%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM518+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 : n016.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 08:39:41 AM UTC 2026 % Result : Theorem 35.63s 35.86s % Output : Proof 35.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM518+3 : 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 % 0.16/0.34 % Computer : n016.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 11:27:24 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 35.63/35.86 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 35.63/35.86 --- Run --no-e-matching --full-saturate-quant at 6... % 35.63/35.86 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 35.63/35.86 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 35.63/35.86 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 35.63/35.86 % SZS status Theorem % 35.63/35.86 % SZS output start Proof % 35.63/35.86 ( % 35.63/35.86 (declare-sort $$unsorted 0) % 35.63/35.86 (declare-const tptp.xr $$unsorted) % 35.63/35.86 (declare-const tptp.xk $$unsorted) % 35.63/35.86 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 35.63/35.86 (declare-const tptp.xm $$unsorted) % 35.63/35.86 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 35.63/35.86 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 35.63/35.86 (declare-const tptp.xn $$unsorted) % 35.63/35.86 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 35.63/35.86 (declare-const tptp.sz00 $$unsorted) % 35.63/35.86 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 35.63/35.86 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 35.63/35.86 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 35.63/35.86 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 35.63/35.86 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 35.63/35.86 (declare-const tptp.sz10 $$unsorted) % 35.63/35.86 (declare-const tptp.xp $$unsorted) % 35.63/35.86 (define @t1 () (@var "W0" $$unsorted)) % 35.63/35.86 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 35.63/35.86 (define @t3 () (@list @t1)) % 35.63/35.86 (define @t4 () (tptp.aNaturalNumber0 tptp.sz00)) % 35.63/35.86 (define @t5 () (@var "W1" $$unsorted)) % 35.63/35.86 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 35.63/35.86 (define @t7 () (tptp.aNaturalNumber0 @t5)) % 35.63/35.86 (define @t8 () (and @t2 @t7)) % 35.63/35.86 (define @t9 () (@list @t1 @t5)) % 35.63/35.86 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 35.63/35.86 (define @t11 () (tptp.sdtpldt0 @t5 @t1)) % 35.63/35.86 (define @t12 () (@var "W2" $$unsorted)) % 35.63/35.86 (define @t13 () (tptp.sdtpldt0 @t5 @t12)) % 35.63/35.86 (define @t14 () (tptp.sdtpldt0 @t6 @t12)) % 35.63/35.86 (define @t15 () (tptp.aNaturalNumber0 @t12)) % 35.63/35.86 (define @t16 () (and @t2 @t7 @t15)) % 35.63/35.86 (define @t17 () (@list @t1 @t5 @t12)) % 35.63/35.86 (define @t18 () (tptp.sdtasdt0 @t5 @t1)) % 35.63/35.86 (define @t19 () (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1))) % 35.63/35.86 (define @t20 () (tptp.sdtasdt0 @t1 tptp.sz00)) % 35.63/35.86 (define @t21 () (and (= @t20 tptp.sz00) @t19)) % 35.63/35.86 (define @t22 () (=> @t2 @t21)) % 35.63/35.86 (define @t23 () (forall @t3 @t22)) % 35.63/35.86 (define @t24 () (tptp.sdtasdt0 @t12 @t1)) % 35.63/35.86 (define @t25 () (tptp.sdtasdt0 @t1 @t12)) % 35.63/35.86 (define @t26 () (= @t5 @t12)) % 35.63/35.86 (define @t27 () (tptp.sdtpldt0 @t12 @t1)) % 35.63/35.86 (define @t28 () (tptp.sdtpldt0 @t1 @t12)) % 35.63/35.86 (define @t29 () (= @t18 @t24)) % 35.63/35.86 (define @t30 () (= @t10 @t25)) % 35.63/35.86 (define @t31 () (and @t7 @t15)) % 35.63/35.86 (define @t32 () (= @t1 tptp.sz00)) % 35.63/35.86 (define @t33 () (not @t32)) % 35.63/35.86 (define @t34 () (= @t5 tptp.sz00)) % 35.63/35.86 (define @t35 () (and @t15 (= @t28 @t5))) % 35.63/35.86 (define @t36 () (@list @t12)) % 35.63/35.86 (define @t37 () (tptp.sdtlseqdt0 @t1 @t5)) % 35.63/35.86 (define @t38 () (= @t1 @t5)) % 35.63/35.86 (define @t39 () (tptp.sdtlseqdt0 @t5 @t1)) % 35.63/35.86 (define @t40 () (and @t37 @t39)) % 35.63/35.86 (define @t41 () (=> @t40 @t38)) % 35.63/35.86 (define @t42 () (forall @t9 (=> @t8 @t41))) % 35.63/35.86 (define @t43 () (tptp.sdtlseqdt0 @t1 @t12)) % 35.63/35.86 (define @t44 () (tptp.sdtlseqdt0 @t5 @t12)) % 35.63/35.86 (define @t45 () (and @t37 @t44)) % 35.63/35.86 (define @t46 () (=> @t45 @t43)) % 35.63/35.86 (define @t47 () (forall @t17 (=> @t16 @t46))) % 35.63/35.86 (define @t48 () (= @t5 @t1)) % 35.63/35.86 (define @t49 () (tptp.sdtpldt0 @t12 @t5)) % 35.63/35.86 (define @t50 () (and (not @t38) @t37)) % 35.63/35.86 (define @t51 () (= @t1 tptp.sz10)) % 35.63/35.86 (define @t52 () (tptp.iLess0 @t1 @t5)) % 35.63/35.86 (define @t53 () (and @t15 (= @t5 @t25))) % 35.63/35.86 (define @t54 () (tptp.doDivides0 @t1 @t5)) % 35.63/35.86 (define @t55 () (tptp.sdtsldt0 @t5 @t1)) % 35.63/35.86 (define @t56 () (and @t33 @t54)) % 35.63/35.86 (define @t57 () (tptp.doDivides0 @t1 @t12)) % 35.63/35.86 (define @t58 () (tptp.doDivides0 @t1 @t13)) % 35.63/35.86 (define @t59 () (not @t34)) % 35.63/35.86 (define @t60 () (and @t54 @t59)) % 35.63/35.86 (define @t61 () (=> @t60 @t37)) % 35.63/35.86 (define @t62 () (=> @t8 @t61)) % 35.63/35.86 (define @t63 () (forall @t9 @t62)) % 35.63/35.86 (define @t64 () (tptp.doDivides0 @t5 @t1)) % 35.63/35.86 (define @t65 () (@list @t5)) % 35.63/35.86 (define @t66 () (not @t51)) % 35.63/35.86 (define @t67 () (tptp.aNaturalNumber0 tptp.xp)) % 35.63/35.86 (define @t68 () (tptp.aNaturalNumber0 tptp.xn)) % 35.63/35.86 (define @t69 () (@var "W3" $$unsorted)) % 35.63/35.86 (define @t70 () (tptp.sdtasdt0 @t12 @t69)) % 35.63/35.86 (define @t71 () (tptp.aNaturalNumber0 @t69)) % 35.63/35.86 (define @t72 () (@list @t69)) % 35.63/35.86 (define @t73 () (@var "W4" $$unsorted)) % 35.63/35.86 (define @t74 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 35.63/35.86 (define @t75 () (tptp.sdtasdt0 tptp.xp @t1)) % 35.63/35.86 (define @t76 () (tptp.sdtpldt0 tptp.xp @t1)) % 35.63/35.86 (define @t77 () (tptp.sdtlseqdt0 tptp.xn tptp.xp)) % 35.63/35.86 (define @t78 () (= tptp.xk tptp.sz10)) % 35.63/35.86 (define @t79 () (= tptp.xk tptp.sz00)) % 35.63/35.86 (define @t80 () (tptp.sdtasdt0 tptp.xr @t1)) % 35.63/35.86 (define @t81 () (tptp.aNaturalNumber0 tptp.xr)) % 35.63/35.86 (define @t82 () (and (exists @t3 (and @t2 (= tptp.xn @t80))) (tptp.doDivides0 tptp.xr tptp.xn))) % 35.63/35.86 (define @t83 () (tptp.sdtsldt0 tptp.xn tptp.xr)) % 35.63/35.86 (define @t84 () (tptp.sdtlseqdt0 @t83 tptp.xn)) % 35.63/35.86 (define @t85 () (tptp.sdtasdt0 tptp.xr @t83)) % 35.63/35.86 (define @t86 () (= tptp.xn @t85)) % 35.63/35.86 (define @t87 () (tptp.aNaturalNumber0 @t83)) % 35.63/35.86 (define @t88 () (= @t83 tptp.xn)) % 35.63/35.86 (define @t89 () (and @t87 @t86)) % 35.63/35.86 (define @t90 () (=> @t89 @t88)) % 35.63/35.86 (define @t91 () (not @t90)) % 35.63/35.86 (define @t92 () (tptp.sdtasdt0 @t83 tptp.xm)) % 35.63/35.86 (define @t93 () (tptp.doDivides0 tptp.xp tptp.xm)) % 35.63/35.86 (define @t94 () (= tptp.xm @t75)) % 35.63/35.86 (define @t95 () (and @t2 @t94)) % 35.63/35.86 (define @t96 () (exists @t3 @t95)) % 35.63/35.86 (define @t97 () (and @t96 @t93)) % 35.63/35.86 (define @t98 () (tptp.doDivides0 tptp.xp @t83)) % 35.63/35.86 (define @t99 () (and @t2 (= @t83 @t75))) % 35.63/35.86 (define @t100 () (exists @t3 @t99)) % 35.63/35.86 (define @t101 () (and @t87 @t86 @t100 @t98)) % 35.63/35.86 (define @t102 () (or @t101 @t97)) % 35.63/35.86 (define @t103 () (tptp.doDivides0 tptp.xp tptp.xn)) % 35.63/35.86 (define @t104 () (= tptp.xn @t75)) % 35.63/35.86 (define @t105 () (and @t2 @t104)) % 35.63/35.86 (define @t106 () (exists @t3 @t105)) % 35.63/35.86 (define @t107 () (or @t106 @t103 @t96 @t93)) % 35.63/35.86 (define @t108 () (not @t107)) % 35.63/35.86 (define @t109 () (forall @t3 (not @t95))) % 35.63/35.86 (define @t110 () (not @t109)) % 35.63/35.86 (define @t111 () (forall @t3 (not @t105))) % 35.63/35.86 (define @t112 () (not @t111)) % 35.63/35.86 (define @t113 () (tptp.sdtasdt0 