%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : COM149+1 : TPTP v9.2.1. Released v6.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/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 08:10:35 AM UTC 2026 % Result : Theorem 0.44s 0.67s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM149+1 : TPTP v9.2.1. Released v6.4.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n016.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Mon Jun 1 20:31:09 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.67 % SZS status Theorem % 0.44/0.67 % SZS output start Proof % 0.44/0.67 ( % 0.44/0.67 (declare-sort $$unsorted 0) % 0.44/0.67 (declare-const tptp.varrow (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.vgetSomeExp (-> $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.vsomeExp (-> $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.vnoExp $$unsorted) % 0.44/0.67 (declare-const tptp.vsubst (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.vgensym (-> $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.vapp (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.visValue (-> $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.vempty $$unsorted) % 0.44/0.67 (declare-const tptp.vbind (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.vnoType $$unsorted) % 0.44/0.67 (declare-const tptp.visFreeVar (-> $$unsorted $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.vtcheck (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.vsomeType (-> $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.visSomeExp (-> $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.vvar (-> $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.vlookup (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.vabs (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.visSomeType (-> $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.vreduce (-> $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.vgetSomeType (-> $$unsorted $$unsorted)) % 0.44/0.67 (define @t1 () (@var "VVar1" $$unsorted)) % 0.44/0.67 (define @t2 () (@var "VVar0" $$unsorted)) % 0.44/0.67 (define @t3 () (tptp.vvar @t2)) % 0.44/0.67 (define @t4 () (= @t3 (tptp.vvar @t1))) % 0.44/0.67 (define @t5 () (= @t2 @t1)) % 0.44/0.67 (define @t6 () (@var "VExp1" $$unsorted)) % 0.44/0.67 (define @t7 () (@var "VTyp1" $$unsorted)) % 0.44/0.67 (define @t8 () (@var "VExp0" $$unsorted)) % 0.44/0.67 (define @t9 () (@var "VTyp0" $$unsorted)) % 0.44/0.67 (define @t10 () (tptp.vabs @t2 @t9 @t8)) % 0.44/0.67 (define @t11 () (= @t10 (tptp.vabs @t1 @t7 @t6))) % 0.44/0.67 (define @t12 () (= @t8 @t6)) % 0.44/0.67 (define @t13 () (= @t9 @t7)) % 0.44/0.67 (define @t14 () (and @t5 @t13 @t12)) % 0.44/0.67 (define @t15 () (@var "VExp3" $$unsorted)) % 0.44/0.67 (define @t16 () (@var "VExp2" $$unsorted)) % 0.44/0.67 (define @t17 () (tptp.vapp @t8 @t6)) % 0.44/0.67 (define @t18 () (= @t17 (tptp.vapp @t16 @t15))) % 0.44/0.67 (define @t19 () (and (= @t8 @t16) (= @t6 @t15))) % 0.44/0.67 (define @t20 () (tptp.visValue @t8)) % 0.44/0.67 (define @t21 () (@var "Ve" $$unsorted)) % 0.44/0.67 (define @t22 () (@var "VS" $$unsorted)) % 0.44/0.67 (define @t23 () (@var "Vx" $$unsorted)) % 0.44/0.67 (define @t24 () (tptp.vabs @t23 @t22 @t21)) % 0.44/0.67 (define @t25 () (= @t8 @t24)) % 0.44/0.67 (define @t26 () (not @t20)) % 0.44/0.67 (define @t27 () (tptp.vvar @t23)) % 0.44/0.67 (define @t28 () (= @t8 @t27)) % 0.44/0.67 (define @t29 () (@var "Ve2" $$unsorted)) % 0.44/0.67 (define @t30 () (@var "Ve1" $$unsorted)) % 0.44/0.67 (define @t31 () (tptp.vapp @t30 @t29)) % 0.44/0.67 (define @t32 () (= @t8 @t31)) % 0.44/0.67 (define @t33 () (@var "Vv" $$unsorted)) % 0.44/0.67 (define @t34 () (= @t23 @t33)) % 0.44/0.67 (define @t35 () (tptp.visFreeVar @t2 @t8)) % 0.44/0.67 (define @t36 () (= @t2 @t33)) % 0.44/0.67 (define @t37 () (tptp.visFreeVar @t33 @t21)) % 0.44/0.67 (define @t38 () (and (not @t34) @t37)) % 0.44/0.67 (define @t39 () (@var "VT" $$unsorted)) % 0.44/0.67 (define @t40 () (or (tptp.visFreeVar @t33 @t30) (tptp.visFreeVar @t33 @t29))) % 0.44/0.67 (define @t41 () (= tptp.vempty tptp.vempty)) % 0.44/0.67 (define @t42 () (@var "VCtx1" $$unsorted)) % 0.44/0.67 (define @t43 () (@var "VCtx0" $$unsorted)) % 0.44/0.67 (define @t44 () (tptp.vbind @t2 @t9 @t43)) % 0.44/0.67 (define @t45 () (= @t44 (tptp.vbind @t1 @t7 @t42))) % 0.44/0.67 (define @t46 () (and @t5 @t13 (= @t43 @t42))) % 0.44/0.67 (define @t47 () (= tptp.vnoType tptp.vnoType)) % 0.44/0.67 (define @t48 () (tptp.vsomeType @t9)) % 0.44/0.67 (define @t49 () (= @t48 (tptp.vsomeType @t7))) % 0.44/0.67 (define @t50 () (@var "VOptTyp0" $$unsorted)) % 0.44/0.67 (define @t51 () (tptp.visSomeType @t50)) % 0.44/0.67 (define @t52 () (= @t50 (tptp.vsomeType @t21))) % 0.44/0.67 (define @t53 () (@var "RESULT" $$unsorted)) % 0.44/0.67 (define @t54 () (= @t53 @t21)) % 0.44/0.67 (define @t55 () (= @t53 tptp.vnoType)) % 0.44/0.67 (define @t56 () (tptp.vlookup @t2 @t43)) % 0.44/0.67 (define @t57 () (= @t53 @t56)) % 0.44/0.67 (define @t58 () (=> @t57 @t55)) % 0.44/0.67 (define @t59 () (= @t43 tptp.vempty)) % 0.44/0.67 (define @t60 () (= @t2 @t23)) % 0.44/0.67 (define @t61 () (and @t60 @t59)) % 0.44/0.67 (define @t62 () (=> @t61 @t58)) % 0.44/0.67 (define @t63 () (@list @t23 @t2 @t43 @t53)) % 0.44/0.67 (define @t64 () (forall @t63 @t62)) % 0.44/0.67 (define @t65 () (@var "VTy" $$unsorted)) % 0.44/0.67 (define @t66 () (= @t53 (tptp.vsomeType @t65))) % 0.44/0.67 (define @t67 () (@var "Vy" $$unsorted)) % 0.44/0.67 (define @t68 () (= @t23 @t67)) % 0.44/0.67 (define @t69 () (@var "VC" $$unsorted)) % 0.44/0.67 (define @t70 () (tptp.vbind @t67 @t65 @t69)) % 0.44/0.67 (define @t71 () (= @t43 @t70)) % 0.44/0.67 (define @t72 () (and @t60 @t71)) % 0.44/0.67 (define @t73 () (tptp.vlookup @t23 @t69)) % 0.44/0.67 (define @t74 () (= @t53 @t73)) % 0.44/0.67 (define @t75 () (not @t68)) % 0.44/0.67 (define @t76 () (@list @t23)) % 0.44/0.67 (define @t77 () (@var "VTx" $$unsorted)) % 0.44/0.67 (define @t78 () (tptp.vbind @t23 @t77 @t69)) % 0.44/0.67 (define @t79 () (tptp.vtcheck (tptp.vbind @t23 @t77 @t70) @t21 @t39)) % 0.44/0.67 (define @t80 () (@list @t67 @t65 @t23 @t77 @t69 @t21 @t39)) % 0.44/0.67 (define @t81 () (tptp.vsubst @t2 @t8 @t6)) % 0.44/0.67 (define @t82 () (= @t53 @t81)) % 0.44/0.67 (define @t83 () (tptp.vvar @t67)) % 0.44/0.67 (define @t84 () (= @t6 @t83)) % 0.44/0.67 (define @t85 () (= @t8 @t21)) % 0.44/0.67 (define @t86 () (and @t60 @t85 @t84)) % 0.44/0.67 (define @t87 () (= @t53 @t83)) % 0.44/0.67 (define @t88 () (tptp.vsubst @t23 @t21 @t30)) % 0.44/0.67 (define @t89 () (= @t53 (tptp.vapp @t88 (tptp.vsubst @t23 @t21 @t29)))) % 0.44/0.67 (define @t90 () (= @t6 @t31)) % 0.44/0.67 (define @t91 () (tptp.vabs @t67 @t39 @t30)) % 0.44/0.67 (define @t92 () (= @t53 @t91)) % 0.44/0.67 (define @t93 () (= @t6 @t91)) % 0.44/0.67 (define @t94 () (and @t60 @t85 @t93)) % 0.44/0.67 (define @t95 () (@var "Vfresh" $$unsorted)) % 0.44/0.67 (define @t96 () (= @t53 (tptp.vsubst @t23 @t21 (tptp.vabs @t95 @t39 (tptp.vsubst @t67 (tptp.vvar @t95) @t30))))) % 0.44/0.67 (define @t97 () (= @t95 (tptp.vgensym (tptp.vapp (tptp.vapp @t21 @t30) @t27)))) % 0.44/0.67 (define @t98 () (tptp.visFreeVar @t67 @t21)) % 0.44/0.67 (define @t99 () (= @t53 (tptp.vabs @t67 @t39 @t88))) % 0.44/0.67 (define @t100 () (not @t98)) % 0.44/0.67 (define @t101 () (= tptp.vnoExp tptp.vnoExp)) % 0.44/0.67 (define @t102 () (tptp.vsomeExp @t8)) % 0.44/0.67 (define @t103 () (= @t102 (tptp.vsomeExp @t6))) % 0.44/0.67 (define @t104 () (@var "VOptExp0" $$unsorted)) % 0.44/0.67 (define @t105 () (tptp.visSomeExp @t104)) % 0.44/0.67 (define @t106 () (= @t104 (tptp.vsomeExp @t21))) % 0.44/0.67 (define @t107 () (= @t53 tptp.vnoExp)) % 0.44/0.67 (define @t108 () (tptp.vreduce @t8)) % 0.44/0.67 (define @t109 () (= @t53 @t108)) % 0.44/0.67 (define @t110 () (=> @t109 @t107)) % 0.44/0.67 (define @t111 () (@var "Ve2red" $$unsorted)) % 0.44/0.67 (define @t112 () (tptp.vabs @t23 @t22 @t30)) % 0.44/0.67 (define @t113 () (= @t53 (tptp.vsomeExp (tptp.vapp @t112 (tptp.vgetSomeExp @t111))))) % 0.44/0.67 (define @t114 () (tptp.visSomeExp @t111)) % 0.44/0.67 (define @t115 () (= @t111 (tptp.vreduce @t29))) % 0.44/0.67 (define @t116 () (= @t8 (tptp.vapp @t112 @t29))) % 0.44/0.67 (define @t117 () (= @t53 (tptp.vsomeExp (tptp.vsubst @t23 @t29 @t30)))) % 0.44/0.67 (define @t118 () (tptp.visValue @t29)) % 0.44/0.67 (define @t119 () (not @t114)) % 0.44/0.67 (define @t120 () (not @t118)) % 0.44/0.67 (define @t121 () (@var "Ve1red" $$unsorted)) % 0.44/0.67 (define @t122 () (= @t53 (tptp.vsomeExp (tptp.vapp (tptp.vgetSomeExp @t121) @t29)))) % 0.44/0.67 (define @t123 () (tptp.visSomeExp @t121)) % 0.44/0.67 (define @t124 () (= @t121 (tptp.vreduce @t30))) % 0.44/0.67 (define @t125 () (@var "VVe10" $$unsorted)) % 0.44/0.67 (define @t126 () (@var "VVS0" $$unsorted)) % 0.44/0.67 (define @t127 () (@var "VVx0" $$unsorted)) % 0.44/0.67 (define @t128 () (forall (@list @t127 @t126 @t125) (not (= @t30 (tptp.vabs @t127 @t126 @t125))))) % 0.44/0.67 (define @t129 () (and @t32 @t128)) % 0.44/0.67 (define @t130 () (not @t123)) % 0.44/0.67 (define @t131 () (@var "VTyp3" $$unsorted)) % 0.44/0.67 (define @t132 () (@var "VTyp2" $$unsorted)) % 0.44/0.67 (define @t133 () (= (tptp.varrow @t9 @t7) (tptp.varrow @t132 @t131))) % 0.44/0.67 (define @t134 () (and (= @t9 @t132) (= @t7 @t131))) % 0.44/0.67 (define @t135 () (= @t73 (tptp.vsomeType @t39))) % 0.44/0.67 (define @t136 () (tptp.varrow @t22 @t39)) % 0.44/0.67 (define @t137 () (tptp.vtcheck (tptp.vbind @t23 @t22 @t69) @t21 @t39)) % 0.44/0.67 (define @t138 () (tptp.vtcheck @t69 @t29 @t22)) % 0.44/0.67 (define @t139 () (tptp.vtcheck @t69 @t30 @t136)) % 0.44/0.67 (define @t140 () (and @t139 @t138)) % 0.44/0.67 (define @t141 () (= @t21 @t31)) % 0.44/0.67 (define @t142 () (and @t141 @t139 @t138)) % 0.44/0.67 (define @t143 () (@list @t30 @t29 @t22)) % 0.44/0.67 (define @t144 () (exists @t143 @t142)) % 0.44/0.67 (define @t145 () (@var "VT2" $$unsorted)) % 0.44/0.67 (define @t146 () (@var "VT1" $$unsorted)) % 0.44/0.67 (define @t147 () (tptp.vtcheck (tptp.vbind @t23 @t146 @t69) @t29 @t145)) % 0.44/0.67 (define @t148 () (tptp.varrow @t146 @t145)) % 0.44/0.67 (define @t149 () (= @t39 @t148)) % 0.44/0.67 (define @t150 () (tptp.vabs @t23 @t146 @t29)) % 0.44/0.67 (define @t151 () (= @t21 @t150)) % 0.44/0.67 (define @t152 () (and @t151 @t149 @t147)) % 0.44/0.67 (define @t153 () (@list @t23 @t29 @t146 @t145)) % 0.44/0.67 (define @t154 () (exists @t153 @t152)) % 0.44/0.67 (define @t155 () (= @t21 @t27)) % 0.44/0.67 (define @t156 () (and @t155 @t135)) % 0.44/0.67 (define @t157 () (exists @t76 @t156)) % 0.44/0.67 (define @t158 () (or @t157 @t154 @t144)) % 0.44/0.67 (define @t159 () (tptp.vtcheck @t69 @t21 @t39)) % 0.44/0.67 (define @t160 () (=> @t159 @t158)) % 0.44/0.67 (define @t161 () (@list @t21 @t39 @t69)) % 0.44/0.67 (define @t162 () (forall @t161 @t160)) % 0.44/0.67 (define @t163 () (@list @t23 @t22 @t69 @t21 @t39)) % 0.44/0.67 (define @t164 () (@var "Veout" $$unsorted)) % 0.44/0.67 (define @t165 () (tptp.vsomeExp @t164)) % 0.44/0.67 (define @t166 () (= (tptp.vreduce @t27) @t165)) % 0.44/0.67 (define @t167 () (@list @t164)) % 0.44/0.67 (define @t168 () (exists @t167 @t166)) % 0.44/0.67 (define @t169 () (tptp.visValue @t27)) % 0.44/0.67 (define @t170 () (not @t169)) % 0.44/0.67 (define @t171 () (tptp.vtcheck tptp.vempty @t27 @t39)) % 0.44/0.67 (define @t172 () (and @t171 @t170)) % 0.44/0.67 (define @t173 () (=> @t172 @t168)) % 0.44/0.67 (define @t174 () (@list @t39 @t23)) % 0.44/0.67 (define @t175 () (forall @t174 @t173)) % 0.44/0.67 (define @t176 () (not @t175)) % 0.44/0.67 (define @t177 () (not (forall @t167 (not @t166)))) % 0.44/0.67 (define @t178 () (not @t171)) % 0.44/0.67 (define @t179 () (or @t178 @t169 @t177)) % 0.44/0.67 (define @t180 () (forall @t174 @t179)) % 0.44/0.67 (define @t181 () (@quantifiers_skolemize @t180 0)) % 0.44/0.67 (define @t182 () (tptp.vlookup @t23 tptp.vempty)) % 0.44/0.67 (define @t183 () (= tptp.vnoType @t182)) % 0.44/0.67 (define @t184 () (not (= @t182 @t182))) % 0.44/0.67 (define @t185 () (or @t184 @t183)) % 0.44/0.67 (define @t186 () (= tptp.vnoType @t53)) % 0.44/0.67 (define @t187 () (not (= @t53 @t182))) % 0.44/0.67 (define @t188 () (or @t187 @t187 @t186)) % 0.44/0.67 (define @t189 () (@list @t53)) % 0.44/0.67 (define @t190 () (or @t187 @t186)) % 0.44/0.67 (define @t191 () (forall @t189 @t190)) % 0.44/0.67 (define @t192 () (forall @t76 @t191)) % 0.44/0.67 (define @t193 () (@list @t23 @t53)) % 0.44/0.67 (define @t194 () (not @t41)) % 0.44/0.67 (define @t195 () (or @t194 @t187 @t186)) % 0.44/0.67 (define @t196 () (not (= @t53 (tptp.vlookup @t23 @t43)))) % 0.44/0.67 (define @t197 () (= tptp.vempty @t43)) % 0.44/0.67 (define @t198 () (not @t197)) % 0.44/0.67 (define @t199 () (@list @t43)) % 0.44/0.67 (define @t200 () (or @t198 @t198 @t196 @t186)) % 0.44/0.67 (define @t201 () (or @t198 @t196 @t186)) % 0.44/0.67 (define @t202 () (forall @t199 @t201)) % 0.44/0.67 (define @t203 () (forall @t193 @t202)) % 0.44/0.67 (define @t204 () (forall (@list @t23 @t53 @t43) @t201)) % 0.44/0.67 (define @t205 () (@list @t23 @t43 @t53)) % 0.44/0.67 (define @t206 () (not (= @t23 @t23))) % 0.44/0.67 (define @t207 () (or @t206 @t198 @t196 @t186)) % 0.44/0.67 (define @t208 () (not @t57)) % 0.44/0.67 (define @t209 () (not @t60)) % 0.44/0.67 (define @t210 () (or @t209 @t209 @t198 @t208 @t186)) % 0.44/0.67 (define @t211 () (@list @t2)) % 0.44/0.67 (define @t212 () (or @t209 @t198 @t208 @t186)) % 0.44/0.67 (define @t213 () (forall @t211 @t212)) % 0.44/0.67 (define @t214 () (forall @t205 @t213)) % 0.44/0.67 (define @t215 () (forall (@list @t23 @t43 @t53 @t2) @t212)) % 0.44/0.67 (define @t216 () (=> @t57 @t186)) % 0.44/0.67 (define @t217 () (and @t60 @t197)) % 0.44/0.67 (define @t218 () (tptp.vsomeType @t181)) % 0.44/0.67 (define @t219 () (not (= @t182 @t218))) % 0.44/0.67 (define @t220 () (@quantifiers_skolemize @t180 1)) % 0.44/0.67 (define @t221 () (tptp.vvar @t220)) % 0.44/0.67 (define @t222 () (forall @t76 (or (not (= @t27 @t221)) @t219))) % 0.44/0.67 (define @t223 () (@quantifiers_skolemize @t222 0)) % 0.44/0.67 (define @t224 () (not @t138)) % 0.44/0.67 (define @t225 () (not @t139)) % 0.44/0.67 (define @t226 () (not @t141)) % 0.44/0.67 (define @t227 () (or @t226 @t225 @t224)) % 0.44/0.67 (define @t228 () (not (forall @t143 @t227))) % 0.44/0.67 (define @t229 () (not @t147)) % 0.44/0.67 (define @t230 () (not @t149)) % 0.44/0.67 (define @t231 () (not @t151)) % 0.44/0.67 (define @t232 () (or @t231 @t230 @t229)) % 0.44/0.67 (define @t233 () (not (forall @t153 @t232))) % 0.44/0.67 (define @t234 () (not (forall @t76 (or (not @t155) (not @t135))))) % 0.44/0.67 (define @t235 () (not @t159)) % 0.44/0.67 (define @t236 () (or @t235 @t234 @t233 @t228)) % 0.44/0.67 (define @t237 () (or @t234 @t233 @t228)) % 0.44/0.67 (define @t238 () (forall @t143 (not @t142))) % 0.44/0.67 (define @t239 () (not @t238)) % 0.44/0.67 (define @t240 () (forall @t153 (not @t152))) % 0.44/0.67 (define @t241 () (not @t240)) % 0.44/0.67 (define @t242 () (forall @t76 (not @t156))) % 0.44/0.67 (define @t243 () (not @t242)) % 0.44/0.67 (define @t244 () (not (tptp.vtcheck tptp.vempty @t29 @t22))) % 0.44/0.67 (define @t245 () (not (tptp.vtcheck tptp.vempty @t30 (tptp.varrow @t22 @t181)))) % 0.44/0.67 (define @t246 () (not (= @t221 @t31))) % 0.44/0.67 (define @t247 () (or @t246 @t245 @t244)) % 0.44/0.67 (define @t248 () (forall @t143 @t247)) % 0.44/0.67 (define @t249 () (not @t248)) % 0.44/0.67 (define @t250 () (not (tptp.vtcheck (tptp.vbind @t23 @t146 tptp.vempty) @t29 @t145))) % 0.44/0.67 (define @t251 () (not (= @t181 @t148))) % 0.44/0.67 (define @t252 () (not (= @t221 @t150))) % 0.44/0.67 (define @t253 () (or @t252 @t251 @t250)) % 0.44/0.67 (define @t254 () (forall @t153 @t253)) % 0.44/0.67 (define @t255 () (not @t254)) % 0.44/0.67 (define @t256 () (not (= @t221 @t27))) % 0.44/0.67 (define @t257 () (or @t256 @t219)) % 0.44/0.67 (define @t258 () (forall @t76 @t257)) % 0.44/0.67 (define @t259 () (not @t258)) % 0.44/0.67 (define @t260 () (tptp.vtcheck tptp.vempty @t221 @t181)) % 0.44/0.67 (define @t261 () (not @t260)) % 0.44/0.67 (define @t262 () (or @t261 @t259 @t255 @t249)) % 0.44/0.67 (define @t263 () (forall @t161 @t236)) % 0.44/0.67 (define @t264 () (forall @t143 (or (not (= @t31 @t221)) @t245 @t244))) % 0.44/0.67 (define @t265 () (not @t264)) % 0.44/0.67 (define @t266 () (forall @t153 (or (not (= @t150 @t221)) (not (= @t148 @t181)) @t250))) % 0.44/0.67 (define @t267 () (not @t266)) % 0.44/0.67 (define @t268 () (not @t222)) % 0.44/0.67 (define @t269 () (or @t261 @t268 @t267 @t265)) % 0.44/0.67 (define @t270 () (@list false)) % 0.44/0.67 (define @t271 () (@quantifiers_skolemize @t264 1)) % 0.44/0.67 (define @t272 () (@quantifiers_skolemize @t264 0)) % 0.44/0.67 (define @t273 () (tptp.vapp @t272 @t271)) % 0.44/0.67 (define @t274 () (= @t221 @t273)) % 0.44/0.67 (define @t275 () (@quantifiers_skolemize @t264 2)) % 0.44/0.67 (define @t276 () (not (tptp.vtcheck tptp.vempty @t271 @t275))) % 0.44/0.67 (define @t277 () (not (tptp.vtcheck tptp.vempty @t272 (tptp.varrow @t275 @t181)))) % 0.44/0.67 (define @t278 () (not @t274)) % 0.44/0.67 (define @t279 () (or @t278 @t277 @t276)) % 0.44/0.67 (define @t280 () (@list true)) % 0.44/0.67 (define @t281 () (not @t279)) % 0.44/0.67 (define @t282 () (not (= @t273 @t221))) % 0.44/0.67 (define @t283 () (or @t282 @t277 @t276)) % 0.44/0.67 (define @t284 () (not @t283)) % 0.44/0.67 (define @t285 () (@quantifiers_skolemize @t266 1)) % 0.44/0.67 (define @t286 () (@quantifiers_skolemize @t266 2)) % 0.44/0.67 (define @t287 () (@quantifiers_skolemize @t266 0)) % 0.44/0.67 (define @t288 () (tptp.vabs @t287 @t286 @t285)) % 0.44/0.67 (define @t289 () (= @t221 @t288)) % 0.44/0.67 (define @t290 () (@quantifiers_skolemize @t266 3)) % 0.44/0.67 (define @t291 () (not (tptp.vtcheck (tptp.vbind @t287 @t286 tptp.vempty) @t285 @t290))) % 0.44/0.67 (define @t292 () (tptp.varrow @t286 @t290)) % 0.44/0.67 (define @t293 () (not @t289)) % 0.44/0.67 (define @t294 () (or @t293 (not (= @t181 @t292)) @t291)) % 0.44/0.67 (define @t295 () (not @t294)) % 0.44/0.67 (define @t296 () (not (= @t292 @t181))) % 0.44/0.67 (define @t297 () (not (= @t288 @t221))) % 0.44/0.67 (define @t298 () (or @t297 @t296 @t291)) % 0.44/0.67 (define @t299 () (not @t298)) % 0.44/0.67 (define @t300 () (tptp.vreduce @t221)) % 0.44/0.67 (define @t301 () (tptp.visValue @t221)) % 0.44/0.67 (define @t302 () (or @t261 @t301 (not (forall @t167 (not (= @t165 @t300)))))) % 0.44/0.67 (define @t303 () (not @t302)) % 0.44/0.67 (define @t304 () (not @t180)) % 0.44/0.67 (define @t305 () (not (= @t300 @t165))) % 0.44/0.67 (define @t306 () (forall @t167 @t305)) % 0.44/0.67 (define @t307 () (not @t306)) % 