @t24) (= @t12 @t23)) @t22)))) % 0.73/0.92 (assume @p15 (forall @t3 (=> @t2 (=> @t28 (forall (@list @t4 @t13) (=> (and @t7 @t16) (=> (or @t26 @t25) @t22))))))) % 0.73/0.92 (assume @p16 (forall @t9 (=> @t8 (=> (= @t5 tptp.sz00) (and @t27 @t29))))) % 0.73/0.92 (assume @p17 (forall @t9 (=> @t8 (=> (= @t11 tptp.sz00) (or @t27 @t29))))) % 0.73/0.92 (assume @p18 (forall @t9 (=> @t8 (= @t32 (exists @t31 @t30))))) % 0.73/0.92 (assume @p19 (forall @t9 (=> @t8 (=> @t32 (forall @t31 (= (= @t13 (tptp.sdtmndt0 @t4 @t1)) @t30)))))) % 0.73/0.92 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.73/0.92 (assume @p21 (forall @t9 (=> @t8 (=> (and @t32 @t34) @t33)))) % 0.73/0.92 (assume @p22 (forall @t18 (=> @t17 (=> (and @t32 @t35) (tptp.sdtlseqdt0 @t1 @t13))))) % 0.73/0.92 (assume @p23 (forall @t9 (=> @t8 (or @t32 (and (not @t36) @t34))))) % 0.73/0.92 (assume @p24 @t49) % 0.73/0.92 (assume @p25 (forall @t18 (=> @t17 (=> (and @t28 (not @t22) @t35) (and (not @t26) (tptp.sdtlseqdt0 @t11 @t21) (not @t25) (tptp.sdtlseqdt0 @t19 @t20)))))) % 0.73/0.92 (assume @p26 (forall @t3 (=> @t2 (or @t27 @t50 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 0.73/0.92 (assume @p27 (forall @t9 (=> @t8 (=> @t28 (tptp.sdtlseqdt0 @t4 @t19))))) % 0.73/0.92 (assume @p28 (forall @t9 (=> @t8 (=> @t51 true)))) % 0.73/0.92 (assume @p29 (forall @t9 (=> @t8 (=> @t46 @t51)))) % 0.73/0.92 (assume @p30 (forall @t9 (=> @t8 (= @t53 (exists @t31 @t52))))) % 0.73/0.92 (assume @p31 (forall @t9 (=> @t8 (=> @t55 (forall @t31 (= (= @t13 @t54) @t52)))))) % 0.73/0.92 (assume @p32 (forall @t18 (=> @t17 (=> (and @t53 (tptp.doDivides0 @t4 @t13)) @t56)))) % 0.73/0.92 (assume @p33 (forall @t18 (=> @t17 (=> (and @t53 @t56) @t57)))) % 0.73/0.92 (assume @p34 (forall @t18 (=> @t17 (=> (and @t53 @t57) @t56)))) % 0.73/0.92 (assume @p35 (forall @t9 (=> @t8 (=> (and @t53 (not @t29)) @t32)))) % 0.73/0.92 (assume @p36 (forall @t9 (=> @t8 (=> @t55 (forall @t31 (=> @t16 (= (tptp.sdtasdt0 @t13 @t54) (tptp.sdtsldt0 (tptp.sdtasdt0 @t13 @t4) @t1)))))))) % 0.73/0.92 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t28 @t60 (forall @t59 (=> (and @t7 @t58) (or (= @t4 tptp.sz10) @t36)))))))) % 0.73/0.92 (assume @p38 (forall @t3 (=> (and @t2 @t28 @t60) (exists @t59 (and @t7 @t58 (tptp.isPrime0 @t4)))))) % 0.73/0.92 (assume @p39 (and @t63 @t62 @t61)) % 0.73/0.92 (assume @p40 (forall @t18 (=> @t17 (=> (and (or (and (not (= @t13 tptp.sz00)) (not (= @t13 tptp.sz10)) (forall @t67 (=> (and @t66 (exists (@list @t70) (and (tptp.aNaturalNumber0 @t70) (= @t13 (tptp.sdtasdt0 @t64 @t70)))) (tptp.doDivides0 @t64 @t13)) (or (= @t64 tptp.sz10) (= @t64 @t13))))) (tptp.isPrime0 @t13)) (or (exists @t67 (and @t66 (= @t11 @t65))) (tptp.doDivides0 @t13 @t11))) (=> (tptp.iLess0 @t15 @t69) (or (and (exists @t67 (and @t66 (= @t1 @t65))) (tptp.doDivides0 @t13 @t1)) (and (exists @t67 (and @t66 (= @t4 @t65))) (tptp.doDivides0 @t13 @t4)))))))) % 0.73/0.92 (assume @p41 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t59 (and @t7 (= tptp.xp @t11))) (tptp.doDivides0 @t1 