%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : COM141+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 : n006.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 0.37s 0.68s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM141+1 : TPTP v9.2.1. Released v6.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n006.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 : Mon Jun 1 20:30:34 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.68 % SZS status Theorem % 0.37/0.68 % SZS output start Proof % 0.37/0.68 ( % 0.37/0.68 (declare-sort $$unsorted 0) % 0.37/0.68 (declare-const tptp.veabs $$unsorted) % 0.37/0.68 (declare-const tptp.varrow (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.vgetSomeExp (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.vsomeExp (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.vnoExp $$unsorted) % 0.37/0.68 (declare-const tptp.vsubst (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.vgensym (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.vapp (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.visValue (-> $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.vempty $$unsorted) % 0.37/0.68 (declare-const tptp.vbind (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.vnoType $$unsorted) % 0.37/0.68 (declare-const tptp.visFreeVar (-> $$unsorted $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.vtcheck (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.vsomeType (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.visSomeExp (-> $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.vvar (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.vlookup (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.vabs (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.visSomeType (-> $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.vreduce (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.vgetSomeType (-> $$unsorted $$unsorted)) % 0.37/0.68 (define @t1 () (@var "VVar1" $$unsorted)) % 0.37/0.68 (define @t2 () (@var "VVar0" $$unsorted)) % 0.37/0.68 (define @t3 () (tptp.vvar @t2)) % 0.37/0.68 (define @t4 () (= @t3 (tptp.vvar @t1))) % 0.37/0.68 (define @t5 () (= @t2 @t1)) % 0.37/0.68 (define @t6 () (@var "VExp1" $$unsorted)) % 0.37/0.68 (define @t7 () (@var "VTyp1" $$unsorted)) % 0.37/0.68 (define @t8 () (@var "VExp0" $$unsorted)) % 0.37/0.68 (define @t9 () (@var "VTyp0" $$unsorted)) % 0.37/0.68 (define @t10 () (tptp.vabs @t2 @t9 @t8)) % 0.37/0.68 (define @t11 () (= @t10 (tptp.vabs @t1 @t7 @t6))) % 0.37/0.68 (define @t12 () (= @t8 @t6)) % 0.37/0.68 (define @t13 () (= @t9 @t7)) % 0.37/0.68 (define @t14 () (and @t5 @t13 @t12)) % 0.37/0.68 (define @t15 () (@var "VExp3" $$unsorted)) % 0.37/0.68 (define @t16 () (@var "VExp2" $$unsorted)) % 0.37/0.68 (define @t17 () (tptp.vapp @t8 @t6)) % 0.37/0.68 (define @t18 () (= @t17 (tptp.vapp @t16 @t15))) % 0.37/0.68 (define @t19 () (and (= @t8 @t16) (= @t6 @t15))) % 0.37/0.68 (define @t20 () (tptp.visValue @t8)) % 0.37/0.68 (define @t21 () (@var "Ve" $$unsorted)) % 0.37/0.68 (define @t22 () (@var "VS" $$unsorted)) % 0.37/0.68 (define @t23 () (@var "Vx" $$unsorted)) % 0.37/0.68 (define @t24 () (tptp.vabs @t23 @t22 @t21)) % 0.37/0.68 (define @t25 () (= @t8 @t24)) % 0.37/0.68 (define @t26 () (not @t20)) % 0.37/0.68 (define @t27 () (tptp.vvar @t23)) % 0.37/0.68 (define @t28 () (= @t8 @t27)) % 0.37/0.68 (define @t29 () (@var "Ve2" $$unsorted)) % 0.37/0.68 (define @t30 () (@var "Ve1" $$unsorted)) % 0.37/0.68 (define @t31 () (tptp.vapp @t30 @t29)) % 0.37/0.68 (define @t32 () (= @t8 @t31)) % 0.37/0.68 (define @t33 () (@var "Vv" $$unsorted)) % 0.37/0.68 (define @t34 () (= @t23 @t33)) % 0.37/0.68 (define @t35 () (tptp.visFreeVar @t2 @t8)) % 0.37/0.68 (define @t36 () (= @t2 @t33)) % 0.37/0.68 (define @t37 () (tptp.visFreeVar @t33 @t21)) % 0.37/0.68 (define @t38 () (and (not @t34) @t37)) % 0.37/0.68 (define @t39 () (@var "VT" $$unsorted)) % 0.37/0.68 (define @t40 () (or (tptp.visFreeVar @t33 @t30) (tptp.visFreeVar @t33 @t29))) % 0.37/0.68 (define @t41 () (= tptp.vempty tptp.vempty)) % 0.37/0.68 (define @t42 () (@var "VCtx1" $$unsorted)) % 0.37/0.68 (define @t43 () (@var "VCtx0" $$unsorted)) % 0.37/0.68 (define @t44 () (tptp.vbind @t2 @t9 @t43)) % 0.37/0.68 (define @t45 () (= @t44 (tptp.vbind @t1 @t7 @t42))) % 0.37/0.68 (define @t46 () (and @t5 @t13 (= @t43 @t42))) % 0.37/0.68 (define @t47 () (= tptp.vnoType tptp.vnoType)) % 0.37/0.68 (define @t48 () (tptp.vsomeType @t9)) % 0.37/0.68 (define @t49 () (= @t48 (tptp.vsomeType @t7))) % 0.37/0.68 (define @t50 () (@var "VOptTyp0" $$unsorted)) % 0.37/0.68 (define @t51 () (tptp.visSomeType @t50)) % 0.37/0.68 (define @t52 () (= @t50 (tptp.vsomeType @t21))) % 0.37/0.68 (define @t53 () (@var "RESULT" $$unsorted)) % 0.37/0.68 (define @t54 () (= @t53 @t21)) % 0.37/0.68 (define @t55 () (= @t53 tptp.vnoType)) % 0.37/0.68 (define @t56 () (tptp.vlookup @t2 @t43)) % 0.37/0.68 (define @t57 () (= @t53 @t56)) % 0.37/0.68 (define @t58 () (= @t43 tptp.vempty)) % 0.37/0.68 (define @t59 () (= @t2 @t23)) % 0.37/0.68 (define @t60 () (@var "VTy" $$unsorted)) % 0.37/0.68 (define @t61 () (= @t53 (tptp.vsomeType @t60))) % 0.37/0.68 (define @t62 () (@var "Vy" $$unsorted)) % 0.37/0.68 (define @t63 () (= @t23 @t62)) % 0.37/0.68 (define @t64 () (@var "VC" $$unsorted)) % 0.37/0.68 (define @t65 () (tptp.vbind @t62 @t60 @t64)) % 0.37/0.68 (define @t66 () (= @t43 @t65)) % 0.37/0.68 (define @t67 () (and @t59 @t66)) % 0.37/0.68 (define @t68 () (tptp.vlookup @t23 @t64)) % 0.37/0.68 (define @t69 () (= @t53 @t68)) % 0.37/0.68 (define @t70 () (not @t63)) % 0.37/0.68 (define @t71 () (@list @t23)) % 0.37/0.68 (define @t72 () (@var "VTx" $$unsorted)) % 0.37/0.68 (define @t73 () (tptp.vbind @t23 @t72 @t64)) % 0.37/0.68 (define @t74 () (tptp.vtcheck (tptp.vbind @t23 @t72 @t65) @t21 @t39)) % 0.37/0.68 (define @t75 () (@list @t62 @t60 @t23 @t72 @t64 @t21 @t39)) % 0.37/0.68 (define @t76 () (tptp.vsubst @t2 @t8 @t6)) % 0.37/0.68 (define @t77 () (= @t53 @t76)) % 0.37/0.68 (define @t78 () (tptp.vvar @t62)) % 0.37/0.68 (define @t79 () (= @t6 @t78)) % 0.37/0.68 (define @t80 () (= @t8 @t21)) % 0.37/0.68 (define @t81 () (and @t59 @t80 @t79)) % 0.37/0.68 (define @t82 () (= @t53 @t78)) % 0.37/0.68 (define @t83 () (tptp.vsubst @t23 @t21 @t30)) % 0.37/0.68 (define @t84 () (= @t53 (tptp.vapp @t83 (tptp.vsubst @t23 @t21 @t29)))) % 0.37/0.68 (define @t85 () (= @t6 @t31)) % 0.37/0.68 (define @t86 () (tptp.vabs @t62 @t39 @t30)) % 0.37/0.68 (define @t87 () (= @t53 @t86)) % 0.37/0.68 (define @t88 () (= @t6 @t86)) % 0.37/0.68 (define @t89 () (and @t59 @t80 @t88)) % 0.37/0.68 (define @t90 () (@var "Vfresh" $$unsorted)) % 0.37/0.68 (define @t91 () (= @t53 (tptp.vsubst @t23 @t21 (tptp.vabs @t90 @t39 (tptp.vsubst @t62 (tptp.vvar @t90) @t30))))) % 0.37/0.68 (define @t92 () (= @t90 (tptp.vgensym (tptp.vapp (tptp.vapp @t21 @t30) @t27)))) % 0.37/0.68 (define @t93 () (tptp.visFreeVar @t62 @t21)) % 0.37/0.68 (define @t94 () (= @t53 (tptp.vabs @t62 @t39 @t83))) % 0.37/0.68 (define @t95 () (not @t93)) % 0.37/0.68 (define @t96 () (= tptp.vnoExp tptp.vnoExp)) % 0.37/0.68 (define @t97 () (tptp.vsomeExp @t8)) % 0.37/0.68 (define @t98 () (= @t97 (tptp.vsomeExp @t6))) % 0.37/0.68 (define @t99 () (@var "VOptExp0" $$unsorted)) % 0.37/0.68 (define @t100 () (tptp.visSomeExp @t99)) % 0.37/0.68 (define @t101 () (= @t99 (tptp.vsomeExp @t21))) % 0.37/0.68 (define @t102 () (= @t53 tptp.vnoExp)) % 0.37/0.68 (define @t103 () (tptp.vreduce @t8)) % 0.37/0.68 (define @t104 () (= @t53 @t103)) % 0.37/0.68 (define @t105 () (=> @t104 @t102)) % 0.37/0.68 (define @t106 () (@var "Ve2red" $$unsorted)) % 0.37/0.68 (define @t107 () (tptp.vabs @t23 @t22 @t30)) % 0.37/0.68 (define @t108 () (= @t53 (tptp.vsomeExp (tptp.vapp @t107 (tptp.vgetSomeExp @t106))))) % 0.37/0.68 (define @t109 () (tptp.visSomeExp @t106)) % 0.37/0.68 (define @t110 () (= @t106 (tptp.vreduce @t29))) % 0.37/0.68 (define @t111 () (= @t8 (tptp.vapp @t107 @t29))) % 0.37/0.68 (define @t112 () (= @t53 (tptp.vsomeExp (tptp.vsubst @t23 @t29 @t30)))) % 0.37/0.68 (define @t113 () (tptp.visValue @t29)) % 0.37/0.68 (define @t114 () (not @t109)) % 0.37/0.68 (define @t115 () (not @t113)) % 0.37/0.68 (define @t116 () (@var "Ve1red" $$unsorted)) % 0.37/0.68 (define @t117 () (= @t53 (tptp.vsomeExp (tptp.vapp (tptp.vgetSomeExp @t116) @t29)))) % 0.37/0.68 (define @t118 () (tptp.visSomeExp @t116)) % 0.37/0.68 (define @t119 () (= @t116 (tptp.vreduce @t30))) % 0.37/0.68 (define @t120 () (@var "VVe10" $$unsorted)) % 0.37/0.68 (define @t121 () (@var "VVS0" $$unsorted)) % 0.37/0.68 (define @t122 () (@var "VVx0" $$unsorted)) % 0.37/0.68 (define @t123 () (forall (@list @t122 @t121 @t120) (not (= @t30 (tptp.vabs @t122 @t121 @t120))))) % 0.37/0.68 (define @t124 () (and @t32 @t123)) % 0.37/0.68 (define @t125 () (not @t118)) % 0.37/0.68 (define @t126 () (@var "VTyp3" $$unsorted)) % 0.37/0.68 (define @t127 () (@var "VTyp2" $$unsorted)) % 0.37/0.68 (define @t128 () (= (tptp.varrow @t9 @t7) (tptp.varrow @t127 @t126))) % 0.37/0.68 (define @t129 () (and (= @t9 @t127) (= @t7 @t126))) % 0.37/0.68 (define @t130 () (= @t68 (tptp.vsomeType @t39))) % 0.37/0.68 (define @t131 () (tptp.varrow @t22 @t39)) % 0.37/0.68 (define @t132 () (tptp.vbind @t23 @t22 @t64)) % 0.37/0.68 (define @t133 () (tptp.vtcheck @t64 @t29 @t22)) % 0.37/0.68 (define @t134 () (tptp.vtcheck @t64 @t30 @t131)) % 0.37/0.68 (define @t135 () (@var "VT2" $$unsorted)) % 0.37/0.68 (define @t136 () (@var "VT1" $$unsorted)) % 0.37/0.68 (define @t137 () (= @t68 tptp.vnoType)) % 0.37/0.68 (define @t138 () (@var "VS1" $$unsorted)) % 0.37/0.68 (define @t139 () (tptp.vabs @t62 @t138 tptp.veabs)) % 0.37/0.68 (define @t140 () (tptp.vtcheck @t132 @t139 @t39)) % 0.37/0.68 (define @t141 () (tptp.vtcheck @t64 @t139 @t39)) % 0.37/0.68 (define @t142 () (and @t70 @t137 @t141)) % 0.37/0.68 (define @t143 () (=> @t142 @t140)) % 0.37/0.68 (define @t144 () (@list @t23 @t22 @t64 @t62 @t138 @t39)) % 0.37/0.68 (define @t145 () (forall @t144 @t143)) % 0.37/0.68 (define @t146 () (and @t63 @t137 @t141)) % 0.37/0.68 (define @t147 () (=> @t146 @t140)) % 0.37/0.68 (define @t148 () (forall @t144 @t147)) % 0.37/0.68 (define @t149 () (and @t137 @t141)) % 0.37/0.68 (define @t150 () (=> @t149 @t140)) % 0.37/0.68 (define @t151 () (forall @t144 @t150)) % 0.37/0.68 (define @t152 () (not @t151)) % 0.37/0.68 (define @t153 () (not @t141)) % 0.37/0.68 (define @t154 () (= tptp.vnoType @t68)) % 0.37/0.68 (define @t155 () (not @t154)) % 0.37/0.68 (define @t156 () (or @t155 @t153 @t140)) % 0.37/0.68 (define @t157 () (or @t155 @t153)) % 0.37/0.68 (define @t158 () (and @t154 @t141)) % 0.37/0.68 (define @t159 () (not @t158)) % 0.37/0.68 (define @t160 () (forall @t144 @t156)) % 0.37/0.68 (define @t161 () (@quantifiers_skolemize @t160 2)) % 0.37/0.68 (define @t162 () (@quantifiers_skolemize @t160 0)) % 0.37/0.68 (define @t163 () (= tptp.vnoType (tptp.vlookup @t162 @t161))) % 0.37/0.68 (define @t164 () (@quantifiers_skolemize @t160 5)) % 0.37/0.68 (define @t165 () (@quantifiers_skolemize @t160 4)) % 0.37/0.68 (define @t166 () (@quantifiers_skolemize @t160 3)) % 0.37/0.68 (define @t167 () (tptp.vabs @t166 @t165 tptp.veabs)) % 0.37/0.68 (define @t168 () (@quantifiers_skolemize @t160 1)) % 0.37/0.68 (define @t169 () (tptp.vbind @t162 @t168 @t161)) % 0.37/0.68 (define @t170 () (tptp.vtcheck @t169 @t167 @t164)) % 0.37/0.68 (define @t171 () (tptp.vtcheck @t161 @t167 @t164)) % 0.37/0.68 (define @t172 () (not @t171)) % 0.37/0.68 (define @t173 () (not @t163)) % 0.37/0.68 (define @t174 () (or @t173 @t172 @t170)) % 0.37/0.68 (define @t175 () (@list true)) % 0.37/0.68 (define @t176 () (@list @t174)) % 0.37/0.68 (define @t177 () (tptp.vtcheck (tptp.vbind @t62 @t22 @t64) @t139 @t39)) % 0.37/0.68 (define @t178 () (not (= tptp.vnoType (tptp.vlookup @t62 @t64)))) % 0.37/0.68 (define @t179 () (not (= @t62 @t62))) % 0.37/0.68 (define @t180 () (or @t179 @t178 @t153 @t177)) % 0.37/0.68 (define @t181 () (@list @t22 @t64 @t62 @t138 @t39)) % 0.37/0.68 (define @t182 () (or @t70 @t70 @t155 @t153 @t140)) % 0.37/0.68 (define @t183 () (or @t70 @t155 @t153 @t140)) % 0.37/0.68 (define @t184 () (forall @t71 @t183)) % 0.37/0.68 (define @t185 () (forall @t181 @t184)) % 0.37/0.68 (define @t186 () (forall (@list @t22 @t64 @t62 @t138 @t39 @t23) @t183)) % 0.37/0.68 (define @t187 () (or @t70 @t155 @t153)) % 0.37/0.68 (define @t188 () (and @t63 @t154 @t141)) % 0.37/0.68 (define @t189 () (not @t70)) % 0.37/0.68 (define @t190 () (or @t189 @t155 @t153)) % 0.37/0.68 (define @t191 () (and @t70 @t154 @t141)) % 0.37/0.68 (define @t192 () (= @t162 @t166)) % 0.37/0.68 (define @t193 () (or @t192 @t173 @t172 @t170)) % 0.37/0.68 (define @t194 () (tptp.vabs @t162 @t165 tptp.veabs)) % 0.37/0.68 (define @t195 () (tptp.vtcheck @t169 @t194 @t164)) % 0.37/0.68 (define @t196 () (tptp.vtcheck @t161 @t194 @t164)) % 0.37/0.68 (define @t197 () (not @t196)) % 0.37/0.68 (define @t198 () (or @t173 @t197 @t195)) % 0.37/0.68 (assume @p1 (forall (@list @t2 @t1) (and (=> @t4 @t5) (=> @t5 @t4)))) % 0.37/0.68 (assume @p2 (forall (@list @t2 @t9 @t8 @t1 @t7 @t6) (and (=> @t11 @t14) (=> @t14 @t11)))) % 0.37/0.68 (assume @p3 (forall (@list @t8 @t6 @t16 @t15) (and (=> @t18 @t19) (=> @t19 @t18)))) % 0.37/0.68 (assume @p4 (forall (@list @t2 @t1 @t9 @t8) (not (= @t3 (tptp.vabs @t1 @t9 @t8))))) % 0.37/0.68 (assume @p5 (forall (@list @t2 @t8 @t6) (not (= @t3 @t17)))) % 0.37/0.68 (assume @p6 (forall (@list @t2 @t9 @t8 @t6 @t16) (not (= @t10 (tptp.vapp @t6 @t16))))) % 0.37/0.68 (assume @p7 (forall (@list @t23 @t22 @t21 @t8) (=> @t25 @t20))) % 0.37/0.68 (assume @p8 (forall (@list @t23 @t8) (=> @t28 @t26))) % 0.37/0.68 (assume @p9 (forall (@list @t30 @t29 @t8) (=> @t32 @t26))) % 0.37/0.68 (assume @p10 (forall (@list @t2 @t8 @t23 @t33) (=> (and @t36 @t28) (and (=> @t34 @t35) (=> @t35 @t34))))) % 0.37/0.68 (assume @p11 (forall (@list @t39 @t2 @t8 @t23 @t33 @t21) (=> (and @t36 (= @t8 (tptp.vabs @t23 @t39 @t21))) (and (=> @t38 @t35) (=> @t35 @t38))))) % 0.37/0.68 (assume @p12 (forall (@list @t2 @t8 @t30 @t33 @t29) (=> (and @t36 @t32) (and (=> @t40 @t35) (=> @t35 @t40))))) % 0.37/0.68 (assume @p13 (and (=> @t41 true) (=> true @t41))) % 0.37/0.68 (assume @p14 (forall (@list @t2 @t9 @t43 @t1 @t7 @t42) (and (=> @t45 @t46) (=> @t46 @t45)))) % 0.37/0.68 (assume @p15 (and (=> @t47 true) (=> true @t47))) % 0.37/0.68 (assume @p16 (forall (@list @t9 @t7) (and (=> @t49 @t13) (=> @t13 @t49)))) % 0.37/0.68 (assume @p17 (forall (@list @t2 @t9 @t43) (not (= tptp.vempty @t44)))) % 0.37/0.68 (assume @p18 (forall (@list @t9) (not (= tptp.vnoType @t48)))) % 0.37/0.68 (assume @p19 (forall (@list @t50) (=> (= @t50 tptp.vnoType) (not @t51)))) % 0.37/0.68 (assume @p20 (forall (@list @t21 @t50) (=> @t52 @t51))) % 0.37/0.68 (assume @p21 (forall (@list @t50 @t53 @t21) (=> @t52 (=> (= @t53 (tptp.vgetSomeType @t50)) @t54)))) % 0.37/0.68 (assume @p22 (forall (@list @t23 @t2 @t43 @t53) (=> (and @t59 @t58) (=> @t57 @t55)))) % 0.37/0.68 (assume @p23 (forall (@list @t64 @t23 @t62 @t2 @t43 @t53 @t60) (=> @t67 (=> @t63 (=> @t57 @t61))))) % 0.37/0.68 (assume @p24 (forall (@list @t60 @t62 @t2 @t43 @t53 @t23 @t64) (=> @t67 (=> @t70 (=> @t57 @t69))))) % 0.37/0.68 (assume @p25 (forall (@list @t2 @t43 @t53) (=> (= @t56 @t53) (or (exists @t71 (and @t59 @t58 @t55)) (exists (@list @t64 @t23 @t62 @t60) (and @t59 @t66 @t63 @t61)) (exists (@list @t60 @t62 @t23 @t64) (and @t59 @t66 @t70 @t69)))))) % 0.37/0.68 (assume @p26 (forall @t75 (=> (and @t63 @t74) (tptp.vtcheck @t73 @t21 @t39)))) % 0.37/0.68 (assume @p27 (forall @t75 (=> (and @t70 @t74) (tptp.vtcheck (tptp.vbind @t62 @t60 @t73) @t21 @t39)))) % 0.37/0.68 (assume @p28 (forall (@list @t33 @t21) (=> (= (tptp.vgensym @t21) @t33) (not @t37)))) % 0.37/0.68 (assume @p29 (forall (@list @t23 @t62 @t2 @t8 @t6 @t53 @t21) (=> @t81 (=> @t63 (=> @t77 @t54))))) % 0.37/0.68 (assume @p30 (forall (@list @t21 @t23 @t2 @t8 @t6 @t53 @t62) (=> @t81 (=> @t70 (=> @t77 @t82))))) % 0.37/0.68 (assume @p31 (forall (@list @t2 @t8 @t6 @t53 @t30 @t23 @t21 @t29) (=> (and @t59 @t80 @t85) (=> @t77 @t84)))) % 0.37/0.68 (assume @p32 (forall (@list @t21 @t23 @t2 @t8 @t6 @t53 @t62 @t39 @t30) (=> @t89 (=> @t63 (=> @t77 @t87))))) % 0.37/0.68 (assume @p33 (forall (@list @t2 @t8 @t6 @t53 @t23 @t21 @t39 @t62 @t90 @t30) (=> @t89 (=> (and @t70 @t93 @t92) (=> @t77 @t91))))) % 0.37/0.68 (assume @p34 (forall (@list @t2 @t8 @t6 @t53 @t62 @t39 @t23 @t21 @t30) (=> @t89 (=> (and @t70 @t95) (=> @t77 @t94))))) % 0.37/0.68 (assume @p35 (forall (@list @t2 @t8 @t6 @t53) (=> (= @t76 @t53) (or (exists (@list @t23 @t62 @t21) (and @t59 @t80 @t79 @t63 @t54)) (exists (@list @t21 @t23 @t62) (and @t59 @t80 @t79 @t70 @t82)) (exists (@list @t30 @t23 @t21 @t29) (and @t59 @t80 @t85 @t84)) (exists (@list @t21 @t23 @t62 @t39 @t30) (and @t59 @t80 @t88 @t63 @t87)) (exists (@list @t23 @t21 @t39 @t62 @t90 @t30) (and @t59 @t80 @t88 @t70 @t93 @t92 @t91)) (exists (@list @t62 @t39 @t23 @t21 @t30) (and @t59 @t80 @t88 @t70 @t95 @t94)))))) % 0.37/0.68 (assume @p36 (and (=> @t96 true) (=> true @t96))) % 0.37/0.68 (assume @p37 (forall (@list @t8 @t6) (and (=> @t98 @t12) (=> @t12 @t98)))) % 0.37/0.68 (assume @p38 (forall (@list @t8) (not (= tptp.vnoExp @t97)))) % 0.37/0.68 (assume @p39 (forall (@list @t99) (=> (= @t99 tptp.vnoExp) (not @t100)))) % 0.37/0.68 (assume @p40 (forall (@list @t21 @t99) (=> @t101 @t100))) % 0.37/0.68 (assume @p41 (forall (@list @t99 @t53 @t21) (=> @t101 (=> (= @t53 (tptp.vgetSomeExp @t99)) @t54)))) % 0.37/0.68 (assume @p42 (forall (@list @t23 @t8 @t53) (=> @t28 @t105))) % 0.37/0.68 (assume @p43 (forall (@list @t23 @t22 @t21 @t8 @t53) (=> @t25 @t105))) % 0.37/0.68 (assume @p44 (forall (@list @t29 @t8 @t53 @t23 @t22 @t30 @t106) (=> @t111 (=> (and @t110 @t109) (=> @t104 @t108))))) % 0.37/0.68 (assume @p45 (forall (@list @t22 @t106 @t8 @t53 @t23 @t29 @t30) (=> @t111 (=> (and @t110 @t114 @t113) (=> @t104 @t112))))) % 0.37/0.68 (assume @p46 (forall (@list @t23 @t22 @t30 @t106 @t29 @t8 @t53) (=> @t111 (=> (and @t110 @t114 @t115) @t105)))) % 0.37/0.68 (assume @p47 (forall (@list @t30 @t8 @t53 @t116 @t29) (=> @t124 (=> (and @t119 @t118) (=> @t104 @t117))))) % 0.37/0.68 (assume @p48 (forall (@list @t29 @t30 @t116 @t8 @t53) (=> @t124 (=> (and @t119 @t125) @t105)))) % 0.37/0.68 (assume @p49 (forall (@list @t8 @t53) (=> (= @t103 @t53) (or (exists @t71 (and @t28 @t102)) (exists (@list @t23 @t22 @t21) (and @t25 @t102)) (exists (@list @t29 @t23 @t22 @t30 @t106) (and @t111 @t110 @t109 @t108)) (exists (@list @t22 @t106 @t23 @t29 @t30) (and @t111 @t110 @t114 @t113 @t112)) (exists (@list @t23 @t22 @t30 @t106 @t29) (and @t111 @t110 @t114 @t115 @t102)) (exists (@list @t30 @t116 @t29) (and @t32 @t123 @t119 @t118 @t117)) (exists (@list @t29 @t30 @t116) (and @t32 @t123 @t119 @t125 @t102)))))) % 0.37/0.68 (assume @p50 (forall (@list @t9 @t7 @t127 @t126) (and (=> @t128 @t129) (=> @t129 @t128)))) % 0.37/0.68 (assume @p51 (forall (@list @t64 @t23 @t39) (=> @t130 (tptp.vtcheck @t64 @t27 @t39)))) % 0.37/0.68 (assume @p52 (forall (@list @t64 @t23 @t21 @t22 @t39) (=> (tptp.vtcheck @t132 @t21 @t39) (tptp.vtcheck @t64 @t24 @t131)))) % 0.37/0.68 (assume @p53 (forall (@list @t22 @t64 @t30 @t29 @t39) (=> (and @t134 @t133) (tptp.vtcheck @t64 @t31 @t39)))) % 0.37/0.68 (assume @p54 (forall (@list @t21 @t39 @t64) (=> (tptp.vtcheck @t64 @t21 @t39) (or (exists @t71 (and (= @t21 @t27) @t130)) (exists (@list @t23 @t29 @t136 @t135) (and (= @t21 (tptp.vabs @t23 @t136 @t29)) (= @t39 (tptp.varrow @t136 @t135)) (tptp.vtcheck (tptp.vbind @t23 @t136 @t64) @t29 @t135))) (exists (@list @t30 @t29 @t22) (and (= @t21 @t31) @t134 @t133)))))) % 0.37/0.68 (assume @p55 (forall (@list @t23 @t22 @t64 @t39) (=> (and @t137 (tptp.vtcheck @t64 tptp.veabs @t39)) (tptp.vtcheck @t132 tptp.veabs @t39)))) % 0.37/0.68 (assume @p56 @t145) % 0.37/0.68 (assume @p57 @t148) % 0.37/0.68 (assume @p58 @t152) % 0.37/0.68 (assume @p59 true) % 0.37/0.68 (step @p60 :rule aci_norm :args ((= (or @t157 @t140) @t156))) % 0.37/0.68 (step @p61 :rule refl :args (@t140)) % 0.37/0.68 (step @p62 :rule bool-and-de-morgan :args (@t154 @t141 true)) % 0.37/0.68 (step @p63 :rule nary_cong :premises (@p62 @p61) :args ((or @t159 @t140))) % 0.37/0.68 (step @p64 :rule trans :premises (@p63 @p60)) % 0.37/0.68 (step @p65 :rule bool-impl-elim :args (@t158 @t140)) % 0.37/0.68 (step @p66 :rule trans :premises (@p65 @p64)) % 0.37/0.68 (step @p67 :rule cong :premises (@p66) :args ((forall @t144 (=> @t158 @t140)))) % 0.37/0.68 (step @p68 :rule refl :args (@t140)) % 0.37/0.68 (step @p69 :rule refl :args (@t141)) % 0.37/0.68 (step @p70 :rule eq-symm :args (@t68 tptp.vnoType)) % 0.37/0.68 (step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t149)) % 0.37/0.68 (step @p72 :rule cong :premises (@p71 @p68) :args (@t150)) % 0.37/0.68 (step @p73 :rule cong :premises (@p72) :args (@t151)) % 0.37/0.68 (step @p74 :rule trans :premises (@p73 @p67)) % 0.37/0.68 (step @p75 :rule cong :premises (@p74) :args (@t152)) % 0.37/0.68 (step @p76 :rule eq_resolve :premises (@p58 @p75)) % 0.37/0.68 (step @p77 :rule skolemize :premises (@p76)) % 0.37/0.68 (step @p78 :rule bool-double-not-elim :args (@t163)) % 0.37/0.68 (step @p79 :rule refl :args (@t174)) % 0.37/0.68 (step @p80 :rule nary_cong :premises (@p79 @p78) :args ((or @t174 (not @t173)))) % 0.37/0.68 (step @p81 :rule cnf_or_neg :args (@t174 0)) % 0.37/0.68 (step @p82 :rule eq_resolve :premises (@p81 @p80)) % 0.37/0.68 (step @p83 :rule reordering :premises (@p82) :args ((or @t163 @t174))) % 0.37/0.68 (step @p84 :rule chain_m_resolution :premises (@p83 @p77) :args (@t163 @t175 @t176)) % 0.37/0.68 (step @p85 :rule aci_norm :args ((= (or false @t178 @t153 @t177) (or @t178 @t153 @t177)))) % 0.37/0.68 (step @p86 :rule refl :args (@t177)) % 0.37/0.68 (step @p87 :rule refl :args (@t153)) % 0.37/0.68 (step @p88 :rule refl :args (@t178)) % 0.37/0.68 (step @p89 :rule evaluate :args ((not true))) % 0.37/0.68 (step @p90 :rule eq-refl :args (@t62)) % 0.37/0.68 (step @p91 :rule cong :premises (@p90) :args (@t179)) % 0.37/0.68 (step @p92 :rule trans :premises (@p91 @p89)) % 0.37/0.68 (step @p93 :rule nary_cong :premises (@p92 @p88 @p87 @p86) :args (@t180)) % 0.37/0.68 (step @p94 :rule trans :premises (@p93 @p85)) % 0.37/0.68 (step @p95 :rule cong :premises (@p94) :args ((forall @t181 @t180))) % 0.37/0.68 (step @p96 :rule quant-var-elim-eq :args ((= (forall @t71 @t182) @t180))) % 0.37/0.68 (step @p97 :rule aci_norm :args ((= @t183 @t182))) % 0.37/0.68 (step @p98 :rule cong :premises (@p97) :args (@t184)) % 0.37/0.68 (step @p99 :rule trans :premises (@p98 @p96)) % 0.37/0.68 (step @p100 :rule cong :premises (@p99) :args (@t185)) % 0.37/0.68 (step @p101 :rule quant-merge-prenex :args ((= @t185 @t186))) % 0.37/0.68 (step @p102 :rule symm :premises (@p101)) % 0.37/0.68 (step @p103 :rule quant_var_reordering :args ((= (forall @t144 @t183) @t186))) % 0.37/0.68 (step @p104 :rule trans :premises (@p103 @p102 @p100)) % 0.37/0.68 (step @p105 :rule trans :premises (@p104 @p95)) % 0.37/0.68 (step @p106 :rule aci_norm :args ((= (or @t187 @t140) @t183))) % 0.37/0.68 (step @p107 :rule aci_norm :args ((= (or @t70 @t157) @t187))) % 0.37/0.68 (step @p108 :rule refl :args (@t70)) % 0.37/0.68 (step @p109 :rule nary_cong :premises (@p108 @p62) :args ((or @t70 @t159))) % 0.37/0.68 (step @p110 :rule bool-and-de-morgan :args (@t63 @t154 (and @t141))) % 0.37/0.68 (step @p111 :rule trans :premises (@p110 @p109)) % 0.37/0.68 (step @p112 :rule trans :premises (@p111 @p107)) % 0.37/0.68 (step @p113 :rule nary_cong :premises (@p112 @p61) :args ((or (not @t188) @t140))) % 0.37/0.68 (step @p114 :rule trans :premises (@p113 @p106)) % 0.37/0.68 (step @p115 :rule bool-impl-elim :args (@t188 @t140)) % 0.37/0.68 (step @p116 :rule trans :premises (@p115 @p114)) % 0.37/0.68 (step @p117 :rule cong :premises (@p116) :args ((forall @t144 (=> @t188 @t140)))) % 0.37/0.68 (step @p118 :rule trans :premises (@p117 @p105)) % 0.37/0.68 (step @p119 :rule refl :args (@t63)) % 0.37/0.68 (step @p120 :rule nary_cong :premises (@p119 @p70 @p69) :args (@t146)) % 0.37/0.68 (step @p121 :rule cong :premises (@p120 @p68) :args (@t147)) % 0.37/0.68 (step @p122 :rule cong :premises (@p121) :args (@t148)) % 0.37/0.68 (step @p123 :rule trans :premises (@p122 @p118)) % 0.37/0.68 (step @p124 :rule eq_resolve :premises (@p57 @p123)) % 0.37/0.68 (step @p125 :rule instantiate :premises (@p124) :args ((@list @t168 @t161 @t162 @t165 @t164))) % 0.37/0.68 (step @p126 :rule cnf_or_neg :args (@t174 2)) % 0.37/0.68 (step @p127 :rule chain_m_resolution :premises (@p126 @p77) :args ((not @t170) @t175 @t176)) % 0.37/0.68 (step @p128 :rule false_intro :premises (@p127)) % 0.37/0.68 (step @p129 :rule refl :args (@t164)) % 0.37/0.68 (step @p130 :rule refl :args (tptp.veabs)) % 0.37/0.68 (step @p131 :rule refl :args (@t165)) % 0.37/0.68 (step @p132 :rule aci_norm :args ((= (or (or @t63 @t155 @t153) @t140) (or @t63 @t155 @t153 @t140)))) % 