%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL951^24 : 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 : n015.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 0.29s 0.58s % Output : Proof 0.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL951^24 : 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 % 0.10/0.36 % Computer : n015.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Sat Sep 5 06:13:27 UTC 2026 % 0.10/0.37 % CPUTime : % 0.14/0.45 %----Proving TH0 % 0.29/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.29/0.58 % SZS status Theorem % 0.29/0.58 % SZS output start Proof % 0.29/0.58 ( % 0.29/0.58 (declare-sort $$unsorted 0) % 0.29/0.58 (declare-sort tptp.mworld 0) % 0.29/0.58 (declare-const tptp.mactual tptp.mworld) % 0.29/0.58 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.29/0.58 (declare-const tptp.eiw_di (-> $$unsorted tptp.mworld Bool)) % 0.29/0.58 (declare-const tptp.in (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.29/0.58 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.29/0.58 (declare-const tptp.empty (-> $$unsorted tptp.mworld Bool)) % 0.29/0.58 (declare-const tptp.empty_set $$unsorted) % 0.29/0.58 (declare-const tptp.qmltpeq (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.29/0.58 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.29/0.58 (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)))))) % 0.29/0.58 (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))))))) % 0.29/0.58 (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))))))) % 0.29/0.58 (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))))))) % 0.29/0.58 (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))))))) % 0.29/0.58 (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)))))))) % 0.29/0.58 (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)))))))) % 0.29/0.58 (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)))))))) % 0.29/0.58 (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)))))))) % 0.29/0.58 (define @t1 () (@var "V" tptp.mworld)) % 0.29/0.58 (define @t2 () (@var "W" tptp.mworld)) % 0.29/0.58 (define @t3 () (_ (_ tptp.mrel @t2) @t1)) % 0.29/0.58 (define @t4 () (@var "X" $$unsorted)) % 0.29/0.58 (define @t5 () (_ tptp.eiw_di @t4)) % 0.29/0.58 (define @t6 () (_ @t5 @t2)) % 0.29/0.58 (define @t7 () (@list @t4)) % 0.29/0.58 (define @t8 () (@list @t2)) % 0.29/0.58 (define @t9 () (@var "__flatten_var_0" tptp.mworld)) % 0.29/0.58 (define @t10 () (_ tptp.qmltpeq @t4)) % 0.29/0.58 (define @t11 () (@list @t4 @t9)) % 0.29/0.58 (define @t12 () (@var "Y" $$unsorted)) % 0.29/0.58 (define @t13 () (_ tptp.qmltpeq @t12)) % 0.29/0.58 (define @t14 () (_ tptp.mbox (_ @t10 @t12))) % 0.29/0.58 (define @t15 () (@list @t12 @t9)) % 0.29/0.58 (define @t16 () (@var "Z" $$unsorted)) % 0.29/0.58 (define @t17 () (@var "B" $$unsorted)) % 0.29/0.58 (define @t18 () (_ tptp.singleton @t17)) % 0.29/0.58 (define @t19 () (@var "A" $$unsorted)) % 0.29/0.58 (define @t20 () (_ tptp.qmltpeq @t19)) % 0.29/0.58 (define @t21 () (_ tptp.mbox (_ @t20 @t17))) % 0.29/0.58 (define @t22 () (@list @t17 @t9)) % 0.29/0.58 (define @t23 () (@list @t19 @t9)) % 0.29/0.58 (define @t24 () (_ tptp.mbox (_ tptp.empty @t19))) % 0.29/0.58 (define @t25 () (_ tptp.mand @t21)) % 0.29/0.58 (define @t26 () (@var "C" $$unsorted)) % 0.29/0.58 (define @t27 () (_ tptp.in @t17)) % 0.29/0.58 (define @t28 () (_ tptp.in @t19)) % 0.29/0.58 (define @t29 () (@list @t26 @t9)) % 0.29/0.58 (define @t30 () (_ tptp.in @t26)) % 0.29/0.58 (define @t31 () (_ @t30 @t19)) % 0.29/0.58 (define @t32 () (_ tptp.mbox @t31)) % 0.29/0.58 (define @t33 () (_ (_ tptp.qmltpeq @t26) @t17)) % 0.29/0.58 (define @t34 () (lambda @t29 (_ (_ tptp.mbox (_ tptp.mnot (_ (_ tptp.mand @t32) (_ tptp.mbox (_ tptp.mnot (_ tptp.mbox @t33)))))) @t9))) % 0.29/0.58 (define @t35 () (_ @t20 tptp.empty_set)) % 0.29/0.58 (define @t36 () (_ @t20 @t18)) % 0.29/0.58 (define @t37 () (lambda @t22 (_ (_ tptp.mbox (_ tptp.mnot (_ (_ tptp.mand (_ tptp.mbox (_ tptp.mnot (_ tptp.mbox @t36)))) (_ (_ tptp.mand (_ tptp.mbox (_ tptp.mnot (_ tptp.mbox @t35)))) (_ tptp.mbox (_ tptp.mforall_di @t34)))))) @t9))) % 0.29/0.58 (define @t38 () (lambda @t23 (_ (_ tptp.mbox (_ tptp.mforall_di @t37)) @t9))) % 0.29/0.58 (define @t39 () (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di @t38)))) % 0.29/0.58 (define @t40 () (not @t39)) % 0.29/0.58 (define @t41 () (@var "Phi" (-> tptp.mworld Bool))) % 0.29/0.58 (define @t42 () (lambda (@list @t41) (_ @t41 tptp.mactual))) % 0.29/0.58 (define @t43 () (@var "A" (-> tptp.mworld Bool))) % 0.29/0.58 (define @t44 () (_ @t43 @t2)) % 0.29/0.58 (define @t45 () (lambda (@list @t43 @t2) (not @t44))) % 0.29/0.58 (define @t46 () (@var "B" (-> tptp.mworld Bool))) % 0.29/0.58 (define @t47 () (_ @t46 @t2)) % 0.29/0.58 (define @t48 () (@list @t43 @t46 @t2)) % 0.29/0.58 (define @t49 () (lambda @t48 (and @t44 @t47))) % 0.29/0.58 (define @t50 () (lambda @t48 (or @t44 @t47))) % 0.29/0.58 (define @t51 () (lambda @t48 (=> @t44 @t47))) % 0.29/0.58 (define @t52 () (lambda @t48 (= @t44 @t47))) % 0.29/0.58 (define @t53 () (_ @t41 @t1)) % 0.29/0.58 (define @t54 () (@list @t1)) % 0.29/0.58 (define @t55 () (forall @t54 (=> @t3 @t53))) % 0.29/0.58 (define @t56 () (@list @t41 @t2)) % 0.29/0.58 (define @t57 () (lambda @t56 @t55)) % 0.29/0.58 (define @t58 () (lambda @t56 (exists @t54 (and @t3 @t53)))) % 0.29/0.58 (define @t59 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.29/0.58 (define @t60 () (_ (_ @t59 @t4) @t2)) % 0.29/0.58 (define @t61 () (forall @t7 (=> @t6 @t60))) % 0.29/0.58 (define @t62 () (@list @t59 @t2)) % 0.29/0.58 (define @t63 () (lambda @t62 @t61)) % 0.29/0.58 (define @t64 () (lambda @t62 (exists @t7 (and @t6 @t60)))) % 0.29/0.58 (define @t65 () (@var "BOUND_VARIABLE_10807" tptp.mworld)) % 0.29/0.58 (define @t66 () (@var "BOUND_VARIABLE_11267" $$unsorted)) % 0.29/0.58 (define @t67 () (@var "BOUND_VARIABLE_10943" $$unsorted)) % 0.29/0.58 (define @t68 () (@var "BOUND_VARIABLE_10844" tptp.mworld)) % 0.29/0.58 (define @t69 () (not (tptp.mrel @t68 @t65))) % 0.29/0.58 (define @t70 () (@list @t65)) % 0.29/0.58 (define @t71 () (@var "BOUND_VARIABLE_10945" tptp.mworld)) % 0.29/0.58 (define @t72 () (not (tptp.mrel @t71 @t68))) % 0.29/0.58 (define @t73 () (@list @t68)) % 0.29/0.58 (define @t74 () (@var "BOUND_VARIABLE_10856" tptp.mworld)) % 0.29/0.58 (define @t75 () (@var "BOUND_VARIABLE_11263" $$unsorted)) % 0.29/0.58 (define @t76 () (not (tptp.mrel @t71 @t74))) % 0.29/0.58 (define @t77 () (@list @t74)) % 0.29/0.58 (define @t78 () (@var "BOUND_VARIABLE_10999" tptp.mworld)) % 0.29/0.58 (define @t79 () (not (tptp.mrel @t78 @t71))) % 0.29/0.58 (define @t80 () (not (tptp.eiw_di @t67 @t78))) % 0.29/0.58 (define @t81 () (@var "BOUND_VARIABLE_11269" tptp.mworld)) % 0.29/0.58 (define @t82 () (@list @t78 @t67 @t71)) % 0.29/0.58 (define @t83 () (not (forall @t82 (or (not (tptp.mrel @t81 @t78)) @t80 @t79 (not (forall @t77 (or @t76 (tptp.in @t67 @t75 @t74)))) (not (forall @t73 (or @t72 (not (forall @t70 (or @t69 (tptp.qmltpeq @t67 @t66 @t65))))))))))) % 0.29/0.58 (define @t84 () (@var "BOUND_VARIABLE_10755" tptp.mworld)) % 0.29/0.58 (define @t85 () (@var "BOUND_VARIABLE_11010" tptp.mworld)) % 0.29/0.58 (define @t86 () (not (tptp.mrel @t85 @t84))) % 0.29/0.58 (define @t87 () (@list @t84)) % 0.29/0.58 (define @t88 () (@list @t85)) % 0.29/0.58 (define @t89 () (not (forall @t88 (or (not (tptp.mrel @t81 @t85)) (not (forall @t87 (or @t86 (tptp.qmltpeq @t75 tptp.empty_set @t84)))))))) % 0.29/0.58 (define @t90 () (@var "BOUND_VARIABLE_10708" tptp.mworld)) % 0.29/0.58 (define @t91 () (@var "BOUND_VARIABLE_11022" tptp.mworld)) % 0.29/0.58 (define @t92 () (not (tptp.mrel @t91 @t90))) % 0.29/0.58 (define @t93 () (@list @t90)) % 0.29/0.58 (define @t94 () (@list @t91)) % 0.29/0.58 (define @t95 () (not (forall @t94 (or (not (tptp.mrel @t81 @t91)) (not (forall @t93 (or @t92 (tptp.qmltpeq @t75 (tptp.singleton @t66) @t90)))))))) % 0.29/0.58 (define @t96 () (@var "BOUND_VARIABLE_11265" tptp.mworld)) % 0.29/0.58 (define @t97 () (not (tptp.mrel @t96 @t81))) % 0.29/0.58 (define @t98 () (not (tptp.eiw_di @t66 @t96))) % 0.29/0.58 (define @t99 () (not (tptp.mrel @t1 @t96))) % 0.29/0.58 (define @t100 () (not (tptp.eiw_di @t75 @t1))) % 0.29/0.58 (define @t101 () (@list @t1 @t75 @t96 @t66 @t81)) % 0.29/0.58 (define @t102 () (tptp.mrel @t2 @t1)) % 0.29/0.58 (define @t103 () (not @t102)) % 0.29/0.58 (define @t104 () (or @t103 @t100 @t99 @t98 @t97 @t95 @t89 @t83)) % 0.29/0.58 (define @t105 () (lambda @t8 (forall @t101 @t104))) % 0.29/0.58 (define @t106 () (_ @t105 tptp.mactual)) % 0.29/0.58 (define @t107 () (or @t100 @t99 @t98 @t97 @t95 @t89 @t83)) % 0.29/0.58 (define @t108 () (or @t103 @t107)) % 0.29/0.58 (define @t109 () (forall @t101 @t108)) % 0.29/0.58 (define @t110 () (@list @t75 @t96 @t66 @t81)) % 0.29/0.58 (define @t111 () (forall @t110 @t108)) % 0.29/0.58 (define @t112 () (forall @t110 @t107)) % 0.29/0.58 (define @t113 () (@var "BOUND_VARIABLE_11210" tptp.mworld)) % 0.29/0.58 (define @t114 () (@var "BOUND_VARIABLE_11208" $$unsorted)) % 0.29/0.58 (define @t115 () (@var "BOUND_VARIABLE_11206" tptp.mworld)) % 0.29/0.58 (define @t116 () (or @t103 @t112)) % 0.29/0.58 (define @t117 () (not (forall @t77 (or @t76 (tptp.in @t67 @t4 @t74))))) % 0.29/0.58 (define @t118 () (not (forall @t82 (or (not (tptp.mrel @t113 @t78)) @t80 @t79 @t117 (not (forall @t73 (or @t72 (not (forall @t70 (or @t69 (tptp.qmltpeq @t67 @t114 @t65))))))))))) % 0.29/0.58 (define @t119 () (not (forall @t87 (or @t86 (tptp.qmltpeq @t4 tptp.empty_set @t84))))) % 0.29/0.58 (define @t120 () (not (forall @t88 (or (not (tptp.mrel @t113 @t85)) @t119)))) % 0.29/0.58 (define @t121 () (not (forall @t94 (or (not (tptp.mrel @t113 @t91)) (not (forall @t93 (or @t92 (tptp.qmltpeq @t4 (tptp.singleton @t114) @t90)))))))) % 0.29/0.58 (define @t122 () (not (tptp.mrel @t115 @t113))) % 0.29/0.58 (define @t123 () (not (tptp.eiw_di @t114 @t115))) % 0.29/0.58 (define @t124 () (not (tptp.eiw_di @t4 @t1))) % 0.29/0.58 (define @t125 () (@list @t4 @t115 @t114 @t113)) % 0.29/0.58 (define @t126 () (forall @t125 (or @t124 (not (tptp.mrel @t1 @t115)) @t123 @t122 @t121 @t120 @t118))) % 0.29/0.58 (define @t127 () (not (tptp.mrel @t2 @t115))) % 0.29/0.58 (define @t128 () (tptp.eiw_di @t4 @t2)) % 0.29/0.58 (define @t129 () (not @t128)) % 0.29/0.58 (define @t130 () (or @t129 @t127 @t123 @t122 @t121 @t120 @t118)) % 0.29/0.58 (define @t131 () (lambda @t8 (forall @t125 @t130))) % 0.29/0.58 (define @t132 () (_ @t131 @t1)) % 0.29/0.58 (define @t133 () (or @t103 @t132)) % 0.29/0.58 (define @t134 () (forall @t54 @t133)) % 0.29/0.58 (define @t135 () (lambda @t8 @t134)) % 0.29/0.58 (define @t136 () (_ @t41 @t1)) % 0.29/0.58 (define @t137 () (lambda @t56 (forall @t54 (or @t103 @t136)))) % 0.29/0.58 (define @t138 () (or @t127 @t123 @t122 @t121 @t120 @t118)) % 0.29/0.58 (define @t139 () (or @t129 @t138)) % 0.29/0.58 (define @t140 () (forall @t125 @t139)) % 0.29/0.58 (define @t141 () (@list @t115 @t114 @t113)) % 0.29/0.58 (define @t142 () (forall @t141 @t139)) % 0.29/0.58 (define @t143 () (forall @t141 @t138)) % 0.29/0.58 (define @t144 () (@var "BOUND_VARIABLE_11131" tptp.mworld)) % 0.29/0.58 (define @t145 () (@var "BOUND_VARIABLE_11129" $$unsorted)) % 0.29/0.58 (define @t146 () (or @t129 @t143)) % 0.29/0.58 (define @t147 () (not (forall @t73 (or @t72 (not (forall @t70 (or @t69 (tptp.qmltpeq @t67 @t145 @t65)))))))) % 0.29/0.58 (define @t148 () (not (tptp.mrel @t144 @t78))) % 0.29/0.58 (define @t149 () (not (tptp.mrel @t144 @t85))) % 0.29/0.58 (define @t150 () (tptp.singleton @t145)) % 0.29/0.58 (define @t151 () (not (tptp.mrel @t144 @t91))) % 0.29/0.58 (define @t152 () (not (tptp.mrel @t1 @t144))) % 0.29/0.58 (define @t153 () (not (tptp.eiw_di @t145 @t1))) % 0.29/0.58 (define @t154 () (@list @t1 @t145 @t144)) % 0.29/0.58 (define @t155 () (forall @t154 (or @t103 @t153 @t152 (not (forall @t94 (or @t151 (not (forall @t93 (or @t92 (tptp.qmltpeq @t4 @t150 @t90))))))) (not (forall @t88 (or @t149 @t119))) (not (forall @t82 (or @t148 @t80 @t79 @t117 @t147)))))) % 0.29/0.58 (define @t156 () (not (forall @t77 (or @t76 (tptp.in @t67 @t19 @t74))))) % 0.29/0.58 (define @t157 () (not (forall @t82 (or @t148 @t80 @t79 @t156 @t147)))) % 0.29/0.58 (define @t158 () (tptp.qmltpeq @t19 tptp.empty_set @t84)) % 0.29/0.58 (define @t159 () (not (forall @t87 (or @t86 @t158)))) % 0.29/0.58 (define @t160 () (not (forall @t88 (or @t149 @t159)))) % 0.29/0.58 (define @t161 () (not (forall @t94 (or @t151 (not (forall @t93 (or @t92 (tptp.qmltpeq @t19 @t150 @t90)))))))) % 0.29/0.58 (define @t162 () (not (tptp.mrel @t9 @t1))) % 0.29/0.58 (define @t163 () (forall @t154 (or @t162 @t153 @t152 @t161 @t160 @t157))) % 0.29/0.58 (define @t164 () (lambda @t23 @t163)) % 0.29/0.58 (define @t165 () (_ @t164 @t4 @t2)) % 0.29/0.58 (define @t166 () (or @t129 @t165)) % 0.29/0.58 (define @t167 () (forall @t7 @t166)) % 0.29/0.58 (define @t168 () (lambda @t8 @t167)) % 0.29/0.58 (define @t169 () (_ @t59 @t4 @t2)) % 0.29/0.58 (define @t170 () (lambda @t62 (forall @t7 (or @t129 @t169)))) % 0.29/0.58 (define @t171 () (or @t103 @t153 @t152 @t161 @t160 @t157)) % 0.29/0.58 (define @t172 () (or @t153 @t152 @t161 @t160 @t157)) % 0.29/0.58 (define @t173 () (or @t103 @t172)) % 0.29/0.58 (define @t174 () (forall @t154 @t173)) % 0.29/0.58 (define @t175 () (@list @t145 @t144)) % 0.29/0.58 (define @t176 () (forall @t175 @t173)) % 0.29/0.58 (define @t177 () (forall @t175 @t172)) % 0.29/0.58 (define @t178 () (@var "BOUND_VARIABLE_11092" tptp.mworld)) % 0.29/0.58 (define @t179 () (or @t103 @t177)) % 0.29/0.58 (define @t180 () (not (forall @t73 (or @t72 (not (forall @t70 (or @t69 (tptp.qmltpeq @t67 @t4 @t65)))))))) % 0.29/0.58 (define @t181 () (not (forall @t82 (or (not (tptp.mrel @t178 @t78)) @t80 @t79 @t156 @t180)))) % 0.29/0.58 (define @t182 () (not (forall @t88 (or (not (tptp.mrel @t178 @t85)) @t159)))) % 0.29/0.58 (define @t183 () (not (forall @t93 (or @t92 (tptp.qmltpeq @t19 (tptp.singleton @t4) @t90))))) % 0.29/0.58 (define @t184 () (not (forall @t94 (or (not (tptp.mrel @t178 @t91)) @t183)))) % 0.29/0.58 (define @t185 () (@list @t4 @t178)) % 0.29/0.58 (define @t186 () (forall @t185 (or @t124 (not (tptp.mrel @t1 @t178)) @t184 @t182 @t181))) % 0.29/0.58 (define @t187 () (not (tptp.mrel @t2 @t178))) % 0.29/0.58 (define @t188 () (or @t129 @t187 @t184 @t182 @t181)) % 0.29/0.58 (define @t189 () (lambda @t8 (forall @t185 @t188))) % 0.29/0.58 (define @t190 () (_ @t189 @t1)) % 0.29/0.58 (define @t191 () (or @t103 @t190)) % 0.29/0.58 (define @t192 () (forall @t54 @t191)) % 0.29/0.58 (define @t193 () (lambda @t8 @t192)) % 0.29/0.58 (define @t194 () (or @t187 @t184 @t182 @t181)) % 0.29/0.58 (define @t195 () (or @t129 @t194)) % 0.29/0.58 (define @t196 () (forall @t185 @t195)) % 0.29/0.58 (define @t197 () (@list @t178)) % 0.29/0.58 (define @t198 () (forall @t197 @t195)) % 0.29/0.58 (define @t199 () (forall @t197 @t194)) % 0.29/0.58 (define @t200 () (@list @t1)) % 0.29/0.58 (define @t201 () (or @t129 @t199)) % 0.29/0.58 (define @t202 () (not (tptp.mrel @t1 @t78))) % 0.29/0.58 (define @t203 () (forall @t88 (or (not (tptp.mrel @t1 @t85)) @t159))) % 0.29/0.58 (define @t204 () (not @t203)) % 0.29/0.58 (define @t205 () (not (tptp.mrel @t1 @t91))) % 0.29/0.58 (define @t206 () (forall @t54 (or @t103 (not (forall @t94 (or @t205 @t183))) @t204 (not (forall @t82 (or @t202 @t80 @t79 @t156 @t180)))))) % 0.29/0.58 (define @t207 () (not (forall @t73 (or @t72 (not (forall @t70 (or @t69 (tptp.qmltpeq @t67 @t17 @t65)))))))) % 0.29/0.58 (define @t208 () (forall @t82 (or @t202 @t80 @t79 @t156 @t207))) % 0.29/0.58 (define @t209 () (not @t208)) % 0.29/0.58 (define @t210 () (tptp.singleton @t17)) % 0.29/0.58 (define @t211 () (tptp.qmltpeq @t19 @t210 @t90)) % 0.29/0.58 (define @t212 () (not (forall @t93 (or @t92 @t211)))) % 0.29/0.58 (define @t213 () (forall @t94 (or @t205 @t212))) % 0.29/0.58 (define @t214 () (not @t213)) % 0.29/0.58 (define @t215 () (forall @t54 (or @t162 @t214 @t204 @t209))) % 0.29/0.58 (define @t216 () (lambda @t22 @t215)) % 0.29/0.58 (define @t217 () (_ @t216 @t4 @t2)) % 0.29/0.58 (define @t218 () (or @t129 @t217)) % 0.29/0.58 (define @t219 () (forall @t7 @t218)) % 0.29/0.58 (define @t220 () (lambda @t8 @t219)) % 0.29/0.58 (define @t221 () (or @t103 @t214 @t204 @t209)) % 0.29/0.58 (define @t222 () (or @t214 @t204 @t209)) % 0.29/0.58 (define @t223 () (not (and @t213 @t203 @t208))) % 0.29/0.58 (define @t224 () (or @t103 @t223)) % 