%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL947^10 : TPTP v9.3.1. Released v8.1.0. % 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 : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:24:13 AM UTC 2026 % Result : Theorem 0.52s 0.88s % Output : Proof 0.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL947^10 : TPTP v9.3.1. Released v8.1.0. % 0.00/0.05 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.12/0.38 % Computer : n005.cluster.edu % 0.12/0.38 % Model : x86_64 x86_64 % 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.38 % Memory : 8046.5625MB % 0.12/0.38 % OS : Linux 6.8.0-71-generic % 0.12/0.38 % CPULimit : 300 % 0.12/0.38 % WCLimit : 300 % 0.12/0.38 % DateTime : Sat Sep 5 21:22:35 UTC 2026 % 0.12/0.38 % CPUTime : % 0.23/0.48 %----Proving TH0 % 0.52/0.88 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.52/0.88 % SZS status Theorem % 0.52/0.88 % SZS output start Proof % 0.52/0.88 ( % 0.52/0.88 (declare-sort $$unsorted 0) % 0.52/0.88 (declare-sort tptp.mworld 0) % 0.52/0.88 (declare-const tptp.mactual tptp.mworld) % 0.52/0.88 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.52/0.88 (declare-const tptp.eiw_di (-> $$unsorted tptp.mworld Bool)) % 0.52/0.88 (declare-const tptp.member (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.52/0.88 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.52/0.88 (declare-const tptp.subset (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.52/0.88 (declare-const tptp.qmltpeq (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.52/0.88 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.52/0.88 (define tptp.mnot () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.52/0.88 (define tptp.mand () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.52/0.88 (define tptp.mor () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.52/0.88 (define tptp.mimplies () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.52/0.88 (define tptp.mequiv () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.52/0.88 (define tptp.mbox () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.52/0.88 (define tptp.mdia () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (exists (@list _let_1) (and (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.52/0.88 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.52/0.88 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (and (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.52/0.88 (define @t1 () (@var "W" tptp.mworld)) % 0.52/0.88 (define @t2 () (_ tptp.mrel @t1)) % 0.52/0.88 (define @t3 () (_ @t2 @t1)) % 0.52/0.88 (define @t4 () (@list @t1)) % 0.52/0.88 (define @t5 () (forall @t4 @t3)) % 0.52/0.88 (define @t6 () (@var "U" tptp.mworld)) % 0.52/0.88 (define @t7 () (@var "V" tptp.mworld)) % 0.52/0.88 (define @t8 () (_ @t2 @t7)) % 0.52/0.88 (define @t9 () (@var "X" $$unsorted)) % 0.52/0.88 (define @t10 () (_ (_ tptp.eiw_di @t9) @t1)) % 0.52/0.88 (define @t11 () (@list @t9)) % 0.52/0.88 (define @t12 () (@var "__flatten_var_0" tptp.mworld)) % 0.52/0.88 (define @t13 () (_ tptp.qmltpeq @t9)) % 0.52/0.88 (define @t14 () (@list @t9 @t12)) % 0.52/0.88 (define @t15 () (@var "Y" $$unsorted)) % 0.52/0.88 (define @t16 () (_ tptp.qmltpeq @t15)) % 0.52/0.88 (define @t17 () (_ tptp.mbox (_ @t13 @t15))) % 0.52/0.88 (define @t18 () (@list @t15 @t12)) % 0.52/0.88 (define @t19 () (@var "Z" $$unsorted)) % 0.52/0.88 (define @t20 () (@var "C" $$unsorted)) % 0.52/0.88 (define @t21 () (@var "B" $$unsorted)) % 0.52/0.88 (define @t22 () (_ tptp.union @t21)) % 0.52/0.88 (define @t23 () (_ @t22 @t20)) % 0.52/0.88 (define @t24 () (@var "A" $$unsorted)) % 0.52/0.88 (define @t25 () (_ tptp.mbox (_ (_ tptp.qmltpeq @t24) @t21))) % 0.52/0.88 (define @t26 () (_ tptp.mimplies @t25)) % 0.52/0.88 (define @t27 () (@list @t20 @t12)) % 0.52/0.88 (define @t28 () (@list @t21 @t12)) % 0.52/0.88 (define @t29 () (@list @t24 @t12)) % 0.52/0.88 (define @t30 () (_ tptp.union @t20)) % 0.52/0.88 (define @t31 () (_ @t30 @t21)) % 0.52/0.88 (define @t32 () (_ tptp.mand @t25)) % 0.52/0.88 (define @t33 () (_ tptp.member @t20)) % 0.52/0.88 (define @t34 () (_ tptp.subset @t21)) % 0.52/0.88 (define @t35 () (_ @t34 @t20)) % 0.52/0.88 (define @t36 () (_ tptp.mbox @t35)) % 0.52/0.88 (define @t37 () (_ tptp.subset @t20)) % 0.52/0.88 (define @t38 () (_ tptp.mbox (_ @t37 @t21))) % 0.52/0.88 (define @t39 () (_ tptp.qmltpeq @t23)) % 0.52/0.88 (define @t40 () (_ @t39 @t20)) % 0.52/0.88 (define @t41 () (_ tptp.mimplies @t36)) % 0.52/0.88 (define @t42 () (lambda @t27 (_ (_ tptp.mbox (_ @t41 (_ tptp.mbox @t40))) @t12))) % 0.52/0.88 (define @t43 () (lambda @t28 (_ (_ tptp.mbox (_ tptp.mforall_di @t42)) @t12))) % 0.52/0.88 (define @t44 () (@var "D" $$unsorted)) % 0.52/0.88 (define @t45 () (_ tptp.member @t44)) % 0.52/0.88 (define @t46 () (_ tptp.mbox (_ @t45 @t23))) % 0.52/0.88 (define @t47 () (_ tptp.mbox (_ @t45 @t20))) % 0.52/0.88 (define @t48 () (_ tptp.mbox (_ @t45 @t21))) % 0.52/0.88 (define @t49 () (_ (_ tptp.mor @t48) @t47)) % 0.52/0.88 (define @t50 () (@list @t44 @t12)) % 0.52/0.88 (define @t51 () (_ tptp.mbox (_ (_ tptp.qmltpeq @t21) @t20))) % 0.52/0.88 (define @t52 () (_ (_ tptp.mand @t36) @t38)) % 0.52/0.88 (define @t53 () (_ tptp.mimplies @t51)) % 0.52/0.88 (define @t54 () (_ tptp.mbox (_ (_ tptp.mimplies @t48) @t47))) % 0.52/0.88 (define @t55 () (_ tptp.mbox (_ tptp.mforall_di (lambda @t50 (_ @t54 @t12))))) % 0.52/0.88 (define @t56 () (_ @t34 @t21)) % 0.52/0.88 (define @t57 () (lambda @t28 (_ (_ tptp.mbox @t56) @t12))) % 0.52/0.88 (define @t58 () (_ tptp.mbox (_ tptp.mforall_di (lambda @t50 (_ (_ (_ tptp.mand @t54) (_ tptp.mbox (_ (_ tptp.mimplies @t47) @t48))) @t12))))) % 0.52/0.88 (define @t59 () (_ @t22 @t21)) % 0.52/0.88 (define @t60 () (_ (_ tptp.qmltpeq @t59) @t21)) % 0.52/0.88 (define @t61 () (lambda @t28 (_ (_ tptp.mbox @t60) @t12))) % 0.52/0.88 (define @t62 () (not (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di @t61))))) % 0.52/0.88 (define @t63 () (@var "Phi" (-> tptp.mworld Bool))) % 0.52/0.88 (define @t64 () (lambda (@list @t63) (_ @t63 tptp.mactual))) % 0.52/0.88 (define @t65 () (@var "A" (-> tptp.mworld Bool))) % 0.52/0.88 (define @t66 () (_ @t65 @t1)) % 0.52/0.88 (define @t67 () (lambda (@list @t65 @t1) (not @t66))) % 0.52/0.88 (define @t68 () (@var "B" (-> tptp.mworld Bool))) % 0.52/0.88 (define @t69 () (_ @t68 @t1)) % 0.52/0.88 (define @t70 () (@list @t65 @t68 @t1)) % 0.52/0.88 (define @t71 () (lambda @t70 (and @t66 @t69))) % 0.52/0.88 (define @t72 () (lambda @t70 (or @t66 @t69))) % 0.52/0.88 (define @t73 () (lambda @t70 (=> @t66 @t69))) % 0.52/0.88 (define @t74 () (lambda @t70 (= @t66 @t69))) % 0.52/0.88 (define @t75 () (_ @t63 @t7)) % 0.52/0.88 (define @t76 () (@list @t7)) % 0.52/0.88 (define @t77 () (forall @t76 (=> @t8 @t75))) % 0.52/0.88 (define @t78 () (@list @t63 @t1)) % 0.52/0.88 (define @t79 () (lambda @t78 @t77)) % 0.52/0.88 (define @t80 () (lambda @t78 (exists @t76 (and @t8 @t75)))) % 0.52/0.88 (define @t81 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.52/0.88 (define @t82 () (_ (_ @t81 @t9) @t1)) % 0.52/0.88 (define @t83 () (forall @t11 (=> @t10 @t82))) % 0.52/0.88 (define @t84 () (@list @t81 @t1)) % 0.52/0.88 (define @t85 () (lambda @t84 @t83)) % 0.52/0.88 (define @t86 () (lambda @t84 (exists @t11 (and @t10 @t82)))) % 0.52/0.88 (define @t87 () (@var "BOUND_VARIABLE_13865" tptp.mworld)) % 0.52/0.88 (define @t88 () (@var "BOUND_VARIABLE_13863" $$unsorted)) % 0.52/0.88 (define @t89 () (tptp.subset @t88 @t88 @t87)) % 0.52/0.88 (define @t90 () (not (tptp.mrel @t7 @t87))) % 0.52/0.88 (define @t91 () (not (tptp.eiw_di @t88 @t7))) % 0.52/0.88 (define @t92 () (not (tptp.mrel tptp.mactual @t7))) % 0.52/0.88 (define @t93 () (@list @t7 @t88 @t87)) % 0.52/0.88 (define @t94 () (forall @t93 (or @t92 @t91 @t90 @t89))) % 0.52/0.88 (define @t95 () (tptp.mrel @t1 @t7)) % 0.52/0.88 (define @t96 () (not @t95)) % 0.52/0.88 (define @t97 () (or @t96 @t91 @t90 @t89)) % 0.52/0.88 (define @t98 () (lambda @t4 (forall @t93 @t97))) % 0.52/0.88 (define @t99 () (_ @t98 tptp.mactual)) % 0.52/0.88 (define @t100 () (or @t91 @t90 @t89)) % 0.52/0.88 (define @t101 () (or @t96 @t100)) % 0.52/0.88 (define @t102 () (forall @t93 @t101)) % 0.52/0.88 (define @t103 () (@list @t88 @t87)) % 0.52/0.88 (define @t104 () (forall @t103 @t101)) % 0.52/0.88 (define @t105 () (forall @t103 @t100)) % 0.52/0.88 (define @t106 () (@var "BOUND_VARIABLE_13840" tptp.mworld)) % 0.52/0.88 (define @t107 () (or @t96 @t105)) % 0.52/0.88 (define @t108 () (tptp.subset @t9 @t9 @t106)) % 0.52/0.88 (define @t109 () (not (tptp.eiw_di @t9 @t7))) % 0.52/0.88 (define @t110 () (@list @t9 @t106)) % 0.52/0.88 (define @t111 () (forall @t110 (or @t109 (not (tptp.mrel @t7 @t106)) @t108))) % 0.52/0.88 (define @t112 () (not (tptp.mrel @t1 @t106))) % 0.52/0.88 (define @t113 () (tptp.eiw_di @t9 @t1)) % 0.52/0.88 (define @t114 () (not @t113)) % 0.52/0.88 (define @t115 () (or @t114 @t112 @t108)) % 0.52/0.88 (define @t116 () (lambda @t4 (forall @t110 @t115))) % 0.52/0.88 (define @t117 () (_ @t116 @t7)) % 0.52/0.88 (define @t118 () (or @t96 @t117)) % 0.52/0.88 (define @t119 () (forall @t76 @t118)) % 0.52/0.88 (define @t120 () (lambda @t4 @t119)) % 0.52/0.88 (define @t121 () (_ @t63 @t7)) % 0.52/0.88 (define @t122 () (lambda @t78 (forall @t76 (or @t96 @t121)))) % 0.52/0.88 (define @t123 () (or @t112 @t108)) % 0.52/0.88 (define @t124 () (or @t114 @t123)) % 0.52/0.88 (define @t125 () (forall @t110 @t124)) % 0.52/0.88 (define @t126 () (@list @t106)) % 0.52/0.88 (define @t127 () (forall @t126 @t124)) % 0.52/0.88 (define @t128 () (forall @t126 @t123)) % 0.52/0.88 (define @t129 () (@list @t7)) % 0.52/0.88 (define @t130 () (or @t114 @t128)) % 0.52/0.88 (define @t131 () (forall @t76 (or @t96 (tptp.subset @t9 @t9 @t7)))) % 0.52/0.88 (define @t132 () (tptp.subset @t21 @t21 @t7)) % 0.52/0.88 (define @t133 () (not (tptp.mrel @t12 @t7))) % 0.52/0.88 (define @t134 () (forall @t76 (or @t133 @t132))) % 0.52/0.88 (define @t135 () (lambda @t28 @t134)) % 0.52/0.88 (define @t136 () (_ @t135 @t9 @t1)) % 0.52/0.88 (define @t137 () (or @t114 @t136)) % 0.52/0.88 (define @t138 () (forall @t11 @t137)) % 0.52/0.88 (define @t139 () (lambda @t4 @t138)) % 0.52/0.88 (define @t140 () (_ @t81 @t9 @t1)) % 0.52/0.88 (define @t141 () (lambda @t84 (forall @t11 (or @t114 @t140)))) % 0.52/0.88 (define @t142 () (_ @t56 @t7)) % 0.52/0.88 (define @t143 () (or @t96 @t142)) % 0.52/0.88 (define @t144 () (_ @t56 @t7)) % 0.52/0.88 (define @t145 () (or @t96 @t144)) % 0.52/0.88 (define @t146 () (forall @t76 @t145)) % 0.52/0.88 (define @t147 () (lambda @t4 @t146)) % 0.52/0.88 (define @t148 () (_ @t122 @t56)) % 0.52/0.88 (define @t149 () (not @t8)) % 0.52/0.88 (define @t150 () (or @t149 @t75)) % 0.52/0.88 (define @t151 () (not @t10)) % 0.52/0.88 (define @t152 () (or @t151 @t82)) % 0.52/0.88 (define @t153 () (@var "BOUND_VARIABLE_11639" tptp.mworld)) % 0.52/0.88 (define @t154 () (@var "BOUND_VARIABLE_11635" $$unsorted)) % 0.52/0.88 (define @t155 () (@var "BOUND_VARIABLE_11631" $$unsorted)) % 0.52/0.88 (define @t156 () (tptp.qmltpeq (tptp.union @t155 @t154) @t154 @t153)) % 0.52/0.88 (define @t157 () (@var "BOUND_VARIABLE_11637" tptp.mworld)) % 0.52/0.88 (define @t158 () (not (tptp.mrel @t157 @t153))) % 0.52/0.88 (define @t159 () (@var "BOUND_VARIABLE_11453" tptp.mworld)) % 0.52/0.88 (define @t160 () (@list @t159)) % 0.52/0.88 (define @t161 () (not (forall @t160 (or (not (tptp.mrel @t157 @t159)) (tptp.subset @t155 @t154 @t159))))) % 0.52/0.88 (define @t162 () (@var "BOUND_VARIABLE_11633" tptp.mworld)) % 0.52/0.88 (define @t163 () (not (tptp.mrel @t162 @t157))) % 0.52/0.88 (define @t164 () (not (tptp.eiw_di @t154 @t162))) % 0.52/0.88 (define @t165 () (not (tptp.mrel @t7 @t162))) % 0.52/0.88 (define @t166 () (not (tptp.eiw_di @t155 @t7))) % 0.52/0.88 (define @t167 () (@list @t7 @t155 @t162 @t154 @t157 @t153)) % 0.52/0.88 (define @t168 () (or @t96 @t166 @t165 @t164 @t163 @t161 @t158 @t156)) % 0.52/0.88 (define @t169 () (lambda @t4 (forall @t167 @t168))) % 0.52/0.88 (define @t170 () (_ @t169 tptp.mactual)) % 0.52/0.88 (define @t171 () (or @t166 @t165 @t164 @t163 @t161 @t158 @t156)) % 0.52/0.88 (define @t172 () (or @t96 @t171)) % 0.52/0.88 (define @t173 () (forall @t167 @t172)) % 0.52/0.88 (define @t174 () (@list @t155 @t162 @t154 @t157 @t153)) % 0.52/0.88 (define @t175 () (forall @t174 @t172)) % 0.52/0.88 (define @t176 () (forall @t174 @t171)) % 0.52/0.88 (define @t177 () (@var "BOUND_VARIABLE_11595" tptp.mworld)) % 0.52/0.88 (define @t178 () (@var "BOUND_VARIABLE_11593" tptp.mworld)) % 0.52/0.88 (define @t179 () (@var "BOUND_VARIABLE_11591" $$unsorted)) % 0.52/0.88 (define @t180 () (@var "BOUND_VARIABLE_11589" tptp.mworld)) % 0.52/0.88 (define @t181 () (or @t96 @t176)) % 0.52/0.88 (define @t182 () (tptp.qmltpeq (tptp.union @t9 @t179) @t179 @t177)) % 0.52/0.88 (define @t183 () (not (tptp.mrel @t178 @t177))) % 0.52/0.88 (define @t184 () (not (forall @t160 (or (not (tptp.mrel @t178 @t159)) (tptp.subset @t9 @t179 @t159))))) % 0.52/0.88 (define @t185 () (not (tptp.mrel @t180 @t178))) % 0.52/0.88 (define @t186 () (not (tptp.eiw_di @t179 @t180))) % 0.52/0.88 (define @t187 () (@list @t9 @t180 @t179 @t178 @t177)) % 0.52/0.88 (define @t188 () (forall @t187 (or @t109 (not (tptp.mrel @t7 @t180)) @t186 @t185 @t184 @t183 @t182))) % 0.52/0.88 (define @t189 () (not (tptp.mrel @t1 @t180))) % 0.52/0.88 (define @t190 () (or @t114 @t189 @t186 @t185 @t184 @t183 @t182)) % 0.52/0.88 (define @t191 () (lambda @t4 (forall @t187 @t190))) % 0.52/0.88 (define @t192 () (_ @t191 @t7)) % 0.52/0.88 (define @t193 () (or @t96 @t192)) % 0.52/0.88 (define @t194 () (forall @t76 @t193)) % 0.52/0.88 (define @t195 () (lambda @t4 @t194)) % 0.52/0.88 (define @t196 () (or @t189 @t186 @t185 @t184 @t183 @t182)) % 0.52/0.88 (define @t197 () (or @t114 @t196)) % 0.52/0.88 (define @t198 () (forall @t187 @t197)) % 0.52/0.88 (define @t199 () (@list @t180 @t179 @t178 @t177)) % 0.52/0.88 (define @t200 () (forall @t199 @t197)) % 0.52/0.88 (define @t201 () (forall @t199 @t196)) % 0.52/0.88 (define @t202 () (@var "BOUND_VARIABLE_11546" tptp.mworld)) % 0.52/0.88 (define @t203 () (@var "BOUND_VARIABLE_11544" tptp.mworld)) % 0.52/0.88 (define @t204 () (@var "BOUND_VARIABLE_11542" $$unsorted)) % 0.52/0.88 (define @t205 () (or @t114 @t201)) % 0.52/0.88 (define @t206 () (not (tptp.mrel @t203 @t202))) % 0.52/0.88 (define @t207 () (not (tptp.mrel @t203 @t159))) % 0.52/0.88 (define @t208 () (not (tptp.mrel @t7 @t203))) % 0.52/0.88 (define @t209 () (not (tptp.eiw_di @t204 @t7))) % 0.52/0.88 (define @t210 () (@list @t7 @t204 @t203 @t202)) % 0.52/0.88 (define @t211 () (forall @t210 (or @t96 @t209 @t208 (not (forall @t160 (or @t207 (tptp.subset @t9 @t204 @t159)))) @t206 (tptp.qmltpeq (tptp.union @t9 @t204) @t204 @t202)))) % 0.52/0.88 (define @t212 () (tptp.qmltpeq (tptp.union @t21 @t204) @t204 @t202)) % 0.52/0.88 (define @t213 () (not (forall @t160 (or @t207 (tptp.subset @t21 @t204 @t159))))) % 0.52/0.88 (define @t214 () (forall @t210 (or @t133 @t209 @t208 @t213 @t206 @t212))) % 0.52/0.88 (define @t215 () (lambda @t28 @t214)) % 0.52/0.88 (define @t216 () (_ @t215 @t9 @t1)) % 0.52/0.88 (define @t217 () (or @t114 @t216)) % 0.52/0.88 (define @t218 () (forall @t11 @t217)) % 0.52/0.88 (define @t219 () (lambda @t4 @t218)) % 0.52/0.88 (define @t220 () (or @t96 @t209 @t208 @t213 @t206 @t212)) % 0.52/0.88 (define @t221 () (or @t209 @t208 @t213 @t206 @t212)) % 0.52/0.88 (define @t222 () (or @t96 @t221)) % 0.52/0.88 (define @t223 () (forall @t210 @t222)) % 0.52/0.88 (define @t224 () (@list @t204 @t203 @t202)) % 0.52/0.88 (define @t225 () (forall @t224 @t222)) % 0.52/0.88 (define @t226 () (forall @t224 @t221)) % 0.52/0.88 (define @t227 () (@var "BOUND_VARIABLE_11512" tptp.mworld)) % 0.52/0.88 (define @t228 () (@var "BOUND_VARIABLE_11510" tptp.mworld)) % 0.52/0.88 (define @t229 () (or @t96 @t226)) % 0.52/0.88 (define @t230 () (tptp.union @t21 @t9)) % 0.52/0.88 (define @t231 () (tptp.qmltpeq @t230 @t9 @t227)) % 0.52/0.88 (define @t232 () (not (tptp.mrel @t228 @t227))) % 0.52/0.88 (define @t233 () (tptp.subset @t21 @t9 @t159)) % 0.52/0.88 (define @t234 () (not (forall @t160 (or (not (tptp.mrel @t228 @t159)) @t233)))) % 0.52/0.88 (define @t235 () (@list @t9 @t228 @t227)) % 0.52/0.88 (define @t236 () (forall @t235 (or @t109 (not (tptp.mrel @t7 @t228)) @t234 @t232 @t231))) % 0.52/0.88 (define @t237 () (not (tptp.mrel @t1 @t228))) % 0.52/0.88 (define @t238 () (or @t114 @t237 @t234 @t232 @t231)) % 0.52/0.88 (define @t239 () (lambda @t4 (forall @t235 @t238))) % 0.52/0.88 (define @t240 () (_ @t239 @t7)) % 0.52/0.88 (define @t241 () (or @t96 @t240)) % 0.52/0.88 (define @t242 () (forall @t76 @t241)) % 0.52/0.88 (define @t243 () (lambda @t4 @t242)) % 0.52/0.88 (define @t244 () (or @t237 @t234 @t232 @t231)) % 0.52/0.88 (define @t245 () (or @t114 @t244)) % 0.52/0.88 (define @t246 () (forall @t235 @t245)) % 0.52/0.88 (define @t247 () (@list @t228 @t227)) % 0.52/0.88 (define @t248 () (forall @t247 @t245)) % 0.52/0.88 (define @t249 () (forall @t247 @t244)) % 0.52/0.88 (define @t250 () (@var "BOUND_VARIABLE_11479" tptp.mworld)) % 0.52/0.88 (define @t251 () (or @t114 @t249)) % 0.52/0.88 (define @t252 () (not (tptp.mrel @t7 @t250))) % 0.52/0.88 (define @t253 () (not (tptp.mrel @t7 @t159))) % 0.52/0.88 (define @t254 () (@list @t7 @t250)) % 0.52/0.88 (define @t255 () (forall @t254 (or @t96 (not (forall @t160 (or @t253 @t233))) @t252 (tptp.qmltpeq @t230 @t9 @t250)))) % 0.52/0.88 (define @t256 () (tptp.union @t21 @t20)) % 0.52/0.88 (define @t257 () (tptp.qmltpeq @t256 @t20 @t250)) % 0.52/0.88 (define @t258 () (tptp.subset @t21 @t20 @t159)) % 0.52/0.88 (define @t259 () (forall @t160 (or @t253 @t258))) % 0.52/0.88 (define @t260 () (not @t259)) % 0.52/0.88 (define @t261 () (forall @t254 (or @t133 @t260 @t252 @t257))) % 0.52/0.88 (define @t262 () (lambda @t27 @t261)) % 0.52/0.88 (define @t263 () (_ @t262 @t9 @t1)) % 0.52/0.88 (define @t264 () (or @t114 @t263)) % 0.52/0.88 (define @t265 () (forall @t11 @t264)) % 0.52/0.88 (define @t266 () (lambda @t4 @t265)) % 0.52/0.88 (define @t267 () (or @t96 @t260 @t252 @t257)) % 0.52/0.88 (define @t268 () (or @t252 @t257)) % 0.52/0.88 (define @t269 () (or @t96 @t260 @t268)) % 0.52/0.88 (define @t270 () (forall @t254 @t269)) % 0.52/0.88 (define @t271 () (@list @t250)) % 0.52/0.88 (define @t272 () (forall @t271 @t269)) % 0.52/0.88 (define @t273 () (forall @t271 @t268)) % 0.52/0.88 (define @t274 () (@var "BOUND_VARIABLE_11445" tptp.mworld)) % 0.52/0.88 (define @t275 () (@list @t274)) % 0.52/0.88 (define @t276 () (or @t96 @t260 @t273)) % 0.52/0.88 (define @t277 () (tptp.qmltpeq @t256 @t20 @t274)) % 0.52/0.88 (define @t278 () (@list @t274)) % 0.52/0.88 (define @t279 () (forall @t278 (or (not (tptp.mrel @t7 @t274)) @t277))) % 0.52/0.88 (define @t280 () (or @t96 @t260 @t279)) % 0.52/0.88 (define @t281 () (=> @t259 @t279)) % 0.52/0.88 (define @t282 () (or @t96 @t281)) % 0.52/0.88 (define @t283 () (tptp.qmltpeq @t256 @t20 @t7)) % 0.52/0.88 (define @t284 () (forall @t76 (or @t96 @t283))) % 0.52/0.88 (define @t285 () (tptp.subset @t21 @t20 @t7)) % 0.52/0.88 (define @t286 () (forall @t76 (or @t96 @t285))) % 0.52/0.88 (define @t287 () (@list @t159)) % 0.52/0.88 (define @t288 () (=> @t286 @t284)) % 0.52/0.88 (define @t289 () (lambda @t4 @t288)) % 0.52/0.88 (define @t290 () (or @t96 (_ @t289 @t7))) % 0.52/0.88 (define @t291 () (forall @t76 @t290)) % 0.52/0.88 (define @t292 () (lambda @t4 @t291)) % 0.52/0.88 (define @t293 () (lambda @t4 @t284)) % 0.52/0.88 (define @t294 () (_ @t293 @t1)) % 0.52/0.88 (define @t295 () (=> @t286 @t294)) % 0.52/0.88 (define @t296 () (lambda @t4 @t295)) % 0.52/0.88 (define @t297 () (@list @t68 @t1)) % 0.52/0.88 (define @t298 () (_ @t40 @t7)) % 0.52/0.88 (define @t299 () (or @t96 @t298)) % 0.52/0.88 (define @t300 () (_ @t40 @t7)) % 0.52/0.88 (define @t301 () (or @t96 @t300)) % 0.52/0.88 (define @t302 () (forall @t76 @t301)) % 0.52/0.88 (define @t303 () (lambda @t4 @t302)) % 0.52/0.88 (define @t304 () (_ @t122 @t40)) % 0.52/0.88 (define @t305 () (lambda @t4 @t286)) % 0.52/0.88 (define @t306 () (_ @t305 @t1)) % 0.52/0.88 (define @t307 () (=> @t306 @t69)) % 0.52/0.88 (define @t308 () (lambda @t297 @t307)) % 0.52/0.88 (define @t309 () (_ @t35 @t7)) % 0.52/0.88 (define @t310 () (or @t96 @t309)) % 0.52/0.88 (define @t311 () (_ @t35 @t7)) % 0.52/0.88 (define @t312 () (or @t96 @t311)) % 0.52/0.88 (define @t313 () (forall @t76 @t312)) % 0.52/0.88 (define @t314 () (lambda @t4 @t313)) % 0.52/0.88 (define @t315 () (_ @t122 @t35)) % 0.52/0.88 (define @t316 () (lambda @t27 (_ (_ @t122 (_ (_ @t73 @t315) @t304)) @t12))) % 0.52/0.88 (define @t317 () (@var "BOUND_VARIABLE_14811" tptp.mworld)) % 0.52/0.88 (define @t318 () (@var "BOUND_VARIABLE_14809" $$unsorted)) % 0.52/0.88 (define @t319 () (tptp.qmltpeq (tptp.union @t318 @t318) @t318 @t317)) % 0.52/0.88 (define @t320 () (not (tptp.mrel @t7 @t317))) % 0.52/0.88 (define @t321 () (not (tptp.eiw_di @t318 @t7))) % 0.52/0.88 (define @t322 () (@list @t7 @t318 @t317)) % 0.52/0.88 (define @t323 () (forall @t322 (or @t92 @t321 @t320 @t319))) % 0.52/0.88 (define @t324 () (@quantifiers_skolemize @t323 2)) % 0.52/0.88 (define @t325 () (@quantifiers_skolemize @t323 0)) % 0.52/0.88 (define @t326 () (@quantifiers_skolemize @t323 1)) % 0.52/0.88 (define @t327 () (tptp.mrel @t1 @t1)) % 0.52/0.88 (define @t328 () (or @t96 @t321 @t320 @t319)) % 0.52/0.88 (define @t329 () (lambda @t4 (forall @t322 @t328))) % 0.52/0.88 (define @t330 () (_ @t329 tptp.mactual)) % 0.52/0.88 (define @t331 () (or @t321 @t320 @t319)) % 0.52/0.88 (define @t332 () (or @t96 @t331)) % 0.52/0.88 (define @t333 () (forall @t322 @t332)) % 0.52/0.88 (define @t334 () (@list @t318 @t317)) % 0.52/0.88 (define @t335 () (forall @t334 @t332)) % 0.52/0.88 (define @t336 () (forall @t334 @t331)) % 0.52/0.88 (define @t337 () (@var "BOUND_VARIABLE_14786" tptp.mworld)) % 0.52/0.88 (define @t338 () (or @t96 @t336)) % 0.52/0.88 (define @t339 () (tptp.union @t9 @t9)) % 0.52/0.88 (define @t340 () (tptp.qmltpeq @t339 @t9 @t337)) % 0.52/0.88 (define @t341 () (@list @t9 @t337)) % 0.52/0.88 (define @t342 () (forall @t341 (or @t109 (not (tptp.mrel @t7 @t337)) @t340))) % 0.52/0.88 (define @t343 () (not (tptp.mrel @t1 @t337))) % 0.52/0.88 (define @t344 () (or @t114 @t343 @t340)) % 0.52/0.88 (define @t345 () (lambda @t4 (forall @t341 @t344))) % 0.52/0.88 (define @t346 () (_ @t345 @t7)) % 0.52/0.88 (define @t347 () (or @t96 @t346)) % 0.52/0.88 (define @t348 () (forall @t76 @t347)) % 0.52/0.88 (define @t349 () (lambda @t4 @t348)) % 0.52/0.88 (define @t350 () (or @t343 @t340)) % 0.52/0.88 (define @t351 () (or @t114 @t350)) % 0.52/0.88 (define @t352 () (forall @t341 @t351)) % 0.52/0.88 (define @t353 () (@list @t337)) % 0.52/0.88 (define @t354 () (forall @t353 @t351)) % 0.52/0.88 (define @t355 () (forall @t353 @t350)) % 0.52/0.88 (define @t356 () (or @t114 @t355)) % 0.52/0.88 (define @t357 () (forall @t76 (or @t96 (tptp.qmltpeq @t339 @t9 @t7)))) % 0.52/0.88 (define @t358 () (tptp.union @t21 @t21)) % 0.52/0.88 (define @t359 () (tptp.qmltpeq @t358 @t21 @t7)) % 0.52/0.88 (define @t360 () (forall @t76 (or @t133 @t359))) % 0.52/0.88 (define @t361 () (lambda @t28 @t360)) % 0.52/0.88 (define @t362 () (_ @t361 @t9 @t1)) % 0.52/0.88 (define @t363 () (or @t114 @t362)) % 0.52/0.88 (define @t364 () (forall @t11 @t363)) % 0.52/0.88 (define @t365 () (lambda @t4 @t364)) % 0.52/0.88 (define @t366 () (_ @t60 @t7)) % 0.52/0.88 (define @t367 () (or @t96 @t366)) % 0.52/0.88 (define @t368 () (_ @t60 @t7)) % 0.52/0.88 (define @t369 () (or @t96 @t368)) % 0.52/0.88 (define @t370 () (forall @t76 @t369)) % 0.52/0.88 (define @t371 () (lambda @t4 @t370)) % 0.52/0.88 (define @t372 () (_ @t122 @t60)) % 0.52/0.88 (define @t373 () (lambda @t28 (_ @t372 @t12))) % 0.52/0.88 (define @t374 () (tptp.qmltpeq (tptp.union @t326 @t326) @t326 @t324)) % 0.52/0.88 (define @t375 () (tptp.mrel @t325 @t324)) % 0.52/0.88 (define @t376 () (not @t375)) % 0.52/0.88 (define @t377 () (tptp.eiw_di @t326 @t325)) % 0.52/0.88 (define @t378 () (not @t377)) % 0.52/0.88 (define @t379 () (tptp.mrel tptp.mactual @t325)) % 0.52/0.88 (define @t380 () (not @t379)) % 0.52/0.88 (define @t381 () (or @t380 @t378 @t376 @t374)) % 0.52/0.88 (define @t382 () (@list true)) % 0.52/0.88 (define @t383 () (@list @t381)) % 0.52/0.88 (define @t384 () (forall @t160 (or (not (tptp.mrel @t325 @t159)) (tptp.subset @t326 @t326 @t159)))) % 0.52/0.88 (define @t385 () (not @t384)) % 0.52/0.88 (define @t386 () (tptp.mrel @t325 @t325)) % 0.52/0.88 (define @t387 () (not @t386)) % 0.52/0.88 (define @t388 () (or @t380 @t378 @t387 @t378 @t387 @t385 @t376 @t374)) % 0.52/0.88 (define @t389 () (@var "BOUND_VARIABLE_10574" tptp.mworld)) % 0.52/0.88 (define @t390 () (forall (@list @t389) (or (not (tptp.mrel @t325 @t389)) (tptp.subset @t326 @t326 @t389)))) % 0.52/0.88 (define @t391 () (@quantifiers_skolemize @t390 0)) % 0.52/0.88 (define @t392 () (tptp.subset @t326 @t326 @t391)) % 0.52/0.88 (define @t393 () (tptp.mrel @t325 @t391)) % 0.52/0.88 (define @t394 () (not @t393)) % 0.52/0.88 (define @t395 () (or @t394 @t392)) % 0.52/0.88 (define @t396 () (@list @t395)) % 0.52/0.88 (define @t397 () (or @t380 @t378 @t394 @t392)) % 0.52/0.88 (define @t398 () (not @t397)) % 0.52/0.88 (assume @p1 @t5) % 0.52/0.88 (assume @p2 (forall (@list @t1 @t7 @t6) (=> (and @t8 (_ (_ tptp.mrel @t7) @t6)) (_ @t2 @t6)))) % 0.52/0.88 (assume @p3 (forall @t4 (exists @t11 @t10))) % 0.52/0.88 (assume @p4 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t14 (_ (_ tptp.mbox (_ @t13 @t9)) @t12)))))) % 0.52/0.88 (assume @p5 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t14 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t18 (_ (_ tptp.mbox (_ (_ tptp.mimplies @t17) (_ tptp.mbox (_ @t16 @t9)))) @t12)))) @t12)))))) % 0.52/0.88 (assume @p6 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t14 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t18 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda (@list @t19 @t12) (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ (_ tptp.mand @t17) (_ tptp.mbox (_ @t16 @t19)))) (_ tptp.mbox (_ @t13 @t19)))) @t12)))) @t12)))) @t12)))))) % 0.52/0.88 (assume @p7 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t29 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t28 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mbox (_ @t26 (_ tptp.mbox (_ (_ tptp.qmltpeq (_ (_ tptp.union @t24) @t20)) @t23)))) @t12)))) @t12)))) @t12)))))) % 0.52/0.88 (assume @p8 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t29 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t28 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mbox (_ @t26 (_ tptp.mbox (_ (_ tptp.qmltpeq (_ @t30 @t24)) @t31)))) @t12)))) @t12)))) @t12)))))) % 0.52/0.88 (assume @p9 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t29 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t28 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ @t32 (_ tptp.mbox (_ (_ tptp.member @t24) @t20)))) (_ tptp.mbox (_ (_ tptp.member @t21) @t20)))) @t12)))) @t12)))) @t12)))))) % 0.52/0.88 (assume @p10 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t29 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t28 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ @t32 (_ tptp.mbox (_ @t33 @t24)))) (_ tptp.mbox (_ @t33 @t21)))) @t12)))) @t12)))) @t12)))))) % 0.52/0.88 (assume @p11 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t29 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t28 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ @t32 (_ tptp.mbox (_ (_ tptp.subset @t24) @t20)))) @t36)) @t12)))) @t12)))) @t12)))))) % 0.52/0.88 (assume @p12 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t29 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t28 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ @t32 (_ tptp.mbox (_ @t37 @t24)))) @t38)) @t12)))) @t12)))) @t12)))))) % 