%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL956^18 : 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 : n014.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 11:24:15 AM UTC 2026 % Result : Theorem 0.19s 0.56s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL956^18 : TPTP v9.3.1. Released v8.1.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.09/0.37 % Computer : n014.cluster.edu % 0.09/0.37 % Model : x86_64 x86_64 % 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.37 % Memory : 8046.5625MB % 0.09/0.37 % OS : Linux 6.8.0-71-generic % 0.09/0.37 % CPULimit : 300 % 0.09/0.37 % WCLimit : 300 % 0.09/0.37 % DateTime : Fri Sep 4 23:47:12 UTC 2026 % 0.09/0.37 % CPUTime : % 0.09/0.44 %----Proving TH0 % 0.19/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.19/0.56 % SZS status Theorem % 0.19/0.56 % SZS output start Proof % 0.19/0.56 ( % 0.19/0.56 (declare-sort $$unsorted 0) % 0.19/0.56 (declare-sort tptp.mworld 0) % 0.19/0.56 (declare-const tptp.mactual tptp.mworld) % 0.19/0.56 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.19/0.56 (declare-const tptp.eiw_di (-> $$unsorted tptp.mworld Bool)) % 0.19/0.56 (declare-const tptp.p (-> tptp.mworld Bool)) % 0.19/0.56 (declare-const tptp.big_q (-> $$unsorted tptp.mworld Bool)) % 0.19/0.56 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.19/0.56 (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)))))) % 0.19/0.56 (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))))))) % 0.19/0.56 (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))))))) % 0.19/0.56 (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))))))) % 0.19/0.56 (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))))))) % 0.19/0.56 (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)))))))) % 0.19/0.56 (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)))))))) % 0.19/0.56 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.19/0.56 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (and (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.19/0.56 (define @t1 () (@var "V" tptp.mworld)) % 0.19/0.56 (define @t2 () (@var "W" tptp.mworld)) % 0.19/0.56 (define @t3 () (_ (_ tptp.mrel @t2) @t1)) % 0.19/0.56 (define @t4 () (@var "X" $$unsorted)) % 0.19/0.56 (define @t5 () (_ tptp.eiw_di @t4)) % 0.19/0.56 (define @t6 () (_ @t5 @t2)) % 0.19/0.56 (define @t7 () (@list @t4)) % 0.19/0.56 (define @t8 () (@list @t2)) % 0.19/0.56 (define @t9 () (@var "__flatten_var_0" tptp.mworld)) % 0.19/0.56 (define @t10 () (_ tptp.big_q @t4)) % 0.19/0.56 (define @t11 () (_ tptp.mbox @t10)) % 0.19/0.56 (define @t12 () (_ tptp.mand (_ tptp.mbox tptp.p))) % 0.19/0.56 (define @t13 () (@list @t4 @t9)) % 0.19/0.56 (define @t14 () (lambda @t13 (_ (_ @t12 @t11) @t9))) % 0.19/0.56 (define @t15 () (_ tptp.mexists_di @t14)) % 0.19/0.56 (define @t16 () (lambda @t13 (_ @t11 @t9))) % 0.19/0.56 (define @t17 () (_ @t12 (_ tptp.mexists_di @t16))) % 0.19/0.56 (define @t18 () (not (_ tptp.mlocal (_ (_ tptp.mand (_ tptp.mbox (_ (_ tptp.mimplies @t15) @t17))) (_ tptp.mbox (_ (_ tptp.mimplies @t17) @t15)))))) % 0.19/0.56 (define @t19 () (@var "Phi" (-> tptp.mworld Bool))) % 0.19/0.56 (define @t20 () (lambda (@list @t19) (_ @t19 tptp.mactual))) % 0.19/0.56 (define @t21 () (@var "A" (-> tptp.mworld Bool))) % 0.19/0.56 (define @t22 () (_ @t21 @t2)) % 0.19/0.56 (define @t23 () (lambda (@list @t21 @t2) (not @t22))) % 0.19/0.56 (define @t24 () (@var "B" (-> tptp.mworld Bool))) % 0.19/0.56 (define @t25 () (_ @t24 @t2)) % 0.19/0.56 (define @t26 () (@list @t21 @t24 @t2)) % 0.19/0.56 (define @t27 () (lambda @t26 (and @t22 @t25))) % 0.19/0.56 (define @t28 () (lambda @t26 (or @t22 @t25))) % 0.19/0.56 (define @t29 () (lambda @t26 (=> @t22 @t25))) % 0.19/0.56 (define @t30 () (lambda @t26 (= @t22 @t25))) % 0.19/0.56 (define @t31 () (_ @t19 @t1)) % 0.19/0.56 (define @t32 () (@list @t1)) % 0.19/0.56 (define @t33 () (forall @t32 (=> @t3 @t31))) % 0.19/0.56 (define @t34 () (@list @t19 @t2)) % 0.19/0.56 (define @t35 () (lambda @t34 @t33)) % 0.19/0.56 (define @t36 () (lambda @t34 (exists @t32 (and @t3 @t31)))) % 0.19/0.56 (define @t37 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.19/0.56 (define @t38 () (_ (_ @t37 @t4) @t2)) % 0.19/0.56 (define @t39 () (@list @t37 @t2)) % 0.19/0.56 (define @t40 () (lambda @t39 (forall @t7 (=> @t6 @t38)))) % 0.19/0.56 (define @t41 () (and @t6 @t38)) % 0.19/0.56 (define @t42 () (exists @t7 @t41)) % 0.19/0.56 (define @t43 () (lambda @t39 @t42)) % 0.19/0.56 (define @t44 () (@var "BOUND_VARIABLE_7764" tptp.mworld)) % 0.19/0.56 (define @t45 () (tptp.p @t44)) % 0.19/0.56 (define @t46 () (@var "BOUND_VARIABLE_7752" tptp.mworld)) % 0.19/0.56 (define @t47 () (@var "BOUND_VARIABLE_7802" $$unsorted)) % 0.19/0.56 (define @t48 () (not (tptp.mrel @t1 @t46))) % 0.19/0.56 (define @t49 () (@list @t46)) % 0.19/0.56 (define @t50 () (not (forall @t49 (or @t48 (tptp.big_q @t47 @t46))))) % 0.19/0.56 (define @t51 () (not (tptp.eiw_di @t47 @t1))) % 0.19/0.56 (define @t52 () (tptp.big_q @t4 @t46)) % 0.19/0.56 (define @t53 () (not (tptp.eiw_di @t4 @t1))) % 0.19/0.56 (define @t54 () (forall @t7 (or @t53 (not (forall @t49 (or @t48 @t52)))))) % 0.19/0.56 (define @t55 () (not @t54)) % 0.19/0.56 (define @t56 () (@var "BOUND_VARIABLE_7811" tptp.mworld)) % 0.19/0.56 (define @t57 () (or (not (tptp.mrel @t1 @t56)) (tptp.p @t56))) % 0.19/0.56 (define @t58 () (and @t57 @t55)) % 0.19/0.56 (define @t59 () (@list @t44)) % 0.19/0.56 (define @t60 () (forall @t59 (or (not (tptp.mrel @t1 @t44)) @t45))) % 0.19/0.56 (define @t61 () (not @t60)) % 0.19/0.56 (define @t62 () (not (tptp.mrel tptp.mactual @t1))) % 0.19/0.56 (define @t63 () (@list @t1 @t47 @t56)) % 0.19/0.56 (define @t64 () (forall @t63 (or @t62 @t61 @t58 @t51 @t50))) % 0.19/0.56 (define @t65 () (@quantifiers_skolemize @t64 0)) % 0.19/0.56 (define @t66 () (forall @t59 (or (not (tptp.mrel @t65 @t44)) @t45))) % 0.19/0.56 (define @t67 () (@quantifiers_skolemize @t64 1)) % 0.19/0.56 (define @t68 () (not (tptp.mrel @t65 @t46))) % 0.19/0.56 (define @t69 () (forall @t49 (or @t68 (tptp.big_q @t67 @t46)))) % 0.19/0.56 (define @t70 () (not @t69)) % 0.19/0.56 (define @t71 () (tptp.eiw_di @t67 @t65)) % 0.19/0.56 (define @t72 () (not @t71)) % 0.19/0.56 (define @t73 () (forall @t7 (or (not (tptp.eiw_di @t4 @t65)) (not (forall @t49 (or @t68 @t52)))))) % 0.19/0.56 (define @t74 () (not @t73)) % 0.19/0.56 (define @t75 () (@quantifiers_skolemize @t64 2)) % 0.19/0.56 (define @t76 () (or (not (tptp.mrel @t65 @t75)) (tptp.p @t75))) % 0.19/0.56 (define @t77 () (and @t76 @t74)) % 0.19/0.56 (define @t78 () (not @t66)) % 0.19/0.56 (define @t79 () (or (not (tptp.mrel tptp.mactual @t65)) @t78 @t77 @t72 @t70)) % 0.19/0.56 (define @t80 () (or @t72 @t70)) % 0.19/0.56 (define @t81 () (not @t76)) % 0.19/0.56 (define @t82 () (not @t79)) % 0.19/0.56 (define @t83 () (not @t64)) % 0.19/0.56 (define @t84 () (@list false)) % 0.19/0.56 (define @t85 () (@var "BOUND_VARIABLE_8016" tptp.mworld)) % 0.19/0.56 (define @t86 () (@var "BOUND_VARIABLE_8017" $$unsorted)) % 0.19/0.56 (define @t87 () (@var "BOUND_VARIABLE_8015" tptp.mworld)) % 0.19/0.56 (define @t88 () (not (tptp.mrel @t87 @t85))) % 0.19/0.56 (define @t89 () (@list @t85)) % 0.19/0.56 (define @t90 () (@var "BOUND_VARIABLE_8019" $$unsorted)) % 0.19/0.56 (define @t91 () (@var "BOUND_VARIABLE_8020" tptp.mworld)) % 0.19/0.56 (define @t92 () (@var "BOUND_VARIABLE_8018" tptp.mworld)) % 0.19/0.56 (define @t93 () (@list @t87 @t85 @t86 @t92 @t90 @t91)) % 0.19/0.56 (define @t94 () (@var "BOUND_VARIABLE_7905" tptp.mworld)) % 0.19/0.56 (define @t95 () (@var "BOUND_VARIABLE_7857" tptp.mworld)) % 0.19/0.56 (define @t96 () (@var "BOUND_VARIABLE_7896" $$unsorted)) % 0.19/0.56 (define @t97 () (@var "BOUND_VARIABLE_7846" tptp.mworld)) % 0.19/0.56 (define @t98 () (not (tptp.mrel @t1 @t97))) % 0.19/0.56 (define @t99 () (@list @t97)) % 0.19/0.56 (define @t100 () (not (forall @t99 (or @t98 (tptp.big_q @t96 @t97))))) % 0.19/0.56 (define @t101 () (not (tptp.eiw_di @t96 @t1))) % 0.19/0.56 (define @t102 () (tptp.big_q @t4 @t97)) % 0.19/0.56 (define @t103 () (forall @t7 (or @t53 (not (forall @t99 (or @t98 @t102)))))) % 0.19/0.56 (define @t104 () (not @t103)) % 0.19/0.56 (define @t105 () (or (not (tptp.mrel @t1 @t94)) (tptp.p @t94))) % 0.19/0.56 (define @t106 () (and @t105 @t104)) % 0.19/0.56 (define @t107 () (tptp.p @t95)) % 0.19/0.56 (define @t108 () (@list @t95)) % 0.19/0.56 (define @t109 () (forall @t108 (or (not (tptp.mrel @t1 @t95)) @t107))) % 0.19/0.56 (define @t110 () (not @t109)) % 0.19/0.56 (define @t111 () (@list @t1 @t96 @t94)) % 0.19/0.56 (define @t112 () (forall @t111 (or @t62 @t110 @t106 @t101 @t100))) % 0.19/0.56 (define @t113 () (tptp.mrel @t2 @t1)) % 0.19/0.56 (define @t114 () (not @t113)) % 