%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET002^3 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n023.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:46:51 AM UTC 2026 % Result : Theorem 0.37s 0.65s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET002^3 : TPTP v9.2.1. Released v8.1.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n023.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 14:40:43 EDT 2026 % 0.18/0.35 % CPUTime : % 0.29/0.52 %----Proving TH0 % 0.37/0.65 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.65 % SZS status Theorem % 0.37/0.65 % SZS output start Proof % 0.37/0.65 ( % 0.37/0.65 (declare-sort $$unsorted 0) % 0.37/0.65 (declare-sort tptp.mworld 0) % 0.37/0.65 (declare-const tptp.mactual tptp.mworld) % 0.37/0.65 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.37/0.65 (declare-const tptp.subset (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.37/0.65 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.member (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.37/0.65 (declare-const tptp.qmltpeq (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.37/0.65 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.37/0.65 (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)))))) % 0.37/0.65 (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))))))) % 0.37/0.65 (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))))))) % 0.37/0.65 (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))))))) % 0.37/0.65 (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))))))) % 0.37/0.65 (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)))))))) % 0.37/0.65 (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)))))))) % 0.37/0.65 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.65 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.65 (define @t1 () (@var "V" tptp.mworld)) % 0.37/0.65 (define @t2 () (@var "W" tptp.mworld)) % 0.37/0.65 (define @t3 () (_ (_ tptp.mrel @t2) @t1)) % 0.37/0.65 (define @t4 () (@list @t1)) % 0.37/0.65 (define @t5 () (@list @t2)) % 0.37/0.65 (define @t6 () (@var "__flatten_var_0" tptp.mworld)) % 0.37/0.65 (define @t7 () (@var "X" $$unsorted)) % 0.37/0.65 (define @t8 () (_ tptp.qmltpeq @t7)) % 0.37/0.65 (define @t9 () (@list @t7 @t6)) % 0.37/0.65 (define @t10 () (@var "Y" $$unsorted)) % 0.37/0.65 (define @t11 () (_ tptp.qmltpeq @t10)) % 0.37/0.65 (define @t12 () (_ @t8 @t10)) % 0.37/0.65 (define @t13 () (@list @t10 @t6)) % 0.37/0.65 (define @t14 () (@var "Z" $$unsorted)) % 0.37/0.65 (define @t15 () (@var "C" $$unsorted)) % 0.37/0.65 (define @t16 () (@var "B" $$unsorted)) % 0.37/0.65 (define @t17 () (_ tptp.union @t16)) % 0.37/0.65 (define @t18 () (_ @t17 @t15)) % 0.37/0.65 (define @t19 () (@var "A" $$unsorted)) % 0.37/0.65 (define @t20 () (_ (_ tptp.qmltpeq @t19) @t16)) % 0.37/0.65 (define @t21 () (_ tptp.mimplies @t20)) % 0.37/0.65 (define @t22 () (@list @t15 @t6)) % 0.37/0.65 (define @t23 () (@list @t16 @t6)) % 0.37/0.65 (define @t24 () (@list @t19 @t6)) % 0.37/0.65 (define @t25 () (_ tptp.union @t15)) % 0.37/0.65 (define @t26 () (_ @t25 @t16)) % 0.37/0.65 (define @t27 () (_ tptp.mand @t20)) % 0.37/0.65 (define @t28 () (_ tptp.member @t15)) % 0.37/0.65 (define @t29 () (_ tptp.subset @t16)) % 0.37/0.65 (define @t30 () (_ @t29 @t15)) % 0.37/0.65 (define @t31 () (_ tptp.subset @t15)) % 0.37/0.65 (define @t32 () (_ @t31 @t16)) % 0.37/0.65 (define @t33 () (_ tptp.qmltpeq @t18)) % 0.37/0.65 (define @t34 () (@var "D" $$unsorted)) % 0.37/0.65 (define @t35 () (_ tptp.member @t34)) % 0.37/0.65 (define @t36 () (_ @t35 @t15)) % 0.37/0.65 (define @t37 () (_ @t35 @t16)) % 0.37/0.65 (define @t38 () (_ @t35 @t18)) % 0.37/0.65 (define @t39 () (@list @t34 @t6)) % 0.37/0.65 (define @t40 () (lambda @t39 (_ (_ (_ tptp.mequiv @t38) (_ (_ tptp.mor @t37) @t36)) @t6))) % 0.37/0.65 (define @t41 () (lambda @t22 (_ (_ tptp.mforall_di @t40) @t6))) % 0.37/0.65 (define @t42 () (lambda @t23 (_ (_ tptp.mforall_di @t41) @t6))) % 0.37/0.65 (define @t43 () (_ tptp.qmltpeq @t16)) % 0.37/0.65 (define @t44 () (_ @t43 @t15)) % 0.37/0.65 (define @t45 () (_ tptp.mequiv @t44)) % 0.37/0.65 (define @t46 () (lambda @t39 (_ (_ (_ tptp.mequiv @t37) @t36) @t6))) % 0.37/0.65 (define @t47 () (lambda @t22 (_ (_ @t45 (_ tptp.mforall_di @t46)) @t6))) % 0.37/0.65 (define @t48 () (lambda @t23 (_ (_ tptp.mforall_di @t47) @t6))) % 