%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM482+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 08:39:34 AM UTC 2026 % Result : Theorem 0.45s 0.63s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM482+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 11:23:07 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.45/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.45/0.63 % SZS status Theorem % 0.45/0.63 % SZS output start Proof % 0.45/0.63 ( % 0.45/0.63 (declare-sort $$unsorted 0) % 0.45/0.63 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 0.45/0.63 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.63 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.63 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.63 (declare-const tptp.xk $$unsorted) % 0.45/0.63 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.63 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.63 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.63 (declare-const tptp.sz10 $$unsorted) % 0.45/0.63 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.63 (declare-const tptp.sz00 $$unsorted) % 0.45/0.63 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.45/0.63 (define @t1 () (@var "W0" $$unsorted)) % 0.45/0.63 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 0.45/0.63 (define @t3 () (@list @t1)) % 0.45/0.63 (define @t4 () (tptp.aNaturalNumber0 tptp.sz10)) % 0.45/0.63 (define @t5 () (@var "W1" $$unsorted)) % 0.45/0.63 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.45/0.63 (define @t7 () (tptp.aNaturalNumber0 @t5)) % 0.45/0.63 (define @t8 () (and @t2 @t7)) % 0.45/0.63 (define @t9 () (@list @t1 @t5)) % 0.45/0.63 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.45/0.63 (define @t11 () (tptp.sdtpldt0 @t5 @t1)) % 0.45/0.63 (define @t12 () (@var "W2" $$unsorted)) % 0.45/0.63 (define @t13 () (tptp.sdtpldt0 @t5 @t12)) % 0.45/0.63 (define @t14 () (tptp.aNaturalNumber0 @t12)) % 0.45/0.63 (define @t15 () (and @t2 @t7 @t14)) % 0.45/0.63 (define @t16 () (@list @t1 @t5 @t12)) % 0.45/0.63 (define @t17 () (tptp.sdtasdt0 @t5 @t1)) % 0.45/0.63 (define @t18 () (tptp.sdtasdt0 @t5 @t12)) % 0.45/0.63 (define @t19 () (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1))) % 0.45/0.63 (define @t20 () (tptp.sdtasdt0 @t1 tptp.sz10)) % 0.45/0.63 (define @t21 () (and (= @t20 @t1) @t19)) % 0.45/0.63 (define @t22 () (=> @t2 @t21)) % 0.45/0.63 (define @t23 () (forall @t3 @t22)) % 0.45/0.63 (define @t24 () (tptp.sdtasdt0 @t12 @t1)) % 0.45/0.63 (define @t25 () (tptp.sdtasdt0 @t1 @t12)) % 0.45/0.63 (define @t26 () (= @t5 @t12)) % 0.45/0.63 (define @t27 () (tptp.sdtpldt0 @t12 @t1)) % 0.45/0.63 (define @t28 () (tptp.sdtpldt0 @t1 @t12)) % 0.45/0.63 (define @t29 () (= @t17 @t24)) % 0.45/0.63 (define @t30 () (= @t10 @t25)) % 0.45/0.63 (define @t31 () (= @t1 tptp.sz00)) % 0.45/0.63 (define @t32 () (not @t31)) % 0.45/0.63 (define @t33 () (= @t5 tptp.sz00)) % 0.45/0.63 (define @t34 () (and @t14 (= @t28 @t5))) % 0.45/0.63 (define @t35 () (@list @t12)) % 0.45/0.63 (define @t36 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.45/0.63 (define @t37 () (= @t1 @t5)) % 0.45/0.63 (define @t38 () (tptp.sdtlseqdt0 @t5 @t1)) % 0.45/0.63 (define @t39 () (tptp.sdtlseqdt0 @t5 @t12)) % 0.45/0.63 (define @t40 () (= @t5 @t1)) % 0.45/0.63 (define @t41 () (tptp.sdtpldt0 @t12 @t5)) % 0.45/0.63 (define @t42 () (and (not @t37) @t36)) % 0.45/0.63 (define @t43 () (= @t1 tptp.sz10)) % 0.45/0.63 (define @t44 () (tptp.iLess0 @t1 @t5)) % 0.45/0.63 (define @t45 () (and @t14 (= @t5 @t25))) % 0.45/0.63 (define @t46 () (tptp.doDivides0 @t1 @t5)) % 0.45/0.63 (define @t47 () (tptp.sdtsldt0 @t5 @t1)) % 0.45/0.63 (define @t48 () (and @t32 @t46)) % 0.45/0.63 (define @t49 () (tptp.doDivides0 @t1 @t12)) % 0.45/0.63 (define @t50 () (tptp.doDivides0 @t1 @t13)) % 0.45/0.63 (define @t51 () (not @t33)) % 0.45/0.63 (define @t52 () (= @t5 tptp.sz10)) % 