%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PLA053^4 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n029.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 08:43:30 AM UTC 2026 % Result : Theorem 2.61s 2.83s % Output : Proof 2.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : PLA053^4 : TPTP v9.2.1. Released v8.1.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n029.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 13:04:47 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.50 %----Proving TH0 % 2.61/2.83 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 2.61/2.83 % SZS status Theorem % 2.61/2.83 % SZS output start Proof % 2.61/2.83 ( % 2.61/2.83 (declare-sort $$unsorted 0) % 2.61/2.83 (declare-sort tptp.mworld 0) % 2.61/2.83 (declare-const tptp.mactual tptp.mworld) % 2.61/2.83 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 2.61/2.83 (declare-const tptp.defused (-> $$unsorted tptp.mworld Bool)) % 2.61/2.83 (declare-const tptp.h (-> $$unsorted tptp.mworld Bool)) % 2.61/2.83 (declare-const tptp.bomb (-> $$unsorted tptp.mworld Bool)) % 2.61/2.83 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 2.61/2.83 (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)))))) % 2.61/2.83 (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))))))) % 2.61/2.83 (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))))))) % 2.61/2.83 (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))))))) % 2.61/2.83 (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))))))) % 2.61/2.83 (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)))))))) % 2.61/2.83 (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)))))))) % 2.61/2.83 (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) (_ (_ _let_3 _let_2) _let_1))))))) % 2.61/2.83 (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) (_ (_ _let_3 _let_2) _let_1))))))) % 2.61/2.83 (define @t1 () (@var "W" tptp.mworld)) % 2.61/2.83 (define @t2 () (_ tptp.mrel @t1)) % 2.61/2.83 (define @t3 () (_ @t2 @t1)) % 2.61/2.83 (define @t4 () (@list @t1)) % 2.61/2.83 (define @t5 () (forall @t4 @t3)) % 2.61/2.83 (define @t6 () (@var "U" tptp.mworld)) % 2.61/2.83 (define @t7 () (@var "V" tptp.mworld)) % 2.61/2.83 (define @t8 () (_ @t2 @t7)) % 2.61/2.83 (define @t9 () (@var "__flatten_var_0" tptp.mworld)) % 2.61/2.83 (define @t10 () (@var "B" $$unsorted)) % 2.61/2.83 (define @t11 () (@var "X" $$unsorted)) % 2.61/2.83 (define @t12 () (_ tptp.bomb @t11)) % 2.61/2.83 (define @t13 () (@var "A" $$unsorted)) % 2.61/2.83 (define @t14 () (_ tptp.mand @t12)) % 2.61/2.83 (define @t15 () (@list @t11 @t9)) % 2.61/2.83 (define @t16 () (_ tptp.defused @t11)) % 2.61/2.83 (define @t17 () (@var "D" $$unsorted)) % 2.61/2.83 (define @t18 () (_ tptp.h @t17)) % 2.61/2.83 (define @t19 () (_ (_ tptp.mimplies (_ @t14 @t18)) @t16)) % 2.61/2.83 (define @t20 () (@list @t17 @t9)) % 2.61/2.83 (define @t21 () (lambda @t20 (_ (_ tptp.mbox @t19) @t9))) % 2.61/2.83 (define @t22 () (lambda @t15 (_ (_ tptp.mexists_di @t21) @t9))) % 2.61/2.83 (define @t23 () (lambda @t20 (_ @t19 @t9))) % 2.61/2.83 (define @t24 () (lambda @t15 (_ (_ tptp.mexists_di @t23) @t9))) % 2.61/2.83 (define @t25 () (not (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di @t24))))) % 2.61/2.83 (define @t26 () (@var "Phi" (-> tptp.mworld Bool))) % 2.61/2.83 (define @t27 () (lambda (@list @t26) (_ @t26 tptp.mactual))) % 2.61/2.83 (define @t28 () (@var "A" (-> tptp.mworld Bool))) % 2.61/2.83 (define @t29 () (_ @t28 @t1)) % 2.61/2.83 (define @t30 () (lambda (@list @t28 @t1) (not @t29))) % 2.61/2.83 (define @t31 () (@var "B" (-> tptp.mworld Bool))) % 2.61/2.83 (define @t32 () (_ @t31 @t1)) % 2.61/2.83 (define @t33 () (@list @t28 @t31 @t1)) % 2.61/2.83 (define @t34 () (lambda @t33 (and @t29 @t32))) % 2.61/2.83 (define @t35 () (lambda @t33 (or @t29 @t32))) % 2.61/2.83 (define @t36 () (lambda @t33 (=> @t29 @t32))) % 2.61/2.83 (define @t37 () (lambda @t33 (= @t29 @t32))) % 2.61/2.83 (define @t38 () (_ @t26 @t7)) % 2.61/2.83 (define @t39 () (@list @t7)) % 2.61/2.83 (define @t40 () (forall @t39 (=> @t8 @t38))) % 2.61/2.83 (define @t41 () (@list @t26 @t1)) % 2.61/2.83 (define @t42 () (lambda @t41 @t40)) % 2.61/2.83 (define @t43 () (lambda @t41 (exists @t39 (and @t8 @t38)))) % 2.61/2.83 (define @t44 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 2.61/2.83 (define @t45 () (_ (_ @t44 @t11) @t1)) % 2.61/2.83 (define @t46 () (@list @t11)) % 2.61/2.83 (define @t47 () (forall @t46 @t45)) % 2.61/2.83 (define @t48 () (@list @t44 @t1)) % 2.61/2.83 (define @t49 () (lambda @t48 @t47)) % 2.61/2.83 (define @t50 () (exists @t46 @t45)) % 2.61/2.83 (define @t51 () (lambda @t48 @t50)) % 2.61/2.83 (define @t52 () (@var "BOUND_VARIABLE_8068" $$unsorted)) % 2.61/2.83 (define @t53 () (tptp.defused @t52 @t7)) % 2.61/2.83 (define @t54 () (not (tptp.bomb @t52 @t7))) % 2.61/2.83 (define @t55 () (@var "BOUND_VARIABLE_8017" $$unsorted)) % 2.61/2.83 (define @t56 () (@list @t55)) % 2.61/2.83 (define @t57 () (not (forall @t56 (tptp.h @t55 @t7)))) % 2.61/2.83 (define @t58 () (not (tptp.mrel