tptp.xp tptp.sz00)) % 35.63/35.86 (define @t114 () (= tptp.xn @t113)) % 35.63/35.86 (define @t115 () (not @t114)) % 35.63/35.86 (define @t116 () (not @t4)) % 35.63/35.86 (define @t117 () (or @t116 @t115)) % 35.63/35.86 (define @t118 () (@list false false)) % 35.63/35.86 (define @t119 () (and (= tptp.sz00 @t20) @t19)) % 35.63/35.86 (define @t120 () (= tptp.sz00 @t113)) % 35.63/35.86 (define @t121 () (and @t120 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xp)))) % 35.63/35.86 (define @t122 () (not @t67)) % 35.63/35.86 (define @t123 () (or @t122 @t121)) % 35.63/35.86 (define @t124 () (@list false)) % 35.63/35.86 (define @t125 () (= tptp.sz00 (tptp.sdtasdt0 tptp.xr tptp.sz00))) % 35.63/35.86 (define @t126 () (and @t125 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xr)))) % 35.63/35.86 (define @t127 () (not @t81)) % 35.63/35.86 (define @t128 () (or @t127 @t126)) % 35.63/35.86 (define @t129 () (= tptp.sz00 @t5)) % 35.63/35.86 (define @t130 () (not @t54)) % 35.63/35.86 (define @t131 () (not @t7)) % 35.63/35.86 (define @t132 () (not @t2)) % 35.63/35.86 (define @t133 () (or @t130 @t129 @t37)) % 35.63/35.86 (define @t134 () (or @t132 @t131)) % 35.63/35.86 (define @t135 () (not @t129)) % 35.63/35.86 (define @t136 () (and @t54 @t135)) % 35.63/35.86 (define @t137 () (=> @t136 @t37)) % 35.63/35.86 (define @t138 () (not @t8)) % 35.63/35.86 (define @t139 () (not @t44)) % 35.63/35.86 (define @t140 () (not @t37)) % 35.63/35.86 (define @t141 () (not @t15)) % 35.63/35.86 (define @t142 () (or @t140 @t139 @t43)) % 35.63/35.86 (define @t143 () (or @t132 @t131 @t141)) % 35.63/35.86 (define @t144 () (not @t39)) % 35.63/35.86 (define @t145 () (or @t132 @t131 @t140 @t144 @t38)) % 35.63/35.86 (define @t146 () (or @t140 @t144 @t38)) % 35.63/35.86 (define @t147 () (tptp.sdtlseqdt0 tptp.xn @t83)) % 35.63/35.86 (define @t148 () (not @t147)) % 35.63/35.86 (define @t149 () (not @t84)) % 35.63/35.86 (define @t150 () (not @t68)) % 35.63/35.86 (define @t151 () (not @t87)) % 35.63/35.86 (define @t152 () (or @t151 @t150 @t149 @t148 @t88)) % 35.63/35.86 (define @t153 () (forall @t9 @t145)) % 35.63/35.86 (define @t154 () (= tptp.xn @t83)) % 35.63/35.86 (define @t155 () (or @t151 @t150 @t149 @t148 @t154)) % 35.63/35.86 (define @t156 () (tptp.sdtlseqdt0 tptp.xp @t83)) % 35.63/35.86 (define @t157 () (not @t156)) % 35.63/35.86 (define @t158 () (not @t77)) % 35.63/35.86 (define @t159 () (or @t150 @t122 @t151 @t158 @t157 @t147)) % 35.63/35.86 (define @t160 () (forall @t3 (or @t132 (not @t94)))) % 35.63/35.86 (define @t161 () (not @t160)) % 35.63/35.86 (define @t162 () (and @t161 @t93)) % 35.63/35.86 (define @t163 () (not @t162)) % 35.63/35.86 (define @t164 () (= @t75 @t83)) % 35.63/35.86 (define @t165 () (and @t2 @t164)) % 35.63/35.86 (define @t166 () (forall @t3 (not @t165))) % 35.63/35.86 (define @t167 () (not @t166)) % 35.63/35.86 (define @t168 () (and @t87 @t86 (not (forall @t3 (or @t132 (not @t164)))) @t98)) % 35.63/35.86 (define @t169 () (= tptp.sz00 @t83)) % 35.63/35.86 (define @t170 () (not @t98)) % 35.63/35.86 (define @t171 () (or @t122 @t151 @t170 @t169 @t156)) % 35.63/35.86 (define @t172 () (@list false false false true false)) % 35.63/35.86 (define @t173 () (and @t86 @t169 @t120 @t125)) % 35.63/35.86 (assume @p1 (forall @t3 (=> @t2 true))) % 35.63/35.86 (assume @p2 @t4) % 35.63/35.86 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 35.63/35.86 (assume @p4 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t6)))) % 35.63/35.86 (assume @p5 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t10)))) % 35.63/35.86 (assume @p6 (forall @t9 (=> @t8 (= @t6 @t11)))) % 35.63/35.86 (assume @p7 (forall @t17 (=> @t16 (= @t14 (tptp.sdtpldt0 @t1 @t13))))) % 35.63/35.86 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 35.63/35.86 (assume @p9 (forall @t9 (=> @t8 (= @t10 @t18)))) % 35.63/35.86 (assume @p10 (forall @t17 (=> @t16 (= (tptp.sdtasdt0 @t10 @t12) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t12)))))) % 35.63/35.86 