0.29/0.58 (define @t225 () (not (tptp.mrel @t1 @t71))) % 0.29/0.58 (define @t226 () (not (tptp.eiw_di @t67 @t1))) % 0.29/0.58 (define @t227 () (or @t103 @t226 @t225 @t156 @t207)) % 0.29/0.58 (define @t228 () (@list @t1 @t67 @t71)) % 0.29/0.58 (define @t229 () (forall @t228 @t227)) % 0.29/0.58 (define @t230 () (not (forall @t87 (or (not (tptp.mrel @t1 @t84)) @t158)))) % 0.29/0.58 (define @t231 () (forall @t54 (or @t103 @t230))) % 0.29/0.58 (define @t232 () (not (forall @t93 (or (not (tptp.mrel @t1 @t90)) @t211)))) % 0.29/0.58 (define @t233 () (forall @t54 (or @t103 @t232))) % 0.29/0.58 (define @t234 () (and @t233 @t231 @t229)) % 0.29/0.58 (define @t235 () (not @t234)) % 0.29/0.58 (define @t236 () (lambda @t8 @t235)) % 0.29/0.58 (define @t237 () (or @t103 (_ @t236 @t1))) % 0.29/0.58 (define @t238 () (forall @t54 @t237)) % 0.29/0.58 (define @t239 () (lambda @t8 @t238)) % 0.29/0.58 (define @t240 () (lambda @t8 @t234)) % 0.29/0.58 (define @t241 () (_ @t240 @t2)) % 0.29/0.58 (define @t242 () (not @t241)) % 0.29/0.58 (define @t243 () (lambda @t8 @t242)) % 0.29/0.58 (define @t244 () (and @t231 @t229)) % 0.29/0.58 (define @t245 () (lambda @t8 @t244)) % 0.29/0.58 (define @t246 () (_ @t245 @t2)) % 0.29/0.58 (define @t247 () (and @t233 @t246)) % 0.29/0.58 (define @t248 () (lambda @t8 @t247)) % 0.29/0.58 (define @t249 () (@list @t46 @t2)) % 0.29/0.58 (define @t250 () (lambda @t8 @t229)) % 0.29/0.58 (define @t251 () (_ @t250 @t2)) % 0.29/0.58 (define @t252 () (and @t231 @t251)) % 0.29/0.58 (define @t253 () (lambda @t8 @t252)) % 0.29/0.58 (define @t254 () (or @t226 @t225 @t156 @t207)) % 0.29/0.58 (define @t255 () (or @t103 @t254)) % 0.29/0.58 (define @t256 () (forall @t228 @t255)) % 0.29/0.58 (define @t257 () (@list @t67 @t71)) % 0.29/0.58 (define @t258 () (forall @t257 @t255)) % 0.29/0.58 (define @t259 () (forall @t257 @t254)) % 0.29/0.58 (define @t260 () (@var "BOUND_VARIABLE_10911" tptp.mworld)) % 0.29/0.58 (define @t261 () (or @t103 @t259)) % 0.29/0.58 (define @t262 () (not (forall @t70 (or @t69 (tptp.qmltpeq @t4 @t17 @t65))))) % 0.29/0.58 (define @t263 () (not (forall @t73 (or (not (tptp.mrel @t260 @t68)) @t262)))) % 0.29/0.58 (define @t264 () (tptp.in @t4 @t19 @t74)) % 0.29/0.58 (define @t265 () (not (forall @t77 (or (not (tptp.mrel @t260 @t74)) @t264)))) % 0.29/0.58 (define @t266 () (@list @t4 @t260)) % 0.29/0.58 (define @t267 () (forall @t266 (or @t124 (not (tptp.mrel @t1 @t260)) @t265 @t263))) % 0.29/0.58 (define @t268 () (not (tptp.mrel @t2 @t260))) % 0.29/0.58 (define @t269 () (or @t129 @t268 @t265 @t263)) % 0.29/0.58 (define @t270 () (lambda @t8 (forall @t266 @t269))) % 0.29/0.58 (define @t271 () (_ @t270 @t1)) % 0.29/0.58 (define @t272 () (or @t103 @t271)) % 0.29/0.58 (define @t273 () (forall @t54 @t272)) % 0.29/0.58 (define @t274 () (lambda @t8 @t273)) % 0.29/0.58 (define @t275 () (or @t268 @t265 @t263)) % 0.29/0.58 (define @t276 () (or @t129 @t275)) % 0.29/0.58 (define @t277 () (forall @t266 @t276)) % 0.29/0.58 (define @t278 () (@list @t260)) % 0.29/0.58 (define @t279 () (forall @t278 @t276)) % 0.29/0.58 (define @t280 () (forall @t278 @t275)) % 0.29/0.58 (define @t281 () (or @t129 @t280)) % 0.29/0.58 (define @t282 () (not (tptp.mrel @t1 @t68))) % 0.29/0.58 (define @t283 () (not (tptp.mrel @t1 @t74))) % 0.29/0.58 (define @t284 () (forall @t54 (or @t103 (not (forall @t77 (or @t283 @t264))) (not (forall @t73 (or @t282 @t262)))))) % 0.29/0.58 (define @t285 () (tptp.qmltpeq @t26 @t17 @t65)) % 0.29/0.58 (define @t286 () (not (forall @t70 (or @t69 @t285)))) % 0.29/0.58 (define @t287 () (forall @t73 (or @t282 @t286))) % 0.29/0.58 (define @t288 () (not @t287)) % 0.29/0.58 (define @t289 () (tptp.in @t26 @t19 @t74)) % 0.29/0.58 (define @t290 () (forall @t77 (or @t283 @t289))) % 0.29/0.58 (define @t291 () (not @t290)) % 0.29/0.58 (define @t292 () (forall @t54 (or @t162 @t291 @t288))) % 0.29/0.58 (define @t293 () (lambda @t29 @t292)) % 0.29/0.58 (define @t294 () (_ @t293 @t4 @t2)) % 0.29/0.58 (define @t295 () (or @t129 @t294)) % 0.29/0.58 (define @t296 () (forall @t7 @t295)) % 0.29/0.58 (define @t297 () (lambda @t8 @t296)) % 0.29/0.58 (define @t298 () (or @t103 @t291 @t288)) % 0.29/0.58 (define @t299 () (not (and @t290 @t287))) % 0.29/0.58 (define @t300 () (or @t103 @t299)) % 0.29/0.58 (define @t301 () (not (forall @t70 (or (not (tptp.mrel @t1 @t65)) @t285)))) % 0.29/0.58 (define @t302 () (forall @t54 (or @t103 @t301))) % 0.29/0.58 (define @t303 () (tptp.in @t26 @t19 @t1)) % 0.29/0.58 (define @t304 () (forall @t54 (or @t103 @t303))) % 0.29/0.58 (define @t305 () (and @t304 @t302)) % 0.29/0.58 (define @t306 () (not @t305)) % 0.29/0.58 (define @t307 () (lambda @t8 @t306)) % 0.29/0.58 (define @t308 () (or @t103 (_ @t307 @t1))) % 0.29/0.58 (define @t309 () (forall @t54 @t308)) % 0.29/0.58 (define @t310 () (lambda @t8 @t309)) % 0.29/0.58 (define @t311 () (lambda @t8 @t305)) % 0.29/0.58 (define @t312 () (_ @t311 @t2)) % 0.29/0.58 (define @t313 () (not @t312)) % 0.29/0.58 (define @t314 () (lambda @t8 @t313)) % 0.29/0.58 (define @t315 () (lambda @t8 @t302)) % 0.29/0.58 (define @t316 () (_ @t315 @t2)) % 0.29/0.58 (define @t317 () (and @t304 @t316)) % 0.29/0.58 (define @t318 () (lambda @t8 @t317)) % 0.29/0.58 (define @t319 () (tptp.qmltpeq @t26 @t17 @t1)) % 0.29/0.58 (define @t320 () (forall @t54 (or @t103 @t319))) % 0.29/0.58 (define @t321 () (not @t320)) % 0.29/0.58 (define @t322 () (lambda @t8 @t321)) % 0.29/0.58 (define @t323 () (or @t103 (_ @t322 @t1))) % 0.29/0.58 (define @t324 () (forall @t54 @t323)) % 0.29/0.58 (define @t325 () (lambda @t8 @t324)) % 0.29/0.58 (define @t326 () (lambda @t8 @t320)) % 0.29/0.58 (define @t327 () (_ @t326 @t2)) % 0.29/0.58 (define @t328 () (not @t327)) % 0.29/0.58 (define @t329 () (lambda @t8 @t328)) % 0.29/0.58 (define @t330 () (_ @t33 @t1)) % 0.29/0.58 (define @t331 () (or @t103 @t330)) % 0.29/0.58 (define @t332 () (_ @t33 @t1)) % 0.29/0.58 (define @t333 () (or @t103 @t332)) % 0.29/0.58 (define @t334 () (forall @t54 @t333)) % 0.29/0.58 (define @t335 () (lambda @t8 @t334)) % 0.29/0.58 (define @t336 () (_ @t137 @t33)) % 0.29/0.58 (define @t337 () (lambda @t8 @t304)) % 0.29/0.58 (define @t338 () (_ @t337 @t2)) % 0.29/0.58 (define @t339 () (and @t338 @t47)) % 0.29/0.58 (define @t340 () (lambda @t249 @t339)) % 0.29/0.58 (define @t341 () (_ @t31 @t1)) % 0.29/0.58 (define @t342 () (or @t103 @t341)) % 0.29/0.58 (define @t343 () (_ @t31 @t1)) % 0.29/0.58 (define @t344 () (or @t103 @t343)) % 0.29/0.58 (define @t345 () (forall @t54 @t344)) % 0.29/0.58 (define @t346 () (lambda @t8 @t345)) % 0.29/0.58 (define @t347 () (_ @t137 @t31)) % 0.29/0.58 (define @t348 () (lambda @t29 (_ (_ @t137 (_ @t45 (_ (_ @t49 @t347) (_ @t137 (_ @t45 @t336))))) @t9))) % 0.29/0.58 (define @t349 () (lambda @t8 @t231)) % 0.29/0.58 (define @t350 () (_ @t349 @t2)) % 0.29/0.58 (define @t351 () (and @t350 @t47)) % 0.29/0.58 (define @t352 () (lambda @t249 @t351)) % 0.29/0.58 (define @t353 () (tptp.qmltpeq @t19 tptp.empty_set @t1)) % 0.29/0.58 (define @t354 () (forall @t54 (or @t103 @t353))) % 0.29/0.58 (define @t355 () (not @t354)) % 0.29/0.58 (define @t356 () (lambda @t8 @t355)) % 0.29/0.58 (define @t357 () (or @t103 (_ @t356 @t1))) % 0.29/0.58 (define @t358 () (forall @t54 @t357)) % 0.29/0.58 (define @t359 () (lambda @t8 @t358)) % 0.29/0.58 (define @t360 () (lambda @t8 @t354)) % 0.29/0.58 (define @t361 () (_ @t360 @t2)) % 0.29/0.58 (define @t362 () (not @t361)) % 0.29/0.58 (define @t363 () (lambda @t8 @t362)) % 0.29/0.58 (define @t364 () (_ @t35 @t1)) % 0.29/0.58 (define @t365 () (or @t103 @t364)) % 0.29/0.58 (define @t366 () (_ @t35 @t1)) % 0.29/0.58 (define @t367 () (or @t103 @t366)) % 0.29/0.58 (define @t368 () (forall @t54 @t367)) % 0.29/0.58 (define @t369 () (lambda @t8 @t368)) % 0.29/0.58 (define @t370 () (_ @t137 @t35)) % 0.29/0.58 (define @t371 () (lambda @t8 @t233)) % 0.29/0.58 (define @t372 () (_ @t371 @t2)) % 0.29/0.58 (define @t373 () (and @t372 @t47)) % 0.29/0.58 (define @t374 () (lambda @t249 @t373)) % 0.29/0.58 (define @t375 () (tptp.qmltpeq @t19 @t210 @t1)) % 0.29/0.58 (define @t376 () (forall @t54 (or @t103 @t375))) % 0.29/0.58 (define @t377 () (not @t376)) % 0.29/0.58 (define @t378 () (lambda @t8 @t377)) % 0.29/0.58 (define @t379 () (or @t103 (_ @t378 @t1))) % 0.29/0.58 (define @t380 () (forall @t54 @t379)) % 0.29/0.58 (define @t381 () (lambda @t8 @t380)) % 0.29/0.58 (define @t382 () (lambda @t8 @t376)) % 0.29/0.58 (define @t383 () (_ @t382 @t2)) % 0.29/0.58 (define @t384 () (not @t383)) % 0.29/0.58 (define @t385 () (lambda @t8 @t384)) % 0.29/0.58 (define @t386 () (_ @t36 @t1)) % 0.29/0.58 (define @t387 () (or @t103 @t386)) % 0.29/0.58 (define @t388 () (_ @t36 @t1)) % 0.29/0.58 (define @t389 () (or @t103 @t388)) % 0.29/0.58 (define @t390 () (forall @t54 @t389)) % 0.29/0.58 (define @t391 () (lambda @t8 @t390)) % 0.29/0.58 (define @t392 () (_ @t137 @t36)) % 0.29/0.58 (define @t393 () (lambda @t22 (_ (_ @t137 (_ @t45 (_ (_ @t49 (_ @t137 (_ @t45 @t392))) (_ (_ @t49 (_ @t137 (_ @t45 @t370))) (_ @t137 (_ @t170 @t348)))))) @t9))) % 0.29/0.58 (define @t394 () (lambda @t23 (_ (_ @t137 (_ @t170 @t393)) @t9))) % 0.29/0.58 (define @t395 () (not @t3)) % 0.29/0.58 (define @t396 () (or @t395 @t53)) % 0.29/0.58 (define @t397 () (not @t6)) % 0.29/0.58 (define @t398 () (or @t397 @t60)) % 0.29/0.58 (assume @p1 (forall (@list @t2 @t1) @t3)) % 0.29/0.58 (assume @p2 (forall @t8 (exists @t7 @t6))) % 0.29/0.58 (assume @p3 (forall (@list @t2 @t1 @t4) (=> (and @t6 (_ (_ tptp.mrel @t1) @t2)) (_ @t5 @t1)))) % 0.29/0.58 (assume @p4 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mbox (_ @t10 @t4)) @t9)))))) % 0.29/0.58 (assume @p5 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t15 (_ (_ tptp.mbox (_ (_ tptp.mimplies @t14) (_ tptp.mbox (_ @t13 @t4)))) @t9)))) @t9)))))) % 0.29/0.58 (assume @p6 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t15 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda (@list @t16 @t9) (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ (_ tptp.mand @t14) (_ tptp.mbox (_ @t13 @t16)))) (_ tptp.mbox (_ @t10 @t16)))) @t9)))) @t9)))) @t9)))))) % 0.29/0.58 (assume @p7 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mbox (_ (_ tptp.mimplies @t21) (_ tptp.mbox (_ (_ tptp.qmltpeq (_ tptp.singleton @t19)) @t18)))) @t9)))) @t9)))))) % 0.29/0.58 (assume @p8 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ @t25 @t24)) (_ tptp.mbox (_ tptp.empty @t17)))) @t9)))) @t9)))))) % 0.29/0.58 (assume @p9 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t29 (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ @t25 (_ tptp.mbox (_ @t28 @t26)))) (_ tptp.mbox (_ @t27 @t26)))) @t9)))) @t9)))) @t9)))))) % 0.29/0.58 (assume @p10 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t29 (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ @t25 @t32)) (_ tptp.mbox (_ @t30 @t17)))) @t9)))) @t9)))) @t9)))))) % 0.29/0.58 (assume @p11 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mbox (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mbox (_ (_ tptp.mimplies (_ tptp.mbox (_ @t28 @t17))) (_ tptp.mbox (_ tptp.mnot (_ tptp.mbox (_ @t27 @t19)))))) @t9)))) @t9)))))) % 0.29/0.58 (assume @p12 (_ tptp.mlocal (_ tptp.mbox (_ tptp.empty tptp.empty_set)))) % 0.29/0.58 (assume @p13 (_ tptp.mlocal (_ tptp.mexists_di (lambda @t23 (_ @t24 @t9))))) % 0.29/0.58 (assume @p14 (_ tptp.mlocal (_ tptp.mexists_di (lambda @t23 (_ (_ tptp.mbox (_ tptp.mnot @t24)) @t9))))) % 0.29/0.58 (assume @p15 @t40) % 0.29/0.58 (assume @p16 @t39) % 0.29/0.58 (assume @p17 true) % 0.29/0.58 (step @p18 (= tptp.mlocal @t42) :rule refl :args (@t42)) % 0.29/0.58 (step @p19 (= tptp.mnot @t45) :rule refl :args (@t45)) % 0.29/0.58 (step @p20 (= tptp.mand @t49) :rule refl :args (@t49)) % 0.29/0.58 (step @p21 (= tptp.mor @t50) :rule refl :args (@t50)) % 0.29/0.58 (step @p22 (= tptp.mimplies @t51) :rule refl :args (@t51)) % 0.29/0.58 (step @p23 (= tptp.mequiv @t52) :rule refl :args (@t52)) % 0.29/0.58 (step @p24 (= tptp.mbox @t57) :rule refl :args (@t57)) % 0.29/0.58 (step @p25 (= tptp.mdia @t58) :rule refl :args (@t58)) % 0.29/0.58 (step @p26 (= tptp.mforall_di @t63) :rule refl :args (@t63)) % 0.29/0.58 (step @p27 (= tptp.mexists_di @t64) :rule refl :args (@t64)) % 0.29/0.58 (step @p28 :rule beta-reduce :args ((= @t106 (forall @t101 (or (not (tptp.mrel tptp.mactual @t1)) @t100 @t99 @t98 @t97 @t95 @t89 @t83))))) % 0.29/0.58 (step @p29 :rule beta-reduce :args ((= (_ @t42 @t105) @t106))) % 0.29/0.58 (step @p30 :rule trans :premises (@p29 @p28)) % 0.29/0.58 (step @p31 :rule aci_norm :args ((= @t108 @t104))) % 0.29/0.58 (step @p32 :rule cong :premises (@p31) :args (@t109)) % 0.29/0.58 (step @p33 :rule quant-merge-prenex :args ((= (forall @t54 @t111) @t109))) % 0.29/0.58 (step @p34 :rule alpha_equiv :args (@t112 (@list @t75 @t96 @t66 @t81) (@list @t4 @t115 @t114 @t113))) % 0.29/0.58 (step @p35 :rule refl :args (@t103)) % 0.29/0.58 (step @p36 :rule nary_cong :premises (@p35 @p34) :args (@t116)) % 0.29/0.58 (step @p37 :rule quant-miniscope-or :args ((= @t111 @t116))) % 0.29/0.58 (step @p38 :rule trans :premises (@p37 @p36)) % 0.29/0.58 (step @p39 :rule symm :premises (@p38)) % 0.29/0.58 (step @p40 :rule cong :premises (@p39) :args ((forall @t54 (or @t103 @t126)))) % 0.29/0.58 (step @p41 :rule trans :premises (@p40 @p33)) % 0.29/0.58 (step @p42 :rule trans :premises (@p41 @p32)) % 0.29/0.58 (step @p43 :rule beta-reduce :args ((= @t132 @t126))) % 0.29/0.58 (step @p44 :rule refl :args (@t103)) % 0.29/0.58 (step @p45 :rule nary_cong :premises (@p44 @p43) :args (@t133)) % 0.29/0.58 (step @p46 :rule cong :premises (@p45) :args (@t134)) % 0.29/0.58 (step @p47 :rule trans :premises (@p46 @p42)) % 0.29/0.58 (step @p48 :rule cong :premises (@p47) :args (@t135)) % 0.29/0.58 (step @p49 :rule beta-reduce :args ((= (_ @t137 @t131) @t135))) % 0.29/0.58 (step @p50 :rule trans :premises (@p49 @p48)) % 0.29/0.58 (step @p51 :rule aci_norm :args ((= @t139 @t130))) % 0.29/0.58 (step @p52 :rule cong :premises (@p51) :args (@t140)) % 0.29/0.58 (step @p53 :rule quant-merge-prenex :args ((= (forall @t7 @t142) @t140))) % 0.29/0.58 (step @p54 :rule alpha_equiv :args (@t143 (@list @t115 @t114 @t113) (@list @t1 @t145 @t144))) % 0.29/0.58 (step @p55 :rule refl :args (@t129)) % 0.29/0.58 (step @p56 :rule nary_cong :premises (@p55 @p54) :args (@t146)) % 0.29/0.58 (step @p57 :rule quant-miniscope-or :args ((= @t142 @t146))) % 0.29/0.58 (step @p58 :rule trans :premises (@p57 @p56)) % 0.29/0.58 (step @p59 :rule symm :premises (@p58)) % 0.29/0.58 (step @p60 :rule cong :premises (@p59) :args ((forall @t7 (or @t129 @t155)))) % 0.29/0.58 (step @p61 :rule trans :premises (@p60 @p53)) % 0.29/0.58 (step @p62 :rule trans :premises (@p61 @p52)) % 0.29/0.58 (step @p63 :rule beta-reduce :args ((= @t165 @t155))) % 0.29/0.58 (step @p64 :rule refl :args (@t129)) % 0.29/0.58 (step @p65 :rule nary_cong :premises (@p64 @p63) :args (@t166)) % 0.29/0.58 (step @p66 :rule cong :premises (@p65) :args (@t167)) % 0.29/0.58 (step @p67 :rule trans :premises (@p66 @p62)) % 0.29/0.58 (step @p68 :rule cong :premises (@p67) :args (@t168)) % 0.29/0.58 (step @p69 :rule beta-reduce :args ((= (_ @t170 @t164) @t168))) % 0.29/0.58 (step @p70 :rule trans :premises (@p69 @p68)) % 0.29/0.58 (step @p71 :rule beta-reduce :args ((= (_ (lambda @t8 (forall @t154 @t171)) @t9) @t163))) % 0.29/0.58 (step @p72 :rule refl :args (@t9)) % 0.29/0.58 (step @p73 :rule aci_norm :args ((= @t173 @t171))) % 0.29/0.58 (step @p74 :rule cong :premises (@p73) :args (@t174)) % 0.29/0.58 (step @p75 :rule quant-merge-prenex :args ((= (forall @t54 @t176) @t174))) % 0.29/0.58 (step @p76 :rule alpha_equiv :args (@t177 (@list @t145 @t144) (@list @t4 @t178))) % 0.29/0.58 (step @p77 :rule nary_cong :premises (@p35 @p76) :args (@t179)) % 0.29/0.58 (step @p78 :rule quant-miniscope-or :args ((= @t176 @t179))) % 0.29/0.58 (step @p79 :rule trans :premises (@p78 @p77)) % 0.29/0.58 (step @p80 :rule symm :premises (@p79)) % 0.29/0.58 (step @p81 :rule cong :premises (@p80) :args ((forall @t54 (or @t103 @t186)))) % 0.29/0.58 (step @p82 :rule trans :premises (@p81 @p75)) % 0.29/0.58 (step @p83 :rule trans :premises (@p82 @p74)) % 0.29/0.58 (step @p84 :rule beta-reduce :args ((= @t190 @t186))) % 0.29/0.58 (step @p85 :rule nary_cong :premises (@p44 @p84) :args (@t191)) % 0.29/0.58 (step @p86 :rule cong :premises (@p85) :args (@t192)) % 0.29/0.58 (step @p87 :rule trans :premises (@p86 @p83)) % 0.29/0.58 (step @p88 :rule cong :premises (@p87) :args (@t193)) % 