tptp.mactual @t7))) % 2.61/2.83 (define @t59 () (@list @t7 @t52)) % 2.61/2.83 (define @t60 () (forall @t59 (or @t58 @t57 @t54 @t53))) % 2.61/2.83 (define @t61 () (tptp.mrel @t1 @t7)) % 2.61/2.83 (define @t62 () (not @t61)) % 2.61/2.83 (define @t63 () (or @t62 @t57 @t54 @t53)) % 2.61/2.83 (define @t64 () (lambda @t4 (forall @t59 @t63))) % 2.61/2.83 (define @t65 () (_ @t64 tptp.mactual)) % 2.61/2.83 (define @t66 () (or @t54 @t53)) % 2.61/2.83 (define @t67 () (or @t62 @t57 @t66)) % 2.61/2.83 (define @t68 () (forall @t59 @t67)) % 2.61/2.83 (define @t69 () (@list @t52)) % 2.61/2.83 (define @t70 () (forall @t69 @t67)) % 2.61/2.83 (define @t71 () (forall @t69 @t66)) % 2.61/2.83 (define @t72 () (@list @t11)) % 2.61/2.83 (define @t73 () (or @t62 @t57 @t71)) % 2.61/2.83 (define @t74 () (tptp.defused @t11 @t7)) % 2.61/2.83 (define @t75 () (tptp.bomb @t11 @t7)) % 2.61/2.83 (define @t76 () (not @t75)) % 2.61/2.83 (define @t77 () (forall @t46 (or @t76 @t74))) % 2.61/2.83 (define @t78 () (or @t62 @t57 @t77)) % 2.61/2.83 (define @t79 () (or @t57 @t77)) % 2.61/2.83 (define @t80 () (tptp.defused @t11 @t1)) % 2.61/2.83 (define @t81 () (tptp.bomb @t11 @t1)) % 2.61/2.83 (define @t82 () (tptp.h @t55 @t1)) % 2.61/2.83 (define @t83 () (forall @t56 @t82)) % 2.61/2.83 (define @t84 () (not @t83)) % 2.61/2.83 (define @t85 () (lambda @t4 (or @t84 (forall @t46 (or (not @t81) @t80))))) % 2.61/2.83 (define @t86 () (_ @t85 @t7)) % 2.61/2.83 (define @t87 () (or @t62 @t86)) % 2.61/2.83 (define @t88 () (forall @t39 @t87)) % 2.61/2.83 (define @t89 () (lambda @t4 @t88)) % 2.61/2.83 (define @t90 () (_ @t26 @t7)) % 2.61/2.83 (define @t91 () (lambda @t41 (forall @t39 (or @t62 @t90)))) % 2.61/2.83 (define @t92 () (_ @t16 @t1)) % 2.61/2.83 (define @t93 () (_ @t12 @t1)) % 2.61/2.83 (define @t94 () (not @t93)) % 2.61/2.83 (define @t95 () (or @t94 @t92)) % 2.61/2.83 (define @t96 () (forall @t46 @t95)) % 2.61/2.83 (define @t97 () (or @t84 @t96)) % 2.61/2.83 (define @t98 () (or @t84 @t95)) % 2.61/2.83 (define @t99 () (or @t94 @t84 @t92)) % 2.61/2.83 (define @t100 () (not @t92)) % 2.61/2.83 (define @t101 () (not @t100)) % 2.61/2.83 (define @t102 () (or @t94 @t84 @t101)) % 2.61/2.83 (define @t103 () (not (and @t93 @t83 @t100))) % 2.61/2.83 (define @t104 () (_ @t16 @t9)) % 2.61/2.83 (define @t105 () (_ @t12 @t9)) % 2.61/2.83 (define @t106 () (not (and @t105 (forall @t56 (tptp.h @t55 @t9)) (not @t104)))) % 2.61/2.83 (define @t107 () (lambda @t15 @t106)) % 2.61/2.83 (define @t108 () (_ @t107 @t11 @t1)) % 2.61/2.83 (define @t109 () (forall @t46 @t108)) % 2.61/2.83 (define @t110 () (lambda @t4 @t109)) % 2.61/2.83 (define @t111 () (_ @t44 @t11 @t1)) % 2.61/2.83 (define @t112 () (lambda @t48 (forall @t46 @t111))) % 2.61/2.83 (define @t113 () (_ (_ tptp.h @t55) @t1)) % 2.61/2.83 (define @t114 () (forall @t56 @t113)) % 2.61/2.83 (define @t115 () (@var "BOUND_VARIABLE_7993" $$unsorted)) % 2.61/2.83 (define @t116 () (@list @t115)) % 2.61/2.83 (define @t117 () (forall @t116 @t100)) % 2.61/2.83 (define @t118 () (_ (_ tptp.h @t115) @t1)) % 2.61/2.83 (define @t119 () (forall @t116 @t118)) % 2.61/2.83 (define @t120 () (@list @t115)) % 2.61/2.83 (define @t121 () (forall @t116 @t93)) % 2.61/2.83 (define @t122 () (and @t121 @t119 @t117)) % 2.61/2.83 (define @t123 () (and @t93 @t118 @t100)) % 2.61/2.83 (define @t124 () (and @t93 @t118)) % 2.61/2.83 (define @t125 () (=> @t124 @t92)) % 2.61/2.83 (define @t126 () (=> (and @t105 (_ @t18 @t9)) @t104)) % 2.61/2.83 (define @t127 () (lambda @t20 @t126)) % 2.61/2.83 (define @t128 () (_ @t127 @t115 @t1)) % 2.61/2.83 (define @t129 () (not @t128)) % 2.61/2.83 (define @t130 () (forall @t116 @t129)) % 2.61/2.83 (define @t131 () (not @t130)) % 2.61/2.83 (define @t132 () (lambda @t4 @t131)) % 2.61/2.83 (define @t133 () (forall @t46 (not @t111))) % 2.61/2.83 (define @t134 () (not @t133)) % 2.61/2.83 (define @t135 () (lambda @t48 @t134)) % 2.61/2.83 (define @t136 () (and @t93 (_ @t18 @t1))) % 2.61/2.83 (define @t137 () (lambda @t4 (=> @t136 @t92))) % 2.61/2.83 (define @t138 () (@list @t31 @t1)) % 2.61/2.83 (define @t139 () (lambda @t4 @t136)) % 2.61/2.83 (define @t140 () (_ @t139 @t1)) % 2.61/2.83 (define @t141 () (=> @t140 @t32)) % 2.61/2.83 (define @t142 () (lambda @t138 @t141)) % 2.61/2.83 (define @t143 () (lambda @t138 (and @t93 @t32))) % 2.61/2.83 (define @t144 () (_ @t34 @t12)) % 2.61/2.83 (define @t145 () (_ (_ @t36 (_ @t144 @t18)) @t16)) % 2.61/2.83 (define @t146 () (lambda @t20 (_ @t145 @t9))) % 2.61/2.83 (define @t147 () (lambda @t15 (_ (_ @t135 @t146) @t9))) % 2.61/2.83 (define @t148 () (not @t45)) % 2.61/2.83 (define @t149 () (forall @t46 @t148)) % 2.61/2.83 (define @t150 () (not @t149)) % 2.61/2.83 (define @t151 () (not @t8)) % 2.61/2.83 (define @t152 () (or @t151 @t38)) % 2.61/2.83 (define @t153 () (@quantifiers_skolemize @t60 0)) % 2.61/2.83 (define @t154 () (forall @t56 (tptp.h @t55 @t153))) % 2.61/2.83 (define @t155 () (@quantifiers_skolemize @t60 1)) % 2.61/2.83 (define @t156 () (tptp.defused @t155 @t153)) % 2.61/2.83 (define @t157 () (tptp.bomb @t155 @t153)) % 2.61/2.83 (define @t158 () (not @t157)) % 2.61/2.83 (define @t159 () (not @t154)) % 2.61/2.83 (define @t160 () (tptp.mrel tptp.mactual @t153)) % 2.61/2.83 (define @t161 () (not @t160)) % 2.61/2.83 (define @t162 () (or @t161 @t159 @t158 @t156)) % 2.61/2.83 (define @t163 () (@list true)) % 2.61/2.83 (define @t164 () (@list @t162)) % 2.61/2.83 (define @t165 () (@var "BOUND_VARIABLE_7929" tptp.mworld)) % 2.61/2.83 (define @t166 () (@var "BOUND_VARIABLE_7957" $$unsorted)) % 2.61/2.83 (define @t167 () (@var "BOUND_VARIABLE_7888" $$unsorted)) % 2.61/2.83 (define @t168 () (not (tptp.h @t167 @t165))) % 2.61/2.83 (define @t169 () (not (tptp.mrel @t7 @t165))) % 2.61/2.83 (define @t170 () (@list @t165)) % 2.61/2.83 (define @t171 () (@list @t167)) % 2.61/2.83 (define @t172 () (not (forall @t171 (not (forall @t170 (or @t169 (not (tptp.bomb @t166 @t165)) @t168 (tptp.defused @t166 @t165))))))) % 2.61/2.83 (define @t173 () (@list @t7 @t166)) % 2.61/2.83 (define @t174 () (or @t62 @t172)) % 2.61/2.83 (define @t175 () (forall @t173 @t174)) % 2.61/2.83 (define @t176 () (lambda @t4 @t175)) % 2.61/2.83 (define @t177 () (_ @t176 tptp.mactual)) % 2.61/2.83 (define @t178 () (@list @t166)) % 2.61/2.83 (define @t179 () (forall @t178 @t174)) % 2.61/2.83 (define @t180 () (forall @t178 @t172)) % 2.61/2.83 (define @t181 () (or @t62 @t180)) % 2.61/2.83 (define @t182 () (tptp.defused @t11 @t165)) % 2.61/2.83 (define @t183 () (not (tptp.bomb @t11 @t165))) % 2.61/2.83 (define @t184 () (forall @t46 (not (forall @t171 (not (forall @t170 (or @t169 @t183 @t168 @t182))))))) % 2.61/2.83 (define @t185 () (not (tptp.h @t167 @t7))) % 2.61/2.83 (define @t186 () (forall @t39 (or @t62 @t76 @t185 @t74))) % 2.61/2.83 (define @t187 () (not @t186)) % 2.61/2.83 (define @t188 () (forall @t171 @t187)) % 2.61/2.83 (define @t189 () (not @t188)) % 2.61/2.83 (define @t190 () (forall @t46 @t189)) % 2.61/2.83 (define @t191 () (lambda @t4 @t190)) % 2.61/2.83 (define @t192 () (or @t62 (_ @t191 @t7))) % 2.61/2.83 (define @t193 () (forall @t39 @t192)) % 2.61/2.83 (define @t194 () (lambda @t4 @t193)) % 2.61/2.83 (define @t195 () (not (tptp.mrel @t9 @t7))) % 2.61/2.83 (define @t196 () (not (forall @t171 (not (forall @t39 (or @t195 @t76 @t185 @t74)))))) % 2.61/2.83 (define @t197 () (lambda @t15 @t196)) % 2.61/2.83 (define @t198 () (_ @t197 @t11 @t1)) % 2.61/2.83 (define @t199 () (forall @t46 @t198)) % 2.61/2.83 (define @t200 () (lambda @t4 @t199)) % 2.61/2.83 (define @t201 () (tptp.h @t17 @t7)) % 2.61/2.83 (define @t202 () (not @t201)) % 2.61/2.83 (define @t203 () (forall @t39 (or @t195 @t76 @t202 @t74))) % 2.61/2.83 (define @t204 () (lambda @t20 @t203)) % 2.61/2.83 (define @t205 () (_ @t204 @t167 @t1)) % 2.61/2.83 (define @t206 () (not @t205)) % 2.61/2.83 (define @t207 () (forall @t171 @t206)) % 2.61/2.83 (define @t208 () (not @t207)) % 2.61/2.83 (define @t209 () (lambda @t4 @t208)) % 2.61/2.83 (define @t210 () (_ @t16 @t7)) % 2.61/2.83 (define @t211 () (_ @t18 @t7)) % 2.61/2.83 (define @t212 () (not @t211)) % 2.61/2.83 (define @t213 () (_ @t12 @t7)) % 2.61/2.83 (define @t214 () (not @t213)) % 2.61/2.83 (define @t215 () (or @t62 @t214 @t212 @t210)) % 2.61/2.83 (define @t216 () (or @t214 @t212 @t210)) % 2.61/2.83 (define @t217 () (and @t213 @t211)) % 2.61/2.83 (define @t218 () (=> @t217 @t210)) % 2.61/2.83 (define @t219 () (or @t62 @t218)) % 2.61/2.83 (define @t220 () (_ @t137 @t7)) % 2.61/2.83 (define @t221 () (or @t62 @t220)) % 2.61/2.83 (define @t222 () (forall @t39 @t221)) % 2.61/2.83 (define @t223 () (lambda @t4 @t222)) % 2.61/2.83 (define @t224 () (lambda @t20 (_ (_ @t91 @t145) @t9))) % 2.61/2.83 (define @t225 () (tptp.mrel @t1 @t1)) % 2.61/2.83 (define @t226 () (tptp.defused @t155 @t165)) % 2.61/2.83 (define @t227 () (not (tptp.bomb @t155 @t165))) % 2.61/2.83 (define @t228 () (not (tptp.mrel tptp.mactual @t165))) % 2.61/2.83 (define @t229 () (forall @t171 (not (forall @t170 (or @t228 @t227 @t168 @t226))))) % 2.61/2.83 (define @t230 () (not @t229)) % 2.61/2.83 (define @t231 () (tptp.mrel tptp.mactual tptp.mactual)) % 2.61/2.83 (define @t232 () (not @t231)) % 2.61/2.83 (define @t233 () (or @t232 @t230)) % 2.61/2.83 (define @t234 () (@quantifiers_skolemize @t229 0)) % 2.61/2.83 (define @t235 () (forall @t170 (or @t228 @t227 (not (tptp.h @t234 @t165)) @t226))) % 2.61/2.83 (define @t236 () (not (not @t235))) % 2.61/2.83 (define @t237 () (tptp.h @t234 @t153)) % 2.61/2.83 (define @t238 () (not @t237)) % 2.61/2.83 (define @t239 () (or @t161 @t158 @t238 @t156)) % 2.61/2.83 (assume @p1 @t5) % 2.61/2.83 (assume @p2 (forall (@list @t1 @t7 @t6) (=> (and @t8 (_ (_ tptp.mrel @t7) @t6)) (_ @t2 @t6)))) % 2.61/2.83 (assume @p3 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mexists_di (lambda (@list @t10 @t9) (_ (_ tptp.bomb @t10) @t9)))))) % 2.61/2.83 (assume @p4 (_ tptp.mlocal (_ tptp.mexists_di (lambda (@list @t13 @t9) (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t15 (_ (_ (_ tptp.mimplies (_ @t14 (_ tptp.h @t13))) (_ tptp.mbox @t12)) @t9)))) @t9))))) % 2.61/2.83 (assume @p5 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di @t22)))) % 2.61/2.83 (assume @p6 @t25) % 2.61/2.83 (assume @p7 true) % 2.61/2.83 (step @p8 (= tptp.mlocal @t27) :rule refl :args (@t27)) % 2.61/2.83 (step @p9 (= tptp.mnot @t30) :rule refl :args (@t30)) % 2.61/2.83 (step @p10 (= tptp.mand @t34) :rule refl :args (@t34)) % 2.61/2.83 (step @p11 (= tptp.mor @t35) :rule refl :args (@t35)) % 2.61/2.83 (step @p12 (= tptp.mimplies @t36) :rule refl :args (@t36)) % 2.61/2.83 (step @p13 (= tptp.mequiv @t37) :rule refl :args (@t37)) % 2.61/2.83 (step @p14 (= tptp.mbox @t42) :rule refl :args (@t42)) % 2.61/2.83 (step @p15 (= tptp.mdia @t43) :rule refl :args (@t43)) % 2.61/2.83 (step @p16 (= tptp.mforall_di @t49) :rule refl :args (@t49)) % 2.61/2.83 (step @p17 (= tptp.mexists_di @t51) :rule refl :args (@t51)) % 2.61/2.83 (step @p18 :rule beta-reduce :args ((= @t65 @t60))) % 2.61/2.83 (step @p19 :rule beta-reduce :args ((= (_ @t27 @t64) @t65))) % 2.61/2.83 (step @p20 :rule trans :premises (@p19 @p18)) % 2.61/2.83 (step @p21 :rule aci_norm :args ((= @t67 @t63))) % 2.61/2.83 (step @p22 :rule cong :premises (@p21) :args (@t68)) % 2.61/2.83 (step @p23 :rule quant-merge-prenex :args ((= (forall @t39 @t70) @t68))) % 2.61/2.83 (step @p24 :rule alpha_equiv :args (@t71 (@list @t52) @t72)) % 2.61/2.83 (step @p25 :rule refl :args (@t57)) % 2.61/2.83 (step @p26 :rule refl :args (@t62)) % 2.61/2.83 (step @p27 :rule nary_cong :premises (@p26 @p25 @p24) :args (@t73)) % 2.61/2.83 (step @p28 :rule quant-miniscope-or :args ((= @t70 @t73))) % 2.61/2.83 (step @p29 :rule trans :premises (@p28 @p27)) % 2.61/2.83 (step @p30 :rule symm :premises (@p29)) % 2.61/2.83 (step @p31 :rule cong :premises (@p30) :args ((forall @t39 @t78))) % 2.61/2.83 (step @p32 :rule trans :premises (@p31 @p23)) % 2.61/2.83 (step @p33 :rule trans :premises (@p32 @p22)) % 2.61/2.83 (step @p34 :rule aci_norm :args ((= (or @t62 @t79) @t78))) % 2.61/2.83 (step @p35 :rule beta-reduce :args ((= @t86 @t79))) % 2.61/2.83 (step @p36 :rule refl :args (@t62)) % 2.61/2.83 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t87)) % 2.61/2.83 (step @p38 :rule trans :premises (@p37 @p34)) % 2.61/2.83 (step @p39 :rule cong :premises (@p38) :args (@t88)) % 2.61/2.83 (step @p40 :rule trans :premises (@p39 @p33)) % 2.61/2.83 (step @p41 :rule cong :premises (@p40) :args (@t89)) % 2.61/2.83 (step @p42 :rule beta-reduce :args ((= (_ @t91 @t85) @t89))) % 2.61/2.83 (step @p43 :rule trans :premises (@p42 @p41)) % 2.61/2.83 (step @p44 :rule refl :args (@t80)) % 2.61/2.83 (step @p45 :rule refl :args (@t92)) % 2.61/2.83 (step @p46 :rule cong :premises (@p45 @p44) :args ((= @t92 @t80))) % 2.61/2.83 (step @p47 :rule symm :premises (@p46)) % 2.61/2.83 (step @p48 :rule eq_resolve :premises (@p45 @p47)) % 2.61/2.83 (step @p49 :rule refl :args (@t81)) % 2.61/2.83 (step @p50 :rule refl :args (@t93)) % 2.61/2.83 (step @p51 :rule cong :premises (@p50 @p49) :args ((= @t93 @t81))) % 2.61/2.83 (step @p52 :rule symm :premises (@p51)) % 2.61/2.83 (step @p53 :rule eq_resolve :premises (@p50 @p52)) % 2.61/2.83 (step @p54 :rule cong :premises (@p53) :args (@t94)) % 2.61/2.83 (step @p55 :rule nary_cong :premises (@p54 @p48) :args (@t95)) % 2.61/2.83 (step @p56 :rule cong :premises (@p55) :args (@t96)) % 2.61/2.83 (step @p57 :rule refl :args (@t84)) % 2.61/2.83 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t97)) % 2.61/2.83 (step @p59 :rule quant-miniscope-or :args ((= (forall @t46 @t98) @t97))) % 2.61/2.83 (step @p60 :rule aci_norm :args ((= @t99 @t98))) % 2.61/2.83 (step @p61 :rule cong :premises (@p60) :args ((forall @t46 @t99))) % 2.61/2.83 (step @p62 :rule trans :premises (@p61 @p59)) % 2.61/2.83 (step @p63 :rule trans :premises (@p62 @p58)) % 2.61/2.83 (step @p64 :rule bool-double-not-elim :args (@t92)) % 2.61/2.83 (step @p65 :rule refl :args (@t84)) % 2.61/2.83 (step @p66 :rule refl :args (@t94)) % 2.61/2.83 (step @p67 :rule nary_cong :premises (@p66 @p65 @p64) :args (@t102)) % 2.61/2.83 (step @p68 :rule aci_norm :args ((= (or @t94 (or @t84 @t101)) @t102))) % 2.61/2.83 (step @p69 :rule trans :premises (@p68 @p67)) % 2.61/2.83 (step @p70 :rule bool-and-de-morgan :args (@t83 @t100 true)) % 2.61/2.83 (step @p71 :rule nary_cong :premises (@p66 @p70) :args ((or @t94 (not (and @t83 @t100))))) % 2.61/2.83 (step @p72 :rule bool-and-de-morgan :args (@t93 @t83 (and @t100))) % 2.61/2.83 (step @p73 :rule trans :premises (@p72 @p71)) % 2.61/2.83 (step @p74 :rule trans :premises (@p73 @p69)) % 2.61/2.83 (step @p75 :rule cong :premises (@p74) :args ((forall @t46 @t103))) % 2.61/2.83 (step @p76 :rule trans :premises (@p75 @p63)) % 2.61/2.83 (step @p77 :rule beta-reduce :args ((= @t108 @t103))) % 2.61/2.83 (step @p78 :rule cong :premises (@p77) :args (@t109)) % 2.61/2.83 (step @p79 :rule trans :premises (@p78 @p76)) % 2.61/2.83 (step @p80 :rule cong :premises (@p79) :args (@t110)) % 2.61/2.83 (step @p81 :rule beta-reduce :args ((= (_ @t112 @t107) @t110))) % 2.61/2.83 (step @p82 :rule trans :premises (@p81 @p80)) % 2.61/2.83 (step @p83 :rule beta-reduce :args ((= (_ (lambda @t4 @t103) @t9) @t106))) % 2.61/2.83 (step @p84 :rule refl :args (@t9)) % 2.61/2.83 (step @p85 :rule refl :args (@t100)) % 2.61/2.83 (step @p86 :rule refl :args (@t82)) % 2.61/2.83 (step @p87 :rule refl :args (@t113)) % 2.61/2.83 (step @p88 :rule cong :premises (@p87 @p86) :args ((= @t113 @t82))) % 2.61/2.83 (step @p89 :rule symm :premises (@p88)) % 2.61/2.83 (step @p90 :rule eq_resolve :premises (@p87 @p89)) % 2.61/2.83 (step @p91 :rule cong :premises (@p90) :args (@t114)) % 2.61/2.83 (step @p92 :rule refl :args (@t93)) % 2.61/2.83 (step @p93 :rule nary_cong :premises (@p92 @p91 @p85) :args ((and @t93 @t114 @t100))) % 2.61/2.83 (step @p94 :rule quant-unused-vars :args ((= @t117 @t100))) % 2.61/2.83 (step @p95 :rule alpha_equiv :args (@t119 @t120 (@list @t55))) % 2.61/2.83 (step @p96 :rule quant-unused-vars :args ((= @t121 @t93))) % 2.61/2.83 (step @p97 :rule nary_cong :premises (@p96 @p95 @p94) :args (@t122)) % 2.61/2.83 (step @p98 :rule quant-miniscope-and :args ((= (forall @t116 @t123) @t122))) % 2.61/2.83 (step @p99 :rule trans :premises (@p98 @p97)) % 2.61/2.83 (step @p100 :rule trans :premises (@p99 @p93)) % 2.61/2.83 (step @p101 :rule aci_norm :args ((= (and @t124 @t100) @t123))) % 2.61/2.83 (step @p102 :rule bool-implies-de-morgan :args (@t124 @t92)) % 2.61/2.83 (step @p103 :rule trans :premises (@p102 @p101)) % 2.61/2.83 (step @p104 :rule cong :premises (@p103) :args ((forall @t116 (not @t125)))) % 2.61/2.83 (step @p105 :rule trans :premises (@p104 @p100)) % 2.61/2.83 (step @p106 :rule beta-reduce :args ((= @t128 @t125))) % 2.61/2.83 (step @p107 :rule cong :premises (@p106) :args (@t129)) % 2.61/2.83 (step @p108 :rule cong :premises (@p107) :args (@t130)) % 2.61/2.83 (step @p109 :rule trans :premises (@p108 @p105)) % 2.61/2.83 (step @p110 :rule cong :premises (@p109) :args (@t131)) % 2.61/2.83 (step @p111 :rule cong :premises (@p110) :args (@t132)) % 2.61/2.83 (step @p112 :rule beta-reduce :args ((= (_ (lambda @t48 (not (forall @t116 (not (_ @t44 @t115 @t1))))) @t127) @t132))) % 2.61/2.83 (step @p113 :rule trans :premises (@p112 @p111)) % 2.61/2.83 (step @p114 :rule refl :args (@t127)) % 2.61/2.83 (step @p115 :rule alpha_equiv :args (@t133 @t72 @t120)) % 2.61/2.83 (step @p116 :rule cong :premises (@p115) :args (@t134)) % 2.61/2.83 (step @p117 :rule cong :premises (@p116) :args (@t135)) % 2.61/2.83 (step @p118 :rule ho_cong :premises (@p117 @p114)) % 2.61/2.83 (step @p119 :rule trans :premises (@p118 @p113)) % 2.61/2.83 (step @p120 :rule beta-reduce :args ((= (_ @t137 @t9) @t126))) % 2.61/2.83 (step @p121 :rule beta-reduce :args ((= (_ (lambda @t138 (=> @t136 @t32)) @t16) @t137))) % 2.61/2.83 (step @p122 :rule refl :args (@t16)) % 2.61/2.83 (step @p123 :rule refl :args (@t32)) % 2.61/2.83 (step @p124 :rule beta-reduce :args ((= @t140 @t136))) % 2.61/2.83 (step @p125 :rule cong :premises (@p124 @p123) :args (@t141)) % 2.61/2.83 (step @p126 :rule cong :premises (@p125) :args (@t142)) % 2.61/2.83 (step @p127 :rule beta-reduce :args ((= (_ @t36 @t139) @t142))) % 2.61/2.83 (step @p128 :rule trans :premises (@p127 @p126)) % 2.61/2.83 (step @p129 :rule beta-reduce :args ((= (_ @t143 @t18) @t139))) % 2.61/2.83 (step @p130 :rule refl :args (@t18)) % 2.61/2.83 (step @p131 :rule beta-reduce :args ((= @t144 @t143))) % 2.61/2.83 (step @p132 :rule ho_cong :premises (@p131 @p130)) % 2.61/2.83 (step @p133 :rule trans :premises (@p132 @p129)) % 2.61/2.83 (step @p134 :rule refl :args (@t36)) % 2.61/2.83 (step @p135 :rule ho_cong :premises (@p134 @p133)) % 2.61/2.83 (step @p136 :rule trans :premises (@p135 @p128)) % 2.61/2.83 (step @p137 :rule ho_cong :premises (@p136 @p122)) % 2.61/2.83 (step @p138 :rule trans :premises (@p137 @p121)) % 2.61/2.83 (step @p139 :rule ho_cong :premises (@p138 @p84)) % 2.61/2.83 (step @p140 :rule trans :premises (@p139 @p120)) % 2.61/2.83 (step @p141 :rule cong :premises (@p140) :args (@t146)) % 2.61/2.83 (step @p142 :rule refl :args (@t135)) % 2.61/2.83 (step @p143 :rule ho_cong :premises (@p142 @p141)) % 2.61/2.83 (step @p144 :rule trans :premises (@p143 @p119)) % 2.61/2.83 (step @p145 :rule ho_cong :premises (@p144 @p84)) % 2.61/2.83 (step @p146 :rule trans :premises (@p145 @p83)) % 2.61/2.83 (step @p147 :rule cong :premises (@p146) :args (@t147)) % 2.61/2.83 (step @p148 :rule refl :args (@t112)) % 2.61/2.83 (step @p149 :rule ho_cong :premises (@p148 @p147)) % 2.61/2.83 (step @p150 :rule trans :premises (@p149 @p82)) % 2.61/2.83 (step @p151 :rule refl :args (@t91)) % 2.61/2.83 (step @p152 :rule ho_cong :premises (@p151 @p150)) % 2.61/2.83 (step @p153 :rule trans :premises (@p152 @p43)) % 2.61/2.83 (step @p154 :rule refl :args (@t27)) % 2.61/2.83 (step @p155 :rule ho_cong :premises (@p154 @p153)) % 2.61/2.83 (step @p156 :rule trans :premises (@p155 @p20)) % 2.61/2.83 (step @p157 :rule cong :premises (@p156) :args ((not (_ @t27 (_ @t91 (_ @t112 @t147)))))) % 2.61/2.83 (step @p158 :rule refl :args (@t12)) % 2.61/2.83 (step @p159 :rule ho_cong :premises (@p10 @p158)) % 2.61/2.83 (step @p160 :rule ho_cong :premises (@p159 @p130)) % 2.61/2.83 (step @p161 :rule ho_cong :premises (@p12 @p160)) % 2.61/2.83 (step @p162 :rule ho_cong :premises (@p161 @p122)) % 2.61/2.83 (step @p163 :rule ho_cong :premises (@p162 @p84)) % 2.61/2.83 (step @p164 :rule cong :premises (@p163) :args (@t23)) % 2.61/2.83 (step @p165 :rule refl :args (@t111)) % 2.61/2.83 (step @p166 :rule refl :args (@t45)) % 2.61/2.83 (step @p167 :rule cong :premises (@p166 @p165) :args ((= @t45 @t111))) % 2.61/2.83 (step @p168 :rule symm :premises (@p167)) % 2.61/2.83 (step @p169 :rule eq_resolve :premises (@p166 @p168)) % 2.61/2.83 (step @p170 :rule cong :premises (@p169) :args (@t148)) % 2.61/2.83 (step @p171 :rule cong :premises (@p170) :args (@t149)) % 2.61/2.83 (step @p172 :rule cong :premises (@p171) :args (@t150)) % 2.61/2.83 (step @p173 :rule exists-elim :args ((= @t50 @t150))) % 2.61/2.83 (step @p174 :rule trans :premises (@p173 @p172)) % 2.61/2.83 (step @p175 :rule cong :premises (@p174) :args (@t51)) % 2.61/2.83 (step @p176 :rule trans :premises (@p17 @p175)) % 2.61/2.83 (step @p177 :rule ho_cong :premises (@p176 @p164)) % 2.61/2.83 (step @p178 :rule ho_cong :premises (@p177 @p84)) % 2.61/2.83 (step @p179 :rule cong :premises (@p178) :args (@t24)) % 2.61/2.83 (step @p180 :rule cong :premises (@p169) :args (@t47)) % 2.61/2.83 (step @p181 :rule cong :premises (@p180) :args (@t49)) % 2.61/2.83 (step @p182 :rule trans :premises (@p16 @p181)) % 2.61/2.83 (step @p183 :rule ho_cong :premises (@p182 @p179)) % 2.61/2.83 (step @p184 :rule refl :args (@t90)) % 2.61/2.83 (step @p185 :rule refl :args (@t38)) % 2.61/2.83 (step @p186 :rule cong :premises (@p185 @p184) :args ((= @t38 @t90))) % 2.61/2.83 (step @p187 :rule symm :premises (@p186)) % 2.61/2.83 (step @p188 :rule eq_resolve :premises (@p185 @p187)) % 2.61/2.83 (step @p189 :rule refl :args (@t61)) % 2.61/2.83 (step @p190 :rule refl :args (@t8)) % 2.61/2.83 (step @p191 :rule cong :premises (@p190 @p189) :args ((= @t8 @t61))) % 2.61/2.83 (step @p192 :rule symm :premises (@p191)) % 2.61/2.83 (step @p193 :rule eq_resolve :premises (@p190 @p192)) % 2.61/2.83 (step @p194 :rule cong :premises (@p193) :args (@t151)) % 2.61/2.83 (step @p195 :rule nary_cong :premises (@p194 @p188) :args (@t152)) % 2.61/2.83 (step @p196 :rule cong :premises (@p195) :args ((forall @t39 @t152))) % 2.61/2.83 (step @p197 :rule bool-impl-elim :args (@t8 @t38)) % 2.61/2.83 (step @p198 :rule cong :premises (@p197) :args (@t40)) % 2.61/2.83 (step @p199 :rule trans :premises (@p198 @p196)) % 2.61/2.83 (step @p200 :rule cong :premises (@p199) :args (@t42)) % 2.61/2.83 (step @p201 :rule trans :premises (@p14 @p200)) % 2.61/2.83 (step @p202 :rule ho_cong :premises (@p201 @p183)) % 2.61/2.83 (step @p203 :rule ho_cong :premises (@p8 @p202)) % 2.61/2.83 (step @p204 :rule cong :premises (@p203) :args (@t25)) % 2.61/2.83 (step @p205 :rule trans :premises (@p204 @p157)) % 2.61/2.83 (step @p206 :rule eq_resolve :premises (@p6 @p205)) % 2.61/2.83 (step @p207 :rule skolemize :premises (@p206)) % 2.61/2.83 (step @p208 :rule bool-double-not-elim :args (@t154)) % 2.61/2.83 (step @p209 :rule refl :args (@t162)) % 2.61/2.83 (step @p210 :rule nary_cong :premises (@p209 @p208) :args ((or @t162 (not @t159)))) % 2.61/2.83 (step @p211 :rule cnf_or_neg :args (@t162 1)) % 2.61/2.83 (step @p212 :rule eq_resolve :premises (@p211 @p210)) % 2.61/2.83 (step @p213 :rule reordering :premises (@p212) :args ((or @t154 @t162))) % 2.61/2.83 (step @p214 :rule chain_m_resolution :premises (@p213 @p207) :args (@t154 @t163 @t164)) % 2.61/2.83 (step @p215 :rule beta-reduce :args ((= @t177 (forall @t173 (or @t58 @t172))))) % 2.61/2.83 (step @p216 :rule beta-reduce :args ((= (_ @t27 @t176) @t177))) % 2.61/2.83 (step @p217 :rule trans :premises (@p216 @p215)) % 2.61/2.83 (step @p218 :rule quant-merge-prenex :args ((= (forall @t39 @t179) @t175))) % 2.61/2.83 (step @p219 :rule alpha_equiv :args (@t180 (@list @t166) @t72)) % 2.61/2.83 (step @p220 :rule nary_cong :premises (@p26 @p219) :args (@t181)) % 2.61/2.83 (step @p221 :rule quant-miniscope-or :args ((= @t179 @t181))) % 2.61/2.83 (step @p222 :rule trans :premises (@p221 @p220)) % 2.61/2.83 (step @p223 :rule symm :premises (@p222)) % 2.61/2.83 (step @p224 :rule cong :premises (@p223) :args ((forall @t39 (or @t62 @t184)))) % 2.61/2.83 (step @p225 :rule trans :premises (@p224 @p218)) % 2.61/2.83 (step @p226 :rule beta-reduce :args ((= (_ (lambda @t4 (forall @t46 (not (forall @t171 (not (forall @t170 (or (not (tptp.mrel @t1 @t165)) @t183 @t168 @t182))))))) @t7) @t184))) % 2.61/2.83 (step @p227 :rule refl :args (@t7)) % 2.61/2.83 (step @p228 :rule alpha_equiv :args (@t186 (@list @t7) (@list @t165))) % 2.61/2.83 (step @p229 :rule cong :premises (@p228) :args (@t187)) % 2.61/2.83 (step @p230 :rule cong :premises (@p229) :args (@t188)) % 2.61/2.83 (step @p231 :rule cong :premises (@p230) :args (@t189)) % 2.61/2.83 (step @p232 :rule cong :premises (@p231) :args (@t190)) % 2.61/2.83 (step @p233 :rule cong :premises (@p232) :args (@t191)) % 2.61/2.83 (step @p234 :rule ho_cong :premises (@p233 @p227)) % 2.61/2.83 (step @p235 :rule trans :premises (@p234 @p226)) % 2.61/2.83 (step @p236 :rule nary_cong :premises (@p36 @p235) :args (@t192)) % 2.61/2.83 (step @p237 :rule cong :premises (@p236) :args (@t193)) % 2.61/2.83 (step @p238 :rule trans :premises (@p237 @p225)) % 2.61/2.83 (step @p239 :rule cong :premises (@p238) :args (@t194)) % 2.61/2.83 (step @p240 :rule beta-reduce :args ((= (_ @t91 @t191) @t194))) % 2.61/2.83 (step @p241 :rule trans :premises (@p240 @p239)) % 2.61/2.83 (step @p242 :rule beta-reduce :args ((= @t198 @t189))) % 2.61/2.83 (step @p243 :rule cong :premises (@p242) :args (@t199)) % 2.61/2.83 (step @p244 :rule cong :premises (@p243) :args (@t200)) % 2.61/2.83 (step @p245 :rule beta-reduce :args ((= (_ @t112 @t197) @t200))) % 2.61/2.83 (step @p246 :rule trans :premises (@p245 @p244)) % 2.61/2.83 (step @p247 :rule beta-reduce :args ((= (_ (lambda @t4 @t189) @t9) @t196))) % 2.61/2.83 (step @p248 :rule beta-reduce :args ((= @t205 @t186))) % 2.61/2.83 (step @p249 :rule cong :premises (@p248) :args (@t206)) % 2.61/2.83 (step @p250 :rule cong :premises (@p249) :args (@t207)) % 2.61/2.83 (step @p251 :rule cong :premises (@p250) :args (@t208)) % 2.61/2.83 (step @p252 :rule cong :premises (@p251) :args (@t209)) % 2.61/2.83 (step @p253 :rule beta-reduce :args ((= (_ (lambda @t48 (not (forall @t171 (not (_ @t44 @t167 @t1))))) @t204) @t209))) % 2.61/2.83 (step @p254 :rule trans :premises (@p253 @p252)) % 2.61/2.83 (step @p255 :rule refl :args (@t204)) % 2.61/2.83 (step @p256 :rule alpha_equiv :args (@t133 @t72 (@list @t167))) % 2.61/2.83 (step @p257 :rule cong :premises (@p256) :args (@t134)) % 2.61/2.83 (step @p258 :rule cong :premises (@p257) :args (@t135)) % 2.61/2.83 (step @p259 :rule ho_cong :premises (@p258 @p255)) % 2.61/2.83 (step @p260 :rule trans :premises (@p259 @p254)) % 2.61/2.83 (step @p261 :rule beta-reduce :args ((= (_ (lambda @t4 (forall @t39 (or @t62 @t76 @t202 @t74))) @t9) @t203))) % 2.61/2.83 (step @p262 :rule refl :args (@t74)) % 2.61/2.83 (step @p263 :rule refl :args (@t210)) % 2.61/2.83 (step @p264 :rule cong :premises (@p263 @p262) :args ((= @t210 @t74))) % 2.61/2.83 (step @p265 :rule symm :premises (@p264)) % 2.61/2.83 (step @p266 :rule eq_resolve :premises (@p263 @p265)) % 2.61/2.83 (step @p267 :rule refl :args (@t201)) % 2.61/2.83 (step @p268 :rule refl :args (@t211)) % 2.61/2.83 (step @p269 :rule cong :premises (@p268 @p267) :args ((= @t211 @t201))) % 2.61/2.83 (step @p270 :rule symm :premises (@p269)) % 2.61/2.83 (step @p271 :rule eq_resolve :premises (@p268 @p270)) % 2.61/2.83 (step @p272 :rule cong :premises (@p271) :args (@t212)) % 2.61/2.83 (step @p273 :rule refl :args (@t75)) % 2.61/2.83 (step @p274 :rule refl :args (@t213)) % 2.61/2.83 (step @p275 :rule cong :premises (@p274 @p273) :args ((= @t213 @t75))) % 2.61/2.83 (step @p276 :rule symm :premises (@p275)) % 2.61/2.83 (step @p277 :rule eq_resolve :premises (@p274 @p276)) % 2.61/2.83 (step @p278 :rule cong :premises (@p277) :args (@t214)) % 2.61/2.83 (step @p279 :rule nary_cong :premises (@p26 @p278 @p272 @p266) :args (@t215)) % 2.61/2.83 (step @p280 :rule cong :premises (@p279) :args ((forall @t39 @t215))) % 2.61/2.83 (step @p281 :rule aci_norm :args ((= (or @t62 @t216) @t215))) % 2.61/2.83 (step @p282 :rule aci_norm :args ((= (or (or @t214 @t212) @t210) @t216))) % 2.61/2.83 (step @p283 :rule bool-and-de-morgan :args (@t213 @t211 true)) % 2.61/2.83 (step @p284 :rule nary_cong :premises (@p283 @p263) :args ((or (not @t217) @t210))) % 2.61/2.83 (step @p285 :rule trans :premises (@p284 @p282)) % 2.61/2.83 (step @p286 :rule bool-impl-elim :args (@t217 @t210)) % 2.61/2.83 (step @p287 :rule trans :premises (@p286 @p285)) % 2.61/2.83 (step @p288 :rule nary_cong :premises (@p26 @p287) :args (@t219)) % 2.61/2.83 (step @p289 :rule trans :premises (@p288 @p281)) % 2.61/2.83 (step @p290 :rule cong :premises (@p289) :args ((forall @t39 @t219))) % 2.61/2.83 (step @p291 :rule trans :premises (@p290 @p280)) % 2.61/2.83 (step @p292 :rule beta-reduce :args ((= @t220 @t218))) % 2.61/2.83 (step @p293 :rule nary_cong :premises (@p36 @p292) :args (@t221)) % 2.61/2.83 (step @p294 :rule cong :premises (@p293) :args (@t222)) % 2.61/2.83 (step @p295 :rule trans :premises (@p294 @p291)) % 2.61/2.83 (step @p296 :rule cong :premises (@p295) :args (@t223)) % 2.61/2.83 (step @p297 :rule beta-reduce :args ((= (_ @t91 @t137) @t223))) % 2.61/2.83 (step @p298 :rule trans :premises (@p297 @p296)) % 2.61/2.83 (step @p299 :rule ho_cong :premises (@p151 @p138)) % 2.61/2.83 (step @p300 :rule trans :premises (@p299 @p298)) % 2.61/2.83 (step @p301 :rule ho_cong :premises (@p300 @p84)) % 2.61/2.83 (step @p302 :rule trans :premises (@p301 @p261)) % 2.61/2.83 (step @p303 :rule cong :premises (@p302) :args (@t224)) % 2.61/2.83 (step @p304 :rule ho_cong :premises (@p142 @p303)) % 2.61/2.83 (step @p305 :rule trans :premises (@p304 @p260)) % 2.61/2.83 (step @p306 :rule ho_cong :premises (@p305 @p84)) % 2.61/2.83 (step @p307 :rule trans :premises (@p306 @p247)) % 2.61/2.83 (step @p308 :rule cong :premises (@p307) :args ((lambda @t15 (_ (_ @t135 @t224) @t9)))) % 