0.19/0.56 (define @t115 () (or @t114 @t110 @t106 @t101 @t100)) % 0.19/0.56 (define @t116 () (forall @t111 @t115)) % 0.19/0.56 (define @t117 () (or @t114 @t61 @t58 @t51 @t50)) % 0.19/0.56 (define @t118 () (forall @t63 @t117)) % 0.19/0.56 (define @t119 () (lambda @t8 (and @t118 @t116))) % 0.19/0.56 (define @t120 () (_ @t119 tptp.mactual)) % 0.19/0.56 (define @t121 () (lambda @t8 @t116)) % 0.19/0.56 (define @t122 () (_ @t121 @t2)) % 0.19/0.56 (define @t123 () (and @t118 @t122)) % 0.19/0.56 (define @t124 () (lambda @t8 @t123)) % 0.19/0.56 (define @t125 () (@list @t24 @t2)) % 0.19/0.56 (define @t126 () (or @t101 @t100)) % 0.19/0.56 (define @t127 () (or @t114 @t110 @t126 @t106)) % 0.19/0.56 (define @t128 () (forall @t111 @t127)) % 0.19/0.56 (define @t129 () (forall (@list @t96 @t94) @t127)) % 0.19/0.56 (define @t130 () (@list @t94)) % 0.19/0.56 (define @t131 () (forall @t130 @t104)) % 0.19/0.56 (define @t132 () (forall @t130 @t105)) % 0.19/0.56 (define @t133 () (@list @t95)) % 0.19/0.56 (define @t134 () (and @t132 @t131)) % 0.19/0.56 (define @t135 () (forall @t130 @t106)) % 0.19/0.56 (define @t136 () (forall (@list @t96) @t126)) % 0.19/0.56 (define @t137 () (@list @t4)) % 0.19/0.56 (define @t138 () (or @t114 @t110 @t136 @t135)) % 0.19/0.56 (define @t139 () (and @t109 @t104)) % 0.19/0.56 (define @t140 () (or @t114 @t110 @t103 @t139)) % 0.19/0.56 (define @t141 () (or @t110 @t103 @t139)) % 0.19/0.56 (define @t142 () (or @t110 @t103)) % 0.19/0.56 (define @t143 () (not @t142)) % 0.19/0.56 (define @t144 () (=> @t139 @t143)) % 0.19/0.56 (define @t145 () (or @t114 @t144)) % 0.19/0.56 (define @t146 () (tptp.eiw_di @t4 @t2)) % 0.19/0.56 (define @t147 () (not @t146)) % 0.19/0.56 (define @t148 () (forall @t7 (or @t147 (not (forall @t99 (or (not (tptp.mrel @t2 @t97)) @t102)))))) % 0.19/0.56 (define @t149 () (forall @t108 (or (not (tptp.mrel @t2 @t95)) @t107))) % 0.19/0.56 (define @t150 () (tptp.big_q @t4 @t1)) % 0.19/0.56 (define @t151 () (forall @t32 (or @t114 @t150))) % 0.19/0.56 (define @t152 () (@list @t1)) % 0.19/0.56 (define @t153 () (not @t151)) % 0.19/0.56 (define @t154 () (or @t147 @t153)) % 0.19/0.56 (define @t155 () (forall @t7 @t154)) % 0.19/0.56 (define @t156 () (tptp.p @t1)) % 0.19/0.56 (define @t157 () (forall @t32 (or @t114 @t156))) % 0.19/0.56 (define @t158 () (not @t157)) % 0.19/0.56 (define @t159 () (or @t158 @t155)) % 0.19/0.56 (define @t160 () (not @t159)) % 0.19/0.56 (define @t161 () (not @t155)) % 0.19/0.56 (define @t162 () (and @t157 @t161)) % 0.19/0.56 (define @t163 () (=> @t162 @t160)) % 0.19/0.56 (define @t164 () (lambda @t8 @t163)) % 0.19/0.56 (define @t165 () (or @t114 (_ @t164 @t1))) % 0.19/0.56 (define @t166 () (forall @t32 @t165)) % 0.19/0.56 (define @t167 () (lambda @t8 @t166)) % 0.19/0.56 (define @t168 () (_ @t19 @t1)) % 0.19/0.56 (define @t169 () (lambda @t34 (forall @t32 (or @t114 @t168)))) % 0.19/0.56 (define @t170 () (lambda @t8 @t160)) % 