0.29/0.58 (step @p89 :rule beta-reduce :args ((= (_ @t137 @t189) @t193))) % 0.29/0.58 (step @p90 :rule trans :premises (@p89 @p88)) % 0.29/0.58 (step @p91 :rule aci_norm :args ((= @t195 @t188))) % 0.29/0.58 (step @p92 :rule cong :premises (@p91) :args (@t196)) % 0.29/0.58 (step @p93 :rule quant-merge-prenex :args ((= (forall @t7 @t198) @t196))) % 0.29/0.58 (step @p94 :rule alpha_equiv :args (@t199 (@list @t178) @t200)) % 0.29/0.58 (step @p95 :rule nary_cong :premises (@p55 @p94) :args (@t201)) % 0.29/0.58 (step @p96 :rule quant-miniscope-or :args ((= @t198 @t201))) % 0.29/0.58 (step @p97 :rule trans :premises (@p96 @p95)) % 0.29/0.58 (step @p98 :rule symm :premises (@p97)) % 0.29/0.58 (step @p99 :rule cong :premises (@p98) :args ((forall @t7 (or @t129 @t206)))) % 0.29/0.58 (step @p100 :rule trans :premises (@p99 @p93)) % 0.29/0.58 (step @p101 :rule trans :premises (@p100 @p92)) % 0.29/0.58 (step @p102 :rule beta-reduce :args ((= @t217 @t206))) % 0.29/0.58 (step @p103 :rule nary_cong :premises (@p64 @p102) :args (@t218)) % 0.29/0.58 (step @p104 :rule cong :premises (@p103) :args (@t219)) % 0.29/0.58 (step @p105 :rule trans :premises (@p104 @p101)) % 0.29/0.58 (step @p106 :rule cong :premises (@p105) :args (@t220)) % 0.29/0.58 (step @p107 :rule beta-reduce :args ((= (_ @t170 @t216) @t220))) % 0.29/0.58 (step @p108 :rule trans :premises (@p107 @p106)) % 0.29/0.58 (step @p109 :rule beta-reduce :args ((= (_ (lambda @t8 (forall @t54 @t221)) @t9) @t215))) % 0.29/0.58 (step @p110 :rule aci_norm :args ((= (or @t103 @t222) @t221))) % 0.29/0.58 (step @p111 :rule aci_norm :args ((= (or @t214 (or @t204 @t209)) @t222))) % 0.29/0.58 (step @p112 :rule bool-and-de-morgan :args (@t203 @t208 true)) % 0.29/0.58 (step @p113 :rule refl :args (@t214)) % 0.29/0.58 (step @p114 :rule nary_cong :premises (@p113 @p112) :args ((or @t214 (not (and @t203 @t208))))) % 0.29/0.58 (step @p115 :rule bool-and-de-morgan :args (@t213 @t203 (and @t208))) % 0.29/0.58 (step @p116 :rule trans :premises (@p115 @p114)) % 0.29/0.58 (step @p117 :rule trans :premises (@p116 @p111)) % 0.29/0.58 (step @p118 :rule nary_cong :premises (@p35 @p117) :args (@t224)) % 0.29/0.58 (step @p119 :rule trans :premises (@p118 @p110)) % 0.29/0.58 (step @p120 :rule cong :premises (@p119) :args ((forall @t54 @t224))) % 0.29/0.58 (step @p121 :rule beta-reduce :args ((= (_ (lambda @t8 (not (and (forall @t94 (or (not (tptp.mrel @t2 @t91)) @t212)) (forall @t88 (or (not (tptp.mrel @t2 @t85)) @t159)) (forall @t82 (or (not (tptp.mrel @t2 @t78)) @t80 @t79 @t156 @t207))))) @t1) @t223))) % 0.29/0.58 (step @p122 :rule refl :args (@t1)) % 0.29/0.58 (step @p123 :rule alpha_equiv :args (@t229 @t200 (@list @t78))) % 0.29/0.58 (step @p124 :rule alpha_equiv :args (@t231 @t200 (@list @t85))) % 0.29/0.58 (step @p125 :rule alpha_equiv :args (@t233 @t200 (@list @t91))) % 0.29/0.58 (step @p126 :rule nary_cong :premises (@p125 @p124 @p123) :args (@t234)) % 0.29/0.58 (step @p127 :rule cong :premises (@p126) :args (@t235)) % 0.29/0.58 (step @p128 :rule cong :premises (@p127) :args (@t236)) % 0.29/0.58 (step @p129 :rule ho_cong :premises (@p128 @p122)) % 0.29/0.58 (step @p130 :rule trans :premises (@p129 @p121)) % 0.29/0.58 (step @p131 :rule nary_cong :premises (@p44 @p130) :args (@t237)) % 0.29/0.58 (step @p132 :rule cong :premises (@p131) :args (@t238)) % 0.29/0.58 (step @p133 :rule trans :premises (@p132 @p120)) % 0.29/0.58 (step @p134 :rule cong :premises (@p133) :args (@t239)) % 0.29/0.58 (step @p135 :rule beta-reduce :args ((= (_ @t137 @t236) @t239))) % 0.29/0.58 (step @p136 :rule trans :premises (@p135 @p134)) % 0.29/0.58 (step @p137 :rule beta-reduce :args ((= @t241 @t234))) % 0.29/0.58 (step @p138 :rule cong :premises (@p137) :args (@t242)) % 0.29/0.58 (step @p139 :rule cong :premises (@p138) :args (@t243)) % 0.29/0.58 (step @p140 :rule beta-reduce :args ((= (_ @t45 @t240) @t243))) % 0.29/0.58 (step @p141 :rule trans :premises (@p140 @p139)) % 0.29/0.58 (step @p142 :rule aci_norm :args ((= (and @t233 @t244) @t234))) % 0.29/0.58 (step @p143 :rule beta-reduce :args ((= @t246 @t244))) % 0.29/0.58 (step @p144 :rule refl :args (@t233)) % 0.29/0.58 (step @p145 :rule nary_cong :premises (@p144 @p143) :args (@t247)) % 0.29/0.58 (step @p146 :rule trans :premises (@p145 @p142)) % 0.29/0.58 (step @p147 :rule cong :premises (@p146) :args (@t248)) % 0.29/0.58 (step @p148 :rule beta-reduce :args ((= (_ (lambda @t249 (and @t233 @t47)) @t245) @t248))) % 0.29/0.58 (step @p149 :rule trans :premises (@p148 @p147)) % 0.29/0.58 (step @p150 :rule beta-reduce :args ((= @t251 @t229))) % 0.29/0.58 (step @p151 :rule refl :args (@t231)) % 0.29/0.58 (step @p152 :rule nary_cong :premises (@p151 @p150) :args (@t252)) % 0.29/0.58 (step @p153 :rule cong :premises (@p152) :args (@t253)) % 0.29/0.58 (step @p154 :rule beta-reduce :args ((= (_ (lambda @t249 (and @t231 @t47)) @t250) @t253))) % 0.29/0.58 (step @p155 :rule trans :premises (@p154 @p153)) % 0.29/0.58 (step @p156 :rule aci_norm :args ((= @t255 @t227))) % 0.29/0.58 (step @p157 :rule cong :premises (@p156) :args (@t256)) % 0.29/0.58 (step @p158 :rule quant-merge-prenex :args ((= (forall @t54 @t258) @t256))) % 0.29/0.58 (step @p159 :rule alpha_equiv :args (@t259 (@list @t67 @t71) (@list @t4 @t260))) % 0.29/0.58 (step @p160 :rule nary_cong :premises (@p35 @p159) :args (@t261)) % 0.29/0.58 (step @p161 :rule quant-miniscope-or :args ((= @t258 @t261))) % 0.29/0.58 (step @p162 :rule trans :premises (@p161 @p160)) % 0.29/0.58 (step @p163 :rule symm :premises (@p162)) % 0.29/0.58 (step @p164 :rule cong :premises (@p163) :args ((forall @t54 (or @t103 @t267)))) % 0.29/0.58 (step @p165 :rule trans :premises (@p164 @p158)) % 0.29/0.58 (step @p166 :rule trans :premises (@p165 @p157)) % 0.29/0.58 (step @p167 :rule beta-reduce :args ((= @t271 @t267))) % 0.29/0.58 (step @p168 :rule nary_cong :premises (@p44 @p167) :args (@t272)) % 0.29/0.58 (step @p169 :rule cong :premises (@p168) :args (@t273)) % 0.29/0.58 (step @p170 :rule trans :premises (@p169 @p166)) % 0.29/0.58 (step @p171 :rule cong :premises (@p170) :args (@t274)) % 0.29/0.58 (step @p172 :rule beta-reduce :args ((= (_ @t137 @t270) @t274))) % 0.29/0.58 (step @p173 :rule trans :premises (@p172 @p171)) % 0.29/0.58 (step @p174 :rule aci_norm :args ((= @t276 @t269))) % 0.29/0.58 (step @p175 :rule cong :premises (@p174) :args (@t277)) % 0.29/0.58 (step @p176 :rule quant-merge-prenex :args ((= (forall @t7 @t279) @t277))) % 0.29/0.58 (step @p177 :rule alpha_equiv :args (@t280 (@list @t260) @t200)) % 0.29/0.58 (step @p178 :rule nary_cong :premises (@p55 @p177) :args (@t281)) % 0.29/0.58 (step @p179 :rule quant-miniscope-or :args ((= @t279 @t281))) % 0.29/0.58 (step @p180 :rule trans :premises (@p179 @p178)) % 0.29/0.58 (step @p181 :rule symm :premises (@p180)) % 0.29/0.58 (step @p182 :rule cong :premises (@p181) :args ((forall @t7 (or @t129 @t284)))) % 0.29/0.58 (step @p183 :rule trans :premises (@p182 @p176)) % 0.29/0.58 (step @p184 :rule trans :premises (@p183 @p175)) % 0.29/0.58 (step @p185 :rule beta-reduce :args ((= @t294 @t284))) % 0.29/0.58 (step @p186 :rule nary_cong :premises (@p64 @p185) :args (@t295)) % 0.29/0.58 (step @p187 :rule cong :premises (@p186) :args (@t296)) % 0.29/0.58 (step @p188 :rule trans :premises (@p187 @p184)) % 0.29/0.58 (step @p189 :rule cong :premises (@p188) :args (@t297)) % 0.29/0.58 (step @p190 :rule beta-reduce :args ((= (_ @t170 @t293) @t297))) % 0.29/0.58 (step @p191 :rule trans :premises (@p190 @p189)) % 0.29/0.58 (step @p192 :rule beta-reduce :args ((= (_ (lambda @t8 (forall @t54 @t298)) @t9) @t292))) % 0.29/0.58 (step @p193 :rule aci_norm :args ((= (or @t103 (or @t291 @t288)) @t298))) % 0.29/0.58 (step @p194 :rule bool-and-de-morgan :args (@t290 @t287 true)) % 0.29/0.58 (step @p195 :rule nary_cong :premises (@p35 @p194) :args (@t300)) % 0.29/0.58 (step @p196 :rule trans :premises (@p195 @p193)) % 0.29/0.58 (step @p197 :rule cong :premises (@p196) :args ((forall @t54 @t300))) % 0.29/0.58 (step @p198 :rule beta-reduce :args ((= (_ (lambda @t8 (not (and (forall @t77 (or (not (tptp.mrel @t2 @t74)) @t289)) (forall @t73 (or (not (tptp.mrel @t2 @t68)) @t286))))) @t1) @t299))) % 0.29/0.58 (step @p199 :rule alpha_equiv :args (@t302 @t200 (@list @t68))) % 0.29/0.58 (step @p200 :rule alpha_equiv :args (@t304 @t200 (@list @t74))) % 0.29/0.58 (step @p201 :rule nary_cong :premises (@p200 @p199) :args (@t305)) % 0.29/0.58 (step @p202 :rule cong :premises (@p201) :args (@t306)) % 0.29/0.58 (step @p203 :rule cong :premises (@p202) :args (@t307)) % 0.29/0.58 (step @p204 :rule ho_cong :premises (@p203 @p122)) % 0.29/0.58 (step @p205 :rule trans :premises (@p204 @p198)) % 0.29/0.58 (step @p206 :rule nary_cong :premises (@p44 @p205) :args (@t308)) % 0.29/0.58 (step @p207 :rule cong :premises (@p206) :args (@t309)) 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:premises (@p26 @p464)) % 0.29/0.59 (step @p466 :rule ho_cong :premises (@p465 @p447)) % 0.29/0.59 (step @p467 :rule ho_cong :premises (@p436 @p466)) % 0.29/0.59 (step @p468 :rule refl :args (@t35)) % 0.29/0.59 (step @p469 :rule ho_cong :premises (@p436 @p468)) % 0.29/0.59 (step @p470 :rule ho_cong :premises (@p19 @p469)) % 0.29/0.59 (step @p471 :rule ho_cong :premises (@p436 @p470)) % 0.29/0.59 (step @p472 :rule ho_cong :premises (@p20 @p471)) % 0.29/0.59 (step @p473 :rule ho_cong :premises (@p472 @p467)) % 0.29/0.59 (step @p474 :rule refl :args (@t36)) % 0.29/0.59 (step @p475 :rule ho_cong :premises (@p436 @p474)) % 0.29/0.59 (step @p476 :rule ho_cong :premises (@p19 @p475)) % 0.29/0.59 (step @p477 :rule ho_cong :premises (@p436 @p476)) % 0.29/0.59 (step @p478 :rule ho_cong :premises (@p20 @p477)) % 0.29/0.59 (step @p479 :rule ho_cong :premises (@p478 @p473)) % 0.29/0.59 (step @p480 :rule ho_cong :premises (@p19 @p479)) % 0.29/0.59 (step @p481 :rule ho_cong :premises (@p436 @p480)) % 0.29/0.59 (step @p482 :rule ho_cong :premises (@p481 @p72)) % 0.29/0.59 (step @p483 :rule cong :premises (@p482) :args (@t37)) % 0.29/0.59 (step @p484 :rule ho_cong :premises (@p465 @p483)) % 0.29/0.59 (step @p485 :rule ho_cong :premises (@p436 @p484)) % 0.29/0.59 (step @p486 :rule ho_cong :premises (@p485 @p72)) % 0.29/0.59 (step @p487 :rule cong :premises (@p486) :args (@t38)) % 0.29/0.59 (step @p488 :rule ho_cong :premises (@p465 @p487)) % 0.29/0.59 (step @p489 :rule ho_cong :premises (@p436 @p488)) % 0.29/0.59 (step @p490 :rule ho_cong :premises (@p18 @p489)) % 0.29/0.59 (step @p491 :rule cong :premises (@p490) :args (@t40)) % 0.29/0.59 (step @p492 :rule trans :premises (@p491 @p417)) % 0.29/0.59 (step @p493 :rule eq_resolve :premises (@p15 @p492)) % 0.29/0.59 (step @p494 :rule trans :premises (@p490 @p416)) % 0.29/0.59 (step @p495 :rule eq_resolve :premises (@p16 @p494)) % 0.29/0.59 (step @p496 false :rule contra :premises (@p495 @p493)) % 0.29/0.59 ) % 0.29/0.59 % SZS output end Proof % 0.29/0.59 % cvc5 exiting %------------------------------------------------------------------------------