0.52/0.88 (assume @p13 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di @t43)))) % 0.52/0.88 (assume @p14 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t28 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t50 (_ (_ (_ tptp.mand (_ tptp.mbox (_ (_ tptp.mimplies @t46) @t49))) (_ tptp.mbox (_ (_ tptp.mimplies @t49) @t46))) @t12)))) @t12)))) @t12)))))) % 0.52/0.88 (assume @p15 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t28 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t27 (_ (_ (_ tptp.mand (_ tptp.mbox (_ @t53 @t52))) (_ tptp.mbox (_ (_ tptp.mimplies @t52) @t51))) @t12)))) @t12)))))) % 0.52/0.88 (assume @p16 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t28 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mbox (_ @t39 @t31)) @t12)))) @t12)))))) % 0.52/0.88 (assume @p17 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t28 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t27 (_ (_ (_ tptp.mand (_ tptp.mbox (_ @t41 @t55))) (_ tptp.mbox (_ (_ tptp.mimplies @t55) @t36))) @t12)))) @t12)))))) % 0.52/0.88 (assume @p18 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di @t57)))) % 0.52/0.89 (assume @p19 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t28 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t27 (_ (_ (_ tptp.mand (_ tptp.mbox (_ @t53 @t58))) (_ tptp.mbox (_ (_ tptp.mimplies @t58) @t51))) @t12)))) @t12)))))) % 0.52/0.89 (assume @p20 @t62) % 0.52/0.89 (assume @p21 true) % 0.52/0.89 (step @p22 (= tptp.mlocal @t64) :rule refl :args (@t64)) % 0.52/0.89 (step @p23 (= tptp.mnot @t67) :rule refl :args (@t67)) % 0.52/0.89 (step @p24 (= tptp.mand @t71) :rule refl :args (@t71)) % 0.52/0.89 (step @p25 (= tptp.mor @t72) :rule refl :args (@t72)) % 0.52/0.89 (step @p26 (= tptp.mimplies @t73) :rule refl :args (@t73)) % 0.52/0.89 (step @p27 (= tptp.mequiv @t74) :rule refl :args (@t74)) % 0.52/0.89 (step @p28 (= tptp.mbox @t79) :rule refl :args (@t79)) % 0.52/0.89 (step @p29 (= tptp.mdia @t80) :rule refl :args (@t80)) % 0.52/0.89 (step @p30 (= tptp.mforall_di @t85) :rule refl :args (@t85)) % 0.52/0.89 (step @p31 (= tptp.mexists_di @t86) :rule refl :args (@t86)) % 0.52/0.89 (step @p32 :rule beta-reduce :args ((= @t99 @t94))) % 0.52/0.89 (step @p33 :rule beta-reduce :args ((= (_ @t64 @t98) @t99))) % 0.52/0.89 (step @p34 :rule trans :premises (@p33 @p32)) % 0.52/0.89 (step @p35 :rule aci_norm :args ((= @t101 @t97))) % 0.52/0.89 (step @p36 :rule cong :premises (@p35) :args (@t102)) % 0.52/0.89 (step @p37 :rule quant-merge-prenex :args ((= (forall @t76 @t104) @t102))) % 0.52/0.89 (step @p38 :rule alpha_equiv :args (@t105 (@list @t88 @t87) (@list @t9 @t106))) % 0.52/0.89 (step @p39 :rule refl :args (@t96)) % 0.52/0.89 (step @p40 :rule nary_cong :premises (@p39 @p38) :args (@t107)) % 0.52/0.89 (step @p41 :rule quant-miniscope-or :args ((= @t104 @t107))) % 0.52/0.89 (step @p42 :rule trans :premises (@p41 @p40)) % 0.52/0.89 (step @p43 :rule symm :premises (@p42)) % 0.52/0.89 (step @p44 :rule cong :premises (@p43) :args ((forall @t76 (or @t96 @t111)))) % 0.52/0.89 (step @p45 :rule trans :premises (@p44 @p37)) % 0.52/0.89 (step @p46 :rule trans :premises (@p45 @p36)) % 0.52/0.89 (step @p47 :rule beta-reduce :args ((= @t117 @t111))) % 0.52/0.89 (step @p48 :rule refl :args (@t96)) % 0.52/0.89 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t118)) % 0.52/0.89 (step @p50 :rule cong :premises (@p49) :args (@t119)) % 0.52/0.89 (step @p51 :rule trans :premises (@p50 @p46)) % 0.52/0.89 (step @p52 :rule cong :premises (@p51) :args (@t120)) % 0.52/0.89 (step @p53 :rule beta-reduce :args ((= (_ @t122 @t116) @t120))) % 0.52/0.89 (step @p54 :rule trans :premises (@p53 @p52)) % 0.52/0.89 (step @p55 :rule aci_norm :args ((= @t124 @t115))) % 0.52/0.89 (step @p56 :rule cong :premises (@p55) :args (@t125)) % 0.52/0.89 (step @p57 :rule quant-merge-prenex :args ((= (forall @t11 @t127) @t125))) % 0.52/0.89 (step @p58 :rule alpha_equiv :args (@t128 (@list @t106) @t129)) % 0.52/0.89 (step @p59 :rule refl :args (@t114)) % 0.52/0.89 (step @p60 :rule nary_cong :premises (@p59 @p58) :args (@t130)) % 0.52/0.89 (step @p61 :rule quant-miniscope-or :args ((= @t127 @t130))) % 0.52/0.89 (step @p62 :rule trans :premises (@p61 @p60)) % 0.52/0.89 (step @p63 :rule symm :premises (@p62)) % 0.52/0.89 (step @p64 :rule cong :premises (@p63) :args ((forall @t11 (or @t114 @t131)))) % 0.52/0.89 (step @p65 :rule trans :premises (@p64 @p57)) % 0.52/0.89 (step @p66 :rule trans :premises (@p65 @p56)) % 0.52/0.89 (step @p67 :rule beta-reduce :args ((= @t136 @t131))) % 0.52/0.89 (step @p68 :rule refl :args (@t114)) % 0.52/0.89 (step @p69 :rule nary_cong :premises (@p68 @p67) :args (@t137)) % 0.52/0.89 (step @p70 :rule cong :premises (@p69) :args (@t138)) % 0.52/0.89 (step @p71 :rule trans :premises (@p70 @p66)) % 0.52/0.89 (step @p72 :rule cong :premises (@p71) :args (@t139)) % 0.52/0.89 (step @p73 :rule beta-reduce :args ((= (_ @t141 @t135) @t139))) % 0.52/0.89 (step @p74 :rule trans :premises (@p73 @p72)) % 0.52/0.89 (step @p75 :rule beta-reduce :args ((= (_ (lambda @t4 (forall @t76 (or @t96 @t132))) @t12) @t134))) % 0.52/0.89 (step @p76 :rule refl :args (@t12)) % 0.52/0.89 (step @p77 :rule refl :args (@t132)) % 0.52/0.89 (step @p78 :rule refl :args (@t142)) % 0.52/0.89 (step @p79 :rule cong :premises (@p78 @p77) :args ((= @t142 @t132))) % 0.52/0.89 (step @p80 :rule symm :premises (@p79)) % 0.52/0.89 (step @p81 :rule eq_resolve :premises (@p78 @p80)) % 0.52/0.89 (step @p82 :rule nary_cong :premises (@p39 @p81) :args (@t143)) % 0.52/0.89 (step @p83 :rule cong :premises (@p82) :args ((forall @t76 @t143))) % 0.52/0.89 (step @p84 :rule refl :args (@t144)) % 0.52/0.89 (step @p85 :rule nary_cong :premises (@p48 @p84) :args (@t145)) % 0.52/0.89 (step @p86 :rule cong :premises (@p85) :args (@t146)) % 0.52/0.89 (step @p87 :rule trans :premises (@p86 @p83)) % 0.52/0.89 (step @p88 :rule cong :premises (@p87) :args (@t147)) % 0.52/0.89 (step @p89 :rule beta-reduce :args ((= @t148 @t147))) % 0.52/0.89 (step @p90 :rule trans :premises (@p89 @p88)) % 0.52/0.89 (step @p91 :rule ho_cong :premises (@p90 @p76)) % 0.52/0.89 (step @p92 :rule trans :premises (@p91 @p75)) % 0.52/0.89 (step @p93 :rule cong :premises (@p92) :args ((lambda @t28 (_ @t148 @t12)))) % 0.52/0.89 (step @p94 :rule refl :args (@t141)) % 0.52/0.89 (step @p95 :rule ho_cong :premises (@p94 @p93)) % 0.52/0.89 (step @p96 :rule trans :premises (@p95 @p74)) % 0.52/0.89 (step @p97 :rule refl :args (@t122)) % 0.52/0.89 (step @p98 :rule ho_cong :premises (@p97 @p96)) % 0.52/0.89 (step @p99 :rule trans :premises (@p98 @p54)) % 0.52/0.89 (step @p100 :rule refl :args (@t64)) % 0.52/0.89 (step @p101 :rule ho_cong :premises (@p100 @p99)) % 0.52/0.89 (step @p102 :rule trans :premises (@p101 @p34)) % 0.52/0.89 (step @p103 :rule refl :args (@t56)) % 0.52/0.89 (step @p104 :rule refl :args (@t121)) % 0.52/0.89 (step @p105 :rule refl :args (@t75)) % 0.52/0.89 (step @p106 :rule cong :premises (@p105 @p104) :args ((= @t75 @t121))) % 0.52/0.89 (step @p107 :rule symm :premises (@p106)) % 0.52/0.89 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 0.52/0.89 (step @p109 :rule refl :args (@t95)) % 0.52/0.89 (step @p110 :rule refl :args (@t8)) % 0.52/0.89 (step @p111 :rule cong :premises (@p110 @p109) :args ((= @t8 @t95))) % 0.52/0.89 (step @p112 :rule symm :premises (@p111)) % 0.52/0.89 (step @p113 :rule eq_resolve :premises (@p110 @p112)) % 0.52/0.89 (step @p114 :rule cong :premises (@p113) :args (@t149)) % 0.52/0.89 (step @p115 :rule nary_cong :premises (@p114 @p108) :args (@t150)) % 0.52/0.89 (step @p116 :rule cong :premises (@p115) :args ((forall @t76 @t150))) % 0.52/0.89 (step @p117 :rule bool-impl-elim :args (@t8 @t75)) % 0.52/0.89 (step @p118 :rule cong :premises (@p117) :args (@t77)) % 0.52/0.89 (step @p119 :rule trans :premises (@p118 @p116)) % 0.52/0.89 (step @p120 :rule cong :premises (@p119) :args (@t79)) % 0.52/0.89 (step @p121 :rule trans :premises (@p28 @p120)) % 0.52/0.89 (step @p122 :rule ho_cong :premises (@p121 @p103)) % 0.52/0.89 (step @p123 :rule ho_cong :premises (@p122 @p76)) % 0.52/0.89 (step @p124 :rule cong :premises (@p123) :args (@t57)) % 0.52/0.89 (step @p125 :rule refl :args (@t140)) % 0.52/0.89 (step @p126 :rule refl :args (@t82)) % 0.52/0.89 (step @p127 :rule cong :premises (@p126 @p125) :args ((= @t82 @t140))) % 0.52/0.89 (step @p128 :rule symm :premises (@p127)) % 0.52/0.89 (step @p129 :rule eq_resolve :premises (@p126 @p128)) % 0.52/0.89 (step @p130 :rule refl :args (@t113)) % 0.52/0.89 (step @p131 :rule refl :args (@t10)) % 0.52/0.89 (step @p132 :rule cong :premises (@p131 @p130) :args ((= @t10 @t113))) % 0.52/0.89 (step @p133 :rule symm :premises (@p132)) % 0.52/0.89 (step @p134 :rule eq_resolve :premises (@p131 @p133)) % 0.52/0.89 (step @p135 :rule cong :premises (@p134) :args (@t151)) % 0.52/0.89 (step @p136 :rule nary_cong :premises (@p135 @p129) :args (@t152)) % 0.52/0.89 (step @p137 :rule cong :premises (@p136) :args ((forall @t11 @t152))) % 0.52/0.89 (step @p138 :rule bool-impl-elim :args (@t10 @t82)) % 0.52/0.89 (step @p139 :rule cong :premises (@p138) :args (@t83)) % 0.52/0.89 (step @p140 :rule trans :premises (@p139 @p137)) % 0.52/0.89 (step @p141 :rule cong :premises (@p140) :args (@t85)) % 0.52/0.89 (step @p142 :rule trans :premises (@p30 @p141)) % 0.52/0.89 (step @p143 :rule ho_cong :premises (@p142 @p124)) % 0.52/0.89 (step @p144 :rule ho_cong :premises (@p121 @p143)) % 0.52/0.89 (step @p145 :rule ho_cong :premises (@p22 @p144)) % 0.52/0.89 (step @p146 :rule trans :premises (@p145 @p102)) % 0.52/0.89 (step @p147 :rule eq_resolve :premises (@p18 @p146)) % 0.52/0.89 (step @p148 :rule beta-reduce :args ((= @t170 (forall @t167 (or @t92 @t166 @t165 @t164 @t163 @t161 @t158 @t156))))) % 0.52/0.89 (step @p149 :rule beta-reduce :args ((= (_ @t64 @t169) @t170))) % 0.52/0.89 (step @p150 :rule trans :premises (@p149 @p148)) % 0.52/0.89 (step @p151 :rule aci_norm :args ((= @t172 @t168))) % 0.52/0.89 (step @p152 :rule cong :premises (@p151) :args (@t173)) % 0.52/0.89 (step @p153 :rule quant-merge-prenex :args ((= (forall @t76 @t175) @t173))) % 0.52/0.89 (step @p154 :rule alpha_equiv :args (@t176 (@list @t155 @t162 @t154 @t157 @t153) (@list @t9 @t180 @t179 @t178 @t177))) % 0.52/0.89 (step @p155 :rule nary_cong :premises (@p39 @p154) :args (@t181)) % 0.52/0.89 (step @p156 :rule quant-miniscope-or :args ((= @t175 @t181))) % 0.52/0.89 (step @p157 :rule trans :premises (@p156 @p155)) % 0.52/0.89 (step @p158 :rule symm :premises (@p157)) % 0.52/0.89 (step @p159 :rule cong :premises (@p158) :args ((forall @t76 (or @t96 @t188)))) % 0.52/0.89 (step @p160 :rule trans :premises (@p159 @p153)) % 0.52/0.89 (step @p161 :rule trans :premises (@p160 @p152)) % 0.52/0.89 (step @p162 :rule beta-reduce :args ((= @t192 @t188))) % 0.52/0.89 (step @p163 :rule nary_cong :premises (@p48 @p162) :args (@t193)) % 0.52/0.89 (step @p164 :rule cong :premises (@p163) :args (@t194)) % 0.52/0.89 (step @p165 :rule trans :premises (@p164 @p161)) % 0.52/0.89 (step @p166 :rule cong :premises (@p165) :args (@t195)) % 0.52/0.89 (step @p167 :rule beta-reduce :args ((= (_ @t122 @t191) @t195))) % 0.52/0.89 (step @p168 :rule trans :premises (@p167 @p166)) % 0.52/0.89 (step @p169 :rule aci_norm :args ((= @t197 @t190))) % 0.52/0.89 (step @p170 :rule cong :premises (@p169) :args (@t198)) % 0.52/0.89 (step @p171 :rule quant-merge-prenex :args ((= (forall @t11 @t200) @t198))) % 0.52/0.89 (step @p172 :rule alpha_equiv :args (@t201 (@list @t180 @t179 @t178 @t177) (@list @t7 @t204 @t203 @t202))) % 0.52/0.89 (step @p173 :rule nary_cong :premises (@p59 @p172) :args (@t205)) % 0.52/0.89 (step @p174 :rule quant-miniscope-or :args ((= @t200 @t205))) % 0.52/0.89 (step @p175 :rule trans :premises (@p174 @p173)) % 0.52/0.89 (step @p176 :rule symm :premises (@p175)) % 0.52/0.89 (step @p177 :rule cong :premises (@p176) :args ((forall @t11 (or @t114 @t211)))) % 0.52/0.89 (step @p178 :rule trans :premises (@p177 @p171)) % 0.52/0.89 (step @p179 :rule trans :premises (@p178 @p170)) % 0.52/0.89 (step @p180 :rule beta-reduce :args ((= @t216 @t211))) % 0.52/0.89 (step @p181 :rule nary_cong :premises (@p68 @p180) :args (@t217)) % 0.52/0.89 (step @p182 :rule cong :premises (@p181) :args (@t218)) % 0.52/0.89 (step @p183 :rule trans :premises (@p182 @p179)) % 0.52/0.89 (step @p184 :rule cong :premises (@p183) :args (@t219)) % 0.52/0.89 (step @p185 :rule beta-reduce :args ((= (_ @t141 @t215) @t219))) % 0.52/0.89 (step @p186 :rule trans :premises (@p185 @p184)) % 0.52/0.89 (step @p187 :rule beta-reduce :args ((= (_ (lambda @t4 (forall @t210 @t220)) @t12) @t214))) % 0.52/0.89 (step @p188 :rule aci_norm :args ((= @t222 @t220))) % 0.52/0.89 (step @p189 :rule cong :premises (@p188) :args (@t223)) % 0.52/0.89 (step @p190 :rule quant-merge-prenex :args ((= (forall @t76 @t225) @t223))) % 0.52/0.89 (step @p191 :rule alpha_equiv :args (@t226 (@list @t204 @t203 @t202) (@list @t9 @t228 @t227))) % 0.52/0.89 (step @p192 :rule nary_cong :premises (@p39 @p191) :args (@t229)) % 0.52/0.89 (step @p193 :rule quant-miniscope-or :args ((= @t225 @t229))) % 0.52/0.89 (step @p194 :rule trans :premises (@p193 @p192)) % 0.52/0.89 (step @p195 :rule symm :premises (@p194)) % 0.52/0.89 (step @p196 :rule cong :premises (@p195) :args ((forall @t76 (or @t96 @t236)))) % 0.52/0.89 (step @p197 :rule trans :premises (@p196 @p190)) % 0.52/0.89 (step @p198 :rule trans :premises (@p197 @p189)) % 0.52/0.89 (step @p199 :rule beta-reduce :args ((= @t240 @t236))) % 0.52/0.89 (step @p200 :rule nary_cong :premises (@p48 @p199) :args (@t241)) % 0.52/0.89 (step @p201 :rule cong :premises (@p200) :args (@t242)) % 0.52/0.89 (step @p202 :rule trans :premises (@p201 @p198)) % 0.52/0.89 (step @p203 :rule cong :premises (@p202) :args (@t243)) % 0.52/0.89 (step @p204 :rule beta-reduce :args ((= (_ @t122 @t239) @t243))) % 0.52/0.89 (step @p205 :rule trans :premises (@p204 @p203)) % 0.52/0.89 (step @p206 :rule aci_norm :args ((= @t245 @t238))) % 0.52/0.89 (step @p207 :rule cong :premises (@p206) :args (@t246)) % 0.52/0.89 (step @p208 :rule quant-merge-prenex :args ((= (forall @t11 @t248) @t246))) % 0.52/0.89 (step @p209 :rule alpha_equiv :args (@t249 (@list @t228 @t227) (@list @t7 @t250))) % 0.52/0.89 (step @p210 :rule nary_cong :premises (@p59 @p209) :args (@t251)) % 0.52/0.89 (step @p211 :rule quant-miniscope-or :args ((= @t248 @t251))) % 0.52/0.89 (step @p212 :rule trans :premises (@p211 @p210)) % 0.52/0.89 (step @p213 :rule symm :premises (@p212)) % 0.52/0.89 (step @p214 :rule cong :premises (@p213) :args ((forall @t11 (or @t114 @t255)))) % 0.52/0.89 (step @p215 :rule trans :premises (@p214 @p208)) 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false false) (@list @t379 @t377 @t375 @t374 @t386 @t388))) % 0.52/0.89 (step @p478 :rule alpha_equiv :args (@t390 (@list @t389) @t287)) % 0.52/0.89 (step @p479 :rule equiv_elim1 :premises (@p478)) % 0.52/0.89 (step @p480 :rule chain_m_resolution :premises (@p479 @p477) :args ((not @t390) @t382 (@list @t384))) % 0.52/0.89 (step @p481 :rule skolemize :premises (@p480)) % 0.52/0.89 (step @p482 :rule cnf_or_neg :args (@t395 1)) % 0.52/0.89 (step @p483 :rule chain_m_resolution :premises (@p482 @p481) :args ((not @t392) @t382 @t396)) % 0.52/0.89 (step @p484 :rule bool-double-not-elim :args (@t393)) % 0.52/0.89 (step @p485 :rule refl :args (@t395)) % 0.52/0.89 (step @p486 :rule nary_cong :premises (@p485 @p484) :args ((or @t395 (not @t394)))) % 0.52/0.89 (step @p487 :rule cnf_or_neg :args (@t395 0)) % 0.52/0.89 (step @p488 :rule eq_resolve :premises (@p487 @p486)) % 0.52/0.89 (step @p489 :rule reordering :premises (@p488) :args ((or @t393 @t395))) % 0.52/0.89 (step @p490 :rule chain_m_resolution :premises (@p489 @p481) :args (@t393 @t382 @t396)) % 0.52/0.89 (step @p491 :rule cnf_or_pos :args (@t397)) % 0.52/0.89 (step @p492 :rule reordering :premises (@p491) :args ((or @t380 @t378 @t394 @t392 @t398))) % 0.52/0.89 (step @p493 :rule chain_m_resolution :premises (@p492 @p473 @p467 @p490 @p483) :args (@t398 (@list false false false true) (@list @t379 @t377 @t393 @t392))) % 0.52/0.89 (assume-push @p500 @t94) % 0.52/0.89 (step @p495 :rule instantiate :premises (@p147) :args ((@list @t325 @t326 @t391))) % 0.52/0.89 (step-pop @p501 :rule scope :premises (@p495)) % 0.52/0.89 (step @p496 :rule process_scope :premises (@p501) :args (@t397)) % 0.52/0.89 (step @p498 :rule implies_elim :premises (@p496)) % 0.52/0.89 (step @p499 false :rule chain_m_resolution :premises (@p498 @p493 @p147) :args (false (@list true false) (@list @t397 @t94))) % 0.52/0.89 ) % 0.52/0.89 % SZS output end Proof % 0.52/0.89 % cvc5 exiting %------------------------------------------------------------------------------