0.19/0.56 (define @t171 () (_ @t170 @t2)) % 0.19/0.56 (define @t172 () (=> @t162 @t171)) % 0.19/0.56 (define @t173 () (lambda @t8 @t172)) % 0.19/0.56 (define @t174 () (or @t158 @t154)) % 0.19/0.56 (define @t175 () (or @t147 @t158 @t153)) % 0.19/0.56 (define @t176 () (and @t157 @t151)) % 0.19/0.56 (define @t177 () (or @t147 (not @t176))) % 0.19/0.56 (define @t178 () (not (tptp.mrel @t9 @t1))) % 0.19/0.56 (define @t179 () (forall @t32 (or @t178 @t150))) % 0.19/0.56 (define @t180 () (and (forall @t32 (or @t178 @t156)) @t179)) % 0.19/0.56 (define @t181 () (lambda @t13 @t180)) % 0.19/0.56 (define @t182 () (_ @t181 @t4 @t2)) % 0.19/0.56 (define @t183 () (not @t182)) % 0.19/0.56 (define @t184 () (or @t147 @t183)) % 0.19/0.56 (define @t185 () (forall @t7 @t184)) % 0.19/0.56 (define @t186 () (not @t185)) % 0.19/0.56 (define @t187 () (lambda @t8 @t186)) % 0.19/0.56 (define @t188 () (_ @t37 @t4 @t2)) % 0.19/0.56 (define @t189 () (lambda @t39 (not (forall @t7 (or @t147 (not @t188)))))) % 0.19/0.56 (define @t190 () (lambda @t8 @t151)) % 0.19/0.56 (define @t191 () (_ @t190 @t2)) % 0.19/0.56 (define @t192 () (and @t157 @t191)) % 0.19/0.56 (define @t193 () (lambda @t8 @t192)) % 0.19/0.56 (define @t194 () (lambda @t125 (and @t157 @t25))) % 0.19/0.56 (define @t195 () (_ @t10 @t1)) % 0.19/0.56 (define @t196 () (or @t114 @t195)) % 0.19/0.56 (define @t197 () (_ @t10 @t1)) % 0.19/0.56 (define @t198 () (or @t114 @t197)) % 0.19/0.56 (define @t199 () (forall @t32 @t198)) % 0.19/0.56 (define @t200 () (lambda @t8 @t199)) % 0.19/0.56 (define @t201 () (_ @t169 @t10)) % 0.19/0.56 (define @t202 () (lambda @t8 @t157)) % 0.19/0.56 (define @t203 () (_ @t202 @t2)) % 0.19/0.56 (define @t204 () (and @t203 @t25)) % 0.19/0.56 (define @t205 () (lambda @t125 @t204)) % 0.19/0.56 (define @t206 () (_ @t169 tptp.p)) % 0.19/0.56 (define @t207 () (_ @t27 @t206)) % 0.19/0.56 (define @t208 () (lambda @t13 (_ (_ @t207 @t201) @t9))) % 0.19/0.56 (define @t209 () (lambda @t8 @t162)) % 0.19/0.56 (define @t210 () (_ @t209 @t2)) % 0.19/0.56 (define @t211 () (=> @t210 @t25)) % 0.19/0.56 (define @t212 () (lambda @t125 @t211)) % 0.19/0.56 (define @t213 () (lambda @t8 @t161)) % 0.19/0.56 (define @t214 () (_ @t213 @t2)) % 0.19/0.56 (define @t215 () (and @t157 @t214)) % 0.19/0.56 (define @t216 () (lambda @t8 @t215)) % 0.19/0.56 (define @t217 () (lambda @t13 @t179)) % 0.19/0.56 (define @t218 () (_ @t217 @t4 @t2)) % 0.19/0.56 (define @t219 () (not @t218)) % 0.19/0.56 (define @t220 () (or @t147 @t219)) % 0.19/0.56 (define @t221 () (forall @t7 @t220)) % 0.19/0.56 (define @t222 () (not @t221)) % 0.19/0.56 (define @t223 () (lambda @t8 @t222)) % 0.19/0.56 (define @t224 () (lambda @t13 (_ @t201 @t9))) % 0.19/0.56 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0.19/0.56 (define @t264 () (not @t6)) % 0.19/0.56 (define @t265 () (or @t264 @t263)) % 0.19/0.56 (define @t266 () (forall @t7 (not @t41))) % 0.19/0.56 (define @t267 () (not @t266)) % 0.19/0.56 (assume @p1 (forall (@list @t2 @t1) @t3)) % 0.19/0.56 (assume @p2 (forall @t8 (exists @t7 @t6))) % 0.19/0.56 (assume @p3 (forall (@list @t2 @t1 @t4) (=> (and @t6 @t3) (_ @t5 @t1)))) % 0.19/0.56 (assume @p4 @t18) % 0.19/0.56 (assume @p5 true) % 0.19/0.56 (step @p6 (= tptp.mlocal @t20) :rule refl :args (@t20)) % 0.19/0.56 (step @p7 (= tptp.mnot @t23) :rule refl :args (@t23)) % 0.19/0.56 (step @p8 (= tptp.mand @t27) :rule refl :args (@t27)) % 0.19/0.56 (step @p9 (= tptp.mor @t28) :rule refl :args (@t28)) % 0.19/0.56 (step @p10 (= tptp.mimplies @t29) :rule refl :args (@t29)) % 0.19/0.56 (step @p11 (= tptp.mequiv @t30) :rule refl :args (@t30)) % 0.19/0.56 (step @p12 (= tptp.mbox @t35) :rule refl :args (@t35)) % 0.19/0.56 (step @p13 (= tptp.mdia @t36) :rule refl :args (@t36)) % 0.19/0.56 (step @p14 (= 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skolemize :premises (@p388)) % 0.19/0.56 (step-pop @p389 :rule scope :premises (@p57)) % 0.19/0.56 (step @p58 :rule process_scope :premises (@p389) :args (@t82)) % 0.19/0.56 (step @p60 :rule implies_elim :premises (@p58)) % 0.19/0.56 (step @p61 :rule eq_resolve :premises (@p60 @p55)) % 0.19/0.56 (step @p62 :rule chain_m_resolution :premises (@p61 @p52) :args (@t64 @t84 (@list @t79))) % 0.19/0.56 (step @p63 :rule alpha_equiv :args ((forall (@list @t87 @t86 @t91) (or (not (tptp.mrel tptp.mactual @t87)) (not (forall (@list @t92) (or (not (tptp.mrel @t87 @t92)) (tptp.p @t92)))) (and (or (not (tptp.mrel @t87 @t91)) (tptp.p @t91)) (not (forall (@list @t90) (or (not (tptp.eiw_di @t90 @t87)) (not (forall @t89 (or @t88 (tptp.big_q @t90 @t85)))))))) (not (tptp.eiw_di @t86 @t87)) (not (forall @t89 (or @t88 (tptp.big_q @t86 @t85)))))) @t93 (@list @t1 @t97 @t96 @t95 @t4 @t94))) % 0.19/0.56 (step @p64 :rule alpha_equiv :args (@t64 (@list @t1 @t46 @t47 @t44 @t4 @t56) @t93)) % 0.19/0.56 (step @p65 :rule trans :premises (@p64 @p63)) % 0.19/0.56 (step @p66 :rule equiv_elim1 :premises (@p65)) % 0.19/0.56 (step @p67 :rule reordering :premises (@p66) :args ((or @t112 @t83))) % 0.19/0.56 (step @p68 :rule chain_m_resolution :premises (@p67 @p62) :args (@t112 @t84 (@list @t64))) % 0.19/0.56 (step @p69 :rule beta-reduce :args ((= @t120 (and @t64 @t112)))) % 0.19/0.56 (step @p70 :rule beta-reduce :args ((= (_ @t20 @t119) @t120))) % 0.19/0.56 (step @p71 :rule trans :premises (@p70 @p69)) % 0.19/0.56 (step @p72 :rule beta-reduce :args ((= @t122 @t116))) % 0.19/0.56 (step @p73 :rule refl :args (@t118)) % 0.19/0.56 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t123)) % 0.19/0.56 (step @p75 :rule cong :premises (@p74) :args (@t124)) % 0.19/0.56 (step @p76 :rule beta-reduce :args ((= (_ (lambda @t125 (and @t118 @t25)) @t121) @t124))) % 0.19/0.56 (step @p77 :rule trans :premises (@p76 @p75)) % 0.19/0.56 (step @p78 :rule aci_norm :args ((= @t127 @t115))) % 0.19/0.56 (step @p79 :rule 