2.61/2.83 (step @p309 :rule ho_cong :premises (@p148 @p308)) % 2.61/2.83 (step @p310 :rule trans :premises (@p309 @p246)) % 2.61/2.83 (step @p311 :rule ho_cong :premises (@p151 @p310)) % 2.61/2.83 (step @p312 :rule trans :premises (@p311 @p241)) % 2.61/2.83 (step @p313 :rule ho_cong :premises (@p154 @p312)) % 2.61/2.83 (step @p314 :rule trans :premises (@p313 @p217)) % 2.61/2.83 (step @p315 :rule ho_cong :premises (@p201 @p162)) % 2.61/2.83 (step @p316 :rule ho_cong :premises (@p315 @p84)) % 2.61/2.83 (step @p317 :rule cong :premises (@p316) :args (@t21)) % 2.61/2.83 (step @p318 :rule ho_cong :premises (@p176 @p317)) % 2.61/2.83 (step @p319 :rule ho_cong :premises (@p318 @p84)) % 2.61/2.83 (step @p320 :rule cong :premises (@p319) :args (@t22)) % 2.61/2.83 (step @p321 :rule ho_cong :premises (@p182 @p320)) % 2.61/2.83 (step @p322 :rule ho_cong :premises (@p201 @p321)) % 2.61/2.83 (step @p323 :rule ho_cong :premises (@p8 @p322)) % 2.61/2.83 (step @p324 :rule trans :premises (@p323 @p314)) % 2.61/2.83 (step @p325 :rule eq_resolve :premises (@p5 @p324)) % 2.61/2.83 (step @p326 :rule instantiate :premises (@p325) :args ((@list tptp.mactual @t155))) % 2.61/2.83 (step @p327 :rule refl :args (@t225)) % 2.61/2.83 (step @p328 :rule refl :args (@t3)) % 2.61/2.83 (step @p329 :rule cong :premises (@p328 @p327) :args ((= @t3 @t225))) % 2.61/2.83 (step @p330 :rule symm :premises (@p329)) % 2.61/2.83 (step @p331 :rule eq_resolve :premises (@p328 @p330)) % 2.61/2.83 (step @p332 :rule cong :premises (@p331) :args (@t5)) % 2.61/2.83 (step @p333 :rule eq_resolve :premises (@p1 @p332)) % 2.61/2.83 (step @p334 :rule instantiate :premises (@p333) :args ((@list tptp.mactual))) % 2.61/2.83 (step @p335 :rule cnf_or_pos :args (@t233)) % 2.61/2.83 (step @p336 :rule reordering :premises (@p335) :args ((or @t232 @t230 (not @t233)))) % 2.61/2.83 (step @p337 :rule chain_m_resolution :premises (@p336 @p334 @p326) :args (@t230 (@list false false) (@list @t231 @t233))) % 2.61/2.83 (step @p338 :rule refl :args (@t235)) % 2.61/2.83 (step @p339 :rule bool-double-not-elim :args (@t229)) % 2.61/2.83 (step @p340 :rule nary_cong :premises (@p339 @p338) :args ((or (not @t230) @t235))) % 2.61/2.83 (step @p341 :rule bool-double-not-elim :args (@t235)) % 2.61/2.83 (step @p342 :rule refl :args (@t230)) % 2.61/2.83 (step @p343 :rule cong :premises (@p342 @p341) :args ((=> @t230 @t236))) % 2.61/2.83 (assume-push @p376 @t230) % 2.61/2.83 (step @p345 :rule skolemize :premises (@p337)) % 2.61/2.83 (step-pop @p377 :rule scope :premises (@p345)) % 2.61/2.83 (step @p346 :rule process_scope :premises (@p377) :args (@t236)) % 2.61/2.83 (step @p348 :rule eq_resolve :premises (@p346 @p343)) % 2.61/2.83 (step @p349 :rule implies_elim :premises (@p348)) % 2.61/2.83 (step @p350 :rule eq_resolve :premises (@p349 @p340)) % 2.61/2.83 (step @p351 :rule chain_m_resolution :premises (@p350 @p337) :args (@t235 @t163 (@list @t229))) % 2.61/2.83 (step @p352 :rule instantiate :premises (@p351) :args ((@list @t153))) % 2.61/2.83 (step @p353 :rule cnf_or_neg :args (@t162 3)) % 2.61/2.83 (step @p354 :rule chain_m_resolution :premises (@p353 @p207) :args ((not @t156) @t163 @t164)) % 2.61/2.83 (step @p355 :rule bool-double-not-elim :args (@t157)) % 2.61/2.83 (step @p356 :rule nary_cong :premises (@p209 @p355) :args ((or @t162 (not @t158)))) % 2.61/2.83 (step @p357 :rule cnf_or_neg :args (@t162 2)) % 2.61/2.83 (step @p358 :rule eq_resolve :premises (@p357 @p356)) % 2.61/2.83 (step @p359 :rule reordering :premises (@p358) :args ((or @t157 @t162))) % 2.61/2.83 (step @p360 :rule chain_m_resolution :premises (@p359 @p207) :args (@t157 @t163 @t164)) % 2.61/2.83 (step @p361 :rule bool-double-not-elim :args (@t160)) % 2.61/2.83 (step @p362 :rule nary_cong :premises (@p209 @p361) :args ((or @t162 (not @t161)))) % 2.61/2.84 (step @p363 :rule cnf_or_neg :args (@t162 0)) % 2.61/2.84 (step @p364 :rule eq_resolve :premises (@p363 @p362)) % 2.61/2.84 (step @p365 :rule reordering :premises (@p364) :args ((or @t160 @t162))) % 2.61/2.84 (step @p366 :rule chain_m_resolution :premises (@p365 @p207) :args (@t160 @t163 @t164)) % 2.61/2.84 (step @p367 :rule cnf_or_pos :args (@t239)) % 2.61/2.84 (step @p368 :rule reordering :premises (@p367) :args ((or @t161 @t158 @t156 @t238 (not @t239)))) % 2.61/2.84 (step @p369 :rule chain_m_resolution :premises (@p368 @p366 @p360 @p354 @p352) :args (@t238 (@list false false true false) (@list @t160 @t157 @t156 @t239))) % 2.61/2.84 (assume-push @p378 @t154) % 2.61/2.84 (step @p371 :rule instantiate :premises (@p214) :args ((@list @t234))) % 2.61/2.84 (step-pop @p379 :rule scope :premises (@p371)) % 2.61/2.84 (step @p372 :rule process_scope :premises (@p379) :args (@t237)) % 2.61/2.84 (step @p374 :rule implies_elim :premises (@p372)) % 2.61/2.84 (step @p375 false :rule chain_m_resolution :premises (@p374 @p369 @p214) :args (false (@list true false) (@list @t237 @t154))) % 2.61/2.84 ) % 2.61/2.84 % SZS output end Proof % 2.61/2.84 % cvc5 exiting %------------------------------------------------------------------------------