%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : COM147+1 : TPTP v9.2.1. Released v6.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n005.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 0.63s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM147+1 : TPTP v9.2.1. Released v6.4.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n005.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 20:30:33 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.63 % SZS status Theorem % 0.44/0.63 % SZS output start Proof % 0.44/0.63 ( % 0.44/0.63 (declare-sort $$unsorted 0) % 0.44/0.63 (declare-const tptp.varrow (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.vgetSomeExp (-> $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.vsomeExp (-> $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.vnoExp $$unsorted) % 0.44/0.63 (declare-const tptp.ve1 $$unsorted) % 0.44/0.63 (declare-const tptp.vsubst (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.vgensym (-> $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.vapp (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.visValue (-> $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.vempty $$unsorted) % 0.44/0.63 (declare-const tptp.vbind (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.vnoType $$unsorted) % 0.44/0.63 (declare-const tptp.visFreeVar (-> $$unsorted $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.vtcheck (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.vsomeType (-> $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.visSomeExp (-> $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.vvar (-> $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.vlookup (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.vabs (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.visSomeType (-> $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.vreduce (-> $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.vgetSomeType (-> $$unsorted $$unsorted)) % 0.44/0.63 (define @t1 () (@var "VVar1" $$unsorted)) % 0.44/0.63 (define @t2 () (@var "VVar0" $$unsorted)) % 0.44/0.63 (define @t3 () (tptp.vvar @t2)) % 0.44/0.63 (define @t4 () (= @t3 (tptp.vvar @t1))) % 0.44/0.63 (define @t5 () (= @t2 @t1)) % 0.44/0.63 (define @t6 () (@var "VExp1" $$unsorted)) % 0.44/0.63 (define @t7 () (@var "VTyp1" $$unsorted)) % 0.44/0.63 (define @t8 () (@var "VExp0" $$unsorted)) % 0.44/0.63 (define @t9 () (@var "VTyp0" $$unsorted)) % 0.44/0.63 (define @t10 () (tptp.vabs @t2 @t9 @t8)) % 0.44/0.63 (define @t11 () (= @t10 (tptp.vabs @t1 @t7 @t6))) % 0.44/0.63 (define @t12 () (= @t8 @t6)) % 0.44/0.63 (define @t13 () (= @t9 @t7)) % 0.44/0.63 (define @t14 () (and @t5 @t13 @t12)) % 0.44/0.63 (define @t15 () (@var "VExp3" $$unsorted)) % 0.44/0.63 (define @t16 () (@var "VExp2" $$unsorted)) % 