0.44/0.67 (define @t308 () (or @t261 @t301 @t307)) % 0.44/0.67 (define @t309 () (not @t308)) % 0.44/0.67 (define @t310 () (tptp.vlookup @t223 tptp.vempty)) % 0.44/0.67 (define @t311 () (= @t218 @t310)) % 0.44/0.67 (define @t312 () (not @t311)) % 0.44/0.67 (define @t313 () (tptp.vvar @t223)) % 0.44/0.67 (define @t314 () (or (not (= @t221 @t313)) @t312)) % 0.44/0.67 (define @t315 () (not @t314)) % 0.44/0.67 (define @t316 () (not (= @t310 @t218))) % 0.44/0.67 (define @t317 () (not (= @t313 @t221))) % 0.44/0.67 (define @t318 () (or @t317 @t316)) % 0.44/0.67 (define @t319 () (not @t318)) % 0.44/0.67 (define @t320 () (= tptp.vnoType @t310)) % 0.44/0.67 (define @t321 () (not @t320)) % 0.44/0.67 (define @t322 () (= tptp.vnoType @t218)) % 0.44/0.67 (define @t323 () (not @t322)) % 0.44/0.67 (define @t324 () (and @t320 @t311 @t323)) % 0.44/0.67 (assume @p1 (forall (@list @t2 @t1) (and (=> @t4 @t5) (=> @t5 @t4)))) % 0.44/0.67 (assume @p2 (forall (@list @t2 @t9 @t8 @t1 @t7 @t6) (and (=> @t11 @t14) (=> @t14 @t11)))) % 0.44/0.67 (assume @p3 (forall (@list @t8 @t6 @t16 @t15) (and (=> @t18 @t19) (=> @t19 @t18)))) % 0.44/0.67 (assume @p4 (forall (@list @t2 @t1 @t9 @t8) (not (= @t3 (tptp.vabs @t1 @t9 @t8))))) % 0.44/0.67 (assume @p5 (forall (@list @t2 @t8 @t6) (not (= @t3 @t17)))) % 0.44/0.67 (assume @p6 (forall (@list @t2 @t9 @t8 @t6 @t16) (not (= @t10 (tptp.vapp @t6 @t16))))) % 0.44/0.67 (assume @p7 (forall (@list @t23 @t22 @t21 @t8) (=> @t25 @t20))) % 0.44/0.67 (assume @p8 (forall (@list @t23 @t8) (=> @t28 @t26))) % 0.44/0.67 (assume @p9 (forall (@list @t30 @t29 @t8) (=> @t32 @t26))) % 0.44/0.67 (assume @p10 (forall (@list @t2 @t8 @t23 @t33) (=> (and @t36 @t28) (and (=> @t34 @t35) (=> @t35 @t34))))) % 0.44/0.67 (assume @p11 (forall (@list @t39 @t2 @t8 @t23 @t33 @t21) (=> (and @t36 (= @t8 (tptp.vabs @t23 @t39 @t21))) (and (=> @t38 @t35) (=> @t35 @t38))))) % 0.44/0.67 (assume @p12 (forall (@list @t2 @t8 @t30 @t33 @t29) (=> (and @t36 @t32) (and (=> @t40 @t35) (=> @t35 @t40))))) % 0.44/0.67 (assume @p13 (and (=> @t41 true) (=> true @t41))) % 0.44/0.67 (assume @p14 (forall (@list @t2 @t9 @t43 @t1 @t7 @t42) (and (=> @t45 @t46) (=> @t46 @t45)))) % 0.44/0.67 (assume @p15 (and (=> @t47 true) (=> true @t47))) % 0.44/0.67 (assume @p16 (forall (@list @t9 @t7) (and (=> @t49 @t13) (=> @t13 @t49)))) % 0.44/0.67 (assume @p17 (forall (@list @t2 @t9 @t43) (not (= tptp.vempty @t44)))) % 0.44/0.67 (assume @p18 (forall (@list @t9) (not (= tptp.vnoType @t48)))) % 0.44/0.67 (assume @p19 (forall (@list @t50) (=> (= @t50 tptp.vnoType) (not @t51)))) % 0.44/0.67 (assume @p20 (forall (@list @t21 @t50) (=> @t52 @t51))) % 0.44/0.67 (assume @p21 (forall (@list @t50 @t53 @t21) (=> @t52 (=> (= @t53 (tptp.vgetSomeType @t50)) @t54)))) % 0.44/0.67 (assume @p22 @t64) % 0.44/0.67 (assume @p23 (forall (@list @t69 @t23 @t67 @t2 @t43 @t53 @t65) (=> @t72 (=> @t68 (=> @t57 @t66))))) % 0.44/0.67 (assume @p24 (forall (@list @t65 @t67 @t2 @t43 @t53 @t23 @t69) (=> @t72 (=> @t75 (=> @t57 @t74))))) % 0.44/0.67 (assume @p25 (forall (@list @t2 @t43 @t53) (=> (= @t56 @t53) (or (exists @t76 (and @t60 @t59 @t55)) (exists (@list @t69 @t23 @t67 @t65) (and @t60 @t71 @t68 @t66)) (exists (@list @t65 @t67 @t23 @t69) (and @t60 @t71 @t75 @t74)))))) % 0.44/0.67 (assume @p26 (forall @t80 (=> (and @t68 @t79) (tptp.vtcheck @t78 @t21 @t39)))) % 0.44/0.67 (assume @p27 (forall @t80 (=> (and @t75 @t79) (tptp.vtcheck (tptp.vbind @t67 @t65 @t78) @t21 @t39)))) % 0.44/0.67 (assume @p28 (forall (@list @t33 @t21) (=> (= (tptp.vgensym @t21) @t33) (not @t37)))) % 0.44/0.67 (assume @p29 (forall (@list @t23 @t67 @t2 @t8 @t6 @t53 @t21) (=> @t86 (=> @t68 (=> @t82 @t54))))) % 0.44/0.67 (assume @p30 (forall (@list @t21 @t23 @t2 @t8 @t6 @t53 @t67) (=> @t86 (=> @t75 (=> @t82 @t87))))) % 0.44/0.67 (assume @p31 (forall (@list @t2 @t8 @t6 @t53 @t30 @t23 @t21 @t29) (=> (and @t60 @t85 @t90) (=> @t82 @t89)))) % 0.44/0.67 (assume @p32 (forall (@list @t21 @t23 @t2 @t8 @t6 @t53 @t67 @t39 @t30) (=> @t94 (=> @t68 (=> @t82 @t92))))) % 0.44/0.67 (assume @p33 (forall (@list @t2 @t8 @t6 @t53 @t23 @t21 @t39 @t67 @t95 @t30) (=> @t94 (=> (and @t75 @t98 @t97) (=> @t82 @t96))))) % 0.44/0.67 (assume @p34 (forall (@list @t2 @t8 @t6 @t53 @t67 @t39 @t23 @t21 @t30) (=> @t94 (=> (and @t75 @t100) (=> @t82 @t99))))) % 0.44/0.67 (assume @p35 (forall (@list @t2 @t8 @t6 @t53) (=> (= @t81 @t53) (or (exists (@list @t23 @t67 @t21) (and @t60 @t85 @t84 @t68 @t54)) (exists (@list @t21 @t23 @t67) (and @t60 @t85 @t84 @t75 @t87)) (exists (@list @t30 @t23 @t21 @t29) (and @t60 @t85 @t90 @t89)) (exists (@list @t21 @t23 @t67 @t39 @t30) (and @t60 @t85 @t93 @t68 @t92)) (exists (@list @t23 @t21 @t39 @t67 @t95 @t30) (and @t60 @t85 @t93 @t75 @t98 @t97 @t96)) (exists (@list @t67 @t39 @t23 @t21 @t30) (and @t60 @t85 @t93 @t75 @t100 @t99)))))) % 0.44/0.67 (assume @p36 (and (=> @t101 true) (=> true @t101))) % 0.44/0.67 (assume @p37 (forall (@list @t8 @t6) (and (=> @t103 @t12) (=> @t12 @t103)))) % 0.44/0.67 (assume @p38 (forall (@list @t8) (not (= tptp.vnoExp @t102)))) % 0.44/0.67 (assume @p39 (forall (@list @t104) (=> (= @t104 tptp.vnoExp) (not @t105)))) % 0.44/0.67 (assume @p40 (forall (@list @t21 @t104) (=> @t106 @t105))) % 0.44/0.67 (assume @p41 (forall (@list @t104 @t53 @t21) (=> @t106 (=> (= @t53 (tptp.vgetSomeExp @t104)) @t54)))) % 0.44/0.67 (assume @p42 (forall (@list @t23 @t8 @t53) (=> @t28 @t110))) % 0.44/0.67 (assume @p43 (forall (@list @t23 @t22 @t21 @t8 @t53) (=> @t25 @t110))) % 0.44/0.67 (assume @p44 (forall (@list @t29 @t8 @t53 @t23 @t22 @t30 @t111) (=> @t116 (=> (and @t115 @t114) (=> @t109 @t113))))) % 0.44/0.67 (assume @p45 (forall (@list @t22 @t111 @t8 @t53 @t23 @t29 @t30) (=> @t116 (=> (and @t115 @t119 @t118) (=> @t109 @t117))))) % 0.44/0.67 (assume @p46 (forall (@list @t23 @t22 @t30 @t111 @t29 @t8 @t53) (=> @t116 (=> (and @t115 @t119 @t120) @t110)))) % 0.44/0.67 (assume @p47 (forall (@list @t30 @t8 @t53 @t121 @t29) (=> @t129 (=> (and @t124 @t123) (=> @t109 @t122))))) % 0.44/0.67 (assume @p48 (forall (@list @t29 @t30 @t121 @t8 @t53) (=> @t129 (=> (and @t124 @t130) @t110)))) % 0.44/0.67 (assume @p49 (forall (@list @t8 @t53) (=> (= @t108 @t53) (or (exists @t76 (and @t28 @t107)) (exists (@list @t23 @t22 @t21) (and @t25 @t107)) (exists (@list @t29 @t23 @t22 @t30 @t111) (and @t116 @t115 @t114 @t113)) (exists (@list @t22 @t111 @t23 @t29 @t30) (and @t116 @t115 @t119 @t118 @t117)) (exists (@list @t23 @t22 @t30 @t111 @t29) (and @t116 @t115 @t119 @t120 @t107)) (exists (@list @t30 @t121 @t29) (and @t32 @t128 @t124 @t123 @t122)) (exists (@list @t29 @t30 @t121) (and @t32 @t128 @t124 @t130 @t107)))))) % 0.44/0.67 (assume @p50 (forall (@list @t9 @t7 @t132 @t131) (and (=> @t133 @t134) (=> @t134 @t133)))) % 0.44/0.67 (assume @p51 (forall (@list @t69 @t23 @t39) (=> @t135 (tptp.vtcheck @t69 @t27 @t39)))) % 0.44/0.67 (assume @p52 (forall (@list @t69 @t23 @t21 @t22 @t39) (=> @t137 (tptp.vtcheck @t69 @t24 @t136)))) % 0.44/0.67 (assume @p53 (forall (@list @t22 @t69 @t30 @t29 @t39) (=> @t140 (tptp.vtcheck @t69 @t31 @t39)))) % 0.44/0.67 (assume @p54 @t162) % 0.44/0.67 (assume @p55 (forall @t163 (=> (and (= @t73 tptp.vnoType) @t159) @t137))) % 0.44/0.67 (assume @p56 (forall @t163 (=> (and (not (tptp.visFreeVar @t23 @t21)) @t137) @t159))) % 0.44/0.67 (assume @p57 @t176) % 0.44/0.67 (assume @p58 true) % 0.44/0.67 (step @p59 :rule instantiate :premises (@p18) :args ((@list @t181))) % 0.44/0.67 (step @p60 :rule aci_norm :args ((= (or false @t183) @t183))) % 0.44/0.67 (step @p61 :rule refl :args (@t183)) % 