0.45/0.63 (define @t53 () (or @t52 @t40)) % 0.45/0.63 (define @t54 () (tptp.doDivides0 @t5 @t1)) % 0.45/0.63 (define @t55 () (@list @t5)) % 0.45/0.63 (define @t56 () (not @t43)) % 0.45/0.63 (define @t57 () (tptp.isPrime0 @t1)) % 0.45/0.63 (define @t58 () (tptp.aNaturalNumber0 tptp.xk)) % 0.45/0.63 (define @t59 () (@var "W3" $$unsorted)) % 0.45/0.63 (define @t60 () (= @t1 @t18)) % 0.45/0.63 (define @t61 () (and @t14 @t60)) % 0.45/0.63 (define @t62 () (exists @t35 @t61)) % 0.45/0.63 (define @t63 () (= tptp.xk tptp.sz10)) % 0.45/0.63 (define @t64 () (= tptp.xk tptp.sz00)) % 0.45/0.63 (define @t65 () (and @t7 @t62 @t54)) % 0.45/0.63 (define @t66 () (=> @t65 @t53)) % 0.45/0.63 (define @t67 () (forall @t55 @t66)) % 0.45/0.63 (define @t68 () (and @t32 @t56 @t67)) % 0.45/0.63 (define @t69 () (or @t68 @t57)) % 0.45/0.63 (define @t70 () (tptp.doDivides0 @t1 tptp.xk)) % 0.45/0.63 (define @t71 () (and @t7 (= tptp.xk @t10))) % 0.45/0.63 (define @t72 () (exists @t55 @t71)) % 0.45/0.63 (define @t73 () (or @t72 @t70)) % 0.45/0.63 (define @t74 () (and @t2 @t73 @t69)) % 0.45/0.63 (define @t75 () (exists @t3 @t74)) % 0.45/0.63 (define @t76 () (tptp.isPrime0 tptp.xk)) % 0.45/0.63 (define @t77 () (= @t1 tptp.xk)) % 0.45/0.63 (define @t78 () (or @t43 @t77)) % 0.45/0.63 (define @t79 () (and @t2 @t73)) % 0.45/0.63 (define @t80 () (=> @t79 @t78)) % 0.45/0.63 (define @t81 () (forall @t3 @t80)) % 0.45/0.63 (define @t82 () (and @t81 @t76)) % 0.45/0.63 (define @t83 () (=> @t82 @t75)) % 0.45/0.63 (define @t84 () (not @t83)) % 0.45/0.63 (define @t85 () (not @t57)) % 0.45/0.63 (define @t86 () (@var "BOUND_VARIABLE_8212" $$unsorted)) % 0.45/0.63 (define @t87 () (tptp.sdtasdt0 @t5 @t86)) % 0.45/0.63 (define @t88 () (not (= @t1 @t87))) % 0.45/0.63 (define @t89 () (not (tptp.aNaturalNumber0 @t86))) % 0.45/0.63 (define @t90 () (= tptp.sz10 @t5)) % 0.45/0.63 (define @t91 () (not @t54)) % 0.45/0.63 (define @t92 () (not @t7)) % 0.45/0.63 (define @t93 () (or @t92 @t91 @t90 @t37 @t89 @t88)) % 0.45/0.63 (define @t94 () (@list @t5 @t86)) % 0.45/0.63 (define @t95 () (forall @t94 @t93)) % 0.45/0.63 (define @t96 () (not @t95)) % 0.45/0.63 (define @t97 () (and (or @t31 @t43 @t96) @t85)) % 0.45/0.63 (define @t98 () (not @t70)) % 0.45/0.63 (define @t99 () (@var "BOUND_VARIABLE_8240" $$unsorted)) % 0.45/0.63 (define @t100 () (tptp.sdtasdt0 @t1 @t99)) % 0.45/0.63 (define @t101 () (not (= @t100 tptp.xk))) % 0.45/0.63 (define @t102 () (not (tptp.aNaturalNumber0 @t99))) % 0.45/0.63 (define @t103 () (or @t102 @t101)) % 0.45/0.63 (define @t104 () (and @t103 @t98)) % 0.45/0.63 (define @t105 () (not @t2)) % 0.45/0.63 (define @t106 () (or @t105 @t104 @t97)) % 0.45/0.63 (define @t107 () (@list @t1 @t99)) % 0.45/0.63 (define @t108 () (forall @t107 @t106)) % 0.45/0.63 (define @t109 () (@list @t99)) % 0.45/0.63 (define @t110 () (forall @t109 @t106)) % 0.45/0.63 (define @t111 () (forall @t109 @t98)) % 0.45/0.63 (define @t112 () (forall @t109 @t103)) % 0.45/0.63 (define @t113 () (@list @t5)) % 0.45/0.63 (define @t114 () (and @t112 @t111)) % 0.45/0.63 (define @t115 () (forall @t109 @t104)) % 0.45/0.63 (define @t116 () (or @t105 @t115 @t97)) % 0.45/0.63 (define @t117 () (= @t10 tptp.xk)) % 0.45/0.63 (define @t118 () (forall @t55 (or @t92 (not @t117)))) % 0.45/0.63 (define @t119 () (and @t118 @t98)) % 0.45/0.63 (define @t120 () (not @t56)) % 0.45/0.63 (define @t121 () (not @t32)) % 0.45/0.63 (define @t122 () (or @t121 @t120 @t96)) % 0.45/0.63 (define @t123 () (and @t32 @t56 @t95)) % 0.45/0.63 (define @t124 () (not @t118)) % 0.45/0.63 (define @t125 () (or @t123 @t57)) % 0.45/0.63 (define @t126 () (not @t125)) % 0.45/0.63 (define @t127 () (or @t124 @t70)) % 0.45/0.63 (define @t128 () (not @t127)) % 0.45/0.63 (define @t129 () (or @t105 @t128 @t126)) % 0.45/0.63 (define @t130 () (and @t2 @t127 @t125)) % 0.45/0.63 (define @t131 () (forall @t3 (not @t130))) % 0.45/0.63 (define @t132 () (not @t131)) % 0.45/0.63 (define @t133 () (or @t89 @t88)) % 0.45/0.63 (define @t134 () (or @t92 @t133 @t91 @t90 @t37)) % 0.45/0.63 (define @t135 () (forall @t94 @t134)) % 0.45/0.63 (define @t136 () (@list @t86)) % 0.45/0.63 (define @t137 () (forall @t136 @t134)) % 0.45/0.63 (define @t138 () (forall @t136 @t133)) % 0.45/0.63 (define @t139 () (or @t92 @t138 @t91 @t90 @t37)) % 0.45/0.63 (define @t140 () (forall @t35 (or (not @t14) (not @t60)))) % 0.45/0.63 (define @t141 () (or @t92 @t140 @t91 @t90 @t37)) % 0.45/0.63 (define @t142 () (or @t90 @t37)) % 0.45/0.63 (define @t143 () (not @t140)) % 0.45/0.63 (define @t144 () (not @t143)) % 0.45/0.63 (define @t145 () (or @t92 @t144 @t91)) % 0.45/0.63 (define @t146 () (and @t7 @t143 @t54)) % 0.45/0.63 (define @t147 () (forall @t35 (not @t61))) % 0.45/0.63 (define @t148 () (not @t147)) % 0.45/0.63 (define @t149 () (and @t7 @t117)) % 0.45/0.63 (define @t150 () (forall @t55 (not @t149))) % 0.45/0.63 (define @t151 () (not @t150)) % 0.45/0.63 (define @t152 () (@var "BOUND_VARIABLE_8186" $$unsorted)) % 0.45/0.63 (define @t153 () (tptp.sdtasdt0 @t1 @t152)) % 0.45/0.63 (define @t154 () (not (= @t153 tptp.xk))) % 0.45/0.63 (define @t155 () (not (tptp.aNaturalNumber0 @t152))) % 0.45/0.63 (define @t156 () (or @t155 @t154)) % 0.45/0.63 (define @t157 () (and @t156 @t98)) % 0.45/0.63 (define @t158 () (or @t105 @t157 @t43 @t77)) % 0.45/0.63 (define @t159 () (forall (@list @t1 @t152) @t158)) % 0.45/0.63 (define @t160 () (@list @t152)) % 0.45/0.63 (define @t161 () (forall @t160 @t158)) % 0.45/0.63 (define @t162 () (forall @t160 @t98)) % 0.45/0.63 (define @t163 () (forall @t160 @t156)) % 0.45/0.63 (define @t164 () (and @t163 @t162)) % 0.45/0.63 (define @t165 () (forall @t160 @t157)) % 0.45/0.63 (define @t166 () (or @t105 @t165 @t43 @t77)) % 0.45/0.63 (define @t167 () (or @t105 @t119 @t43 @t77)) % 0.45/0.63 (define @t168 () (and @t2 @t127)) % 0.45/0.63 (define @t169 () (not @t76)) % 0.45/0.63 (define @t170 () (not (= tptp.xk @t87))) % 0.45/0.63 (define @t171 () (not (tptp.doDivides0 @t5 tptp.xk))) % 0.45/0.63 (define @t172 () (or @t92 @t171 @t90 (= tptp.xk @t5) @t89 @t170)) % 0.45/0.63 (define @t173 () (forall @t94 @t172)) % 0.45/0.63 (define @t174 () (not @t173)) % 0.45/0.63 (define @t175 () (or @t64 @t63 @t174)) % 0.45/0.63 (define @t176 () (and @t175 @t169)) % 0.45/0.63 (define @t177 () (= tptp.xk (tptp.sdtasdt0 tptp.xk tptp.sz10))) % 0.45/0.63 (define @t178 () (not @t177)) % 0.45/0.63 (define @t179 () (not @t4)) % 0.45/0.63 (define @t180 () (or @t179 @t178)) % 0.45/0.63 (define @t181 () (and @t180 (not (tptp.doDivides0 tptp.xk tptp.xk)))) % 0.45/0.63 (define @t182 () (not @t58)) % 0.45/0.63 (define @t183 () (or @t182 @t181 @t176)) % 0.45/0.63 (define @t184 () (forall @t107 (or @t105 (and (or @t102 (not (= tptp.xk @t100))) @t98) @t97))) % 0.45/0.63 (define @t185 () (and (or (= tptp.sz00 tptp.xk) (= tptp.sz10 tptp.xk) (not (forall @t94 (or @t92 @t171 @t90 (= @t5 tptp.xk) @t89 @t170)))) @t169)) % 0.45/0.63 (define @t186 () (or @t182 @t181 @t185)) % 0.45/0.63 (define @t187 () (@list false)) % 0.45/0.63 (define @t188 () (not @t185)) % 0.45/0.63 (define @t189 () (and (= @t1 @t20) @t19)) % 0.45/0.63 (define @t190 () (and @t177 (= tptp.xk (tptp.sdtasdt0 tptp.sz10 tptp.xk)))) % 0.45/0.63 (define @t191 () (or @t182 @t190)) % 0.45/0.63 (define @t192 () (@list false false)) % 0.45/0.63 (define @t193 () (not @t180)) % 0.45/0.63 (define @t194 () (not @t181)) % 0.45/0.63 (assume @p1 (forall @t3 (=> @t2 true))) % 0.45/0.63 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 0.45/0.63 (assume @p3 (and @t4 (not (= tptp.sz10 tptp.sz00)))) % 0.45/0.63 (assume @p4 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t6)))) % 0.45/0.63 (assume @p5 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t10)))) % 0.45/0.63 (assume @p6 (forall @t9 (=> @t8 (= @t6 @t11)))) % 0.45/0.63 (assume @p7 (forall @t16 (=> @t15 (= (tptp.sdtpldt0 @t6 @t12) (tptp.sdtpldt0 @t1 @t13))))) % 0.45/0.63 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.45/0.63 (assume @p9 (forall @t9 (=> @t8 (= @t10 @t17)))) % 0.45/0.63 (assume @p10 (forall @t16 (=> @t15 (= (tptp.sdtasdt0 @t10 @t12) (tptp.sdtasdt0 @t1 @t18))))) % 0.45/0.63 (assume @p11 @t23) % 0.45/0.63 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.45/0.63 (assume @p13 (forall @t16 (=> @t15 (and (= (tptp.sdtasdt0 @t1 @t13) (tptp.sdtpldt0 @t10 @t25)) (= (tptp.sdtasdt0 @t13 @t1) (tptp.sdtpldt0 @t17 @t24)))))) % 0.45/0.63 (assume @p14 (forall @t16 (=> @t15 (=> (or (= @t6 @t28) (= @t11 @t27)) @t26)))) % 0.45/0.63 (assume @p15 (forall @t3 (=> @t2 (=> @t32 (forall (@list @t5 @t12) (=> (and @t7 @t14) (=> (or @t30 @t29) @t26))))))) % 0.45/0.63 (assume @p16 (forall @t9 (=> @t8 (=> (= @t6 tptp.sz00) (and @t31 @t33))))) % 0.45/0.63 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t31 @t33))))) % 0.45/0.63 (assume @p18 (forall @t9 (=> @t8 (= @t36 (exists @t35 @t34))))) % 0.45/0.63 (assume @p19 (forall @t9 (=> @t8 (=> @t36 (forall @t35 (= (= @t12 (tptp.sdtmndt0 @t5 @t1)) @t34)))))) % 0.45/0.63 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.45/0.63 (assume @p21 (forall @t9 (=> @t8 (=> (and @t36 @t38) @t37)))) % 0.45/0.63 (assume @p22 (forall @t16 (=> @t15 (=> (and @t36 @t39) (tptp.sdtlseqdt0 @t1 @t12))))) % 0.45/0.63 (assume @p23 (forall @t9 (=> @t8 (or @t36 (and (not @t40) @t38))))) % 0.45/0.63 (assume @p24 (forall @t9 (=> @t8 (=> @t42 (forall @t35 (=> @t14 (and (not (= @t27 @t41)) (tptp.sdtlseqdt0 @t27 @t41) (not (= @t28 @t13)) (tptp.sdtlseqdt0 @t28 @t13)))))))) % 0.45/0.63 (assume @p25 (forall @t16 (=> @t15 (=> (and @t32 (not @t26) @t39) (and (not @t30) (tptp.sdtlseqdt0 @t10 @t25) (not @t29) (tptp.sdtlseqdt0 @t17 @t24)))))) % 0.45/0.63 (assume @p26 (forall @t3 (=> @t2 (or @t31 @t43 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 0.45/0.63 (assume @p27 (forall @t9 (=> @t8 (=> @t32 (tptp.sdtlseqdt0 @t5 @t17))))) % 0.45/0.63 (assume @p28 (forall @t9 (=> @t8 (=> @t44 true)))) % 0.45/0.63 (assume @p29 (forall @t9 (=> @t8 (=> @t42 @t44)))) % 0.45/0.63 (assume @p30 (forall @t9 (=> @t8 (= @t46 (exists @t35 @t45))))) % 0.45/0.63 (assume @p31 (forall @t9 (=> @t8 (=> @t48 (forall @t35 (= (= @t12 @t47) @t45)))))) % 0.45/0.63 (assume @p32 (forall @t16 (=> @t15 (=> (and @t46 (tptp.doDivides0 @t5 @t12)) @t49)))) % 0.45/0.63 (assume @p33 (forall @t16 (=> @t15 (=> (and @t46 @t49) @t50)))) % 0.45/0.63 (assume @p34 (forall @t16 (=> @t15 (=> (and @t46 @t50) @t49)))) % 0.45/0.63 (assume @p35 (forall @t9 (=> @t8 (=> (and @t46 @t51) @t36)))) % 0.45/0.63 (assume @p36 (forall @t9 (=> @t8 (=> @t48 (forall @t35 (=> @t14 (= (tptp.sdtasdt0 @t12 @t47) (tptp.sdtsldt0 (tptp.sdtasdt0 @t12 @t5) @t1)))))))) % 0.45/0.63 (assume @p37 (forall @t3 (=> @t2 (= @t57 (and @t32 @t56 (forall @t55 (=> (and @t7 @t54) @t53))))))) % 0.45/0.63 (assume @p38 @t58) % 0.45/0.63 (assume @p39 (forall @t3 (=> (and @t2 @t32 @t56) (=> (tptp.iLess0 @t1 tptp.xk) (exists @t55 (and @t7 @t62 @t54 @t51 (not @t52) (forall @t35 (=> (and @t14 (or (exists (@list @t59) (and (tptp.aNaturalNumber0 @t59) (= @t5 (tptp.sdtasdt0 @t12 @t59)))) (tptp.doDivides0 @t12 @t5))) (or (= @t12 tptp.sz10) (= @t12 @t5)))) (tptp.isPrime0 @t5))))))) % 0.45/0.63 (assume @p40 (and (not @t64) (not @t63))) % 0.45/0.63 (assume @p41 @t84) % 0.45/0.63 (assume @p42 true) % 0.45/0.63 (step @p43 :rule refl :args (@t97)) % 0.45/0.63 (step @p44 :rule refl :args (@t98)) % 0.45/0.63 (step @p45 :rule eq-symm :args (@t100 tptp.xk)) % 0.45/0.63 (step @p46 :rule cong :premises (@p45) :args (@t101)) % 0.45/0.63 (step @p47 :rule refl :args (@t102)) % 0.45/0.63 (step @p48 :rule nary_cong :premises (@p47 @p46) :args (@t103)) % 0.45/0.63 (step @p49 :rule nary_cong :premises (@p48 @p44) :args (@t104)) % 0.45/0.63 (step @p50 :rule refl :args (@t105)) % 0.45/0.63 (step @p51 :rule nary_cong :premises (@p50 @p49 @p43) :args (@t106)) % 0.45/0.63 (step @p52 :rule cong :premises (@p51) :args (@t108)) % 0.45/0.63 (step @p53 :rule quant-merge-prenex :args ((= (forall @t3 @t110) @t108))) % 0.45/0.63 (step @p54 :rule refl :args (@t97)) % 0.45/0.63 (step @p55 :rule quant-unused-vars :args ((= @t111 @t98))) % 0.45/0.63 (step @p56 :rule alpha_equiv :args (@t112 (@list @t99) @t113)) % 0.45/0.63 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t114)) % 0.45/0.63 (step @p58 :rule quant-miniscope-and :args ((= @t115 @t114))) % 0.45/0.63 (step @p59 :rule trans :premises (@p58 @p57)) % 0.45/0.63 (step @p60 :rule refl :args (@t105)) % 0.45/0.63 (step @p61 :rule nary_cong :premises (@p60 @p59 @p54) :args (@t116)) % 0.45/0.63 (step @p62 :rule quant-miniscope-or :args ((= @t110 @t116))) % 0.45/0.63 (step @p63 :rule trans :premises (@p62 @p61)) % 0.45/0.63 (step @p64 :rule symm :premises (@p63)) % 0.45/0.63 (step @p65 :rule cong :premises (@p64) :args ((forall @t3 (or @t105 @t119 @t97)))) % 0.45/0.63 (step @p66 :rule trans :premises (@p65 @p53)) % 0.45/0.63 (step @p67 :rule trans :premises (@p66 @p52)) % 0.45/0.63 (step @p68 :rule refl :args (@t85)) % 0.45/0.63 (step @p69 :rule refl :args (@t96)) % 0.45/0.63 (step @p70 :rule bool-double-not-elim :args (@t43)) % 0.45/0.63 (step @p71 :rule bool-double-not-elim :args (@t31)) % 0.45/0.63 (step @p72 :rule nary_cong :premises (@p71 @p70 @p69) :args (@t122)) % 0.45/0.63 (step @p73 :rule aci_norm :args ((= (or @t121 (or @t120 @t96)) @t122))) % 0.45/0.63 (step @p74 :rule trans :premises (@p73 @p72)) % 0.45/0.63 (step @p75 :rule bool-and-de-morgan :args (@t56 @t95 true)) % 0.45/0.63 (step @p76 :rule refl :args (@t121)) % 0.45/0.63 (step @p77 :rule nary_cong :premises (@p76 @p75) :args ((or @t121 (not (and @t56 @t95))))) % 0.45/0.63 (step @p78 :rule bool-and-de-morgan :args (@t32 @t56 (and @t95))) % 0.45/0.63 (step @p79 :rule trans :premises (@p78 @p77)) % 0.45/0.63 (step @p80 :rule trans :premises (@p79 @p74)) % 0.45/0.63 (step @p81 :rule nary_cong :premises (@p80 @p68) :args ((and (not @t123) @t85))) % 0.45/0.63 (step @p82 :rule bool-or-de-morgan :args (@t123 @t57 false)) % 0.45/0.63 (step @p83 :rule trans :premises (@p82 @p81)) % 0.45/0.63 (step @p84 :rule refl :args (@t98)) % 0.45/0.63 (step @p85 :rule bool-double-not-elim :args (@t118)) % 0.45/0.63 (step @p86 :rule nary_cong :premises (@p85 @p84) :args ((and (not @t124) @t98))) % 0.45/0.63 (step @p87 :rule bool-or-de-morgan :args (@t124 @t70 false)) % 0.45/0.63 (step @p88 :rule trans :premises (@p87 @p86)) % 0.45/0.63 (step @p89 :rule nary_cong :premises (@p60 @p88 @p83) :args (@t129)) % 0.45/0.63 (step @p90 :rule aci_norm :args ((= (or @t105 (or @t128 @t126)) @t129))) % 0.45/0.63 (step @p91 :rule bool-and-de-morgan :args (@t127 @t125 true)) % 0.45/0.63 (step @p92 :rule nary_cong :premises (@p60 @p91) :args ((or @t105 (not (and @t127 @t125))))) % 0.45/0.63 (step @p93 :rule bool-and-de-morgan :args (@t2 @t127 (and @t125))) % 0.45/0.63 (step @p94 :rule trans :premises (@p93 @p92)) % 0.45/0.63 (step @p95 :rule trans :premises (@p94 @p90)) % 0.45/0.63 (step @p96 :rule trans :premises (@p95 @p89)) % 0.45/0.63 (step @p97 :rule cong :premises (@p96) :args (@t131)) % 0.45/0.63 (step @p98 :rule trans :premises (@p97 @p67)) % 0.45/0.63 (step @p99 :rule cong :premises (@p98) :args (@t132)) % 0.45/0.63 (step @p100 :rule exists-elim :args ((= (exists @t3 @t130) @t132))) % 0.45/0.63 (step @p101 :rule trans :premises (@p100 @p99)) % 0.45/0.63 (step @p102 :rule refl :args (@t57)) % 0.45/0.63 (step @p103 :rule aci_norm :args ((= @t134 @t93))) % 0.45/0.63 (step @p104 :rule cong :premises (@p103) :args (@t135)) % 0.45/0.63 (step @p105 :rule quant-merge-prenex :args ((= (forall @t55 @t137) @t135))) % 0.45/0.63 (step @p106 :rule refl :args (@t37)) % 0.45/0.63 (step @p107 :rule refl :args (@t90)) % 0.45/0.63 (step @p108 :rule refl :args (@t91)) % 