0.44/0.63 (define @t17 () (tptp.vapp @t8 @t6)) % 0.44/0.63 (define @t18 () (= @t17 (tptp.vapp @t16 @t15))) % 0.44/0.63 (define @t19 () (and (= @t8 @t16) (= @t6 @t15))) % 0.44/0.63 (define @t20 () (tptp.visValue @t8)) % 0.44/0.63 (define @t21 () (@var "Ve" $$unsorted)) % 0.44/0.63 (define @t22 () (@var "VS" $$unsorted)) % 0.44/0.63 (define @t23 () (@var "Vx" $$unsorted)) % 0.44/0.63 (define @t24 () (tptp.vabs @t23 @t22 @t21)) % 0.44/0.63 (define @t25 () (= @t8 @t24)) % 0.44/0.63 (define @t26 () (@list @t23 @t22 @t21 @t8)) % 0.44/0.63 (define @t27 () (forall @t26 (=> @t25 @t20))) % 0.44/0.63 (define @t28 () (not @t20)) % 0.44/0.63 (define @t29 () (tptp.vvar @t23)) % 0.44/0.63 (define @t30 () (= @t8 @t29)) % 0.44/0.63 (define @t31 () (@var "Ve2" $$unsorted)) % 0.44/0.63 (define @t32 () (@var "Ve1" $$unsorted)) % 0.44/0.63 (define @t33 () (tptp.vapp @t32 @t31)) % 0.44/0.63 (define @t34 () (= @t8 @t33)) % 0.44/0.63 (define @t35 () (@var "Vv" $$unsorted)) % 0.44/0.63 (define @t36 () (= @t23 @t35)) % 0.44/0.63 (define @t37 () (tptp.visFreeVar @t2 @t8)) % 0.44/0.63 (define @t38 () (= @t2 @t35)) % 0.44/0.63 (define @t39 () (tptp.visFreeVar @t35 @t21)) % 0.44/0.63 (define @t40 () (and (not @t36) @t39)) % 0.44/0.63 (define @t41 () (@var "VT" $$unsorted)) % 0.44/0.63 (define @t42 () (or (tptp.visFreeVar @t35 @t32) (tptp.visFreeVar @t35 @t31))) % 0.44/0.63 (define @t43 () (= tptp.vempty tptp.vempty)) % 0.44/0.63 (define @t44 () (@var "VCtx1" $$unsorted)) % 0.44/0.63 (define @t45 () (@var "VCtx0" $$unsorted)) % 0.44/0.63 (define @t46 () (tptp.vbind @t2 @t9 @t45)) % 0.44/0.63 (define @t47 () (= @t46 (tptp.vbind @t1 @t7 @t44))) % 0.44/0.63 (define @t48 () (and @t5 @t13 (= @t45 @t44))) % 0.44/0.63 (define @t49 () (= tptp.vnoType tptp.vnoType)) % 0.44/0.63 (define @t50 () (tptp.vsomeType @t9)) % 0.44/0.63 (define @t51 () (= @t50 (tptp.vsomeType @t7))) % 0.44/0.63 (define @t52 () (@var "VOptTyp0" $$unsorted)) % 0.44/0.63 (define @t53 () (tptp.visSomeType @t52)) % 0.44/0.63 (define @t54 () (= @t52 (tptp.vsomeType @t21))) % 0.44/0.63 (define @t55 () (@var "RESULT" $$unsorted)) % 0.44/0.63 (define @t56 () (= @t55 @t21)) % 0.44/0.63 (define @t57 () (= @t55 tptp.vnoType)) % 0.44/0.63 (define @t58 () (tptp.vlookup @t2 @t45)) % 0.44/0.63 (define @t59 () (= @t55 @t58)) % 0.44/0.63 (define @t60 () (= @t45 tptp.vempty)) % 0.44/0.63 (define @t61 () (= @t2 @t23)) % 0.44/0.63 (define @t62 () (@var "VTy" $$unsorted)) % 0.44/0.63 (define @t63 () (= @t55 (tptp.vsomeType @t62))) % 0.44/0.63 (define @t64 () (@var "Vy" $$unsorted)) % 0.44/0.63 (define @t65 () (= @t23 @t64)) % 0.44/0.63 (define @t66 () (@var "VC" $$unsorted)) % 0.44/0.63 (define @t67 () (tptp.vbind @t64 @t62 @t66)) % 0.44/0.63 (define @t68 () (= @t45 @t67)) % 0.44/0.63 (define @t69 () (and @t61 @t68)) % 0.44/0.63 (define @t70 () (tptp.vlookup @t23 @t66)) % 0.44/0.63 (define @t71 () (= @t55 @t70)) % 0.44/0.63 (define @t72 () (not @t65)) % 0.44/0.63 (define @t73 () (@list @t23)) % 0.44/0.63 (define @t74 () (@var "VTx" $$unsorted)) % 0.44/0.63 (define @t75 () (tptp.vbind @t23 @t74 @t66)) % 0.44/0.63 (define @t76 () (tptp.vtcheck (tptp.vbind @t23 @t74 @t67) @t21 @t41)) % 0.44/0.63 (define @t77 () (@list @t64 @t62 @t23 @t74 @t66 @t21 @t41)) % 0.44/0.63 (define @t78 () (tptp.vsubst @t2 @t8 @t6)) % 0.44/0.63 (define @t79 () (= @t55 @t78)) % 0.44/0.63 (define @t80 () (tptp.vvar @t64)) % 0.44/0.63 (define @t81 () (= @t6 @t80)) % 0.44/0.63 (define @t82 () (= @t8 @t21)) % 0.44/0.63 (define @t83 () (and @t61 @t82 @t81)) % 0.44/0.63 (define @t84 () (= @t55 @t80)) % 0.44/0.63 (define @t85 () (tptp.vsubst @t23 @t21 @t32)) % 0.44/0.63 (define @t86 () (= @t55 (tptp.vapp @t85 (tptp.vsubst @t23 @t21 @t31)))) % 0.44/0.63 (define @t87 () (= @t6 @t33)) % 0.44/0.63 (define @t88 () (tptp.vabs @t64 @t41 @t32)) % 0.44/0.63 (define @t89 () (= @t55 @t88)) % 0.44/0.63 (define @t90 () (= @t6 @t88)) % 0.44/0.63 (define @t91 () (and @t61 @t82 @t90)) % 0.44/0.63 (define @t92 () (@var "Vfresh" $$unsorted)) % 0.44/0.63 (define @t93 () (= @t55 (tptp.vsubst @t23 @t21 (tptp.vabs @t92 @t41 (tptp.vsubst @t64 (tptp.vvar @t92) @t32))))) % 0.44/0.63 (define @t94 () (= @t92 (tptp.vgensym (tptp.vapp (tptp.vapp @t21 @t32) @t29)))) % 0.44/0.63 (define @t95 () (tptp.visFreeVar @t64 @t21)) % 0.44/0.63 (define @t96 () (= @t55 (tptp.vabs @t64 @t41 @t85))) % 0.44/0.63 (define @t97 () (not @t95)) % 0.44/0.63 (define @t98 () (= tptp.vnoExp tptp.vnoExp)) % 0.44/0.63 (define @t99 () (tptp.vsomeExp @t8)) % 0.44/0.63 (define @t100 () (= @t99 (tptp.vsomeExp @t6))) % 0.44/0.63 (define @t101 () (@list @t8)) % 0.44/0.63 (define @t102 () (@var "VOptExp0" $$unsorted)) % 0.44/0.63 (define @t103 () (tptp.visSomeExp @t102)) % 0.44/0.63 (define @t104 () (= @t102 (tptp.vsomeExp @t21))) % 0.44/0.63 (define @t105 () (= @t55 tptp.vnoExp)) % 0.44/0.63 (define @t106 () (tptp.vreduce @t8)) % 0.44/0.63 (define @t107 () (= @t55 @t106)) % 0.44/0.63 (define @t108 () (=> @t107 @t105)) % 0.44/0.63 (define @t109 () (@var "Ve2red" $$unsorted)) % 0.44/0.63 (define @t110 () (tptp.vabs @t23 @t22 @t32)) % 0.44/0.63 (define @t111 () (= @t55 (tptp.vsomeExp (tptp.vapp @t110 (tptp.vgetSomeExp @t109))))) % 0.44/0.63 (define @t112 () (tptp.visSomeExp @t109)) % 0.44/0.63 (define @t113 () (= @t109 (tptp.vreduce @t31))) % 0.44/0.63 (define @t114 () (= @t8 (tptp.vapp @t110 @t31))) % 0.44/0.63 (define @t115 () (= @t55 (tptp.vsomeExp (tptp.vsubst @t23 @t31 @t32)))) % 0.44/0.63 (define @t116 () (tptp.visValue @t31)) % 0.44/0.63 (define @t117 () (not @t112)) % 0.44/0.63 (define @t118 () (not @t116)) % 0.44/0.63 (define @t119 () (@var "Ve1red" $$unsorted)) % 0.44/0.63 (define @t120 () (= @t55 (tptp.vsomeExp (tptp.vapp (tptp.vgetSomeExp @t119) @t31)))) % 0.44/0.63 (define @t121 () (tptp.visSomeExp @t119)) % 0.44/0.63 (define @t122 () (= @t119 (tptp.vreduce @t32))) % 0.44/0.63 (define @t123 () (@var "VVe10" $$unsorted)) % 0.44/0.63 (define @t124 () (@var "VVS0" $$unsorted)) % 0.44/0.63 (define @t125 () (@var "VVx0" $$unsorted)) % 0.44/0.63 (define @t126 () (forall (@list @t125 @t124 @t123) (not (= @t32 (tptp.vabs @t125 @t124 @t123))))) % 0.44/0.63 (define @t127 () (and @t34 @t126)) % 0.44/0.63 (define @t128 () (not @t121)) % 0.44/0.63 (define @t129 () (@list @t23 @t22 @t21)) % 0.44/0.63 (define @t130 () (@var "VTyp3" $$unsorted)) % 0.44/0.63 (define @t131 () (@var "VTyp2" $$unsorted)) % 0.44/0.63 (define @t132 () (= (tptp.varrow @t9 @t7) (tptp.varrow @t131 @t130))) % 0.44/0.63 (define @t133 () (and (= @t9 @t131) (= @t7 @t130))) % 0.44/0.63 (define @t134 () (= @t70 (tptp.vsomeType @t41))) % 0.44/0.63 (define @t135 () (tptp.varrow @t22 @t41)) % 0.44/0.63 (define @t136 () (tptp.vtcheck (tptp.vbind @t23 @t22 @t66) @t21 @t41)) % 0.44/0.63 (define @t137 () (tptp.vtcheck @t66 @t31 @t22)) % 0.44/0.63 (define @t138 () (tptp.vtcheck @t66 @t32 @t135)) % 0.44/0.63 (define @t139 () (@var "VT2" $$unsorted)) % 0.44/0.63 (define @t140 () (@var "VT1" $$unsorted)) % 0.44/0.63 (define @t141 () (tptp.vtcheck @t66 @t21 @t41)) % 0.44/0.63 (define @t142 () (@list @t23 @t22 @t66 @t21 @t41)) % 0.44/0.63 (define @t143 () (@var "Veout" $$unsorted)) % 0.44/0.63 (define @t144 () (tptp.vsomeExp @t143)) % 0.44/0.63 (define @t145 () (@list @t143)) % 0.44/0.63 (define @t146 () (tptp.vabs @t23 @t22 tptp.ve1)) % 0.44/0.63 (define @t147 () (tptp.vreduce @t146)) % 0.44/0.63 (define @t148 () (exists @t145 (= @t147 @t144))) % 0.44/0.63 (define @t149 () (tptp.visValue @t146)) % 0.44/0.63 (define @t150 () (not @t149)) % 0.44/0.63 (define @t151 () (@var "VTin" $$unsorted)) % 0.44/0.63 (define @t152 () (tptp.vtcheck tptp.vempty @t146 @t151)) % 0.44/0.63 (define @t153 () (and @t152 @t150)) % 0.44/0.63 (define @t154 () (=> @t153 @t148)) % 0.44/0.63 (define @t155 () (@list @t151 @t23 @t22)) % 0.44/0.63 (define @t156 () (forall @t155 @t154)) % 0.44/0.63 (define @t157 () (not @t156)) % 0.44/0.63 (define @t158 () (tptp.visValue @t24)) % 0.44/0.63 (define @t159 () (not (= @t24 @t24))) % 0.44/0.63 (define @t160 () (or @t159 @t158)) % 0.44/0.63 (define @t161 () (not @t25)) % 0.44/0.63 (define @t162 () (or @t161 @t161 @t20)) % 0.44/0.63 (define @t163 () (or @t161 @t20)) % 0.44/0.63 (define @t164 () (forall @t101 @t163)) % 0.44/0.63 (define @t165 () (forall @t129 @t164)) % 0.44/0.63 (define @t166 () (= @t144 @t147)) % 0.44/0.63 (define @t167 () (not (forall @t145 (not @t166)))) % 0.44/0.63 (define @t168 () (not @t152)) % 0.44/0.63 (define @t169 () (or @t168 @t149 @t167)) % 