%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL952^12 : TPTP v9.3.1. 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 : n003.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 11:24:14 AM UTC 2026 % Result : Theorem 0.21s 0.56s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL952^12 : TPTP v9.3.1. Released v8.1.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.09/0.37 % Computer : n003.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 : Sat Sep 5 12:33:06 UTC 2026 % 0.09/0.37 % CPUTime : % 0.09/0.45 %----Proving TH0 % 0.21/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.21/0.56 % SZS status Theorem % 0.21/0.56 % SZS output start Proof % 0.21/0.56 ( % 0.21/0.56 (declare-sort $$unsorted 0) % 0.21/0.56 (declare-sort tptp.mworld 0) % 0.21/0.56 (declare-const tptp.mactual tptp.mworld) % 0.21/0.56 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.21/0.56 (declare-const tptp.eiw_di (-> $$unsorted tptp.mworld Bool)) % 0.21/0.56 (declare-const tptp.empty (-> $$unsorted tptp.mworld Bool)) % 0.21/0.56 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 0.21/0.56 (declare-const tptp.in (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.21/0.56 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.21/0.56 (declare-const tptp.qmltpeq (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.21/0.56 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.21/0.56 (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)))))) % 0.21/0.56 (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))))))) % 0.21/0.56 (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))))))) % 0.21/0.56 (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))))))) % 0.21/0.56 (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))))))) % 0.21/0.56 (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)))))))) % 0.21/0.56 (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)))))))) % 0.21/0.56 (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)))))))) % 0.21/0.56 (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)))))))) % 0.21/0.56 (define @t1 () (@var "V" tptp.mworld)) % 0.21/0.56 (define @t2 () (@var "W" tptp.mworld)) % 0.21/0.56 (define @t3 () (_ (_ tptp.mrel @t2) @t1)) % 0.21/0.56 (define @t4 () (@var "X" $$unsorted)) % 0.21/0.56 (define @t5 () (_ (_ tptp.eiw_di @t4) @t2)) % 0.21/0.56 (define @t6 () (@list @t4)) % 0.21/0.56 (define @t7 () (@list @t2)) % 0.21/0.56 (define @t8 () (@var "__flatten_var_0" tptp.mworld)) % 0.21/0.56 (define @t9 () (_ tptp.qmltpeq @t4)) % 0.21/0.56 (define @t10 () (@list @t4 @t8)) % 0.21/0.56 (define @t11 () (@var "Y" $$unsorted)) % 0.21/0.56 (define @t12 () (_ tptp.qmltpeq @t11)) % 0.21/0.56 (define @t13 () (_ tptp.mbox (_ @t9 @t11))) % 0.21/0.56 (define @t14 () (@list @t11 @t8)) % 0.21/0.56 (define @t15 () (@var "Z" $$unsorted)) % 0.21/0.56 (define @t16 () (@var "C" $$unsorted)) % 0.21/0.56 (define @t17 () (@var "B" $$unsorted)) % 0.21/0.56 (define @t18 () (_ tptp.set_intersection2 @t17)) % 0.21/0.56 (define @t19 () (@var "A" $$unsorted)) % 0.21/0.56 (define @t20 () (_ tptp.set_intersection2 @t19)) % 0.21/0.56 (define @t21 () (_ tptp.mbox (_ (_ tptp.qmltpeq @t19) @t17))) % 0.21/0.56 (define @t22 () (_ tptp.mimplies @t21)) % 0.21/0.56 (define @t23 () (@list @t16 @t8)) % 0.21/0.56 (define @t24 () (@list @t17 @t8)) % 0.21/0.56 (define @t25 () (@list @t19 @t8)) % 0.21/0.56 (define @t26 () (_ tptp.set_intersection2 @t16)) % 0.21/0.56 (define @t27 () (_ tptp.singleton @t17)) % 0.21/0.56 (define @t28 () (_ tptp.mbox (_ tptp.empty @t19))) % 0.21/0.56 (define @t29 () (_ tptp.mand @t21)) % 0.21/0.56 (define @t30 () (_ tptp.in @t17)) % 0.21/0.56 (define @t31 () (_ tptp.in @t19)) % 0.21/0.56 (define @t32 () (_ tptp.in @t16)) % 0.21/0.56 (define @t33 () (_ @t30 @t19)) % 0.21/0.56 (define @t34 () (_ tptp.mbox @t33)) % 0.21/0.56 (define @t35 () (_ @t20 @t27)) % 0.21/0.56 (define @t36 () (_ (_ tptp.qmltpeq @t35) @t27)) % 0.21/0.56 (define @t37 () (lambda @t24 (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ tptp.mbox @t36)) @t34)) @t8))) % 0.21/0.56 (define @t38 () (lambda @t25 (_ (_ tptp.mbox (_ tptp.mforall_di @t37)) @t8))) % 0.21/0.56 (define @t39 () (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di @t38)))) % 0.21/0.56 (define @t40 () (not @t39)) % 0.21/0.56 (define @t41 () (@var "Phi" (-> tptp.mworld Bool))) % 0.21/0.56 (define @t42 () (lambda (@list @t41) (_ @t41 tptp.mactual))) % 0.21/0.56 (define @t43 () (@var "A" (-> tptp.mworld Bool))) % 0.21/0.56 (define @t44 () (_ @t43 @t2)) % 0.21/0.56 (define @t45 () (lambda (@list @t43 @t2) (not @t44))) % 0.21/0.56 (define @t46 () (@var "B" (-> tptp.mworld Bool))) % 0.21/0.56 (define @t47 () (_ @t46 @t2)) % 0.21/0.56 (define @t48 () (@list @t43 @t46 @t2)) % 0.21/0.56 (define @t49 () (lambda @t48 (and @t44 @t47))) % 0.21/0.56 (define @t50 () (lambda @t48 (or @t44 @t47))) % 0.21/0.56 (define @t51 () (lambda @t48 (=> @t44 @t47))) % 0.21/0.56 (define @t52 () (lambda @t48 (= @t44 @t47))) % 0.21/0.56 (define @t53 () (_ @t41 @t1)) % 0.21/0.56 (define @t54 () (@list @t1)) % 0.21/0.56 (define @t55 () (forall @t54 (=> @t3 @t53))) % 0.21/0.56 (define @t56 () (@list @t41 @t2)) % 0.21/0.56 (define @t57 () (lambda @t56 @t55)) % 0.21/0.56 (define @t58 () (lambda @t56 (exists @t54 (and @t3 @t53)))) % 0.21/0.56 (define @t59 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.21/0.56 (define @t60 () (_ (_ @t59 @t4) @t2)) % 0.21/0.56 (define @t61 () (forall @t6 (=> @t5 @t60))) % 0.21/0.56 (define @t62 () (@list @t59 @t2)) % 0.21/0.56 (define @t63 () (lambda @t62 @t61)) % 0.21/0.56 (define @t64 () (lambda @t62 (exists @t6 (and @t5 @t60)))) % 0.21/0.56 (define @t65 () (@var "BOUND_VARIABLE_11992" tptp.mworld)) % 0.21/0.56 (define @t66 () (@var "BOUND_VARIABLE_11984" $$unsorted)) % 0.21/0.56 (define @t67 () (@var "BOUND_VARIABLE_11988" $$unsorted)) % 0.21/0.56 (define @t68 () (tptp.in @t67 @t66 @t65)) % 0.21/0.56 (define @t69 () (@var "BOUND_VARIABLE_11990" tptp.mworld)) % 0.21/0.56 (define @t70 () (not (tptp.mrel @t69 @t65))) % 0.21/0.56 (define @t71 () (@var "BOUND_VARIABLE_11803" tptp.mworld)) % 0.21/0.56 (define @t72 () (tptp.singleton @t67)) % 0.21/0.56 (define @t73 () (@list @t71)) % 0.21/0.56 (define @t74 () (not (forall @t73 (or (not (tptp.mrel @t69 @t71)) (tptp.qmltpeq (tptp.set_intersection2 @t66 @t72) @t72 @t71))))) % 0.21/0.56 (define @t75 () (@var "BOUND_VARIABLE_11986" tptp.mworld)) % 0.21/0.56 (define @t76 () (not (tptp.mrel @t75 @t69))) % 0.21/0.56 (define @t77 () (not (tptp.eiw_di @t67 @t75))) % 0.21/0.56 (define @t78 () (not (tptp.mrel @t1 @t75))) % 0.21/0.56 (define @t79 () (not (tptp.eiw_di @t66 @t1))) % 0.21/0.56 (define @t80 () (@list @t1 @t66 @t75 @t67 @t69 @t65)) % 0.21/0.56 (define @t81 () (tptp.mrel @t2 @t1)) % 0.21/0.56 (define @t82 () (not @t81)) % 0.21/0.56 (define @t83 () (or @t82 @t79 @t78 @t77 @t76 @t74 @t70 @t68)) % 0.21/0.56 (define @t84 () (lambda @t7 (forall @t80 @t83))) % 0.21/0.56 (define @t85 () (_ @t84 tptp.mactual)) % 0.21/0.56 (define @t86 () (or @t79 @t78 @t77 @t76 @t74 @t70 @t68)) % 0.21/0.56 (define @t87 () (or @t82 @t86)) % 0.21/0.56 (define @t88 () (forall @t80 @t87)) % 0.21/0.56 (define @t89 () (@list @t66 @t75 @t67 @t69 @t65)) % 0.21/0.56 (define @t90 () (forall @t89 @t87)) % 0.21/0.56 (define @t91 () (forall @t89 @t86)) % 0.21/0.56 (define @t92 () (@var "BOUND_VARIABLE_11947" tptp.mworld)) % 0.21/0.56 (define @t93 () (@var "BOUND_VARIABLE_11945" tptp.mworld)) % 0.21/0.56 (define @t94 () (@var "BOUND_VARIABLE_11943" $$unsorted)) % 0.21/0.56 (define @t95 () (@var "BOUND_VARIABLE_11941" tptp.mworld)) % 0.21/0.56 (define @t96 () (or @t82 @t91)) % 0.21/0.56 (define @t97 () (tptp.in @t94 @t4 @t92)) % 0.21/0.56 (define @t98 () (not (tptp.mrel @t93 @t92))) % 0.21/0.56 (define @t99 () (tptp.singleton @t94)) % 0.21/0.56 (define @t100 () (not (forall @t73 (or (not (tptp.mrel @t93 @t71)) (tptp.qmltpeq (tptp.set_intersection2 @t4 @t99) @t99 @t71))))) % 0.21/0.56 (define @t101 () (not (tptp.mrel @t95 @t93))) % 0.21/0.56 (define @t102 () (not (tptp.eiw_di @t94 @t95))) % 0.21/0.56 (define @t103 () (not (tptp.eiw_di @t4 @t1))) % 0.21/0.56 (define @t104 () (@list @t4 @t95 @t94 @t93 @t92)) % 0.21/0.56 (define @t105 () (forall @t104 (or @t103 (not (tptp.mrel @t1 @t95)) @t102 @t101 @t100 @t98 @t97))) % 0.21/0.56 (define @t106 () (not (tptp.mrel @t2 @t95))) % 0.21/0.56 (define @t107 () (tptp.eiw_di @t4 @t2)) % 0.21/0.56 (define @t108 () (not @t107)) % 0.21/0.56 (define @t109 () (or @t108 @t106 @t102 @t101 @t100 @t98 @t97)) % 0.21/0.56 (define @t110 () (lambda @t7 (forall @t104 @t109))) % 0.21/0.56 (define @t111 () (_ @t110 @t1)) % 0.21/0.56 (define @t112 () (or @t82 @t111)) % 0.21/0.56 (define @t113 () (forall @t54 @t112)) % 0.21/0.56 (define @t114 () (lambda @t7 @t113)) % 0.21/0.56 (define @t115 () (_ @t41 @t1)) % 0.21/0.56 (define @t116 () (lambda @t56 (forall @t54 (or @t82 @t115)))) % 0.21/0.56 (define @t117 () (or @t106 @t102 @t101 @t100 @t98 @t97)) % 0.21/0.56 (define @t118 () (or @t108 @t117)) % 0.21/0.56 (define @t119 () (forall @t104 @t118)) % 0.21/0.56 (define @t120 () (@list @t95 @t94 @t93 @t92)) % 0.21/0.56 (define @t121 () (forall @t120 @t118)) % 0.21/0.56 (define @t122 () (forall @t120 @t117)) % 0.21/0.56 (define @t123 () (@var "BOUND_VARIABLE_11897" tptp.mworld)) % 0.21/0.56 (define @t124 () (@var "BOUND_VARIABLE_11895" tptp.mworld)) % 0.21/0.56 (define @t125 () (@var "BOUND_VARIABLE_11893" $$unsorted)) % 