tptp.xp))) (or @t50 (= @t1 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists @t3 (and @t2 (= @t71 @t72))) (tptp.doDivides0 tptp.xp @t71))) % 0.73/0.92 (assume @p42 (and (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xp @t1) tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn))) % 0.73/0.92 (assume @p43 (and @t73 (= (tptp.sdtpldt0 tptp.xp tptp.xr) tptp.xn) (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp)))) % 0.73/0.92 (assume @p44 (and (not @t75) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xr @t1) tptp.xn))) @t74)) % 0.73/0.92 (assume @p45 (and (exists @t3 (and @t2 (= @t76 @t72))) (tptp.doDivides0 tptp.xp @t76))) % 0.73/0.92 (assume @p46 @t86) % 0.73/0.92 (assume @p47 true) % 0.73/0.92 (step @p48 :rule aci_norm :args ((= @t99 @t97))) % 0.73/0.92 (step @p49 :rule cong :premises (@p48) :args (@t101)) % 0.73/0.92 (step @p50 :rule quant-merge-prenex :args ((= (forall @t9 @t103) @t101))) % 0.73/0.92 (step @p51 :rule alpha_equiv :args (@t104 (@list @t87) (@list @t13))) % 0.73/0.92 (step @p52 :rule refl :args (@t94)) % 0.73/0.92 (step @p53 :rule refl :args (@t33)) % 0.73/0.92 (step @p54 :rule refl :args (@t95)) % 0.73/0.92 (step @p55 :rule refl :args (@t96)) % 0.73/0.92 (step @p56 :rule nary_cong :premises (@p55 @p54 @p53 @p52 @p51) :args (@t105)) % 0.73/0.92 (step @p57 :rule quant-miniscope-or :args ((= @t103 @t105))) % 0.73/0.92 (step @p58 :rule trans :premises (@p57 @p56)) % 0.73/0.92 (step @p59 :rule symm :premises (@p58)) % 0.73/0.92 (step @p60 :rule cong :premises (@p59) :args ((forall @t9 @t108))) % 0.73/0.92 (step @p61 :rule trans :premises (@p60 @p50)) % 0.73/0.92 (step @p62 :rule trans :premises (@p61 @p49)) % 0.73/0.92 (step @p63 :rule aci_norm :args ((= (or @t110 @t109) @t108))) % 0.73/0.92 (step @p64 :rule aci_norm :args ((= (or (or @t33 @t94) @t107) @t109))) % 0.73/0.92 (step @p65 :rule refl :args (@t107)) % 0.73/0.92 (step @p66 :rule bool-double-not-elim :args (@t33)) % 0.73/0.92 (step @p67 :rule nary_cong :premises (@p66 @p52) :args ((or (not @t45) @t94))) % 0.73/0.92 (step @p68 :rule bool-and-de-morgan :args (@t45 @t32 true)) % 0.73/0.92 (step @p69 :rule trans :premises (@p68 @p67)) % 0.73/0.92 (step @p70 :rule nary_cong :premises (@p69 @p65) :args ((or (not @t46) @t107))) % 0.73/0.92 (step @p71 :rule trans :premises (@p70 @p64)) % 0.73/0.92 (step @p72 :rule bool-impl-elim :args (@t46 @t107)) % 0.73/0.92 (step @p73 :rule trans :premises (@p72 @p71)) % 0.73/0.92 (step @p74 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 0.73/0.92 (step @p75 :rule nary_cong :premises (@p74 @p73) :args ((or @t112 @t111))) % 0.73/0.92 (step @p76 :rule trans :premises (@p75 @p63)) % 0.73/0.92 (step @p77 :rule bool-impl-elim :args (@t8 @t111)) % 0.73/0.92 (step @p78 :rule trans :premises (@p77 @p76)) % 0.73/0.92 (step @p79 :rule cong :premises (@p78) :args ((forall @t9 (=> @t8 @t111)))) % 0.73/0.92 (step @p80 :rule trans :premises (@p79 @p62)) % 0.73/0.92 (step @p81 :rule bool-impl-elim :args (@t16 @t106)) % 0.73/0.92 (step @p82 :rule cong :premises (@p81) :args ((forall @t31 (=> @t16 @t106)))) % 0.73/0.92 (step @p83 :rule refl :args (@t37)) % 0.73/0.92 (step @p84 :rule eq-symm :args (@t24 @t14)) % 0.73/0.92 (step @p85 :rule cong :premises (@p84) :args (@t38)) % 0.73/0.92 (step @p86 :rule refl :args (@t40)) % 0.73/0.92 (step @p87 :rule refl :args (@t41)) % 0.73/0.92 (step @p88 :rule nary_cong :premises (@p87 @p86 @p85 @p83) :args (@t42)) % 0.73/0.92 (step @p89 :rule refl :args (@t16)) % 0.73/0.92 (step @p90 :rule cong :premises (@p89 @p88) :args (@t43)) % 0.73/0.92 (step @p91 :rule cong :premises (@p90) :args (@t44)) % 0.73/0.92 (step @p92 :rule trans :premises (@p91 @p82)) % 0.73/0.92 (step @p93 :rule refl :args (@t46)) % 0.73/0.92 (step @p94 :rule cong :premises (@p93 @p92) :args (@t47)) % 0.73/0.92 (step @p95 :rule refl :args (@t8)) % 0.73/0.92 (step @p96 :rule cong :premises (@p95 @p94) :args (@t48)) % 0.73/0.92 (step @p97 :rule cong :premises (@p96) :args (@t49)) % 0.73/0.92 (step @p98 :rule trans :premises (@p97 @p80)) % 0.73/0.92 (step @p99 :rule eq_resolve :premises (@p24 @p98)) % 0.73/0.92 (step @p100 :rule refl :args (@t79)) % 0.73/0.92 (step @p101 :rule refl :args (@t114)) % 0.73/0.92 (step @p102 :rule refl :args (@t117)) % 0.73/0.92 (step @p103 :rule eq-symm :args (@t116 @t115)) % 0.73/0.92 (step @p104 :rule cong :premises (@p103) :args (@t118)) % 0.73/0.92 (step @p105 :rule nary_cong :premises (@p104 @p102 @p101 @p100) :args (@t119)) % 0.73/0.92 (step @p106 :rule refl :args (@t120)) % 0.73/0.92 (step @p107 :rule refl :args (@t122)) % 0.73/0.92 (step @p108 :rule eq-symm :args (@t77 @t68)) % 0.73/0.92 (step @p109 :rule refl :args (@t124)) % 0.73/0.92 (step @p110 :rule refl :args (@t126)) % 0.73/0.92 (step @p111 :rule nary_cong :premises (@p110 @p109 @p108 @p107 @p106 @p105) :args (@t127)) % 0.73/0.92 (step @p112 :rule refl :args (@t128)) % 0.73/0.92 (step @p113 :rule cong :premises (@p112 @p111) :args ((=> @t128 @t127))) % 0.73/0.92 (assume-push @p206 @t128) % 0.73/0.92 (step @p115 :rule instantiate :premises (@p99) :args ((@list @t77 @t68 tptp.xp))) % 0.73/0.92 (step-pop @p207 :rule scope :premises (@p115)) % 0.73/0.92 (step @p116 :rule process_scope :premises (@p207) :args (@t127)) % 0.73/0.92 (step @p118 :rule eq_resolve :premises (@p116 @p113)) % 0.73/0.92 (step @p119 :rule implies_elim :premises (@p118)) % 0.73/0.92 (step @p120 :rule chain_m_resolution :premises (@p119 @p99) :args (@t131 @t132 @t133)) % 0.73/0.92 (step @p121 :rule refl :args (@t121)) % 0.73/0.92 (step @p122 :rule refl :args (@t134)) % 0.73/0.92 (step @p123 :rule refl :args (@t137)) % 0.73/0.92 (step @p124 :rule eq-symm :args (@t136 @t135)) % 0.73/0.92 (step @p125 :rule cong :premises (@p124) :args (@t138)) % 0.73/0.92 (step @p126 :rule nary_cong :premises (@p125 @p123 @p122 @p121) :args (@t139)) % 0.73/0.92 (step @p127 :rule refl :args (@t140)) % 0.73/0.92 (step @p128 :rule refl :args (@t141)) % 0.73/0.92 (step @p129 :rule eq-symm :args (tptp.xr tptp.xn)) % 0.73/0.92 (step @p130 :rule refl :args (@t142)) % 0.73/0.92 (step @p131 :rule refl :args (@t143)) % 0.73/0.92 (step @p132 :rule nary_cong :premises (@p131 @p130 @p129 @p128 @p127 @p126) :args (@t144)) % 0.73/0.92 (step @p133 :rule cong :premises (@p112 @p132) :args ((=> @t128 @t144))) % 0.73/0.92 (assume-push @p208 @t128) % 0.73/0.92 (step @p135 :rule instantiate :premises (@p99) :args ((@list tptp.xr tptp.xn tptp.xm))) % 0.73/0.92 (step-pop @p209 :rule scope :premises (@p135)) % 0.73/0.92 (step @p136 :rule process_scope :premises (@p209) :args (@t144)) % 0.73/0.92 (step @p138 :rule eq_resolve :premises (@p136 @p133)) % 0.73/0.92 (step @p139 :rule implies_elim :premises (@p138)) % 0.73/0.92 (step @p140 :rule chain_m_resolution :premises (@p139 @p99) :args (@t147 @t132 @t133)) % 0.73/0.92 (step @p141 :rule and_elim :premises (@p44) :args (2)) % 0.73/0.92 (step @p142 :rule and_elim :premises (@p43) :args (0)) % 0.73/0.92 (step @p143 :rule and_elim :premises (@p39) :args (1)) % 0.73/0.92 (step @p144 :rule and_elim :premises (@p39) :args (0)) % 0.73/0.92 (step @p145 :rule and_elim :premises (@p44) :args (0)) % 0.73/0.92 (step @p146 :rule symm :premises (@p145)) % 0.73/0.92 (step @p147 :rule cnf_or_pos :args (@t147)) % 0.73/0.92 (step @p148 :rule reordering :premises (@p147) :args ((or @t146 @t142 @t140 @t143 @t141 @t145 (not @t147)))) % 0.73/0.92 (step @p149 :rule chain_m_resolution :premises (@p148 @p146 @p144 @p143 @p142 @p141 @p140) :args (@t145 (@list true false false false false false) (@list @t146 @t63 @t62 @t73 @t74 @t147))) % 0.73/0.92 (step @p150 :rule cnf_and_pos :args (@t145 2)) % 0.73/0.92 (step @p151 :rule reordering :premises (@p150) :args ((or @t134 @t148))) % 0.73/0.92 (step @p152 :rule chain_m_resolution :premises (@p151 @p149) :args (@t134 @t132 @t149)) % 0.73/0.92 (step @p153 :rule cnf_and_pos :args (@t145 3)) % 0.73/0.92 (step @p154 :rule reordering :premises (@p153) :args ((or @t121 @t148))) % 0.73/0.92 (step @p155 :rule chain_m_resolution :premises (@p154 @p149) :args (@t121 @t132 @t149)) % 0.73/0.92 (step @p156 :rule aci_norm :args ((= (or @t110 @t6) (or @t96 @t95 @t6)))) % 0.73/0.92 (step @p157 :rule refl :args (@t6)) % 0.73/0.92 (step @p158 :rule nary_cong :premises (@p74 @p157) :args ((or @t112 @t6))) % 0.73/0.92 (step @p159 :rule trans :premises (@p158 @p156)) % 0.73/0.92 (step @p160 :rule bool-impl-elim :args (@t8 @t6)) % 0.73/0.92 (step @p161 :rule trans :premises (@p160 @p159)) % 0.73/0.92 (step @p162 :rule cong :premises (@p161) :args (@t10)) % 0.73/0.92 (step @p163 :rule eq_resolve :premises (@p4 @p162)) % 0.73/0.92 (step @p164 :rule instantiate :premises (@p163) :args ((@list tptp.xr tptp.xm))) % 0.73/0.92 (step @p165 :rule cnf_or_pos :args (@t150)) % 0.73/0.92 (step @p166 :rule reordering :premises (@p165) :args ((or @t140 @t143 @t125 (not @t150)))) % 0.73/0.92 (step @p167 :rule chain_m_resolution :premises (@p166 @p143 @p142 @p164) :args (@t125 @t151 (@list @t62 @t73 @t150))) % 0.73/0.92 (step @p168 :rule instantiate :premises (@p163) :args ((@list tptp.xn tptp.xm))) % 0.73/0.92 (step @p169 :rule cnf_or_pos :args (@t152)) % 0.73/0.92 (step @p170 :rule reordering :premises (@p169) :args ((or @t142 @t140 @t123 (not @t152)))) % 0.73/0.92 (step @p171 :rule chain_m_resolution :premises (@p170 @p144 @p143 @p168) :args (@t123 @t151 (@list @t63 @t62 @t152))) % 0.73/0.92 (step @p172 :rule and_elim :premises (@p39) :args (2)) % 0.73/0.92 (step @p173 :rule cnf_or_pos :args (@t131)) % 0.73/0.92 (step @p174 :rule reordering :premises (@p173) :args ((or @t120 @t124 @t126 @t122 @t130 @t129 (not @t131)))) % 0.73/0.92 (step @p175 :rule chain_m_resolution :premises (@p174 @p172 @p171 @p167 @p155 @p152 @p120) :args (@t129 (@list false false false false true false) (@list @t61 @t123 @t125 @t121 @t130 @t131))) % 0.73/0.92 (step @p176 :rule cnf_and_pos :args (@t129 3)) % 0.73/0.92 (step @p177 :rule reordering :premises (@p176) :args ((or @t79 @t153))) % 0.73/0.92 (step @p178 :rule chain_m_resolution :premises (@p177 @p175) :args (@t79 @t132 @t154)) % 0.73/0.92 (step @p179 :rule cnf_and_pos :args (@t129 2)) % 0.73/0.92 (step @p180 :rule reordering :premises (@p179) :args ((or @t114 @t153))) % 0.73/0.92 (step @p181 :rule chain_m_resolution :premises (@p180 @p175) :args (@t114 @t132 @t154)) % 0.73/0.92 (step @p182 :rule refl :args (@t157)) % 0.73/0.92 (step @p183 :rule bool-double-not-elim :args (@t113)) % 0.73/0.92 (step @p184 :rule nary_cong :premises (@p183 @p182) :args ((or (not @t114) @t157))) % 0.73/0.92 (step @p185 :rule bool-and-de-morgan :args (@t2 @t155 true)) % 0.73/0.92 (step @p186 :rule cong :premises (@p185) :args (@t159)) % 0.73/0.92 (step @p187 :rule cong :premises (@p186) :args (@t160)) % 0.73/0.92 (step @p188 :rule exists-elim :args ((= (exists @t3 @t158) @t160))) % 0.73/0.92 (step @p189 :rule trans :premises (@p188 @p187)) % 0.73/0.92 (step @p190 :rule eq-symm :args (@t80 @t69)) % 0.73/0.92 (step @p191 :rule refl :args (@t2)) % 0.73/0.92 (step @p192 :rule nary_cong :premises (@p191 @p190) :args (@t81)) % 0.73/0.92 (step @p193 :rule cong :premises (@p192) :args (@t82)) % 0.73/0.93 (step @p194 :rule trans :premises (@p193 @p189)) % 0.73/0.93 (step @p195 :rule nary_cong :premises (@p194 @p100) :args (@t83)) % 0.73/0.93 (step @p196 :rule eq-symm :args (@t78 @t69)) % 0.73/0.93 (step @p197 :rule cong :premises (@p196) :args (@t84)) % 0.73/0.93 (step @p198 :rule nary_cong :premises (@p197 @p195) :args (@t85)) % 0.73/0.93 (step @p199 :rule cong :premises (@p198) :args (@t86)) % 0.73/0.93 (step @p200 :rule eq_resolve :premises (@p46 @p199)) % 0.73/0.93 (step @p201 :rule not_and :premises (@p200)) % 0.73/0.93 (step @p202 :rule eq_resolve :premises (@p201 @p184)) % 0.73/0.93 (step @p203 :rule chain_m_resolution :premises (@p202 @p181) :args (@t157 (@list true) (@list @t113))) % 0.73/0.93 (step @p204 :rule cnf_or_neg :args (@t156 1)) % 0.73/0.93 (step @p205 false :rule chain_m_resolution :premises (@p204 @p203 @p178) :args (false (@list true false) (@list @t156 @t79))) % 0.73/0.93 ) % 0.73/0.93 % SZS output end Proof % 0.73/0.93 % cvc5 exiting %------------------------------------------------------------------------------