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 35.63/35.86 (assume @p12 @t23) % 35.63/35.86 (assume @p13 (forall @t17 (=> @t16 (and (= (tptp.sdtasdt0 @t1 @t13) (tptp.sdtpldt0 @t10 @t25)) (= (tptp.sdtasdt0 @t13 @t1) (tptp.sdtpldt0 @t18 @t24)))))) % 35.63/35.86 (assume @p14 (forall @t17 (=> @t16 (=> (or (= @t6 @t28) (= @t11 @t27)) @t26)))) % 35.63/35.86 (assume @p15 (forall @t3 (=> @t2 (=> @t33 (forall (@list @t5 @t12) (=> @t31 (=> (or @t30 @t29) @t26))))))) % 35.63/35.86 (assume @p16 (forall @t9 (=> @t8 (=> (= @t6 tptp.sz00) (and @t32 @t34))))) % 35.63/35.86 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t32 @t34))))) % 35.63/35.86 (assume @p18 (forall @t9 (=> @t8 (= @t37 (exists @t36 @t35))))) % 35.63/35.86 (assume @p19 (forall @t9 (=> @t8 (=> @t37 (forall @t36 (= (= @t12 (tptp.sdtmndt0 @t5 @t1)) @t35)))))) % 35.63/35.86 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 35.63/35.86 (assume @p21 @t42) % 35.63/35.86 (assume @p22 @t47) % 35.63/35.86 (assume @p23 (forall @t9 (=> @t8 (or @t37 (and (not @t48) @t39))))) % 35.63/35.86 (assume @p24 (forall @t9 (=> @t8 (=> @t50 (forall @t36 (=> @t15 (and (not (= @t27 @t49)) (tptp.sdtlseqdt0 @t27 @t49) (not (= @t28 @t13)) (tptp.sdtlseqdt0 @t28 @t13)))))))) % 35.63/35.86 (assume @p25 (forall @t17 (=> @t16 (=> (and @t33 (not @t26) @t44) (and (not @t30) (tptp.sdtlseqdt0 @t10 @t25) (not @t29) (tptp.sdtlseqdt0 @t18 @t24)))))) % 35.63/35.86 (assume @p26 (forall @t3 (=> @t2 (or @t32 @t51 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 35.63/35.86 (assume @p27 (forall @t9 (=> @t8 (=> @t33 (tptp.sdtlseqdt0 @t5 @t18))))) % 35.63/35.86 (assume @p28 (forall @t9 (=> @t8 (=> @t52 true)))) % 35.63/35.86 (assume @p29 (forall @t9 (=> @t8 (=> @t50 @t52)))) % 35.63/35.86 (assume @p30 (forall @t9 (=> @t8 (= @t54 (exists @t36 @t53))))) % 35.63/35.86 (assume @p31 (forall @t9 (=> @t8 (=> @t56 (forall @t36 (= (= @t12 @t55) @t53)))))) % 35.63/35.86 (assume @p32 (forall @t17 (=> @t16 (=> (and @t54 (tptp.doDivides0 @t5 @t12)) @t57)))) % 35.63/35.86 (assume @p33 (forall @t17 (=> @t16 (=> (and @t54 @t57) @t58)))) % 35.63/35.86 (assume @p34 (forall @t17 (=> @t16 (=> (and @t54 @t58) @t57)))) % 35.63/35.86 (assume @p35 @t63) % 35.63/35.86 (assume @p36 (forall @t9 (=> @t8 (=> @t56 (forall @t36 (=> @t15 (= (tptp.sdtasdt0 @t12 @t55) (tptp.sdtsldt0 (tptp.sdtasdt0 @t12 @t5) @t1)))))))) % 35.63/35.86 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t33 @t66 (forall @t65 (=> (and @t7 @t64) (or (= @t5 tptp.sz10) @t48)))))))) % 35.63/35.86 (assume @p38 (forall @t3 (=> (and @t2 @t33 @t66) (exists @t65 (and @t7 @t64 (tptp.isPrime0 @t5)))))) % 35.63/35.86 (assume @p39 (and @t68 (tptp.aNaturalNumber0 tptp.xm) @t67)) % 35.63/35.86 (assume @p40 (forall @t17 (=> @t16 (=> (and (or (and (not (= @t12 tptp.sz00)) (not (= @t12 tptp.sz10)) (forall @t72 (=> (and @t71 (exists (@list @t73) (and (tptp.aNaturalNumber0 @t73) (= @t12 (tptp.sdtasdt0 @t69 @t73)))) (tptp.doDivides0 @t69 @t12)) (or (= @t69 tptp.sz10) (= @t69 @t12))))) (tptp.isPrime0 @t12)) (or (exists @t72 (and @t71 (= @t10 @t70))) (tptp.doDivides0 @t12 @t10))) (=> (tptp.iLess0 @t14 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (and (exists @t72 (and @t71 (= @t1 @t70))) (tptp.doDivides0 @t12 @t1)) (and (exists @t72 (and @t71 (= @t5 @t70))) (tptp.doDivides0 @t12 @t5)))))))) % 35.63/35.86 (assume @p41 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t65 (and @t7 (= tptp.xp @t10))) (tptp.doDivides0 @t1 tptp.xp))) (or @t51 (= @t1 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists @t3 (and @t2 (= @t74 @t75))) (tptp.doDivides0 tptp.xp @t74))) % 35.63/35.86 (assume @p42 (not (or (exists @t3 (and @t2 (= @t76 tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn)))) % 35.63/35.86 (assume @p43 (not (or (exists @t3 (and @t2 (= @t76 tptp.xm))) (tptp.sdtlseqdt0 tptp.xp tptp.xm)))) % 35.63/35.86 (assume @p44 (and (not (= tptp.xn tptp.xp)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xn @t1) tptp.xp))) @t77 (not (= tptp.xm tptp.xp)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xm @t1) tptp.xp))) (tptp.sdtlseqdt0 tptp.xm tptp.xp))) % 35.63/35.86 (assume @p45 (and (tptp.aNaturalNumber0 tptp.xk) (= @t74 (tptp.sdtasdt0 tptp.xp tptp.xk)) (= tptp.xk (tptp.sdtsldt0 @t74 tptp.xp)))) % 35.63/35.86 (assume @p46 (not (or @t79 @t78))) % 35.63/35.86 (assume @p47 (and (not @t79) (not @t78))) % 35.63/35.86 (assume @p48 (and @t81 (exists @t3 (and @t2 (= tptp.xk @t80))) (tptp.doDivides0 tptp.xr tptp.xk) (not (= tptp.xr tptp.sz00)) (not (= tptp.xr tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t65 (and @t7 (= tptp.xr @t10))) (tptp.doDivides0 @t1 tptp.xr))) (or @t51 (= @t1 tptp.xr)))) (tptp.isPrime0 tptp.xr))) % 35.63/35.86 (assume @p49 (and (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xr @t1) tptp.xk))) (exists @t3 (and @t2 (= @t74 @t80))) (tptp.doDivides0 tptp.xr @t74))) % 35.63/35.86 (assume @p50 (and (not (= tptp.xk tptp.xp)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xk @t1) tptp.xp))) (tptp.sdtlseqdt0 tptp.xk tptp.xp))) % 35.63/35.86 (assume @p51 (or @t82 (and (exists @t3 (and @t2 (= tptp.xm @t80))) (tptp.doDivides0 tptp.xr tptp.xm)))) % 35.63/35.86 (assume @p52 @t82) % 35.63/35.86 (assume @p53 (and @t91 @t87 @t86 (exists @t3 (and @t2 (= (tptp.sdtpldt0 @t83 @t1) tptp.xn))) @t84)) % 35.63/35.86 (assume @p54 (and @t87 @t86 (exists @t3 (and @t2 (= @t92 @t75))) (tptp.doDivides0 tptp.xp @t92))) % 35.63/35.86 (assume @p55 @t102) % 35.63/35.86 (assume @p56 @t108) % 35.63/35.86 (assume @p57 true) % 35.63/35.86 (step @p58 :rule eq-symm :args (@t83 tptp.xn)) % 35.63/35.86 (step @p59 :rule refl :args (@t89)) % 35.63/35.86 (step @p60 :rule cong :premises (@p59 @p58) :args (@t90)) % 35.63/35.86 (step @p61 :rule cong :premises (@p60) :args (@t91)) % 35.63/35.86 (step @p62 :rule and_elim :premises (@p53) :args (0)) % 35.63/35.86 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 35.63/35.86 (step @p64 :rule not_implies_elim1 :premises (@p63)) % 35.63/35.86 (step @p65 :rule and_elim :premises (@p64) :args (1)) % 35.63/35.86 (step @p66 :rule refl :args (@t93)) % 35.63/35.86 (step @p67 :rule bool-and-de-morgan :args (@t2 @t94 true)) % 35.63/35.86 (step @p68 :rule cong :premises (@p67) :args (@t109)) % 35.63/35.86 (step @p69 :rule cong :premises (@p68) :args (@t110)) % 35.63/35.86 (step @p70 :rule exists-elim :args ((= @t96 @t110))) % 35.63/35.86 (step @p71 :rule trans :premises (@p70 @p69)) % 35.63/35.86 (step @p72 :rule refl :args (@t103)) % 35.63/35.86 (step @p73 :rule bool-and-de-morgan :args (@t2 @t104 true)) % 35.63/35.86 (step @p74 :rule cong :premises (@p73) :args (@t111)) % 35.63/35.86 (step @p75 :rule cong :premises (@p74) :args (@t112)) % 35.63/35.86 (step @p76 :rule exists-elim :args ((= @t106 @t112))) % 35.63/35.86 (step @p77 :rule trans :premises (@p76 @p75)) % 35.63/35.86 (step @p78 :rule nary_cong :premises (@p77 @p72 @p71 @p66) :args (@t107)) % 35.63/35.86 (step @p79 :rule cong :premises (@p78) :args (@t108)) % 35.63/35.86 (step @p80 :rule eq_resolve :premises (@p56 @p79)) % 35.63/35.86 (step @p81 :rule not_or_elim :premises (@p80) :args (0)) % 35.63/35.86 (step @p82 :rule not_not_elim :premises (@p81)) % 35.63/35.86 (step @p83 :rule instantiate :premises (@p82) :args ((@list tptp.sz00))) % 35.63/35.86 (step @p84 :rule cnf_or_pos :args (@t117)) % 35.63/35.86 (step @p85 :rule reordering :premises (@p84) :args ((or @t116 @t115 (not @t117)))) % 35.63/35.86 (step @p86 :rule chain_m_resolution :premises (@p85 @p2 @p83) :args (@t115 @t118 (@list @t4 @t117))) % 35.63/35.86 (step @p87 :rule bool-impl-elim :args (@t2 @t119)) % 35.63/35.86 (step @p88 :rule cong :premises (@p87) :args ((forall @t3 (=> @t2 @t119)))) % 35.63/35.86 (step @p89 :rule refl :args (@t19)) % 35.63/35.86 (step @p90 :rule eq-symm :args (@t20 tptp.sz00)) % 35.63/35.86 (step @p91 :rule nary_cong :premises (@p90 @p89) :args (@t21)) % 35.63/35.86 (step @p92 :rule refl :args (@t2)) % 35.63/35.86 (step @p93 :rule cong :premises (@p92 @p91) :args (@t22)) % 35.63/35.86 (step @p94 :rule cong :premises (@p93) :args (@t23)) % 