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0.19/0.56 (step @p328 :rule cong :premises (@p327) :args (@t261)) % 0.19/0.56 (step @p329 :rule nary_cong :premises (@p328 @p322) :args (@t262)) % 0.19/0.56 (step @p330 :rule cong :premises (@p329) :args ((forall @t32 @t262))) % 0.19/0.56 (step @p331 :rule bool-impl-elim :args (@t3 @t31)) % 0.19/0.56 (step @p332 :rule cong :premises (@p331) :args (@t33)) % 0.19/0.56 (step @p333 :rule trans :premises (@p332 @p330)) % 0.19/0.56 (step @p334 :rule cong :premises (@p333) :args (@t35)) % 0.19/0.56 (step @p335 :rule trans :premises (@p12 @p334)) % 0.19/0.56 (step @p336 :rule ho_cong :premises (@p335 @p317)) % 0.19/0.56 (step @p337 :rule refl :args (tptp.p)) % 0.19/0.56 (step @p338 :rule ho_cong :premises (@p335 @p337)) % 0.19/0.56 (step @p339 :rule ho_cong :premises (@p8 @p338)) % 0.19/0.56 (step @p340 :rule ho_cong :premises (@p339 @p336)) % 0.19/0.56 (step @p341 :rule ho_cong :premises (@p340 @p166)) % 0.19/0.56 (step @p342 :rule cong :premises (@p341) :args (@t14)) % 0.19/0.56 (step @p343 :rule refl :args (@t188)) % 0.19/0.56 (step @p344 :rule refl :args (@t38)) % 0.19/0.56 (step @p345 :rule cong :premises (@p344 @p343) :args ((= @t38 @t188))) % 0.19/0.56 (step @p346 :rule symm :premises (@p345)) % 0.19/0.56 (step @p347 :rule eq_resolve :premises (@p344 @p346)) % 0.19/0.56 (step @p348 :rule cong :premises (@p347) :args (@t263)) % 0.19/0.56 (step @p349 :rule refl :args (@t146)) % 0.19/0.56 (step @p350 :rule refl :args (@t6)) % 0.19/0.56 (step @p351 :rule cong :premises (@p350 @p349) :args ((= @t6 @t146))) % 0.19/0.56 (step @p352 :rule symm :premises (@p351)) % 0.19/0.56 (step @p353 :rule eq_resolve :premises (@p350 @p352)) % 0.19/0.56 (step @p354 :rule cong :premises (@p353) :args (@t264)) % 0.19/0.56 (step @p355 :rule nary_cong :premises (@p354 @p348) :args (@t265)) % 0.19/0.56 (step @p356 :rule cong :premises (@p355) :args ((forall @t7 @t265))) % 0.19/0.56 (step @p357 :rule bool-and-de-morgan :args (@t6 @t38 true)) % 0.19/0.56 (step @p358 :rule cong :premises (@p357) 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ho_cong :premises (@p373 @p369)) % 0.19/0.56 (step @p375 :rule ho_cong :premises (@p335 @p374)) % 0.19/0.56 (step @p376 :rule ho_cong :premises (@p8 @p375)) % 0.19/0.56 (step @p377 :rule ho_cong :premises (@p376 @p372)) % 0.19/0.56 (step @p378 :rule ho_cong :premises (@p6 @p377)) % 0.19/0.56 (step @p379 :rule cong :premises (@p378) :args (@t18)) % 0.19/0.56 (step @p380 :rule trans :premises (@p379 @p316)) % 0.19/0.56 (step @p381 :rule eq_resolve :premises (@p4 @p380)) % 0.19/0.56 (step @p382 :rule not_and :premises (@p381)) % 0.19/0.56 (step @p383 false :rule chain_m_resolution :premises (@p382 @p68 @p62) :args (false (@list false false) (@list @t112 @t64))) % 0.19/0.56 ) % 0.19/0.56 % SZS output end Proof % 0.19/0.56 % cvc5 exiting %------------------------------------------------------------------------------