0.21/0.56 (define @t126 () (or @t108 @t122)) % 0.21/0.56 (define @t127 () (not (tptp.mrel @t124 @t123))) % 0.21/0.56 (define @t128 () (tptp.singleton @t125)) % 0.21/0.56 (define @t129 () (not (tptp.mrel @t124 @t71))) % 0.21/0.56 (define @t130 () (not (tptp.mrel @t1 @t124))) % 0.21/0.56 (define @t131 () (not (tptp.eiw_di @t125 @t1))) % 0.21/0.56 (define @t132 () (@list @t1 @t125 @t124 @t123)) % 0.21/0.56 (define @t133 () (forall @t132 (or @t82 @t131 @t130 (not (forall @t73 (or @t129 (tptp.qmltpeq (tptp.set_intersection2 @t4 @t128) @t128 @t71)))) @t127 (tptp.in @t125 @t4 @t123)))) % 0.21/0.56 (define @t134 () (tptp.in @t125 @t19 @t123)) % 0.21/0.56 (define @t135 () (not (forall @t73 (or @t129 (tptp.qmltpeq (tptp.set_intersection2 @t19 @t128) @t128 @t71))))) % 0.21/0.56 (define @t136 () (not (tptp.mrel @t8 @t1))) % 0.21/0.56 (define @t137 () (forall @t132 (or @t136 @t131 @t130 @t135 @t127 @t134))) % 0.21/0.56 (define @t138 () (lambda @t25 @t137)) % 0.21/0.56 (define @t139 () (_ @t138 @t4 @t2)) % 0.21/0.56 (define @t140 () (or @t108 @t139)) % 0.21/0.56 (define @t141 () (forall @t6 @t140)) % 0.21/0.56 (define @t142 () (lambda @t7 @t141)) % 0.21/0.56 (define @t143 () (_ @t59 @t4 @t2)) % 0.21/0.56 (define @t144 () (lambda @t62 (forall @t6 (or @t108 @t143)))) % 0.21/0.56 (define @t145 () (or @t82 @t131 @t130 @t135 @t127 @t134)) % 0.21/0.56 (define @t146 () (or @t131 @t130 @t135 @t127 @t134)) % 0.21/0.56 (define @t147 () (or @t82 @t146)) % 0.21/0.56 (define @t148 () (forall @t132 @t147)) % 0.21/0.56 (define @t149 () (@list @t125 @t124 @t123)) % 0.21/0.56 (define @t150 () (forall @t149 @t147)) % 0.21/0.56 (define @t151 () (forall @t149 @t146)) % 0.21/0.56 (define @t152 () (@var "BOUND_VARIABLE_11863" tptp.mworld)) % 0.21/0.56 (define @t153 () (@var "BOUND_VARIABLE_11861" tptp.mworld)) % 0.21/0.56 (define @t154 () (or @t82 @t151)) % 0.21/0.56 (define @t155 () (tptp.in @t4 @t19 @t152)) % 0.21/0.56 (define @t156 () (not (tptp.mrel @t153 @t152))) % 0.21/0.56 (define @t157 () (tptp.singleton @t4)) % 0.21/0.56 (define @t158 () (tptp.qmltpeq (tptp.set_intersection2 @t19 @t157) @t157 @t71)) % 0.21/0.56 (define @t159 () (not (forall @t73 (or (not (tptp.mrel @t153 @t71)) @t158)))) % 0.21/0.56 (define @t160 () (@list @t4 @t153 @t152)) % 0.21/0.56 (define @t161 () (forall @t160 (or @t103 (not (tptp.mrel @t1 @t153)) @t159 @t156 @t155))) % 0.21/0.56 (define @t162 () (not (tptp.mrel @t2 @t153))) % 0.21/0.56 (define @t163 () (or @t108 @t162 @t159 @t156 @t155)) % 0.21/0.56 (define @t164 () (lambda @t7 (forall @t160 @t163))) % 0.21/0.56 (define @t165 () (_ @t164 @t1)) % 0.21/0.56 (define @t166 () (or @t82 @t165)) % 0.21/0.56 (define @t167 () (forall @t54 @t166)) % 0.21/0.56 (define @t168 () (lambda @t7 @t167)) % 0.21/0.56 (define @t169 () (or @t162 @t159 @t156 @t155)) % 0.21/0.56 (define @t170 () (or @t108 @t169)) % 0.21/0.56 (define @t171 () (forall @t160 @t170)) % 0.21/0.56 (define @t172 () (@list @t153 @t152)) % 0.21/0.56 (define @t173 () (forall @t172 @t170)) % 0.21/0.56 (define @t174 () (forall @t172 @t169)) % 0.21/0.56 (define @t175 () (@var "BOUND_VARIABLE_11829" tptp.mworld)) % 0.21/0.56 (define @t176 () (or @t108 @t174)) % 0.21/0.56 (define @t177 () (not (tptp.mrel @t1 @t175))) % 0.21/0.56 (define @t178 () (not (tptp.mrel @t1 @t71))) % 0.21/0.56 (define @t179 () (@list @t1 @t175)) % 0.21/0.56 (define @t180 () (forall @t179 (or @t82 (not (forall @t73 (or @t178 @t158))) @t177 (tptp.in @t4 @t19 @t175)))) % 0.21/0.56 (define @t181 () (tptp.in @t17 @t19 @t175)) % 0.21/0.56 (define @t182 () (tptp.singleton @t17)) % 0.21/0.56 (define @t183 () (tptp.set_intersection2 @t19 @t182)) % 0.21/0.56 (define @t184 () (tptp.qmltpeq @t183 @t182 @t71)) % 0.21/0.56 (define @t185 () (forall @t73 (or @t178 @t184))) % 0.21/0.56 (define @t186 () (not @t185)) % 0.21/0.56 (define @t187 () (forall @t179 (or @t136 @t186 @t177 @t181))) % 0.21/0.56 (define @t188 () (lambda @t24 @t187)) % 0.21/0.56 (define @t189 () (_ @t188 @t4 @t2)) % 0.21/0.56 (define @t190 () (or @t108 @t189)) % 0.21/0.56 (define @t191 () (forall @t6 @t190)) % 0.21/0.56 (define @t192 () (lambda @t7 @t191)) % 0.21/0.56 (define @t193 () (or @t82 @t186 @t177 @t181)) % 0.21/0.56 (define @t194 () (or @t177 @t181)) % 0.21/0.56 (define @t195 () (or @t82 @t186 @t194)) % 0.21/0.56 (define @t196 () (forall @t179 @t195)) % 0.21/0.56 (define @t197 () (@list @t175)) % 0.21/0.56 (define @t198 () (forall @t197 @t195)) % 0.21/0.56 (define @t199 () (forall @t197 @t194)) % 0.21/0.56 (define @t200 () (@var "BOUND_VARIABLE_11795" tptp.mworld)) % 0.21/0.56 (define @t201 () (@list @t200)) % 0.21/0.56 (define @t202 () (or @t82 @t186 @t199)) % 0.21/0.56 (define @t203 () (tptp.in @t17 @t19 @t200)) % 