0.45/0.63 (step @p109 :rule alpha_equiv :args (@t138 (@list @t86) (@list @t12))) % 0.45/0.63 (step @p110 :rule refl :args (@t92)) % 0.45/0.63 (step @p111 :rule nary_cong :premises (@p110 @p109 @p108 @p107 @p106) :args (@t139)) % 0.45/0.63 (step @p112 :rule quant-miniscope-or :args ((= @t137 @t139))) % 0.45/0.63 (step @p113 :rule trans :premises (@p112 @p111)) % 0.45/0.63 (step @p114 :rule symm :premises (@p113)) % 0.45/0.63 (step @p115 :rule cong :premises (@p114) :args ((forall @t55 @t141))) % 0.45/0.63 (step @p116 :rule trans :premises (@p115 @p105)) % 0.45/0.63 (step @p117 :rule trans :premises (@p116 @p104)) % 0.45/0.63 (step @p118 :rule aci_norm :args ((= (or (or @t92 @t140 @t91) @t142) @t141))) % 0.45/0.63 (step @p119 :rule refl :args (@t142)) % 0.45/0.63 (step @p120 :rule bool-double-not-elim :args (@t140)) % 0.45/0.63 (step @p121 :rule nary_cong :premises (@p110 @p120 @p108) :args (@t145)) % 0.45/0.63 (step @p122 :rule aci_norm :args ((= (or @t92 (or @t144 @t91)) @t145))) % 0.45/0.63 (step @p123 :rule trans :premises (@p122 @p121)) % 0.45/0.63 (step @p124 :rule bool-and-de-morgan :args (@t143 @t54 true)) % 0.45/0.63 (step @p125 :rule nary_cong :premises (@p110 @p124) :args ((or @t92 (not (and @t143 @t54))))) % 0.45/0.63 (step @p126 :rule bool-and-de-morgan :args (@t7 @t143 (and @t54))) % 0.45/0.63 (step @p127 :rule trans :premises (@p126 @p125)) % 0.45/0.63 (step @p128 :rule trans :premises (@p127 @p123)) % 0.45/0.63 (step @p129 :rule nary_cong :premises (@p128 @p119) :args ((or (not @t146) @t142))) % 0.45/0.63 (step @p130 :rule trans :premises (@p129 @p118)) % 0.45/0.63 (step @p131 :rule bool-impl-elim :args (@t146 @t142)) % 0.45/0.63 (step @p132 :rule trans :premises (@p131 @p130)) % 0.45/0.63 (step @p133 :rule cong :premises (@p132) :args ((forall @t55 (=> @t146 @t142)))) % 0.45/0.63 (step @p134 :rule trans :premises (@p133 @p117)) % 0.45/0.63 (step @p135 :rule eq-symm :args (@t5 @t1)) % 0.45/0.63 (step @p136 :rule eq-symm :args (@t5 tptp.sz10)) % 0.45/0.63 (step @p137 :rule nary_cong :premises (@p136 @p135) :args (@t53)) % 0.45/0.63 (step @p138 :rule refl :args (@t54)) % 0.45/0.63 (step @p139 :rule bool-and-de-morgan :args (@t14 @t60 true)) % 0.45/0.63 (step @p140 :rule cong :premises (@p139) :args (@t147)) % 0.45/0.63 (step @p141 :rule cong :premises (@p140) :args (@t148)) % 0.45/0.63 (step @p142 :rule exists-elim :args ((= @t62 @t148))) % 0.45/0.63 (step @p143 :rule trans :premises (@p142 @p141)) % 0.45/0.63 (step @p144 :rule refl :args (@t7)) % 0.45/0.63 (step @p145 :rule nary_cong :premises (@p144 @p143 @p138) :args (@t65)) % 0.45/0.63 (step @p146 :rule cong :premises (@p145 @p137) :args (@t66)) % 0.45/0.63 (step @p147 :rule cong :premises (@p146) :args (@t67)) % 0.45/0.63 (step @p148 :rule trans :premises (@p147 @p134)) % 0.45/0.63 (step @p149 :rule refl :args (@t56)) % 0.45/0.63 (step @p150 :rule refl :args (@t32)) % 0.45/0.63 (step @p151 :rule nary_cong :premises (@p150 @p149 @p148) :args (@t68)) % 0.45/0.63 (step @p152 :rule nary_cong :premises (@p151 @p102) :args (@t69)) % 0.45/0.63 (step @p153 :rule refl :args (@t70)) % 0.45/0.63 (step @p154 :rule bool-and-de-morgan :args (@t7 @t117 true)) % 0.45/0.63 (step @p155 :rule cong :premises (@p154) :args (@t150)) % 0.45/0.63 (step @p156 :rule cong :premises (@p155) :args (@t151)) % 0.45/0.63 (step @p157 :rule exists-elim :args ((= (exists @t55 @t149) @t151))) % 0.45/0.63 (step @p158 :rule trans :premises (@p157 @p156)) % 0.45/0.63 (step @p159 :rule eq-symm :args (tptp.xk @t10)) % 0.45/0.63 (step @p160 :rule nary_cong :premises (@p144 @p159) :args (@t71)) % 0.45/0.63 (step @p161 :rule cong :premises (@p160) :args (@t72)) % 0.45/0.63 (step @p162 :rule trans :premises (@p161 @p158)) % 0.45/0.63 (step @p163 :rule nary_cong :premises (@p162 @p153) :args (@t73)) % 0.45/0.63 (step @p164 :rule refl :args (@t2)) % 0.45/0.63 (step @p165 :rule nary_cong :premises (@p164 @p163 @p152) :args (@t74)) % 0.45/0.63 (step @p166 :rule cong :premises (@p165) :args (@t75)) % 0.45/0.63 (step @p167 :rule trans :premises (@p166 @p101)) % 0.45/0.63 (step @p168 :rule refl :args (@t76)) % 0.45/0.63 (step @p169 :rule refl :args (@t77)) % 0.45/0.63 (step @p170 :rule refl :args (@t43)) % 0.45/0.63 (step @p171 :rule eq-symm :args (@t153 tptp.xk)) % 0.45/0.63 (step @p172 :rule cong :premises (@p171) :args (@t154)) % 0.45/0.63 (step @p173 :rule refl :args (@t155)) % 0.45/0.63 (step @p174 :rule nary_cong :premises (@p173 @p172) :args (@t156)) % 0.45/0.63 (step @p175 :rule nary_cong :premises (@p174 @p44) :args (@t157)) % 0.45/0.63 (step @p176 :rule nary_cong :premises (@p50 @p175 @p170 @p169) :args (@t158)) % 0.45/0.63 (step @p177 :rule cong :premises (@p176) :args (@t159)) % 0.45/0.63 (step @p178 :rule quant-merge-prenex :args ((= (forall @t3 @t161) @t159))) % 0.45/0.63 (step @p179 :rule refl :args (@t77)) % 0.45/0.63 (step @p180 :rule refl :args (@t43)) % 0.45/0.63 (step @p181 :rule quant-unused-vars :args ((= @t162 @t98))) % 0.45/0.63 (step @p182 :rule alpha_equiv :args (@t163 (@list @t152) @t113)) % 0.45/0.63 (step @p183 :rule nary_cong :premises (@p182 @p181) :args (@t164)) % 0.45/0.63 (step @p184 :rule quant-miniscope-and :args ((= @t165 @t164))) % 0.45/0.63 (step @p185 :rule trans :premises (@p184 @p183)) % 0.45/0.63 (step @p186 :rule nary_cong :premises (@p60 @p185 @p180 @p179) :args (@t166)) % 0.45/0.63 (step @p187 :rule quant-miniscope-or :args ((= @t161 @t166))) % 0.45/0.63 (step @p188 :rule trans :premises (@p187 @p186)) % 0.45/0.63 (step @p189 :rule symm :premises (@p188)) % 0.45/0.63 (step @p190 :rule cong :premises (@p189) :args ((forall @t3 @t167))) % 0.45/0.63 (step @p191 :rule trans :premises (@p190 @p178)) % 0.45/0.63 (step @p192 :rule trans :premises (@p191 @p177)) % 0.45/0.63 (step @p193 :rule aci_norm :args ((= (or (or @t105 @t119) @t78) @t167))) % 0.45/0.63 (step @p194 :rule refl :args (@t78)) % 0.45/0.63 (step @p195 :rule nary_cong :premises (@p60 @p88) :args ((or @t105 @t128))) % 0.45/0.63 (step @p196 :rule bool-and-de-morgan :args (@t2 @t127 true)) % 0.45/0.63 (step @p197 :rule trans :premises (@p196 @p195)) % 0.45/0.63 (step @p198 :rule nary_cong :premises (@p197 @p194) :args ((or (not @t168) @t78))) % 0.45/0.63 (step @p199 :rule trans :premises (@p198 @p193)) % 0.45/0.63 (step @p200 :rule bool-impl-elim :args (@t168 @t78)) % 0.45/0.63 (step @p201 :rule trans :premises (@p200 @p199)) % 0.45/0.63 (step @p202 :rule cong :premises (@p201) :args ((forall @t3 (=> @t168 @t78)))) % 0.45/0.63 (step @p203 :rule trans :premises (@p202 @p192)) % 0.45/0.63 (step @p204 :rule refl :args (@t78)) % 0.45/0.63 (step @p205 :rule nary_cong :premises (@p164 @p163) :args (@t79)) % 0.45/0.63 (step @p206 :rule cong :premises (@p205 @p204) :args (@t80)) % 0.45/0.63 (step @p207 :rule cong :premises (@p206) :args (@t81)) % 0.45/0.63 (step @p208 :rule trans :premises (@p207 @p203)) % 0.45/0.63 (step @p209 :rule nary_cong :premises (@p208 @p168) :args (@t82)) % 0.45/0.63 (step @p210 :rule cong :premises (@p209 @p167) :args (@t83)) % 0.45/0.63 (step @p211 :rule cong :premises (@p210) :args (@t84)) % 0.45/0.63 (step @p212 :rule eq_resolve :premises (@p41 @p211)) % 0.45/0.63 (step @p213 :rule not_implies_elim2 :premises (@p212)) % 0.45/0.63 (step @p214 :rule not_not_elim :premises (@p213)) % 0.45/0.63 (step @p215 :rule refl :args (@t169)) % 0.45/0.63 (step @p216 :rule refl :args (@t170)) % 0.45/0.63 (step @p217 :rule refl :args (@t89)) % 0.45/0.63 (step @p218 :rule eq-symm :args (tptp.xk @t5)) % 0.45/0.63 (step @p219 :rule refl :args (@t90)) % 0.45/0.63 (step @p220 :rule refl :args (@t171)) % 0.45/0.63 (step @p221 :rule refl :args (@t92)) % 0.45/0.63 (step @p222 :rule nary_cong :premises (@p221 @p220 @p219 @p218 @p217 @p216) :args (@t172)) % 0.45/0.63 (step @p223 :rule cong :premises (@p222) :args (@t173)) % 0.45/0.63 (step @p224 :rule cong :premises (@p223) :args (@t174)) % 0.45/0.63 (step @p225 :rule eq-symm :args (tptp.xk tptp.sz10)) % 0.45/0.63 (step @p226 :rule eq-symm :args (tptp.xk tptp.sz00)) % 0.45/0.63 (step @p227 :rule nary_cong :premises (@p226 @p225 @p224) :args (@t175)) % 0.45/0.63 (step @p228 :rule nary_cong :premises (@p227 @p215) :args (@t176)) % 0.45/0.63 (step @p229 :rule refl :args (@t181)) % 0.45/0.63 (step @p230 :rule refl :args (@t182)) % 0.45/0.63 (step @p231 :rule nary_cong :premises (@p230 @p229 @p228) :args (@t183)) % 0.45/0.63 (step @p232 :rule refl :args (@t184)) % 0.45/0.63 (step @p233 :rule cong :premises (@p232 @p231) :args ((=> @t184 @t183))) % 0.45/0.63 (assume-push @p272 @t184) % 0.45/0.63 (step @p235 :rule instantiate :premises (@p214) :args ((@list tptp.xk tptp.sz10))) % 0.45/0.63 (step-pop @p273 :rule scope :premises (@p235)) % 0.45/0.63 (step @p236 :rule process_scope :premises (@p273) :args (@t183)) % 0.45/0.63 (step @p238 :rule eq_resolve :premises (@p236 @p233)) % 0.45/0.63 (step @p239 :rule implies_elim :premises (@p238)) % 0.45/0.63 (step @p240 :rule chain_m_resolution :premises (@p239 @p214) :args (@t186 @t187 (@list @t184))) % 0.45/0.63 (step @p241 :rule not_implies_elim1 :premises (@p212)) % 0.45/0.63 (step @p242 :rule and_elim :premises (@p241) :args (1)) % 0.45/0.63 (step @p243 :rule cnf_and_pos :args (@t185 1)) % 0.45/0.63 (step @p244 :rule reordering :premises (@p243) :args ((or @t169 @t188))) % 0.45/0.63 (step @p245 :rule chain_m_resolution :premises (@p244 @p242) :args (@t188 @t187 (@list @t76))) % 0.45/0.63 (step @p246 :rule bool-impl-elim :args (@t2 @t189)) % 0.45/0.63 (step @p247 :rule cong :premises (@p246) :args ((forall @t3 (=> @t2 @t189)))) % 0.45/0.63 (step @p248 :rule refl :args (@t19)) % 0.45/0.63 (step @p249 :rule eq-symm :args (@t20 @t1)) % 0.45/0.63 (step @p250 :rule nary_cong :premises (@p249 @p248) :args (@t21)) % 0.45/0.63 (step @p251 :rule cong :premises (@p164 @p250) :args (@t22)) % 0.45/0.63 (step @p252 :rule cong :premises (@p251) :args (@t23)) % 0.45/0.63 (step @p253 :rule trans :premises (@p252 @p247)) % 0.45/0.63 (step @p254 :rule eq_resolve :premises (@p11 @p253)) % 0.45/0.63 (step @p255 :rule instantiate :premises (@p254) :args ((@list tptp.xk))) % 0.45/0.63 (step @p256 :rule cnf_or_pos :args (@t191)) % 0.45/0.63 (step @p257 :rule reordering :premises (@p256) :args ((or @t182 @t190 (not @t191)))) % 0.45/0.63 (step @p258 :rule chain_m_resolution :premises (@p257 @p38 @p255) :args (@t190 @t192 (@list @t58 @t191))) % 0.45/0.63 (step @p259 :rule cnf_and_pos :args (@t190 0)) % 0.45/0.63 (step @p260 :rule reordering :premises (@p259) :args ((or @t177 (not @t190)))) % 0.45/0.63 (step @p261 :rule chain_m_resolution :premises (@p260 @p258) :args (@t177 @t187 (@list @t190))) % 0.45/0.63 (step @p262 :rule and_elim :premises (@p3) :args (0)) % 0.45/0.63 (step @p263 :rule cnf_or_pos :args (@t180)) % 0.45/0.63 (step @p264 :rule reordering :premises (@p263) :args ((or @t179 @t178 @t193))) % 0.45/0.63 (step @p265 :rule chain_m_resolution :premises (@p264 @p262 @p261) :args (@t193 @t192 (@list @t4 @t177))) % 0.45/0.63 (step @p266 :rule cnf_and_pos :args (@t181 0)) % 0.45/0.63 (step @p267 :rule reordering :premises (@p266) :args ((or @t180 @t194))) % 0.45/0.63 (step @p268 :rule chain_m_resolution :premises (@p267 @p265) :args (@t194 (@list true) (@list @t180))) % 0.45/0.63 (step @p269 :rule cnf_or_pos :args (@t186)) % 0.45/0.63 (step @p270 :rule reordering :premises (@p269) :args ((or @t182 @t181 @t185 (not @t186)))) % 0.45/0.63 (step @p271 false :rule chain_m_resolution :premises (@p270 @p268 @p245 @p240 @p38) :args (false (@list true true false false) (@list @t181 @t185 @t186 @t58))) % 0.45/0.63 ) % 0.45/0.63 % SZS output end Proof % 0.45/0.63 % cvc5 exiting %------------------------------------------------------------------------------