0.44/0.67 (step @p62 :rule evaluate :args ((not true))) % 0.44/0.67 (step @p63 :rule eq-refl :args (@t182)) % 0.44/0.67 (step @p64 :rule cong :premises (@p63) :args (@t184)) % 0.44/0.67 (step @p65 :rule trans :premises (@p64 @p62)) % 0.44/0.67 (step @p66 :rule nary_cong :premises (@p65 @p61) :args (@t185)) % 0.44/0.67 (step @p67 :rule trans :premises (@p66 @p60)) % 0.44/0.67 (step @p68 :rule cong :premises (@p67) :args ((forall @t76 @t185))) % 0.44/0.67 (step @p69 :rule quant-var-elim-eq :args ((= (forall @t189 @t188) @t185))) % 0.44/0.67 (step @p70 :rule aci_norm :args ((= @t190 @t188))) % 0.44/0.67 (step @p71 :rule cong :premises (@p70) :args (@t191)) % 0.44/0.67 (step @p72 :rule trans :premises (@p71 @p69)) % 0.44/0.67 (step @p73 :rule cong :premises (@p72) :args (@t192)) % 0.44/0.67 (step @p74 :rule quant-merge-prenex :args ((= @t192 (forall @t193 @t190)))) % 0.44/0.67 (step @p75 :rule symm :premises (@p74)) % 0.44/0.67 (step @p76 :rule trans :premises (@p75 @p73)) % 0.44/0.67 (step @p77 :rule trans :premises (@p76 @p68)) % 0.44/0.67 (step @p78 :rule aci_norm :args ((= (or false @t187 @t186) @t190))) % 0.44/0.67 (step @p79 :rule refl :args (@t186)) % 0.44/0.67 (step @p80 :rule refl :args (@t187)) % 0.44/0.67 (step @p81 :rule eq-refl :args (tptp.vempty)) % 0.44/0.67 (step @p82 :rule cong :premises (@p81) :args (@t194)) % 0.44/0.67 (step @p83 :rule trans :premises (@p82 @p62)) % 0.44/0.67 (step @p84 :rule nary_cong :premises (@p83 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chain_m_resolution :premises (@p342 @p336) :args (@t311 @t280 (@list @t314))) % 0.44/0.67 (step @p344 :rule refl :args (@t321)) % 0.44/0.67 (step @p345 :rule bool-double-not-elim :args (@t322)) % 0.44/0.67 (step @p346 :rule refl :args (@t312)) % 0.44/0.67 (step @p347 :rule nary_cong :premises (@p346 @p345 @p344) :args ((or @t312 (not @t323) @t321))) % 0.44/0.67 (assume-push @p386 @t320) % 0.44/0.67 (assume-push @p387 @t311) % 0.44/0.67 (assume-push @p388 @t323) % 0.44/0.67 (step @p351 :rule evaluate :args ((= false true))) % 0.44/0.67 (step @p352 :rule symm :premises (@p387)) % 0.44/0.67 (step @p353 :rule trans :premises (@p144 @p352)) % 0.44/0.67 (step @p354 :rule true_intro :premises (@p353)) % 0.44/0.67 (step @p355 :rule false_intro :premises (@p59)) % 0.44/0.67 (step @p356 :rule symm :premises (@p355)) % 0.44/0.67 (step @p357 :rule trans :premises (@p356 @p354)) % 0.44/0.67 (step @p358 false :rule eq_resolve :premises (@p357 @p351)) % 0.44/0.67 (step-pop @p389 :rule scope :premises (@p358)) % 0.44/0.67 (step-pop @p390 :rule scope :premises (@p389)) % 0.44/0.67 (step-pop @p391 :rule scope :premises (@p390)) % 0.44/0.67 (step @p359 :rule process_scope :premises (@p391) :args (false)) % 0.44/0.67 (assume-push @p392 @t311) % 0.44/0.67 (assume-push @p393 @t323) % 0.44/0.67 (assume-push @p394 @t320) % 0.44/0.67 (step @p366 :rule and_intro :premises (@p144 @p392 @p59)) % 0.44/0.67 (step-pop @p395 :rule scope :premises (@p366)) % 0.44/0.67 (step-pop @p396 :rule scope :premises (@p395)) % 0.44/0.67 (step-pop @p397 :rule scope :premises (@p396)) % 0.44/0.67 (step @p367 :rule process_scope :premises (@p397) :args (@t324)) % 0.44/0.67 (step @p371 :rule implies_elim :premises (@p367)) % 0.44/0.67 (step @p372 :rule resolution :premises (@p371 @p359) :args (true @t324)) % 0.44/0.67 (step @p373 :rule not_and :premises (@p372)) % 0.44/0.67 (step @p374 :rule eq_resolve :premises (@p373 @p347)) % 0.44/0.67 (step @p375 false :rule chain_m_resolution :premises (@p374 @p343 @p144 @p59) :args (false (@list false false true) (@list @t311 @t320 @t322))) % 0.44/0.67 ) % 0.44/0.67 % SZS output end Proof % 0.44/0.67 % cvc5 exiting %------------------------------------------------------------------------------