0.44/0.63 (define @t170 () (forall @t155 @t169)) % 0.44/0.63 (define @t171 () (@quantifiers_skolemize @t170 2)) % 0.44/0.63 (define @t172 () (@quantifiers_skolemize @t170 1)) % 0.44/0.63 (define @t173 () (tptp.vabs @t172 @t171 tptp.ve1)) % 0.44/0.63 (define @t174 () (tptp.visValue @t173)) % 0.44/0.63 (define @t175 () (or (not (tptp.vtcheck tptp.vempty @t173 (@quantifiers_skolemize @t170 0))) @t174 (not (forall @t145 (not (= @t144 (tptp.vreduce @t173))))))) % 0.44/0.63 (define @t176 () (forall @t129 @t158)) % 0.44/0.63 (assume @p1 (forall (@list @t2 @t1) (and (=> @t4 @t5) (=> @t5 @t4)))) % 0.44/0.63 (assume @p2 (forall (@list @t2 @t9 @t8 @t1 @t7 @t6) (and (=> @t11 @t14) (=> @t14 @t11)))) % 0.44/0.63 (assume @p3 (forall (@list @t8 @t6 @t16 @t15) (and (=> @t18 @t19) (=> @t19 @t18)))) % 0.44/0.63 (assume @p4 (forall (@list @t2 @t1 @t9 @t8) (not (= @t3 (tptp.vabs @t1 @t9 @t8))))) % 0.44/0.63 (assume @p5 (forall (@list @t2 @t8 @t6) (not (= @t3 @t17)))) % 0.44/0.63 (assume @p6 (forall (@list @t2 @t9 @t8 @t6 @t16) (not (= @t10 (tptp.vapp @t6 @t16))))) % 0.44/0.63 (assume @p7 @t27) % 0.44/0.63 (assume @p8 (forall (@list @t23 @t8) (=> @t30 @t28))) % 0.44/0.63 (assume @p9 (forall (@list @t32 @t31 @t8) (=> @t34 @t28))) % 0.44/0.63 (assume @p10 (forall (@list @t2 @t8 @t23 @t35) (=> (and @t38 @t30) (and (=> @t36 @t37) (=> @t37 @t36))))) % 0.44/0.63 (assume @p11 (forall (@list @t41 @t2 @t8 @t23 @t35 @t21) (=> (and @t38 (= @t8 (tptp.vabs @t23 @t41 @t21))) (and (=> @t40 @t37) (=> @t37 @t40))))) % 0.44/0.63 (assume @p12 (forall (@list @t2 @t8 @t32 @t35 @t31) (=> (and @t38 @t34) (and (=> @t42 @t37) (=> @t37 @t42))))) % 0.44/0.63 (assume @p13 (and (=> @t43 true) (=> true @t43))) % 0.44/0.63 (assume @p14 (forall (@list @t2 @t9 @t45 @t1 @t7 @t44) (and (=> @t47 @t48) (=> @t48 @t47)))) % 0.44/0.63 (assume @p15 (and (=> @t49 true) (=> true @t49))) % 0.44/0.63 (assume @p16 (forall (@list @t9 @t7) (and (=> @t51 @t13) (=> @t13 @t51)))) % 0.44/0.63 (assume @p17 (forall (@list @t2 @t9 @t45) (not (= tptp.vempty @t46)))) % 0.44/0.63 (assume @p18 (forall (@list @t9) (not (= tptp.vnoType @t50)))) % 0.44/0.63 (assume @p19 (forall (@list @t52) (=> (= @t52 tptp.vnoType) (not @t53)))) % 0.44/0.63 (assume @p20 (forall (@list @t21 @t52) (=> @t54 @t53))) % 0.44/0.63 (assume @p21 (forall (@list @t52 @t55 @t21) (=> @t54 (=> (= @t55 (tptp.vgetSomeType @t52)) @t56)))) % 0.44/0.63 (assume @p22 (forall (@list @t23 @t2 @t45 @t55) (=> (and @t61 @t60) (=> @t59 @t57)))) % 0.44/0.63 (assume @p23 (forall (@list @t66 @t23 @t64 @t2 @t45 @t55 @t62) (=> @t69 (=> @t65 (=> @t59 @t63))))) % 0.44/0.63 (assume @p24 (forall (@list @t62 @t64 @t2 @t45 @t55 @t23 @t66) (=> @t69 (=> @t72 (=> @t59 @t71))))) % 0.44/0.63 (assume @p25 (forall (@list @t2 @t45 @t55) (=> (= @t58 @t55) (or (exists @t73 (and @t61 @t60 @t57)) (exists (@list @t66 @t23 @t64 @t62) (and @t61 @t68 @t65 @t63)) (exists (@list @t62 @t64 @t23 @t66) (and @t61 @t68 @t72 @t71)))))) % 0.44/0.63 (assume @p26 (forall @t77 (=> (and @t65 @t76) (tptp.vtcheck @t75 @t21 @t41)))) % 0.44/0.63 (assume @p27 (forall @t77 (=> (and @t72 @t76) (tptp.vtcheck (tptp.vbind @t64 @t62 @t75) @t21 @t41)))) % 0.44/0.63 (assume @p28 (forall (@list @t35 @t21) (=> (= (tptp.vgensym @t21) @t35) (not @t39)))) % 0.44/0.63 (assume @p29 (forall (@list @t23 @t64 @t2 @t8 @t6 @t55 @t21) (=> @t83 (=> @t65 (=> @t79 @t56))))) % 0.44/0.63 (assume @p30 (forall (@list @t21 @t23 @t2 @t8 @t6 @t55 @t64) (=> @t83 (=> @t72 (=> @t79 @t84))))) % 0.44/0.63 (assume @p31 (forall (@list @t2 @t8 @t6 @t55 @t32 @t23 @t21 @t31) (=> (and @t61 @t82 @t87) (=> @t79 @t86)))) % 0.44/0.63 (assume @p32 (forall (@list @t21 @t23 @t2 @t8 @t6 @t55 @t64 @t41 @t32) (=> @t91 (=> @t65 (=> @t79 @t89))))) % 0.44/0.63 (assume @p33 (forall (@list @t2 @t8 @t6 @t55 @t23 @t21 @t41 @t64 @t92 @t32) (=> @t91 (=> (and @t72 @t95 @t94) (=> @t79 @t93))))) % 0.44/0.63 (assume @p34 (forall (@list @t2 @t8 @t6 @t55 @t64 @t41 @t23 @t21 @t32) (=> @t91 (=> (and @t72 @t97) (=> @t79 @t96))))) % 0.44/0.63 (assume @p35 (forall (@list @t2 @t8 @t6 @t55) (=> (= @t78 @t55) (or (exists (@list @t23 @t64 @t21) (and @t61 @t82 @t81 @t65 @t56)) (exists (@list @t21 @t23 @t64) (and @t61 @t82 @t81 @t72 @t84)) (exists (@list @t32 @t23 @t21 @t31) (and @t61 @t82 @t87 @t86)) (exists (@list @t21 @t23 @t64 @t41 @t32) (and @t61 @t82 @t90 @t65 @t89)) (exists (@list @t23 @t21 @t41 @t64 @t92 @t32) (and @t61 @t82 @t90 @t72 @t95 @t94 @t93)) (exists (@list @t64 @t41 @t23 @t21 @t32) (and @t61 @t82 @t90 @t72 @t97 @t96)))))) % 0.44/0.63 (assume @p36 (and (=> @t98 true) (=> true @t98))) % 0.44/0.63 (assume @p37 (forall (@list @t8 @t6) (and (=> @t100 @t12) (=> @t12 @t100)))) % 0.44/0.63 (assume @p38 (forall @t101 (not (= tptp.vnoExp @t99)))) % 0.44/0.63 (assume @p39 (forall (@list @t102) (=> (= @t102 tptp.vnoExp) (not @t103)))) % 0.44/0.63 (assume @p40 (forall (@list @t21 @t102) (=> @t104 @t103))) % 0.44/0.63 (assume @p41 (forall (@list @t102 @t55 @t21) (=> @t104 (=> (= @t55 (tptp.vgetSomeExp @t102)) @t56)))) % 0.44/0.63 (assume @p42 (forall (@list @t23 @t8 @t55) (=> @t30 @t108))) % 0.44/0.63 (assume @p43 (forall (@list @t23 @t22 @t21 @t8 @t55) (=> @t25 @t108))) % 0.44/0.63 (assume @p44 (forall (@list @t31 @t8 @t55 @t23 @t22 @t32 @t109) (=> @t114 (=> (and @t113 @t112) (=> @t107 @t111))))) % 0.44/0.63 (assume @p45 (forall (@list @t22 @t109 @t8 @t55 @t23 @t31 @t32) (=> @t114 (=> (and @t113 @t117 @t116) (=> @t107 @t115))))) % 0.44/0.63 (assume @p46 (forall (@list @t23 @t22 @t32 @t109 @t31 @t8 @t55) (=> @t114 (=> (and @t113 @t117 @t118) @t108)))) % 0.44/0.63 (assume @p47 (forall (@list @t32 @t8 @t55 @t119 @t31) (=> @t127 (=> (and @t122 @t121) (=> @t107 @t120))))) % 0.44/0.63 (assume @p48 (forall (@list @t31 @t32 @t119 @t8 @t55) (=> @t127 (=> (and @t122 @t128) @t108)))) % 0.44/0.63 (assume @p49 (forall (@list @t8 @t55) (=> (= @t106 @t55) (or (exists @t73 (and @t30 @t105)) (exists @t129 (and @t25 @t105)) (exists (@list @t31 @t23 @t22 @t32 @t109) (and @t114 @t113 @t112 @t111)) (exists (@list @t22 @t109 @t23 @t31 @t32) (and @t114 @t113 @t117 @t116 @t115)) (exists (@list @t23 @t22 @t32 @t109 @t31) (and @t114 @t113 @t117 @t118 @t105)) (exists (@list @t32 @t119 @t31) (and @t34 @t126 @t122 @t121 @t120)) (exists (@list @t31 @t32 @t119) (and @t34 @t126 @t122 @t128 @t105)))))) % 0.44/0.63 (assume @p50 (forall (@list @t9 @t7 @t131 @t130) (and (=> @t132 @t133) (=> @t133 @t132)))) % 0.44/0.63 (assume @p51 (forall (@list @t66 @t23 @t41) (=> @t134 (tptp.vtcheck @t66 @t29 @t41)))) % 0.44/0.63 (assume @p52 (forall (@list @t66 @t23 @t21 @t22 @t41) (=> @t136 (tptp.vtcheck @t66 @t24 @t135)))) % 0.44/0.63 (assume @p53 (forall (@list @t22 @t66 @t32 @t31 @t41) (=> (and @t138 @t137) (tptp.vtcheck @t66 @t33 @t41)))) % 0.44/0.63 (assume @p54 (forall (@list @t21 @t41 @t66) (=> @t141 (or (exists @t73 (and (= @t21 @t29) @t134)) (exists (@list @t23 @t31 @t140 @t139) (and (= @t21 (tptp.vabs @t23 @t140 @t31)) (= @t41 (tptp.varrow @t140 @t139)) (tptp.vtcheck (tptp.vbind @t23 @t140 @t66) @t31 @t139))) (exists (@list @t32 @t31 @t22) (and (= @t21 @t33) @t138 @t137)))))) % 0.44/0.63 (assume @p55 (forall @t142 (=> (and (= @t70 tptp.vnoType) @t141) @t136))) % 0.44/0.63 (assume @p56 (forall @t142 (=> (and (not (tptp.visFreeVar @t23 @t21)) @t136) @t141))) % 0.44/0.63 (assume @p57 (forall (@list @t41) (=> (and (tptp.vtcheck tptp.vempty tptp.ve1 @t41) (not (tptp.visValue tptp.ve1))) (exists @t145 (= (tptp.vreduce tptp.ve1) @t144))))) % 0.44/0.63 (assume @p58 @t157) % 0.44/0.63 (assume @p59 true) % 0.44/0.63 (step @p60 :rule aci_norm :args ((= (or false @t158) @t158))) % 0.44/0.63 (step @p61 :rule refl :args (@t158)) % 0.44/0.63 (step @p62 :rule evaluate :args ((not true))) % 0.44/0.63 (step @p63 :rule eq-refl :args (@t24)) % 0.44/0.63 (step @p64 :rule cong :premises (@p63) :args (@t159)) % 0.44/0.63 (step @p65 :rule trans :premises (@p64 @p62)) % 0.44/0.63 (step @p66 :rule nary_cong :premises (@p65 @p61) :args (@t160)) % 0.44/0.63 (step @p67 :rule trans :premises (@p66 @p60)) % 0.44/0.63 (step @p68 :rule cong :premises (@p67) :args ((forall @t129 @t160))) % 0.44/0.63 (step @p69 :rule quant-var-elim-eq :args ((= (forall @t101 @t162) @t160))) % 0.44/0.63 (step @p70 :rule aci_norm :args ((= @t163 @t162))) % 0.44/0.63 (step @p71 :rule cong :premises (@p70) :args (@t164)) % 0.44/0.63 (step @p72 :rule trans :premises (@p71 @p69)) % 0.44/0.63 (step @p73 :rule cong :premises (@p72) :args (@t165)) % 0.44/0.63 (step @p74 :rule quant-merge-prenex :args ((= @t165 (forall @t26 @t163)))) % 0.44/0.63 (step @p75 :rule symm :premises (@p74)) % 0.44/0.63 (step @p76 :rule trans :premises (@p75 @p73)) % 0.44/0.63 (step @p77 :rule trans :premises (@p76 @p68)) % 0.44/0.63 (step @p78 :rule bool-impl-elim :args (@t25 @t20)) % 0.44/0.63 (step @p79 :rule cong :premises (@p78) :args (@t27)) % 0.44/0.63 (step @p80 :rule trans :premises (@p79 @p77)) % 0.44/0.63 (step @p81 :rule eq_resolve :premises (@p7 @p80)) % 0.44/0.63 (step @p82 :rule aci_norm :args ((= (or (or @t168 @t149) @t167) @t169))) % 0.44/0.63 (step @p83 :rule refl :args (@t167)) % 0.44/0.63 (step @p84 :rule bool-double-not-elim :args (@t149)) % 0.44/0.63 (step @p85 :rule refl :args (@t168)) % 0.44/0.63 (step @p86 :rule nary_cong :premises (@p85 @p84) :args ((or @t168 (not @t150)))) % 0.44/0.63 (step @p87 :rule bool-and-de-morgan :args (@t152 @t150 true)) % 0.44/0.63 (step @p88 :rule trans :premises (@p87 @p86)) % 0.44/0.63 (step @p89 :rule nary_cong :premises (@p88 @p83) :args ((or (not @t153) @t167))) % 0.44/0.63 (step @p90 :rule trans :premises (@p89 @p82)) % 0.44/0.63 (step @p91 :rule bool-impl-elim :args (@t153 @t167)) % 0.44/0.63 (step @p92 :rule trans :premises (@p91 @p90)) % 0.44/0.63 (step @p93 :rule cong :premises (@p92) :args ((forall @t155 (=> @t153 @t167)))) % 0.44/0.63 (step @p94 :rule exists-elim :args ((= (exists @t145 @t166) @t167))) % 0.44/0.63 (step @p95 :rule eq-symm :args (@t147 @t144)) % 0.44/0.63 (step @p96 :rule cong :premises (@p95) :args (@t148)) % 0.44/0.63 (step @p97 :rule trans :premises (@p96 @p94)) % 0.44/0.63 (step @p98 :rule refl :args (@t153)) % 0.44/0.63 (step @p99 :rule cong :premises (@p98 @p97) :args (@t154)) % 0.44/0.63 (step @p100 :rule cong :premises (@p99) :args (@t156)) % 0.44/0.63 (step @p101 :rule trans :premises (@p100 @p93)) % 0.44/0.63 (step @p102 :rule cong :premises (@p101) :args (@t157)) % 0.44/0.63 (step @p103 :rule eq_resolve :premises (@p58 @p102)) % 0.44/0.63 (step @p104 :rule skolemize :premises (@p103)) % 0.44/0.63 (step @p105 :rule cnf_or_neg :args (@t175 1)) % 0.44/0.63 (step @p106 :rule chain_m_resolution :premises (@p105 @p104) :args ((not @t174) (@list true) (@list @t175))) % 0.44/0.63 (assume-push @p113 @t176) % 0.44/0.63 (step @p108 :rule instantiate :premises (@p81) :args ((@list @t172 @t171 tptp.ve1))) % 0.44/0.63 (step-pop @p114 :rule scope :premises (@p108)) % 0.44/0.63 (step @p109 :rule process_scope :premises (@p114) :args (@t174)) % 0.44/0.63 (step @p111 :rule implies_elim :premises (@p109)) % 0.44/0.63 (step @p112 false :rule chain_m_resolution :premises (@p111 @p106 @p81) :args (false (@list true false) (@list @t174 @t176))) % 0.44/0.63 ) % 0.44/0.63 % SZS output end Proof % 0.44/0.64 % cvc5 exiting %------------------------------------------------------------------------------