0.37/0.68 (step @p133 :rule refl :args (@t153)) % 0.37/0.68 (step @p134 :rule refl :args (@t155)) % 0.37/0.68 (step @p135 :rule bool-double-not-elim :args (@t63)) % 0.37/0.68 (step @p136 :rule nary_cong :premises (@p135 @p134 @p133) :args (@t190)) % 0.37/0.68 (step @p137 :rule aci_norm :args ((= (or @t189 @t157) @t190))) % 0.37/0.68 (step @p138 :rule trans :premises (@p137 @p136)) % 0.37/0.68 (step @p139 :rule refl :args (@t189)) % 0.37/0.68 (step @p140 :rule nary_cong :premises (@p139 @p62) :args ((or @t189 @t159))) % 0.37/0.68 (step @p141 :rule bool-and-de-morgan :args (@t70 @t154 (and @t141))) % 0.37/0.68 (step @p142 :rule trans :premises (@p141 @p140)) % 0.37/0.68 (step @p143 :rule trans :premises (@p142 @p138)) % 0.37/0.68 (step @p144 :rule nary_cong :premises (@p143 @p61) :args ((or (not @t191) @t140))) % 0.37/0.68 (step @p145 :rule trans :premises (@p144 @p132)) % 0.37/0.68 (step @p146 :rule bool-impl-elim :args (@t191 @t140)) % 0.37/0.68 (step @p147 :rule trans :premises (@p146 @p145)) % 0.37/0.68 (step @p148 :rule cong :premises (@p147) :args ((forall @t144 (=> @t191 @t140)))) % 0.37/0.68 (step @p149 :rule refl :args (@t70)) % 0.37/0.68 (step @p150 :rule nary_cong :premises (@p149 @p70 @p69) :args (@t142)) % 0.37/0.68 (step @p151 :rule cong :premises (@p150 @p68) :args (@t143)) % 0.37/0.68 (step @p152 :rule cong :premises (@p151) :args (@t145)) % 0.37/0.68 (step @p153 :rule trans :premises (@p152 @p148)) % 0.37/0.68 (step @p154 :rule eq_resolve :premises (@p56 @p153)) % 0.37/0.68 (step @p155 :rule instantiate :premises (@p154) :args ((@list @t162 @t168 @t161 @t166 @t165 @t164))) % 0.37/0.68 (step @p156 :rule bool-double-not-elim :args (@t171)) % 0.37/0.68 (step @p157 :rule nary_cong :premises (@p79 @p156) :args ((or @t174 (not @t172)))) % 0.37/0.68 (step @p158 :rule cnf_or_neg :args (@t174 1)) % 0.37/0.68 (step @p159 :rule eq_resolve :premises (@p158 @p157)) % 0.37/0.68 (step @p160 :rule reordering :premises (@p159) :args ((or @t171 @t174))) % 0.37/0.68 (step @p161 :rule chain_m_resolution :premises (@p160 @p77) :args (@t171 @t175 @t176)) % 0.37/0.68 (step @p162 :rule cnf_or_pos :args (@t193)) % 0.37/0.68 (step @p163 :rule reordering :premises (@p162) :args ((or @t173 @t172 @t170 @t192 (not @t193)))) % 0.37/0.68 (step @p164 :rule chain_m_resolution :premises (@p163 @p84 @p161 @p127 @p155) :args (@t192 (@list false false true false) (@list @t163 @t171 @t170 @t193))) % 0.37/0.68 (step @p165 :rule cong :premises (@p164 @p131 @p130) :args (@t194)) % 0.37/0.68 (step @p166 :rule refl :args (@t169)) % 0.37/0.68 (step @p167 :rule cong :premises (@p166 @p165 @p129) :args (@t195)) % 0.37/0.68 (step @p168 :rule trans :premises (@p167 @p128)) % 0.37/0.68 (step @p169 :rule false_elim :premises (@p168)) % 0.37/0.68 (step @p170 :rule true_intro :premises (@p161)) % 0.37/0.68 (step @p171 :rule refl :args (@t161)) % 0.37/0.68 (step @p172 :rule cong :premises (@p171 @p165 @p129) :args (@t196)) % 0.37/0.68 (step @p173 :rule trans :premises (@p172 @p170)) % 0.37/0.68 (step @p174 :rule true_elim :premises (@p173)) % 0.37/0.68 (step @p175 :rule cnf_or_pos :args (@t198)) % 0.37/0.68 (step @p176 :rule reordering :premises (@p175) :args ((or @t173 @t197 @t195 (not @t198)))) % 0.37/0.68 (step @p177 false :rule chain_m_resolution :premises (@p176 @p174 @p169 @p125 @p84) :args (false (@list false true false false) (@list @t196 @t195 @t198 @t163))) % 0.37/0.68 ) % 0.37/0.68 % SZS output end Proof % 0.37/0.68 % cvc5 exiting %------------------------------------------------------------------------------