35.63/35.86 (step @p95 :rule trans :premises (@p94 @p88)) % 35.63/35.86 (step @p96 :rule eq_resolve :premises (@p12 @p95)) % 35.63/35.86 (step @p97 :rule instantiate :premises (@p96) :args ((@list tptp.xp))) % 35.63/35.86 (step @p98 :rule and_elim :premises (@p39) :args (2)) % 35.63/35.86 (step @p99 :rule cnf_or_pos :args (@t123)) % 35.63/35.86 (step @p100 :rule reordering :premises (@p99) :args ((or @t122 @t121 (not @t123)))) % 35.63/35.86 (step @p101 :rule chain_m_resolution :premises (@p100 @p98 @p97) :args (@t121 @t118 (@list @t67 @t123))) % 35.63/35.86 (step @p102 :rule cnf_and_pos :args (@t121 0)) % 35.63/35.86 (step @p103 :rule reordering :premises (@p102) :args ((or @t120 (not @t121)))) % 35.63/35.86 (step @p104 :rule chain_m_resolution :premises (@p103 @p101) :args (@t120 @t124 (@list @t121))) % 35.63/35.86 (step @p105 :rule instantiate :premises (@p96) :args ((@list tptp.xr))) % 35.63/35.86 (step @p106 :rule and_elim :premises (@p48) :args (0)) % 35.63/35.86 (step @p107 :rule cnf_or_pos :args (@t128)) % 35.63/35.86 (step @p108 :rule reordering :premises (@p107) :args ((or @t127 @t126 (not @t128)))) % 35.63/35.86 (step @p109 :rule chain_m_resolution :premises (@p108 @p106 @p105) :args (@t126 @t118 (@list @t81 @t128))) % 35.63/35.86 (step @p110 :rule cnf_and_pos :args (@t126 0)) % 35.63/35.86 (step @p111 :rule reordering :premises (@p110) :args ((or @t125 (not @t126)))) % 35.63/35.86 (step @p112 :rule chain_m_resolution :premises (@p111 @p109) :args (@t125 @t124 (@list @t126))) % 35.63/35.86 (step @p113 :rule aci_norm :args ((= (or @t134 @t133) (or @t132 @t131 @t130 @t129 @t37)))) % 35.63/35.86 (step @p114 :rule aci_norm :args ((= (or (or @t130 @t129) @t37) @t133))) % 35.63/35.86 (step @p115 :rule refl :args (@t37)) % 35.63/35.86 (step @p116 :rule bool-double-not-elim :args (@t129)) % 35.63/35.86 (step @p117 :rule refl :args (@t130)) % 35.63/35.86 (step @p118 :rule nary_cong :premises (@p117 @p116) :args ((or @t130 (not @t135)))) % 35.63/35.86 (step @p119 :rule bool-and-de-morgan :args (@t54 @t135 true)) % 35.63/35.86 (step @p120 :rule trans :premises (@p119 @p118)) % 35.63/35.86 (step @p121 :rule nary_cong :premises (@p120 @p115) :args ((or (not @t136) @t37))) % 35.63/35.86 (step @p122 :rule trans :premises (@p121 @p114)) % 35.63/35.86 (step @p123 :rule bool-impl-elim :args (@t136 @t37)) % 35.63/35.86 (step @p124 :rule trans :premises (@p123 @p122)) % 35.63/35.86 (step @p125 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 35.63/35.86 (step @p126 :rule nary_cong :premises (@p125 @p124) :args ((or @t138 @t137))) % 35.63/35.86 (step @p127 :rule trans :premises (@p126 @p113)) % 35.63/35.86 (step @p128 :rule bool-impl-elim :args (@t8 @t137)) % 35.63/35.86 (step @p129 :rule trans :premises (@p128 @p127)) % 35.63/35.86 (step @p130 :rule cong :premises (@p129) :args ((forall @t9 (=> @t8 @t137)))) % 35.63/35.86 (step @p131 :rule refl :args (@t37)) % 35.63/35.86 (step @p132 :rule eq-symm :args (@t5 tptp.sz00)) % 35.63/35.86 (step @p133 :rule cong :premises (@p132) :args (@t59)) % 35.63/35.86 (step @p134 :rule refl :args (@t54)) % 35.63/35.86 (step @p135 :rule nary_cong :premises (@p134 @p133) :args (@t60)) % 35.63/35.86 (step @p136 :rule cong :premises (@p135 @p131) :args (@t61)) % 35.63/35.86 (step @p137 :rule refl :args (@t8)) % 35.63/35.86 (step @p138 :rule cong :premises (@p137 @p136) :args (@t62)) % 35.63/35.86 (step @p139 :rule cong :premises (@p138) :args (@t63)) % 35.63/35.86 (step @p140 :rule trans :premises (@p139 @p130)) % 35.63/35.86 (step @p141 :rule eq_resolve :premises (@p35 @p140)) % 35.63/35.86 (step @p142 :rule instantiate :premises (@p141) :args ((@list tptp.xp @t83))) % 35.63/35.86 (step @p143 :rule aci_norm :args ((= (or @t143 @t142) (or @t132 @t131 @t141 @t140 @t139 @t43)))) % 35.63/35.86 (step @p144 :rule aci_norm :args ((= (or (or @t140 @t139) @t43) @t142))) % 35.63/35.86 (step @p145 :rule refl :args (@t43)) % 35.63/35.86 (step @p146 :rule bool-and-de-morgan :args (@t37 @t44 true)) % 35.63/35.86 (step @p147 :rule nary_cong :premises (@p146 @p145) :args ((or (not @t45) @t43))) % 35.63/35.86 (step @p148 :rule trans :premises (@p147 @p144)) % 35.63/35.86 (step @p149 :rule bool-impl-elim :args (@t45 @t43)) % 35.63/35.86 (step @p150 :rule trans :premises (@p149 @p148)) % 35.63/35.86 (step @p151 :rule aci_norm :args ((= (or @t132 (or @t131 @t141)) @t143))) % 35.63/35.86 (step @p152 :rule bool-and-de-morgan :args (@t7 @t15 true)) % 35.63/35.86 (step @p153 :rule refl :args (@t132)) % 35.63/35.86 (step @p154 :rule nary_cong :premises (@p153 @p152) :args ((or @t132 (not @t31)))) % 35.63/35.86 (step @p155 :rule bool-and-de-morgan :args (@t2 @t7 (and @t15))) % 35.63/35.86 (step @p156 :rule trans :premises (@p155 @p154)) % 35.63/35.86 (step @p157 :rule trans :premises (@p156 @p151)) % 35.63/35.86 (step @p158 :rule nary_cong :premises (@p157 @p150) :args ((or (not @t16) @t46))) % 35.63/35.86 (step @p159 :rule trans :premises (@p158 @p143)) % 35.63/35.86 (step @p160 :rule bool-impl-elim :args (@t16 @t46)) % 35.63/35.86 (step @p161 :rule trans :premises (@p160 @p159)) % 35.63/35.86 (step @p162 :rule cong :premises (@p161) :args (@t47)) % 35.63/35.86 (step @p163 :rule eq_resolve :premises (@p22 @p162)) % 35.63/35.86 (step @p164 :rule instantiate :premises (@p163) :args ((@list tptp.xn tptp.xp @t83))) % 35.63/35.86 (step @p165 :rule aci_norm :args ((= (or @t134 @t146) @t145))) % 35.63/35.86 (step @p166 :rule aci_norm :args ((= (or (or @t140 @t144) @t38) @t146))) % 35.63/35.86 (step @p167 :rule refl :args (@t38)) % 35.63/35.86 (step @p168 :rule bool-and-de-morgan :args (@t37 @t39 true)) % 35.63/35.86 (step @p169 :rule nary_cong :premises (@p168 @p167) :args ((or (not @t40) @t38))) % 35.63/35.86 (step @p170 :rule trans :premises (@p169 @p166)) % 35.63/35.86 (step @p171 :rule bool-impl-elim :args (@t40 @t38)) % 35.63/35.86 (step @p172 :rule trans :premises (@p171 @p170)) % 35.63/35.86 (step @p173 :rule nary_cong :premises (@p125 @p172) :args ((or @t138 @t41))) % 35.63/35.86 (step @p174 :rule trans :premises (@p173 @p165)) % 35.63/35.86 (step @p175 :rule bool-impl-elim :args (@t8 @t41)) % 35.63/35.86 (step @p176 :rule trans :premises (@p175 @p174)) % 35.63/35.86 (step @p177 :rule cong :premises (@p176) :args (@t42)) % 35.63/35.86 (step @p178 :rule eq_resolve :premises (@p21 @p177)) % 35.63/35.86 (step @p179 :rule refl :args (@t148)) % 35.63/35.86 (step @p180 :rule refl :args (@t149)) % 35.63/35.86 (step @p181 :rule refl :args (@t150)) % 35.63/35.86 (step @p182 :rule refl :args (@t151)) % 35.63/35.86 (step @p183 :rule nary_cong :premises (@p182 @p181 @p180 @p179 @p58) :args (@t152)) % 35.63/35.86 (step @p184 :rule refl :args (@t153)) % 35.63/35.86 (step @p185 :rule cong :premises (@p184 @p183) :args ((=> @t153 @t152))) % 35.63/35.86 (assume-push @p251 @t153) % 35.63/35.86 (step @p187 :rule instantiate :premises (@p178) :args ((@list @t83 tptp.xn))) % 35.63/35.86 (step-pop @p252 :rule scope :premises (@p187)) % 35.63/35.86 (step @p188 :rule process_scope :premises (@p252) :args (@t152)) % 35.63/35.86 (step @p190 :rule eq_resolve :premises (@p188 @p185)) % 35.63/35.86 (step @p191 :rule implies_elim :premises (@p190)) % 35.63/35.86 (step @p192 :rule chain_m_resolution :premises (@p191 @p178) :args (@t155 @t124 (@list @t153))) % 35.63/35.86 (step @p193 :rule and_elim :premises (@p53) :args (4)) % 35.63/35.86 (step @p194 :rule and_elim :premises (@p64) :args (0)) % 35.63/35.86 (step @p195 :rule and_elim :premises (@p39) :args (0)) % 35.63/35.86 (step @p196 :rule not_implies_elim2 :premises (@p63)) % 35.63/35.86 (step @p197 :rule cnf_or_pos :args (@t155)) % 35.63/35.86 (step @p198 :rule reordering :premises (@p197) :args ((or @t154 @t150 @t151 @t149 @t148 (not @t155)))) % 35.63/35.86 (step @p199 :rule chain_m_resolution :premises (@p198 @p196 @p195 @p194 @p193 @p192) :args (@t148 (@list true false false false false) (@list @t154 @t68 @t87 @t84 @t155))) % 35.63/35.86 (step @p200 :rule and_elim :premises (@p44) :args (2)) % 35.63/35.86 (step @p201 :rule cnf_or_pos :args (@t159)) % 35.63/35.86 (step @p202 :rule reordering :premises (@p201) :args ((or @t150 @t122 @t158 @t151 @t147 @t157 (not @t159)))) % 35.63/35.86 (step @p203 :rule chain_m_resolution :premises (@p202 @p195 @p98 @p200 @p194 @p199 @p164) :args (@t157 (@list false false false false true false) (@list @t68 @t67 @t77 @t87 @t147 @t159))) % 35.63/35.86 (step @p204 :rule not_or_elim :premises (@p80) :args (2)) % 35.63/35.86 (step @p205 :rule not_not_elim :premises (@p204)) % 35.63/35.86 (step @p206 :rule cnf_and_pos :args (@t162 0)) % 35.63/35.86 (step @p207 :rule reordering :premises (@p206) :args ((or @t161 @t163))) % 35.63/35.86 (step @p208 :rule chain_m_resolution :premises (@p207 @p205) :args (@t163 @t124 (@list @t160))) % 35.63/35.86 (step @p209 :rule nary_cong :premises (@p71 @p66) :args (@t97)) % 35.63/35.86 (step @p210 :rule refl :args (@t98)) % 35.63/35.86 (step @p211 :rule bool-and-de-morgan :args (@t2 @t164 true)) % 35.63/35.86 (step @p212 :rule cong :premises (@p211) :args (@t166)) % 35.63/35.86 (step @p213 :rule cong :premises (@p212) :args (@t167)) % 35.63/35.86 (step @p214 :rule exists-elim :args ((= (exists @t3 @t165) @t167))) % 35.63/35.86 (step @p215 :rule trans :premises (@p214 @p213)) % 35.63/35.86 (step @p216 :rule eq-symm :args (@t83 @t75)) % 35.63/35.86 (step @p217 :rule nary_cong :premises (@p92 @p216) :args (@t99)) % 35.63/35.86 (step @p218 :rule cong :premises (@p217) :args (@t100)) % 35.63/35.86 (step @p219 :rule trans :premises (@p218 @p215)) % 35.63/35.86 (step @p220 :rule refl :args (@t86)) % 35.63/35.86 (step @p221 :rule refl :args (@t87)) % 35.63/35.86 (step @p222 :rule nary_cong :premises (@p221 @p220 @p219 @p210) :args (@t101)) % 35.63/35.86 (step @p223 :rule nary_cong :premises (@p222 @p209) :args (@t102)) % 35.63/35.86 (step @p224 :rule eq_resolve :premises (@p55 @p223)) % 35.63/35.86 (step @p225 :rule chain_m_resolution :premises (@p224 @p208) :args (@t168 (@list true) (@list @t162))) % 35.63/35.86 (step @p226 :rule cnf_and_pos :args (@t168 3)) % 35.63/35.86 (step @p227 :rule reordering :premises (@p226) :args ((or @t98 (not @t168)))) % 35.63/35.86 (step @p228 :rule chain_m_resolution :premises (@p227 @p225) :args (@t98 @t124 (@list @t168))) % 35.63/35.86 (step @p229 :rule cnf_or_pos :args (@t171)) % 35.63/35.86 (step @p230 :rule reordering :premises (@p229) :args ((or @t122 @t151 @t170 @t169 @t156 (not @t171)))) % 35.63/35.86 (step @p231 :rule chain_m_resolution :premises (@p230 @p98 @p194 @p228 @p203 @p142) :args (@t169 @t172 (@list @t67 @t87 @t98 @t156 @t171))) % 35.63/35.86 (assume-push @p253 @t86) % 35.63/35.86 (assume-push @p254 @t169) % 35.63/35.86 (assume-push @p255 @t120) % 35.63/35.86 (assume-push @p256 @t125) % 35.63/35.86 (step @p236 :rule symm :premises (@p112)) % 35.63/35.86 (step @p237 :rule symm :premises (@p231)) % 35.63/35.86 (step @p238 :rule refl :args (tptp.xr)) % 35.63/35.86 (step @p239 :rule cong :premises (@p238 @p237) :args (@t85)) % 35.63/35.87 (step @p240 :rule trans :premises (@p65 @p239 @p236 @p104)) % 35.63/35.87 (step-pop @p257 :rule scope :premises (@p240)) % 35.63/35.87 (step-pop @p258 :rule scope :premises (@p257)) % 35.63/35.87 (step-pop @p259 :rule scope :premises (@p258)) % 35.63/35.87 (step-pop @p260 :rule scope :premises (@p259)) % 35.63/35.87 (step @p241 :rule process_scope :premises (@p260) :args (@t114)) % 35.63/35.87 (step @p246 :rule implies_elim :premises (@p241)) % 35.63/35.87 (step @p247 :rule cnf_and_neg :args (@t173)) % 35.63/35.87 (step @p248 :rule resolution :premises (@p247 @p246) :args (true @t173)) % 35.63/35.87 (step @p249 :rule reordering :premises (@p248) :args ((or (not @t86) (not @t169) @t114 (not @t120) (not @t125)))) % 35.63/35.87 (step @p250 false :rule chain_m_resolution :premises (@p249 @p231 @p112 @p104 @p86 @p65) :args (false @t172 (@list @t169 @t125 @t120 @t114 @t86))) % 35.63/35.87 ) % 35.63/35.87 % SZS output end Proof % 35.63/35.87 % cvc5 exiting %------------------------------------------------------------------------------