0.21/0.56 (define @t204 () (@list @t200)) % 0.21/0.56 (define @t205 () (forall @t204 (or (not (tptp.mrel @t1 @t200)) @t203))) % 0.21/0.56 (define @t206 () (or @t82 @t186 @t205)) % 0.21/0.56 (define @t207 () (=> @t185 @t205)) % 0.21/0.56 (define @t208 () (or @t82 @t207)) % 0.21/0.56 (define @t209 () (tptp.in @t17 @t19 @t1)) % 0.21/0.56 (define @t210 () (forall @t54 (or @t82 @t209))) % 0.21/0.56 (define @t211 () (@list @t1)) % 0.21/0.56 (define @t212 () (tptp.qmltpeq @t183 @t182 @t1)) % 0.21/0.56 (define @t213 () (forall @t54 (or @t82 @t212))) % 0.21/0.56 (define @t214 () (=> @t213 @t210)) % 0.21/0.56 (define @t215 () (lambda @t7 @t214)) % 0.21/0.56 (define @t216 () (or @t82 (_ @t215 @t1))) % 0.21/0.56 (define @t217 () (forall @t54 @t216)) % 0.21/0.56 (define @t218 () (lambda @t7 @t217)) % 0.21/0.56 (define @t219 () (lambda @t7 @t210)) % 0.21/0.56 (define @t220 () (_ @t219 @t2)) % 0.21/0.56 (define @t221 () (=> @t213 @t220)) % 0.21/0.56 (define @t222 () (lambda @t7 @t221)) % 0.21/0.56 (define @t223 () (@list @t46 @t2)) % 0.21/0.56 (define @t224 () (_ @t33 @t1)) % 0.21/0.56 (define @t225 () (or @t82 @t224)) % 0.21/0.56 (define @t226 () (_ @t33 @t1)) % 0.21/0.56 (define @t227 () (or @t82 @t226)) % 0.21/0.56 (define @t228 () (forall @t54 @t227)) % 0.21/0.56 (define @t229 () (lambda @t7 @t228)) % 0.21/0.56 (define @t230 () (_ @t116 @t33)) % 0.21/0.56 (define @t231 () (lambda @t7 @t213)) % 0.21/0.56 (define @t232 () (_ @t231 @t2)) % 0.21/0.56 (define @t233 () (=> @t232 @t47)) % 0.21/0.56 (define @t234 () (lambda @t223 @t233)) % 0.21/0.56 (define @t235 () (_ @t36 @t1)) % 0.21/0.56 (define @t236 () (or @t82 @t235)) % 0.21/0.56 (define @t237 () (_ @t36 @t1)) % 0.21/0.56 (define @t238 () (or @t82 @t237)) % 0.21/0.56 (define @t239 () (forall @t54 @t238)) % 0.21/0.56 (define @t240 () (lambda @t7 @t239)) % 0.21/0.56 (define @t241 () (_ @t116 @t36)) % 0.21/0.56 (define @t242 () (lambda @t24 (_ (_ @t116 (_ (_ @t51 @t241) @t230)) @t8))) % 0.21/0.56 (define @t243 () (lambda @t25 (_ (_ @t116 (_ @t144 @t242)) @t8))) % 0.21/0.56 (define @t244 () (not @t3)) % 0.21/0.56 (define @t245 () (or @t244 @t53)) % 0.21/0.56 (define @t246 () (not @t5)) % 0.21/0.56 (define @t247 () (or @t246 @t60)) % 0.21/0.56 (assume @p1 (forall (@list @t2 @t1) @t3)) % 0.21/0.56 (assume @p2 (forall @t7 (exists @t6 @t5))) % 0.21/0.56 (assume @p3 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t10 (_ (_ tptp.mbox (_ @t9 @t4)) @t8)))))) % 0.21/0.56 (assume @p4 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t10 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t14 (_ (_ tptp.mbox (_ (_ tptp.mimplies @t13) (_ tptp.mbox (_ @t12 @t4)))) @t8)))) @t8)))))) % 0.21/0.56 (assume @p5 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t10 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t14 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda (@list @t15 @t8) (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ (_ tptp.mand @t13) (_ tptp.mbox (_ @t12 @t15)))) (_ tptp.mbox (_ @t9 @t15)))) @t8)))) @t8)))) @t8)))))) % 0.21/0.56 (assume @p6 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mbox (_ @t22 (_ tptp.mbox (_ (_ tptp.qmltpeq (_ @t20 @t16)) (_ @t18 @t16))))) @t8)))) @t8)))) @t8)))))) % 0.21/0.56 (assume @p7 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mbox (_ @t22 (_ tptp.mbox (_ (_ tptp.qmltpeq (_ @t26 @t19)) (_ @t26 @t17))))) @t8)))) @t8)))) @t8)))))) % 0.21/0.56 (assume @p8 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mbox (_ @t22 (_ tptp.mbox (_ (_ tptp.qmltpeq (_ tptp.singleton @t19)) @t27)))) @t8)))) @t8)))))) % 0.21/0.56 (assume @p9 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ @t29 @t28)) (_ tptp.mbox (_ tptp.empty @t17)))) @t8)))) @t8)))))) % 0.21/0.56 (assume @p10 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ @t29 (_ tptp.mbox (_ @t31 @t16)))) (_ tptp.mbox (_ @t30 @t16)))) @t8)))) @t8)))) @t8)))))) % 0.21/0.56 (assume @p11 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ @t29 (_ tptp.mbox (_ @t32 @t19)))) (_ tptp.mbox (_ @t32 @t17)))) @t8)))) @t8)))) @t8)))))) % 0.21/0.56 (assume @p12 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mbox (_ (_ tptp.qmltpeq (_ @t20 @t17)) (_ @t18 @t19))) @t8)))) @t8)))))) % 0.21/0.56 (assume @p13 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mbox (_ (_ tptp.qmltpeq (_ @t20 @t19)) @t19)) @t8)))) @t8)))))) % 0.21/0.56 (assume @p14 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ tptp.mbox (_ @t31 @t17))) (_ tptp.mbox (_ tptp.mnot @t34)))) @t8)))) @t8)))))) % 0.21/0.56 (assume @p15 (_ tptp.mlocal (_ tptp.mexists_di (lambda @t25 (_ @t28 @t8))))) % 0.21/0.56 (assume @p16 (_ tptp.mlocal (_ tptp.mexists_di (lambda @t25 (_ (_ tptp.mbox (_ tptp.mnot @t28)) @t8))))) % 0.21/0.56 (assume @p17 @t40) % 0.21/0.56 (assume @p18 @t39) % 0.21/0.56 (assume @p19 true) % 0.21/0.56 (step @p20 (= tptp.mlocal @t42) :rule refl :args (@t42)) % 0.21/0.56 (step @p21 (= tptp.mnot @t45) :rule refl :args (@t45)) % 0.21/0.56 (step @p22 (= tptp.mand @t49) :rule refl :args (@t49)) % 0.21/0.56 (step @p23 (= tptp.mor @t50) :rule refl :args (@t50)) % 0.21/0.56 (step @p24 (= tptp.mimplies @t51) :rule refl :args (@t51)) % 0.21/0.56 (step @p25 (= tptp.mequiv @t52) :rule refl :args (@t52)) % 0.21/0.56 (step @p26 (= tptp.mbox @t57) :rule refl :args (@t57)) % 0.21/0.56 (step @p27 (= tptp.mdia @t58) :rule refl :args (@t58)) % 0.21/0.56 (step @p28 (= tptp.mforall_di @t63) :rule refl :args (@t63)) % 0.21/0.56 (step @p29 (= tptp.mexists_di @t64) :rule refl :args (@t64)) % 0.21/0.56 (step @p30 :rule beta-reduce :args ((= @t85 (forall @t80 (or (not (tptp.mrel tptp.mactual @t1)) @t79 @t78 @t77 @t76 @t74 @t70 @t68))))) % 0.21/0.56 (step @p31 :rule beta-reduce :args ((= (_ @t42 @t84) @t85))) % 0.21/0.56 (step @p32 :rule trans :premises (@p31 @p30)) % 0.21/0.56 (step @p33 :rule aci_norm :args ((= @t87 @t83))) % 0.21/0.56 (step @p34 :rule cong :premises (@p33) :args (@t88)) % 0.21/0.56 (step @p35 :rule quant-merge-prenex :args ((= (forall @t54 @t90) @t88))) % 0.21/0.56 (step @p36 :rule alpha_equiv :args (@t91 (@list @t66 @t75 @t67 @t69 @t65) (@list @t4 @t95 @t94 @t93 @t92))) % 0.21/0.56 (step @p37 :rule refl :args (@t82)) % 0.21/0.56 (step @p38 :rule nary_cong :premises (@p37 @p36) :args (@t96)) % 0.21/0.56 (step @p39 :rule quant-miniscope-or :args ((= @t90 @t96))) % 0.21/0.56 (step @p40 :rule trans :premises (@p39 @p38)) % 0.21/0.56 (step @p41 :rule symm :premises (@p40)) % 0.21/0.56 (step @p42 :rule cong :premises (@p41) :args ((forall @t54 (or @t82 @t105)))) % 0.21/0.56 (step @p43 :rule trans :premises (@p42 @p35)) % 0.21/0.56 (step @p44 :rule trans :premises (@p43 @p34)) % 0.21/0.56 (step @p45 :rule beta-reduce :args ((= @t111 @t105))) % 0.21/0.56 (step @p46 :rule refl :args (@t82)) % 0.21/0.56 (step @p47 :rule nary_cong :premises (@p46 @p45) :args (@t112)) % 0.21/0.56 (step @p48 :rule cong :premises (@p47) :args (@t113)) % 0.21/0.56 (step @p49 :rule trans :premises (@p48 @p44)) % 0.21/0.56 (step @p50 :rule cong :premises (@p49) :args (@t114)) % 0.21/0.56 (step @p51 :rule beta-reduce :args ((= (_ @t116 @t110) @t114))) % 0.21/0.56 (step @p52 :rule trans :premises (@p51 @p50)) % 0.21/0.56 (step @p53 :rule aci_norm :args ((= @t118 @t109))) % 0.21/0.56 (step @p54 :rule cong :premises (@p53) :args (@t119)) % 0.21/0.56 (step @p55 :rule quant-merge-prenex :args ((= (forall @t6 @t121) @t119))) % 0.21/0.56 (step @p56 :rule alpha_equiv :args (@t122 (@list @t95 @t94 @t93 @t92) (@list @t1 @t125 @t124 @t123))) % 0.21/0.56 (step @p57 :rule refl :args (@t108)) % 0.21/0.56 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t126)) % 0.21/0.56 (step @p59 :rule quant-miniscope-or :args ((= @t121 @t126))) % 0.21/0.56 (step @p60 :rule trans :premises (@p59 @p58)) % 0.21/0.56 (step @p61 :rule symm :premises (@p60)) % 0.21/0.56 (step @p62 :rule cong :premises (@p61) :args ((forall @t6 (or @t108 @t133)))) % 0.21/0.56 (step @p63 :rule trans :premises (@p62 @p55)) % 0.21/0.56 (step @p64 :rule trans :premises (@p63 @p54)) % 0.21/0.56 (step @p65 :rule beta-reduce :args ((= @t139 @t133))) % 0.21/0.56 (step @p66 :rule refl :args (@t108)) % 0.21/0.56 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t140)) % 0.21/0.56 (step @p68 :rule cong :premises (@p67) :args (@t141)) % 0.21/0.56 (step @p69 :rule trans :premises (@p68 @p64)) % 0.21/0.56 (step @p70 :rule cong :premises (@p69) :args (@t142)) % 0.21/0.56 (step @p71 :rule beta-reduce :args ((= (_ @t144 @t138) @t142))) % 0.21/0.56 (step @p72 :rule trans :premises (@p71 @p70)) % 0.21/0.56 (step @p73 :rule beta-reduce :args ((= (_ (lambda @t7 (forall @t132 @t145)) @t8) @t137))) % 0.21/0.56 (step @p74 :rule refl :args (@t8)) % 0.21/0.56 (step @p75 :rule aci_norm :args ((= @t147 @t145))) % 0.21/0.56 (step @p76 :rule cong :premises (@p75) :args (@t148)) % 0.21/0.56 (step @p77 :rule quant-merge-prenex :args ((= (forall @t54 @t150) @t148))) % 0.21/0.56 (step @p78 :rule alpha_equiv :args (@t151 (@list @t125 @t124 @t123) (@list @t4 @t153 @t152))) % 0.21/0.56 (step @p79 :rule nary_cong :premises (@p37 @p78) :args (@t154)) % 0.21/0.56 (step @p80 :rule quant-miniscope-or :args ((= @t150 @t154))) % 0.21/0.56 (step @p81 :rule trans :premises (@p80 @p79)) % 0.21/0.56 (step @p82 :rule symm :premises (@p81)) % 0.21/0.56 (step @p83 :rule cong :premises (@p82) :args ((forall @t54 (or @t82 @t161)))) % 0.21/0.56 (step @p84 :rule trans :premises (@p83 @p77)) % 0.21/0.56 (step @p85 :rule trans :premises (@p84 @p76)) % 0.21/0.56 (step @p86 :rule beta-reduce :args ((= @t165 @t161))) % 0.21/0.56 (step @p87 :rule nary_cong :premises (@p46 @p86) :args (@t166)) % 0.21/0.56 (step @p88 :rule cong :premises (@p87) :args (@t167)) % 0.21/0.56 (step @p89 :rule trans :premises (@p88 @p85)) % 0.21/0.56 (step @p90 :rule cong :premises (@p89) :args (@t168)) % 0.21/0.56 (step @p91 :rule beta-reduce :args ((= (_ @t116 @t164) @t168))) % 0.21/0.56 (step @p92 :rule trans :premises (@p91 @p90)) % 0.21/0.56 (step @p93 :rule aci_norm :args ((= @t170 @t163))) % 0.21/0.56 (step @p94 :rule cong :premises (@p93) :args (@t171)) % 0.21/0.56 (step @p95 :rule quant-merge-prenex :args ((= (forall @t6 @t173) @t171))) % 0.21/0.56 (step @p96 :rule alpha_equiv :args (@t174 (@list @t153 @t152) (@list @t1 @t175))) % 0.21/0.56 (step @p97 :rule nary_cong :premises (@p57 @p96) :args (@t176)) % 0.21/0.56 (step @p98 :rule quant-miniscope-or :args ((= @t173 @t176))) % 0.21/0.56 (step @p99 :rule trans :premises (@p98 @p97)) % 0.21/0.56 (step @p100 :rule symm :premises (@p99)) % 0.21/0.56 (step @p101 :rule cong :premises (@p100) :args ((forall @t6 (or @t108 @t180)))) % 0.21/0.56 (step @p102 :rule trans :premises (@p101 @p95)) % 0.21/0.56 (step @p103 :rule trans :premises (@p102 @p94)) % 0.21/0.56 (step @p104 :rule beta-reduce :args ((= @t189 @t180))) % 0.21/0.56 (step @p105 :rule nary_cong :premises (@p66 @p104) :args (@t190)) % 0.21/0.56 (step @p106 :rule cong :premises (@p105) :args (@t191)) % 0.21/0.56 (step @p107 :rule trans :premises (@p106 @p103)) % 0.21/0.56 (step @p108 :rule cong :premises (@p107) :args (@t192)) % 0.21/0.56 (step @p109 :rule beta-reduce :args ((= (_ @t144 @t188) @t192))) % 0.21/0.56 (step @p110 :rule trans :premises (@p109 @p108)) % 0.21/0.56 (step @p111 :rule beta-reduce :args ((= (_ (lambda @t7 (forall @t179 @t193)) @t8) @t187))) % 0.21/0.56 (step @p112 :rule aci_norm :args ((= @t195 @t193))) % 0.21/0.56 (step @p113 :rule cong :premises (@p112) :args (@t196)) % 0.21/0.56 (step @p114 :rule quant-merge-prenex :args ((= (forall @t54 @t198) @t196))) % 0.21/0.56 (step @p115 :rule alpha_equiv :args (@t199 (@list @t175) @t201)) % 0.21/0.56 (step @p116 :rule refl :args (@t186)) % 0.21/0.56 (step @p117 :rule nary_cong :premises (@p37 @p116 @p115) :args (@t202)) % 0.21/0.56 (step @p118 :rule quant-miniscope-or :args ((= @t198 @t202))) % 0.21/0.56 (step @p119 :rule trans :premises (@p118 @p117)) % 0.21/0.56 (step @p120 :rule symm :premises (@p119)) % 0.21/0.56 (step @p121 :rule cong :premises (@p120) :args ((forall @t54 @t206))) % 0.21/0.56 (step @p122 :rule trans :premises (@p121 @p114)) % 0.21/0.56 (step @p123 :rule trans :premises (@p122 @p113)) % 0.21/0.56 (step @p124 :rule aci_norm :args ((= (or @t82 (or @t186 @t205)) @t206))) % 0.21/0.56 (step @p125 :rule bool-impl-elim :args (@t185 @t205)) % 0.21/0.56 (step @p126 :rule nary_cong :premises (@p37 @p125) :args (@t208)) % 0.21/0.56 (step @p127 :rule trans :premises (@p126 @p124)) % 0.21/0.56 (step @p128 :rule cong :premises (@p127) :args ((forall @t54 @t208))) % 0.21/0.56 (step @p129 :rule trans :premises (@p128 @p123)) % 0.21/0.56 (step @p130 :rule beta-reduce :args ((= (_ (lambda @t7 (=> (forall @t73 (or (not (tptp.mrel @t2 @t71)) @t184)) (forall @t204 (or (not (tptp.mrel @t2 @t200)) @t203)))) @t1) @t207))) % 0.21/0.56 (step @p131 :rule refl :args (@t1)) % 0.21/0.56 (step @p132 :rule alpha_equiv :args (@t210 @t211 @t201)) % 0.21/0.56 (step @p133 :rule alpha_equiv :args (@t213 @t211 (@list @t71))) % 0.21/0.56 (step @p134 :rule cong :premises (@p133 @p132) :args (@t214)) % 0.21/0.56 (step @p135 :rule cong :premises (@p134) :args (@t215)) % 0.21/0.56 (step @p136 :rule ho_cong :premises (@p135 @p131)) % 0.21/0.56 (step @p137 :rule trans :premises (@p136 @p130)) % 0.21/0.56 (step @p138 :rule nary_cong :premises (@p46 @p137) :args (@t216)) % 0.21/0.56 (step @p139 :rule cong :premises (@p138) :args (@t217)) % 0.21/0.56 (step @p140 :rule trans :premises (@p139 @p129)) % 0.21/0.56 (step @p141 :rule cong :premises (@p140) :args (@t218)) % 0.21/0.56 (step @p142 :rule beta-reduce :args ((= (_ @t116 @t215) @t218))) % 0.21/0.56 (step @p143 :rule trans :premises (@p142 @p141)) % 0.21/0.56 (step @p144 :rule beta-reduce :args ((= @t220 @t210))) % 0.21/0.56 (step @p145 :rule refl :args (@t213)) % 0.21/0.56 (step @p146 :rule cong :premises (@p145 @p144) :args (@t221)) % 0.21/0.56 (step @p147 :rule cong :premises (@p146) :args (@t222)) % 0.21/0.56 (step @p148 :rule beta-reduce :args ((= (_ (lambda @t223 (=> @t213 @t47)) @t219) @t222))) % 0.21/0.56 (step @p149 :rule trans :premises (@p148 @p147)) % 0.21/0.56 (step @p150 :rule refl :args (@t209)) % 0.21/0.56 (step @p151 :rule refl :args (@t224)) % 0.21/0.56 (step @p152 :rule cong :premises (@p151 @p150) :args ((= @t224 @t209))) % 0.21/0.56 (step @p153 :rule symm :premises (@p152)) % 0.21/0.56 (step @p154 :rule eq_resolve :premises (@p151 @p153)) % 0.21/0.56 (step @p155 :rule nary_cong :premises (@p37 @p154) :args (@t225)) % 0.21/0.56 (step @p156 :rule cong :premises (@p155) :args ((forall @t54 @t225))) % 0.21/0.56 (step @p157 :rule refl :args (@t226)) % 0.21/0.56 (step @p158 :rule nary_cong :premises (@p46 @p157) :args (@t227)) % 0.21/0.56 (step @p159 :rule cong :premises (@p158) :args (@t228)) % 0.21/0.56 (step @p160 :rule trans :premises (@p159 @p156)) % 0.21/0.56 (step @p161 :rule cong :premises (@p160) :args (@t229)) % 0.21/0.56 (step @p162 :rule beta-reduce :args ((= @t230 @t229))) % 0.21/0.56 (step @p163 :rule trans :premises (@p162 @p161)) % 0.21/0.56 (step @p164 :rule refl :args (@t47)) % 0.21/0.56 (step @p165 :rule beta-reduce :args ((= @t232 @t213))) % 0.21/0.56 (step @p166 :rule cong :premises (@p165 @p164) :args (@t233)) % 0.21/0.56 (step @p167 :rule cong :premises (@p166) :args (@t234)) % 0.21/0.56 (step @p168 :rule beta-reduce :args ((= (_ @t51 @t231) @t234))) % 0.21/0.56 (step @p169 :rule trans :premises (@p168 @p167)) % 0.21/0.56 (step @p170 :rule refl :args ((tptp.qmltpeq @t35 @t27 @t1))) % 0.21/0.56 (step @p171 :rule refl :args (@t182)) % 0.21/0.56 (step @p172 :rule refl :args ((tptp.set_intersection2 @t19 @t27))) % 0.21/0.56 (step @p173 :rule refl :args (@t19)) % 0.21/0.56 (step @p174 :rule cong :premises (@p173 @p171) :args (@t183)) % 0.21/0.56 (step @p175 :rule trans :premises (@p174 @p172)) % 0.21/0.56 (step @p176 :rule cong :premises (@p175 @p171 @p131) :args (@t212)) % 0.21/0.56 (step @p177 :rule trans :premises (@p176 @p170)) % 0.21/0.56 (step @p178 :rule refl :args (tptp.qmltpeq)) % 0.21/0.56 (step @p179 :rule ho_cong :premises (@p178 @p175)) % 0.21/0.56 (step @p180 :rule ho_cong :premises (@p179 @p171)) % 0.21/0.56 (step @p181 :rule ho_cong :premises (@p180 @p131)) % 0.21/0.56 (step @p182 :rule cong :premises (@p181 @p177) :args ((= (_ (_ (_ tptp.qmltpeq @t183) @t182) @t1) @t212))) % 0.21/0.56 (step @p183 :rule symm :premises (@p182)) % 0.21/0.56 (step @p184 :rule refl :args (@t235)) % 0.21/0.56 (step @p185 :rule eq_resolve :premises (@p184 @p183)) % 0.21/0.56 (step @p186 :rule refl :args (@t27)) % 0.21/0.56 (step @p187 :rule cong :premises (@p186 @p171) :args ((= @t27 @t182))) % 0.21/0.56 (step @p188 :rule symm :premises (@p187)) % 0.21/0.56 (step @p189 :rule eq_resolve :premises (@p186 @p188)) % 0.21/0.56 (step @p190 :rule refl :args (@t20)) % 0.21/0.56 (step @p191 :rule ho_cong :premises (@p190 @p171)) % 0.21/0.56 (step @p192 :rule cong :premises (@p191 @p175) :args ((= (_ @t20 @t182) @t183))) % 0.21/0.56 (step @p193 :rule symm :premises (@p192)) % 0.21/0.56 (step @p194 :rule refl :args (@t35)) % 0.21/0.56 (step @p195 :rule eq_resolve :premises (@p194 @p193)) % 0.21/0.56 (step @p196 :rule ho_cong :premises (@p190 @p189)) % 0.21/0.56 (step @p197 :rule trans :premises (@p196 @p195)) % 0.21/0.56 (step @p198 :rule ho_cong :premises (@p178 @p197)) % 0.21/0.56 (step @p199 :rule ho_cong :premises (@p198 @p189)) % 0.21/0.56 (step @p200 :rule ho_cong :premises (@p199 @p131)) % 0.21/0.56 (step @p201 :rule trans :premises (@p200 @p185)) % 0.21/0.56 (step @p202 :rule nary_cong :premises (@p37 @p201) :args (@t236)) % 0.21/0.56 (step @p203 :rule cong :premises (@p202) :args ((forall @t54 @t236))) % 0.21/0.56 (step @p204 :rule refl :args (@t237)) % 0.21/0.56 (step @p205 :rule nary_cong :premises (@p46 @p204) :args (@t238)) % 0.21/0.56 (step @p206 :rule cong :premises (@p205) :args (@t239)) % 0.21/0.56 (step @p207 :rule trans :premises (@p206 @p203)) % 0.21/0.56 (step @p208 :rule cong :premises (@p207) :args (@t240)) % 0.21/0.56 (step @p209 :rule beta-reduce :args ((= @t241 @t240))) % 0.21/0.56 (step @p210 :rule trans :premises (@p209 @p208)) % 0.21/0.56 (step @p211 :rule refl :args (@t51)) % 0.21/0.56 (step @p212 :rule ho_cong :premises (@p211 @p210)) % 0.21/0.56 (step @p213 :rule trans :premises (@p212 @p169)) % 0.21/0.56 (step @p214 :rule ho_cong :premises (@p213 @p163)) % 0.21/0.56 (step @p215 :rule trans :premises (@p214 @p149)) % 0.21/0.56 (step @p216 :rule refl :args (@t116)) % 0.21/0.56 (step @p217 :rule ho_cong :premises (@p216 @p215)) % 0.21/0.56 (step @p218 :rule trans :premises (@p217 @p143)) % 0.21/0.56 (step @p219 :rule ho_cong :premises (@p218 @p74)) % 0.21/0.56 (step @p220 :rule trans :premises (@p219 @p111)) % 0.21/0.56 (step @p221 :rule cong :premises (@p220) :args (@t242)) % 0.21/0.56 (step @p222 :rule refl :args (@t144)) % 0.21/0.56 (step @p223 :rule ho_cong :premises (@p222 @p221)) % 0.21/0.56 (step @p224 :rule trans :premises (@p223 @p110)) % 0.21/0.56 (step @p225 :rule ho_cong :premises (@p216 @p224)) % 0.21/0.56 (step @p226 :rule trans :premises (@p225 @p92)) % 0.21/0.56 (step @p227 :rule ho_cong :premises (@p226 @p74)) % 0.21/0.56 (step @p228 :rule trans :premises (@p227 @p73)) % 0.21/0.56 (step @p229 :rule cong :premises (@p228) :args (@t243)) % 0.21/0.56 (step @p230 :rule ho_cong :premises (@p222 @p229)) % 0.21/0.56 (step @p231 :rule trans :premises (@p230 @p72)) % 0.21/0.56 (step @p232 :rule ho_cong :premises (@p216 @p231)) % 0.21/0.56 (step @p233 :rule trans :premises (@p232 @p52)) % 0.21/0.56 (step @p234 :rule refl :args (@t42)) % 0.21/0.56 (step @p235 :rule ho_cong :premises (@p234 @p233)) % 0.21/0.56 (step @p236 :rule trans :premises (@p235 @p32)) % 0.21/0.56 (step @p237 :rule cong :premises (@p236) :args ((not (_ @t42 (_ @t116 (_ @t144 @t243)))))) % 0.21/0.56 (step @p238 :rule refl :args (@t33)) % 0.21/0.56 (step @p239 :rule refl :args (@t115)) % 0.21/0.56 (step @p240 :rule refl :args (@t53)) % 0.21/0.56 (step @p241 :rule cong :premises (@p240 @p239) :args ((= @t53 @t115))) % 0.21/0.56 (step @p242 :rule symm :premises (@p241)) % 0.21/0.56 (step @p243 :rule eq_resolve :premises (@p240 @p242)) % 0.21/0.56 (step @p244 :rule refl :args (@t81)) % 0.21/0.56 (step @p245 :rule refl :args (@t3)) % 0.21/0.56 (step @p246 :rule cong :premises (@p245 @p244) :args ((= @t3 @t81))) % 0.21/0.56 (step @p247 :rule symm :premises (@p246)) % 0.21/0.56 (step @p248 :rule eq_resolve :premises (@p245 @p247)) % 0.21/0.56 (step @p249 :rule cong :premises (@p248) :args (@t244)) % 0.21/0.56 (step @p250 :rule nary_cong :premises (@p249 @p243) :args (@t245)) % 0.21/0.56 (step @p251 :rule cong :premises (@p250) :args ((forall @t54 @t245))) % 0.21/0.56 (step @p252 :rule bool-impl-elim :args (@t3 @t53)) % 0.21/0.56 (step @p253 :rule cong :premises (@p252) :args (@t55)) % 0.21/0.56 (step @p254 :rule trans :premises (@p253 @p251)) % 0.21/0.56 (step @p255 :rule cong :premises (@p254) :args (@t57)) % 0.21/0.56 (step @p256 :rule trans :premises (@p26 @p255)) % 0.21/0.56 (step @p257 :rule ho_cong :premises (@p256 @p238)) % 0.21/0.56 (step @p258 :rule refl :args (@t36)) % 0.21/0.56 (step @p259 :rule ho_cong :premises (@p256 @p258)) % 0.21/0.56 (step @p260 :rule ho_cong :premises (@p24 @p259)) % 0.21/0.56 (step @p261 :rule ho_cong :premises (@p260 @p257)) % 0.21/0.56 (step @p262 :rule ho_cong :premises (@p256 @p261)) % 0.21/0.56 (step @p263 :rule ho_cong :premises (@p262 @p74)) % 0.21/0.56 (step @p264 :rule cong :premises (@p263) :args (@t37)) % 0.21/0.56 (step @p265 :rule refl :args (@t143)) % 0.21/0.56 (step @p266 :rule refl :args (@t60)) % 0.21/0.56 (step @p267 :rule cong :premises (@p266 @p265) :args ((= @t60 @t143))) % 0.21/0.56 (step @p268 :rule symm :premises (@p267)) % 0.21/0.56 (step @p269 :rule eq_resolve :premises (@p266 @p268)) % 0.21/0.56 (step @p270 :rule refl :args (@t107)) % 0.21/0.56 (step @p271 :rule refl :args (@t5)) % 0.21/0.56 (step @p272 :rule cong :premises (@p271 @p270) :args ((= @t5 @t107))) % 0.21/0.56 (step @p273 :rule symm :premises (@p272)) % 0.21/0.56 (step @p274 :rule eq_resolve :premises (@p271 @p273)) % 0.21/0.56 (step @p275 :rule cong :premises (@p274) :args (@t246)) % 0.21/0.56 (step @p276 :rule nary_cong :premises (@p275 @p269) :args (@t247)) % 0.21/0.56 (step @p277 :rule cong :premises (@p276) :args ((forall @t6 @t247))) % 0.21/0.56 (step @p278 :rule bool-impl-elim :args (@t5 @t60)) % 0.21/0.56 (step @p279 :rule cong :premises (@p278) :args (@t61)) % 0.21/0.56 (step @p280 :rule trans :premises (@p279 @p277)) % 0.21/0.56 (step @p281 :rule cong :premises (@p280) :args (@t63)) % 0.21/0.56 (step @p282 :rule trans :premises (@p28 @p281)) % 0.21/0.56 (step @p283 :rule ho_cong :premises (@p282 @p264)) % 0.21/0.56 (step @p284 :rule ho_cong :premises (@p256 @p283)) % 0.21/0.56 (step @p285 :rule ho_cong :premises (@p284 @p74)) % 0.21/0.56 (step @p286 :rule cong :premises (@p285) :args (@t38)) % 0.21/0.56 (step @p287 :rule ho_cong :premises (@p282 @p286)) % 0.21/0.56 (step @p288 :rule ho_cong :premises (@p256 @p287)) % 0.21/0.56 (step @p289 :rule ho_cong :premises (@p20 @p288)) % 0.21/0.56 (step @p290 :rule cong :premises (@p289) :args (@t40)) % 0.21/0.56 (step @p291 :rule trans :premises (@p290 @p237)) % 0.21/0.56 (step @p292 :rule eq_resolve :premises (@p17 @p291)) % 0.21/0.56 (step @p293 :rule trans :premises (@p289 @p236)) % 0.21/0.56 (step @p294 :rule eq_resolve :premises (@p18 @p293)) % 0.21/0.56 (step @p295 false :rule contra :premises (@p294 @p292)) % 0.21/0.56 ) % 0.21/0.56 % SZS output end Proof % 0.21/0.56 % cvc5 exiting %------------------------------------------------------------------------------