0.37/0.65 (define @t49 () (lambda @t23 (_ (_ (_ tptp.qmltpeq (_ @t17 @t16)) @t16) @t6))) % 0.37/0.65 (define @t50 () (not (_ tptp.mlocal (_ tptp.mforall_di @t49)))) % 0.37/0.65 (define @t51 () (@var "Phi" (-> tptp.mworld Bool))) % 0.37/0.65 (define @t52 () (lambda (@list @t51) (_ @t51 tptp.mactual))) % 0.37/0.65 (define @t53 () (@var "A" (-> tptp.mworld Bool))) % 0.37/0.65 (define @t54 () (_ @t53 @t2)) % 0.37/0.65 (define @t55 () (lambda (@list @t53 @t2) (not @t54))) % 0.37/0.65 (define @t56 () (@var "B" (-> tptp.mworld Bool))) % 0.37/0.65 (define @t57 () (_ @t56 @t2)) % 0.37/0.65 (define @t58 () (@list @t53 @t56 @t2)) % 0.37/0.65 (define @t59 () (lambda @t58 (and @t54 @t57))) % 0.37/0.65 (define @t60 () (lambda @t58 (or @t54 @t57))) % 0.37/0.65 (define @t61 () (lambda @t58 (=> @t54 @t57))) % 0.37/0.65 (define @t62 () (lambda @t58 (= @t54 @t57))) % 0.37/0.65 (define @t63 () (_ @t51 @t1)) % 0.37/0.65 (define @t64 () (@list @t51 @t2)) % 0.37/0.65 (define @t65 () (lambda @t64 (forall @t4 (=> @t3 @t63)))) % 0.37/0.65 (define @t66 () (lambda @t64 (exists @t4 (and @t3 @t63)))) % 0.37/0.65 (define @t67 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.37/0.65 (define @t68 () (_ (_ @t67 @t7) @t2)) % 0.37/0.65 (define @t69 () (@list @t7)) % 0.37/0.65 (define @t70 () (forall @t69 @t68)) % 0.37/0.65 (define @t71 () (@list @t67 @t2)) % 0.37/0.65 (define @t72 () (lambda @t71 @t70)) % 0.37/0.65 (define @t73 () (lambda @t71 (exists @t69 @t68))) % 0.37/0.65 (define @t74 () (@var "BOUND_VARIABLE_9102" $$unsorted)) % 0.37/0.65 (define @t75 () (@var "BOUND_VARIABLE_9069" $$unsorted)) % 0.37/0.65 (define @t76 () (tptp.union @t7 @t74)) % 0.37/0.65 (define @t77 () (@list @t7 @t74 @t75)) % 0.37/0.65 (define @t78 () (forall @t77 (= (tptp.member @t75 @t76 tptp.mactual) (or (tptp.member @t75 @t7 tptp.mactual) (tptp.member @t75 @t74 tptp.mactual))))) % 0.37/0.65 (define @t79 () (tptp.member @t75 @t7 @t2)) % 0.37/0.65 (define @t80 () (= (tptp.member @t75 @t76 @t2) (or @t79 (tptp.member @t75 @t74 @t2)))) % 0.37/0.65 (define @t81 () (forall @t77 @t80)) % 0.37/0.65 (define @t82 () (lambda @t5 @t81)) % 0.37/0.65 (define @t83 () (_ @t82 tptp.mactual)) % 0.37/0.65 (define @t84 () (@list @t74 @t75)) % 0.37/0.65 (define @t85 () (forall @t84 @t80)) % 0.37/0.65 (define @t86 () (tptp.member @t75 @t16 @t6)) % 0.37/0.65 (define @t87 () (tptp.union @t16 @t7)) % 0.37/0.65 (define @t88 () (@list @t7 @t75)) % 0.37/0.65 (define @t89 () (forall @t88 (= (tptp.member @t75 @t87 @t6) (or @t86 (tptp.member @t75 @t7 @t6))))) % 0.37/0.65 (define @t90 () (@list @t7)) % 0.37/0.65 (define @t91 () (lambda @t23 @t89)) % 0.37/0.65 (define @t92 () (forall @t69 (_ @t91 @t7 @t2))) % 0.37/0.65 (define @t93 () (lambda @t5 @t92)) % 0.37/0.65 (define @t94 () (_ @t67 @t7 @t2)) % 0.37/0.65 (define @t95 () (lambda @t71 (forall @t69 @t94))) % 0.37/0.65 (define @t96 () (= (tptp.member @t75 @t87 @t2) (or (tptp.member @t75 @t16 @t2) @t79))) % 0.37/0.65 (define @t97 () (forall @t88 @t96)) % 0.37/0.65 (define @t98 () (@list @t75)) % 0.37/0.65 (define @t99 () (forall @t98 @t96)) % 0.37/0.65 (define @t100 () (tptp.union @t16 @t15)) % 0.37/0.65 (define @t101 () (tptp.member @t7 @t15 @t6)) % 0.37/0.65 (define @t102 () (tptp.member @t7 @t16 @t6)) % 0.37/0.65 (define @t103 () (forall @t69 (= (tptp.member @t7 @t100 @t6) (or @t102 @t101)))) % 0.37/0.65 (define @t104 () (lambda @t22 @t103)) % 0.37/0.65 (define @t105 () (forall @t69 (_ @t104 @t7 @t2))) % 0.37/0.65 (define @t106 () (lambda @t5 @t105)) % 0.37/0.65 (define @t107 () (tptp.member @t7 @t15 @t2)) % 0.37/0.65 (define @t108 () (tptp.member @t7 @t16 @t2)) % 0.37/0.65 (define @t109 () (tptp.member @t7 @t100 @t2)) % 0.37/0.65 (define @t110 () (_ tptp.member @t7)) % 0.37/0.65 (define @t111 () (_ (_ @t110 @t15) @t2)) % 0.37/0.65 (define @t112 () (_ (_ @t110 @t16) @t2)) % 0.37/0.65 (define @t113 () (or @t112 @t111)) % 0.37/0.65 (define @t114 () (_ (_ @t110 @t18) @t2)) % 0.37/0.65 (define @t115 () (= @t114 @t113)) % 0.37/0.65 (define @t116 () (_ @t36 @t6)) % 0.37/0.65 (define @t117 () (_ @t37 @t6)) % 0.37/0.65 (define @t118 () (= (_ @t38 @t6) (or @t117 @t116))) % 0.37/0.65 (define @t119 () (lambda @t39 @t118)) % 0.37/0.65 (define @t120 () (_ @t119 @t7 @t2)) % 0.37/0.65 (define @t121 () (forall @t69 @t120)) % 0.37/0.65 (define @t122 () (lambda @t5 @t121)) % 0.37/0.65 (define @t123 () (_ @t36 @t2)) % 0.37/0.65 (define @t124 () (_ @t37 @t2)) % 0.37/0.65 (define @t125 () (or @t124 @t123)) % 0.37/0.65 (define @t126 () (_ @t38 @t2)) % 0.37/0.65 (define @t127 () (lambda @t5 @t125)) % 0.37/0.65 (define @t128 () (_ @t127 @t2)) % 0.37/0.65 (define @t129 () (lambda @t5 (= @t128 @t126))) % 0.37/0.65 (define @t130 () (@list @t56 @t2)) % 0.37/0.65 (define @t131 () (lambda @t130 (or @t124 @t57))) % 0.37/0.65 (define @t132 () (_ @t60 @t37)) % 0.37/0.65 (define @t133 () (lambda @t130 (= @t126 @t57))) % 0.37/0.65 (define @t134 () (_ @t62 @t38)) % 0.37/0.65 (define @t135 () (lambda @t39 (_ (_ @t134 (_ @t132 @t36)) @t6))) % 0.37/0.65 (define @t136 () (lambda @t22 (_ (_ @t95 @t135) @t6))) % 0.37/0.65 (define @t137 () (@var "BOUND_VARIABLE_9498" $$unsorted)) % 0.37/0.65 (define @t138 () (@var "BOUND_VARIABLE_9467" $$unsorted)) % 0.37/0.65 (define @t139 () (@list @t138)) % 0.37/0.65 (define @t140 () (@list @t7 @t137)) % 0.37/0.65 (define @t141 () (tptp.member @t138 @t7 @t2)) % 0.37/0.65 (define @t142 () (= (tptp.qmltpeq @t7 @t137 @t2) (forall @t139 (= @t141 (tptp.member @t138 @t137 @t2))))) % 0.37/0.65 (define @t143 () (forall @t140 @t142)) % 0.37/0.65 (define @t144 () (lambda @t5 @t143)) % 0.37/0.65 (define @t145 () (_ @t144 tptp.mactual)) % 0.37/0.65 (define @t146 () (@list @t137)) % 0.37/0.65 (define @t147 () (forall @t146 @t142)) % 0.37/0.65 (define @t148 () (tptp.member @t138 @t16 @t6)) % 0.37/0.65 (define @t149 () (forall @t69 (= (tptp.qmltpeq @t16 @t7 @t6) (forall @t139 (= @t148 (tptp.member @t138 @t7 @t6)))))) % 0.37/0.65 (define @t150 () (lambda @t23 @t149)) % 0.37/0.65 (define @t151 () (forall @t69 (_ @t150 @t7 @t2))) % 0.37/0.65 (define @t152 () (lambda @t5 @t151)) % 0.37/0.65 (define @t153 () (forall @t139 (= (tptp.member @t138 @t16 @t2) @t141))) % 0.37/0.65 (define @t154 () (tptp.qmltpeq @t16 @t7 @t2)) % 0.37/0.65 (define @t155 () (_ (_ @t43 @t7) @t2)) % 0.37/0.65 (define @t156 () (= @t155 @t153)) % 0.37/0.65 (define @t157 () (_ @t44 @t6)) % 0.37/0.65 (define @t158 () (forall @t69 (= @t102 @t101))) % 0.37/0.65 (define @t159 () (= @t157 @t158)) % 0.37/0.65 (define @t160 () (lambda @t22 @t159)) % 0.37/0.65 (define @t161 () (forall @t69 (_ @t160 @t7 @t2))) % 0.37/0.65 (define @t162 () (lambda @t5 @t161)) % 0.37/0.65 (define @t163 () (forall @t69 (= @t108 @t107))) % 0.37/0.65 (define @t164 () (_ @t44 @t2)) % 0.37/0.65 (define @t165 () (lambda @t5 @t163)) % 0.37/0.65 (define @t166 () (_ @t165 @t2)) % 0.37/0.65 (define @t167 () (lambda @t5 (= @t166 @t164))) % 0.37/0.65 (define @t168 () (= @t112 @t111)) % 0.37/0.65 (define @t169 () (= @t117 @t116)) % 0.37/0.65 (define @t170 () (lambda @t39 @t169)) % 0.37/0.65 (define @t171 () (_ @t170 @t7 @t2)) % 0.37/0.65 (define @t172 () (forall @t69 @t171)) % 0.37/0.65 (define @t173 () (lambda @t5 @t172)) % 0.37/0.65 (define @t174 () (lambda @t5 (= @t123 @t124))) % 0.37/0.65 (define @t175 () (lambda @t130 (= @t124 @t57))) % 0.37/0.65 (define @t176 () (_ @t62 @t37)) % 0.37/0.65 (define @t177 () (lambda @t39 (_ (_ @t176 @t36) @t6))) % 0.37/0.65 (define @t178 () (lambda @t130 (= @t164 @t57))) % 0.37/0.65 (define @t179 () (_ @t62 @t44)) % 0.37/0.65 (define @t180 () (lambda @t22 (_ (_ @t179 (_ @t95 @t177)) @t6))) % 0.37/0.65 (define @t181 () (tptp.union @t7 @t7)) % 0.37/0.65 (define @t182 () (forall @t69 (tptp.qmltpeq @t181 @t7 tptp.mactual))) % 0.37/0.65 (define @t183 () (@quantifiers_skolemize @t182 0)) % 0.37/0.65 (define @t184 () (tptp.union @t183 @t183)) % 0.37/0.65 (define @t185 () (tptp.qmltpeq @t181 @t7 @t2)) % 0.37/0.65 (define @t186 () (lambda @t5 (forall @t69 @t185))) % 0.37/0.65 (define @t187 () (_ @t186 tptp.mactual)) % 0.37/0.65 (define @t188 () (_ (_ tptp.union @t7) @t7)) % 0.37/0.65 (define @t189 () (_ (_ (_ tptp.qmltpeq @t188) @t7) @t2)) % 0.37/0.65 (define @t190 () (_ @t49 @t7 @t2)) % 0.37/0.65 (define @t191 () (forall @t69 @t190)) % 0.37/0.65 (define @t192 () (lambda @t5 @t191)) % 0.37/0.65 (define @t193 () (_ @t95 @t49)) % 0.37/0.65 (define @t194 () (forall @t139 (= (tptp.member @t138 @t184 tptp.mactual) (tptp.member @t138 @t183 tptp.mactual)))) % 0.37/0.65 (define @t195 () (tptp.qmltpeq @t184 @t183 tptp.mactual)) % 0.37/0.65 (define @t196 () (= @t195 @t194)) % 0.37/0.65 (define @t197 () (not @t194)) % 0.37/0.65 (define @t198 () (@list true false)) % 0.37/0.65 (define @t199 () (@quantifiers_skolemize @t194 0)) % 0.37/0.65 (define @t200 () (tptp.member @t199 @t183 tptp.mactual)) % 0.37/0.65 (define @t201 () (or @t200 @t200)) % 0.37/0.65 (define @t202 () (tptp.member @t199 @t184 tptp.mactual)) % 0.37/0.65 (define @t203 () (= @t202 @t201)) % 0.37/0.65 (assume @p1 (forall @t5 (exists @t4 @t3))) % 0.37/0.65 (assume @p2 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t9 (_ (_ @t8 @t7) @t6))))) % 0.37/0.65 (assume @p3 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t9 (_ (_ tptp.mforall_di (lambda @t13 (_ (_ (_ tptp.mimplies @t12) (_ @t11 @t7)) @t6))) @t6))))) % 0.37/0.65 (assume @p4 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t9 (_ (_ tptp.mforall_di (lambda @t13 (_ (_ tptp.mforall_di (lambda (@list @t14 @t6) (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t12) (_ @t11 @t14))) (_ @t8 @t14)) @t6))) @t6))) @t6))))) % 0.37/0.65 (assume @p5 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ @t21 (_ (_ tptp.qmltpeq (_ (_ tptp.union @t19) @t15)) @t18)) @t6))) @t6))) @t6))))) % 0.37/0.65 (assume @p6 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ @t21 (_ (_ tptp.qmltpeq (_ @t25 @t19)) @t26)) @t6))) @t6))) @t6))))) % 0.37/0.65 (assume @p7 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ (_ tptp.mimplies (_ @t27 (_ (_ tptp.member @t19) @t15))) (_ (_ tptp.member @t16) @t15)) @t6))) @t6))) @t6))))) % 0.37/0.65 (assume @p8 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ (_ tptp.mimplies (_ @t27 (_ @t28 @t19))) (_ @t28 @t16)) @t6))) @t6))) @t6))))) % 0.37/0.65 (assume @p9 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ (_ tptp.mimplies (_ @t27 (_ (_ tptp.subset @t19) @t15))) @t30) @t6))) @t6))) @t6))))) % 0.37/0.65 (assume @p10 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t24 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ (_ tptp.mimplies (_ @t27 (_ @t31 @t19))) @t32) @t6))) @t6))) @t6))))) % 0.37/0.65 (assume @p11 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ (_ tptp.mimplies @t30) (_ @t33 @t15)) @t6))) @t6))))) % 0.37/0.65 (assume @p12 (_ tptp.mlocal (_ tptp.mforall_di @t42))) % 0.37/0.65 (assume @p13 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ @t45 (_ (_ tptp.mand @t30) @t32)) @t6))) @t6))))) % 0.37/0.65 (assume @p14 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ @t33 @t26) @t6))) @t6))))) % 0.37/0.65 (assume @p15 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ (_ tptp.mequiv @t30) (_ tptp.mforall_di (lambda @t39 (_ (_ (_ tptp.mimplies @t37) @t36) @t6)))) @t6))) @t6))))) % 0.37/0.65 (assume @p16 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ @t29 @t16) @t6))))) % 0.37/0.65 (assume @p17 (_ tptp.mlocal (_ tptp.mforall_di @t48))) % 0.37/0.65 (assume @p18 @t50) % 0.37/0.65 (assume @p19 true) % 0.37/0.65 (step @p20 (= tptp.mlocal @t52) :rule refl :args (@t52)) % 0.37/0.65 (step @p21 (= tptp.mnot @t55) :rule refl :args (@t55)) % 0.37/0.65 (step @p22 (= tptp.mand @t59) :rule refl :args (@t59)) % 0.37/0.65 (step @p23 (= tptp.mor @t60) :rule refl :args (@t60)) % 0.37/0.65 (step @p24 (= tptp.mimplies @t61) :rule refl :args (@t61)) % 0.37/0.65 (step @p25 (= tptp.mequiv @t62) :rule refl :args (@t62)) % 0.37/0.65 (step @p26 (= tptp.mbox @t65) :rule refl :args (@t65)) % 0.37/0.65 (step @p27 (= tptp.mdia @t66) :rule refl :args (@t66)) % 0.37/0.65 (step @p28 (= tptp.mforall_di @t72) :rule refl :args (@t72)) % 0.37/0.65 (step @p29 (= tptp.mexists_di @t73) :rule refl :args (@t73)) % 0.37/0.65 (step @p30 :rule beta-reduce :args ((= @t83 @t78))) % 0.37/0.65 (step @p31 :rule beta-reduce :args ((= (_ @t52 @t82) @t83))) % 0.37/0.65 (step @p32 :rule trans :premises (@p31 @p30)) % 0.37/0.65 (step @p33 :rule quant-merge-prenex :args ((= (forall @t69 @t85) @t81))) % 0.37/0.65 (step @p34 :rule beta-reduce :args ((= (_ (lambda @t23 (forall @t84 (= (tptp.member @t75 (tptp.union @t16 @t74) @t6) (or @t86 (tptp.member @t75 @t74 @t6))))) @t7 @t2) @t85))) % 0.37/0.65 (step @p35 :rule refl :args (@t2)) % 0.37/0.65 (step @p36 :rule refl :args (@t7)) % 0.37/0.65 (step @p37 :rule alpha_equiv :args (@t89 @t90 (@list @t74))) % 0.37/0.65 (step @p38 :rule cong :premises (@p37) :args (@t91)) % 0.37/0.65 (step @p39 :rule ho_cong :premises (@p38 @p36 @p35)) % 0.37/0.65 (step @p40 :rule trans :premises (@p39 @p34)) % 0.37/0.65 (step @p41 :rule cong :premises (@p40) :args (@t92)) % 0.37/0.65 (step @p42 :rule trans :premises (@p41 @p33)) % 0.37/0.65 (step @p43 :rule cong :premises (@p42) :args (@t93)) % 0.37/0.65 (step @p44 :rule beta-reduce :args ((= (_ @t95 @t91) @t93))) % 0.37/0.65 (step @p45 :rule trans :premises (@p44 @p43)) % 0.37/0.65 (step @p46 :rule beta-reduce :args ((= (_ (lambda @t5 @t97) @t6) @t89))) % 0.37/0.65 (step @p47 :rule refl :args (@t6)) % 0.37/0.65 (step @p48 :rule quant-merge-prenex :args ((= (forall @t69 @t99) @t97))) % 0.37/0.65 (step @p49 :rule beta-reduce :args ((= (_ (lambda @t22 (forall @t98 (= (tptp.member @t75 @t100 @t6) (or @t86 (tptp.member @t75 @t15 @t6))))) @t7 @t2) @t99))) % 0.37/0.65 (step @p50 :rule alpha_equiv :args (@t103 @t90 (@list @t75))) % 0.37/0.65 (step @p51 :rule cong :premises (@p50) :args (@t104)) % 0.37/0.65 (step @p52 :rule ho_cong :premises (@p51 @p36 @p35)) % 0.37/0.65 (step @p53 :rule trans :premises (@p52 @p49)) % 0.37/0.65 (step @p54 :rule cong :premises (@p53) :args (@t105)) % 0.37/0.65 (step @p55 :rule trans :premises (@p54 @p48)) % 0.37/0.65 (step @p56 :rule cong :premises (@p55) :args (@t106)) % 0.37/0.65 (step @p57 :rule beta-reduce :args ((= (_ @t95 @t104) @t106))) % 0.37/0.65 (step @p58 :rule trans :premises (@p57 @p56)) % 0.37/0.65 (step @p59 :rule beta-reduce :args ((= (_ (lambda @t5 (forall @t69 (= @t109 (or @t108 @t107)))) @t6) @t103))) % 0.37/0.65 (step @p60 :rule refl :args (@t107)) % 0.37/0.65 (step @p61 :rule refl :args (@t111)) % 0.37/0.65 (step @p62 :rule cong :premises (@p61 @p60) :args ((= @t111 @t107))) % 0.37/0.65 (step @p63 :rule symm :premises (@p62)) % 0.37/0.65 (step @p64 :rule eq_resolve :premises (@p61 @p63)) % 0.37/0.65 (step @p65 :rule refl :args (@t108)) % 0.37/0.65 (step @p66 :rule refl :args (@t112)) % 0.37/0.65 (step @p67 :rule cong :premises (@p66 @p65) :args ((= @t112 @t108))) % 0.37/0.65 (step @p68 :rule symm :premises (@p67)) % 0.37/0.65 (step @p69 :rule eq_resolve :premises (@p66 @p68)) % 0.37/0.65 (step @p70 :rule nary_cong :premises (@p69 @p64) :args (@t113)) % 0.37/0.65 (step @p71 :rule refl :args ((tptp.member @t7 @t18 @t2))) % 0.37/0.65 (step @p72 :rule refl :args (@t100)) % 0.37/0.65 (step @p73 :rule cong :premises (@p36 @p72 @p35) :args (@t109)) % 0.37/0.65 (step @p74 :rule trans :premises (@p73 @p71)) % 0.37/0.65 (step @p75 :rule refl :args (@t110)) % 0.37/0.65 (step @p76 :rule ho_cong :premises (@p75 @p72)) % 0.37/0.65 (step @p77 :rule ho_cong :premises (@p76 @p35)) % 0.37/0.65 (step @p78 :rule cong :premises (@p77 @p74) :args ((= (_ (_ @t110 @t100) @t2) @t109))) % 0.37/0.65 (step @p79 :rule symm :premises (@p78)) % 0.37/0.65 (step @p80 :rule refl :args (@t114)) % 0.37/0.65 (step @p81 :rule eq_resolve :premises (@p80 @p79)) % 0.37/0.65 (step @p82 :rule refl :args (@t18)) % 0.37/0.65 (step @p83 :rule cong :premises (@p82 @p72) :args ((= @t18 @t100))) % 0.37/0.65 (step @p84 :rule symm :premises (@p83)) % 0.37/0.65 (step @p85 :rule eq_resolve :premises (@p82 @p84)) % 0.37/0.65 (step @p86 :rule ho_cong :premises (@p75 @p85)) % 0.37/0.65 (step @p87 :rule ho_cong :premises (@p86 @p35)) % 0.37/0.65 (step @p88 :rule trans :premises (@p87 @p81)) % 0.37/0.65 (step @p89 :rule cong :premises (@p88 @p70) :args (@t115)) % 0.37/0.65 (step @p90 :rule cong :premises (@p89) :args ((forall @t69 @t115))) % 0.37/0.65 (step @p91 :rule beta-reduce :args ((= @t120 @t115))) % 0.37/0.65 (step @p92 :rule cong :premises (@p91) :args (@t121)) % 0.37/0.65 (step @p93 :rule trans :premises (@p92 @p90)) % 0.37/0.65 (step @p94 :rule cong :premises (@p93) :args (@t122)) % 0.37/0.65 (step @p95 :rule beta-reduce :args ((= (_ @t95 @t119) @t122))) % 0.37/0.65 (step @p96 :rule trans :premises (@p95 @p94)) % 0.37/0.65 (step @p97 :rule beta-reduce :args ((= (_ (lambda @t5 (= @t126 @t125)) @t6) @t118))) % 0.37/0.65 (step @p98 :rule beta-reduce :args ((= @t128 @t125))) % 0.37/0.65 (step @p99 :rule refl :args (@t126)) % 0.37/0.65 (step @p100 :rule cong :premises (@p99 @p98) :args ((= @t126 @t128))) % 0.37/0.65 (step @p101 :rule eq-symm :args (@t128 @t126)) % 0.37/0.65 (step @p102 :rule trans :premises (@p101 @p100)) % 0.37/0.65 (step @p103 :rule cong :premises (@p102) :args (@t129)) % 0.37/0.65 (step @p104 :rule beta-reduce :args ((= (_ (lambda @t130 (= @t57 @t126)) @t127) @t129))) % 0.37/0.65 (step @p105 :rule trans :premises (@p104 @p103)) % 0.37/0.65 (step @p106 :rule beta-reduce :args ((= (_ @t131 @t36) @t127))) % 0.37/0.65 (step @p107 :rule refl :args (@t36)) % 0.37/0.65 (step @p108 :rule beta-reduce :args ((= @t132 @t131))) % 0.37/0.65 (step @p109 :rule ho_cong :premises (@p108 @p107)) % 0.37/0.65 (step @p110 :rule trans :premises (@p109 @p106)) % 0.37/0.65 (step @p111 :rule eq-symm :args (@t126 @t57)) % 0.37/0.65 (step @p112 :rule cong :premises (@p111) :args (@t133)) % 0.37/0.65 (step @p113 :rule beta-reduce :args ((= @t134 @t133))) % 0.37/0.65 (step @p114 :rule trans :premises (@p113 @p112)) % 0.37/0.65 (step @p115 :rule ho_cong :premises (@p114 @p110)) % 0.37/0.65 (step @p116 :rule trans :premises (@p115 @p105)) % 0.37/0.65 (step @p117 :rule ho_cong :premises (@p116 @p47)) % 0.37/0.65 (step @p118 :rule trans :premises (@p117 @p97)) % 0.37/0.65 (step @p119 :rule cong :premises (@p118) :args (@t135)) % 0.37/0.65 (step @p120 :rule refl :args (@t95)) % 0.37/0.65 (step @p121 :rule ho_cong :premises (@p120 @p119)) % 0.37/0.65 (step @p122 :rule trans :premises (@p121 @p96)) % 0.37/0.65 (step @p123 :rule ho_cong :premises (@p122 @p47)) % 0.37/0.65 (step @p124 :rule trans :premises (@p123 @p59)) % 0.37/0.65 (step @p125 :rule cong :premises (@p124) :args (@t136)) % 0.37/0.65 (step @p126 :rule ho_cong :premises (@p120 @p125)) % 0.37/0.65 (step @p127 :rule trans :premises (@p126 @p58)) % 0.37/0.65 (step @p128 :rule ho_cong :premises (@p127 @p47)) % 0.37/0.65 (step @p129 :rule trans :premises (@p128 @p46)) % 0.37/0.65 (step @p130 :rule cong :premises (@p129) :args ((lambda @t23 (_ (_ @t95 @t136) @t6)))) % 0.37/0.65 (step @p131 :rule ho_cong :premises (@p120 @p130)) % 0.37/0.65 (step @p132 :rule trans :premises (@p131 @p45)) % 0.37/0.65 (step @p133 :rule refl :args (@t52)) % 0.37/0.65 (step @p134 :rule ho_cong :premises (@p133 @p132)) % 0.37/0.65 (step @p135 :rule trans :premises (@p134 @p32)) % 0.37/0.65 (step @p136 :rule refl :args (@t37)) % 0.37/0.65 (step @p137 :rule ho_cong :premises (@p23 @p136)) % 0.37/0.65 (step @p138 :rule ho_cong :premises (@p137 @p107)) % 0.37/0.65 (step @p139 :rule refl :args (@t38)) % 0.37/0.65 (step @p140 :rule ho_cong :premises (@p25 @p139)) % 0.37/0.65 (step @p141 :rule ho_cong :premises (@p140 @p138)) % 0.37/0.65 (step @p142 :rule ho_cong :premises (@p141 @p47)) % 0.37/0.65 (step @p143 :rule cong :premises (@p142) :args (@t40)) % 0.37/0.65 (step @p144 :rule refl :args (@t94)) % 0.37/0.65 (step @p145 :rule refl :args (@t68)) % 0.37/0.65 (step @p146 :rule cong :premises (@p145 @p144) :args ((= @t68 @t94))) % 0.37/0.65 (step @p147 :rule symm :premises (@p146)) % 0.37/0.65 (step @p148 :rule eq_resolve :premises (@p145 @p147)) % 0.37/0.65 (step @p149 :rule cong :premises (@p148) :args (@t70)) % 0.37/0.65 (step @p150 :rule cong :premises (@p149) :args (@t72)) % 0.37/0.65 (step @p151 :rule trans :premises (@p28 @p150)) % 0.37/0.65 (step @p152 :rule ho_cong :premises (@p151 @p143)) % 0.37/0.65 (step @p153 :rule ho_cong :premises (@p152 @p47)) % 0.37/0.65 (step @p154 :rule cong :premises (@p153) :args (@t41)) % 0.37/0.65 (step @p155 :rule ho_cong :premises (@p151 @p154)) % 0.37/0.65 (step @p156 :rule ho_cong :premises (@p155 @p47)) % 0.37/0.65 (step @p157 :rule cong :premises (@p156) :args (@t42)) % 0.37/0.65 (step @p158 :rule ho_cong :premises (@p151 @p157)) % 0.37/0.65 (step @p159 :rule ho_cong :premises (@p20 @p158)) % 0.37/0.65 (step @p160 :rule trans :premises (@p159 @p135)) % 0.37/0.65 (step @p161 :rule eq_resolve :premises (@p12 @p160)) % 0.37/0.65 (step @p162 :rule beta-reduce :args ((= @t145 (forall @t140 (= (tptp.qmltpeq @t7 @t137 tptp.mactual) (forall @t139 (= (tptp.member @t138 @t7 tptp.mactual) (tptp.member @t138 @t137 tptp.mactual)))))))) % 0.37/0.65 (step @p163 :rule beta-reduce :args ((= (_ @t52 @t144) @t145))) % 0.37/0.65 (step @p164 :rule trans :premises (@p163 @p162)) % 0.37/0.65 (step @p165 :rule quant-merge-prenex :args ((= (forall @t69 @t147) @t143))) % 0.37/0.65 (step @p166 :rule beta-reduce :args ((= (_ (lambda @t23 (forall @t146 (= (tptp.qmltpeq @t16 @t137 @t6) (forall @t139 (= @t148 (tptp.member @t138 @t137 @t6)))))) @t7 @t2) @t147))) % 0.37/0.65 (step @p167 :rule alpha_equiv :args (@t149 @t90 (@list @t137))) % 0.37/0.65 (step @p168 :rule cong :premises (@p167) :args (@t150)) % 0.37/0.65 (step @p169 :rule ho_cong :premises (@p168 @p36 @p35)) % 0.37/0.65 (step @p170 :rule trans :premises (@p169 @p166)) % 0.37/0.65 (step @p171 :rule cong :premises (@p170) :args (@t151)) % 0.37/0.65 (step @p172 :rule trans :premises (@p171 @p165)) % 0.37/0.65 (step @p173 :rule cong :premises (@p172) :args (@t152)) % 0.37/0.65 (step @p174 :rule beta-reduce :args ((= (_ @t95 @t150) @t152))) % 0.37/0.65 (step @p175 :rule trans :premises (@p174 @p173)) % 0.37/0.65 (step @p176 :rule beta-reduce :args ((= (_ (lambda @t5 (forall @t69 (= @t154 @t153))) @t6) @t149))) % 0.37/0.65 (step @p177 :rule refl :args (@t153)) % 0.37/0.65 (step @p178 :rule refl :args (@t154)) % 0.37/0.65 (step @p179 :rule refl :args (@t155)) % 0.37/0.65 (step @p180 :rule cong :premises (@p179 @p178) :args ((= @t155 @t154))) % 0.37/0.65 (step @p181 :rule symm :premises (@p180)) % 0.37/0.65 (step @p182 :rule eq_resolve :premises (@p179 @p181)) % 0.37/0.65 (step @p183 :rule cong :premises (@p182 @p177) :args (@t156)) % 0.37/0.65 (step @p184 :rule cong :premises (@p183) :args ((forall @t69 @t156))) % 0.37/0.65 (step @p185 :rule beta-reduce :args ((= (_ (lambda @t22 (= @t157 (forall @t139 (= @t148 (tptp.member @t138 @t15 @t6))))) @t7 @t2) @t156))) % 0.37/0.65 (step @p186 :rule alpha_equiv :args (@t158 @t90 (@list @t138))) % 0.37/0.65 (step @p187 :rule refl :args (@t157)) % 0.37/0.65 (step @p188 :rule cong :premises (@p187 @p186) :args (@t159)) % 0.37/0.65 (step @p189 :rule cong :premises (@p188) :args (@t160)) % 0.37/0.65 (step @p190 :rule ho_cong :premises (@p189 @p36 @p35)) % 0.37/0.65 (step @p191 :rule trans :premises (@p190 @p185)) % 0.37/0.65 (step @p192 :rule cong :premises (@p191) :args (@t161)) % 0.37/0.65 (step @p193 :rule trans :premises (@p192 @p184)) % 0.37/0.65 (step @p194 :rule cong :premises (@p193) :args (@t162)) % 0.37/0.65 (step @p195 :rule beta-reduce :args ((= (_ @t95 @t160) @t162))) % 0.37/0.65 (step @p196 :rule trans :premises (@p195 @p194)) % 0.37/0.65 (step @p197 :rule beta-reduce :args ((= (_ (lambda @t5 (= @t164 @t163)) @t6) @t159))) % 0.37/0.65 (step @p198 :rule beta-reduce :args ((= @t166 @t163))) % 0.37/0.65 (step @p199 :rule refl :args (@t164)) % 0.37/0.65 (step @p200 :rule cong :premises (@p199 @p198) :args ((= @t164 @t166))) % 0.37/0.65 (step @p201 :rule eq-symm :args (@t166 @t164)) % 0.37/0.65 (step @p202 :rule trans :premises (@p201 @p200)) % 0.37/0.65 (step @p203 :rule cong :premises (@p202) :args (@t167)) % 0.37/0.65 (step @p204 :rule beta-reduce :args ((= (_ (lambda @t130 (= @t57 @t164)) @t165) @t167))) % 0.37/0.65 (step @p205 :rule trans :premises (@p204 @p203)) % 0.37/0.65 (step @p206 :rule cong :premises (@p69 @p64) :args (@t168)) % 0.37/0.65 (step @p207 :rule cong :premises (@p206) :args ((forall @t69 @t168))) % 0.37/0.65 (step @p208 :rule beta-reduce :args ((= @t171 @t168))) % 0.37/0.65 (step @p209 :rule cong :premises (@p208) :args (@t172)) % 0.37/0.65 (step @p210 :rule trans :premises (@p209 @p207)) % 0.37/0.65 (step @p211 :rule cong :premises (@p210) :args (@t173)) % 0.37/0.65 (step @p212 :rule beta-reduce :args ((= (_ @t95 @t170) @t173))) % 0.37/0.65 (step @p213 :rule trans :premises (@p212 @p211)) % 0.37/0.65 (step @p214 :rule beta-reduce :args ((= (_ (lambda @t5 (= @t124 @t123)) @t6) @t169))) % 0.37/0.65 (step @p215 :rule eq-symm :args (@t123 @t124)) % 0.37/0.65 (step @p216 :rule cong :premises (@p215) :args (@t174)) % 0.37/0.65 (step @p217 :rule beta-reduce :args ((= (_ (lambda @t130 (= @t57 @t124)) @t36) @t174))) % 0.37/0.65 (step @p218 :rule trans :premises (@p217 @p216)) % 0.37/0.65 (step @p219 :rule eq-symm :args (@t124 @t57)) % 0.37/0.65 (step @p220 :rule cong :premises (@p219) :args (@t175)) % 0.37/0.65 (step @p221 :rule beta-reduce :args ((= @t176 @t175))) % 0.37/0.65 (step @p222 :rule trans :premises (@p221 @p220)) % 0.37/0.65 (step @p223 :rule ho_cong :premises (@p222 @p107)) % 0.37/0.65 (step @p224 :rule trans :premises (@p223 @p218)) % 0.37/0.65 (step @p225 :rule ho_cong :premises (@p224 @p47)) % 0.37/0.65 (step @p226 :rule trans :premises (@p225 @p214)) % 0.37/0.65 (step @p227 :rule cong :premises (@p226) :args (@t177)) % 0.37/0.65 (step @p228 :rule ho_cong :premises (@p120 @p227)) % 0.37/0.65 (step @p229 :rule trans :premises (@p228 @p213)) % 0.37/0.65 (step @p230 :rule eq-symm :args (@t164 @t57)) % 0.37/0.65 (step @p231 :rule cong :premises (@p230) :args (@t178)) % 0.37/0.65 (step @p232 :rule beta-reduce :args ((= @t179 @t178))) % 0.37/0.65 (step @p233 :rule trans :premises (@p232 @p231)) % 0.37/0.65 (step @p234 :rule ho_cong :premises (@p233 @p229)) % 0.37/0.65 (step @p235 :rule trans :premises (@p234 @p205)) % 0.37/0.65 (step @p236 :rule ho_cong :premises (@p235 @p47)) % 0.37/0.65 (step @p237 :rule trans :premises (@p236 @p197)) % 0.37/0.65 (step @p238 :rule cong :premises (@p237) :args (@t180)) % 0.37/0.65 (step @p239 :rule ho_cong :premises (@p120 @p238)) % 0.37/0.65 (step @p240 :rule trans :premises (@p239 @p196)) % 0.37/0.65 (step @p241 :rule ho_cong :premises (@p240 @p47)) % 0.37/0.65 (step @p242 :rule trans :premises (@p241 @p176)) % 0.37/0.65 (step @p243 :rule cong :premises (@p242) :args ((lambda @t23 (_ (_ @t95 @t180) @t6)))) % 0.37/0.65 (step @p244 :rule ho_cong :premises (@p120 @p243)) % 0.37/0.65 (step @p245 :rule trans :premises (@p244 @p175)) % 0.37/0.65 (step @p246 :rule ho_cong :premises (@p133 @p245)) % 0.37/0.65 (step @p247 :rule trans :premises (@p246 @p164)) % 0.37/0.65 (step @p248 :rule ho_cong :premises (@p25 @p136)) % 0.37/0.65 (step @p249 :rule ho_cong :premises (@p248 @p107)) % 0.37/0.65 (step @p250 :rule ho_cong :premises (@p249 @p47)) % 0.37/0.65 (step @p251 :rule cong :premises (@p250) :args (@t46)) % 0.37/0.65 (step @p252 :rule ho_cong :premises (@p151 @p251)) % 0.37/0.65 (step @p253 :rule refl :args (@t44)) % 0.37/0.65 (step @p254 :rule ho_cong :premises (@p25 @p253)) % 0.37/0.65 (step @p255 :rule ho_cong :premises (@p254 @p252)) % 0.37/0.65 (step @p256 :rule ho_cong :premises (@p255 @p47)) % 0.37/0.65 (step @p257 :rule cong :premises (@p256) :args (@t47)) % 0.37/0.65 (step @p258 :rule ho_cong :premises (@p151 @p257)) % 0.37/0.65 (step @p259 :rule ho_cong :premises (@p258 @p47)) % 0.37/0.65 (step @p260 :rule cong :premises (@p259) :args (@t48)) % 0.37/0.65 (step @p261 :rule ho_cong :premises (@p151 @p260)) % 0.37/0.65 (step @p262 :rule ho_cong :premises (@p20 @p261)) % 0.37/0.65 (step @p263 :rule trans :premises (@p262 @p247)) % 0.37/0.65 (step @p264 :rule eq_resolve :premises (@p17 @p263)) % 0.37/0.65 (step @p265 :rule instantiate :premises (@p264) :args ((@list @t184 @t183))) % 0.37/0.65 (step @p266 :rule beta-reduce :args ((= @t187 @t182))) % 0.37/0.65 (step @p267 :rule beta-reduce :args ((= (_ @t52 @t186) @t187))) % 0.37/0.65 (step @p268 :rule trans :premises (@p267 @p266)) % 0.37/0.65 (step @p269 :rule refl :args ((tptp.qmltpeq @t188 @t7 @t2))) % 0.37/0.65 (step @p270 :rule refl :args (@t181)) % 0.37/0.65 (step @p271 :rule cong :premises (@p270 @p36 @p35) :args (@t185)) % 0.37/0.65 (step @p272 :rule trans :premises (@p271 @p269)) % 0.37/0.65 (step @p273 :rule refl :args (tptp.qmltpeq)) % 0.37/0.65 (step @p274 :rule ho_cong :premises (@p273 @p270)) % 0.37/0.65 (step @p275 :rule ho_cong :premises (@p274 @p36)) % 0.37/0.65 (step @p276 :rule ho_cong :premises (@p275 @p35)) % 0.37/0.65 (step @p277 :rule cong :premises (@p276 @p272) :args ((= (_ (_ (_ tptp.qmltpeq @t181) @t7) @t2) @t185))) % 0.37/0.65 (step @p278 :rule symm :premises (@p277)) % 0.37/0.65 (step @p279 :rule refl :args (@t189)) % 0.37/0.65 (step @p280 :rule eq_resolve :premises (@p279 @p278)) % 0.37/0.65 (step @p281 :rule refl :args (@t188)) % 0.37/0.65 (step @p282 :rule cong :premises (@p281 @p270) :args ((= @t188 @t181))) % 0.37/0.65 (step @p283 :rule symm :premises (@p282)) % 0.37/0.65 (step @p284 :rule eq_resolve :premises (@p281 @p283)) % 0.37/0.65 (step @p285 :rule ho_cong :premises (@p273 @p284)) % 0.37/0.65 (step @p286 :rule ho_cong :premises (@p285 @p36)) % 0.37/0.65 (step @p287 :rule ho_cong :premises (@p286 @p35)) % 0.37/0.65 (step @p288 :rule trans :premises (@p287 @p280)) % 0.37/0.65 (step @p289 :rule cong :premises (@p288) :args ((forall @t69 @t189))) % 0.37/0.65 (step @p290 :rule beta-reduce :args ((= @t190 @t189))) % 0.37/0.65 (step @p291 :rule cong :premises (@p290) :args (@t191)) % 0.37/0.65 (step @p292 :rule trans :premises (@p291 @p289)) % 0.37/0.65 (step @p293 :rule cong :premises (@p292) :args (@t192)) % 0.37/0.65 (step @p294 :rule beta-reduce :args ((= @t193 @t192))) % 0.37/0.65 (step @p295 :rule trans :premises (@p294 @p293)) % 0.37/0.65 (step @p296 :rule ho_cong :premises (@p133 @p295)) % 0.37/0.65 (step @p297 :rule trans :premises (@p296 @p268)) % 0.37/0.65 (step @p298 :rule cong :premises (@p297) :args ((not (_ @t52 @t193)))) % 0.37/0.65 (step @p299 :rule refl :args (@t49)) % 0.37/0.65 (step @p300 :rule ho_cong :premises (@p151 @p299)) % 0.37/0.65 (step @p301 :rule ho_cong :premises (@p20 @p300)) % 0.37/0.65 (step @p302 :rule cong :premises (@p301) :args (@t50)) % 0.37/0.65 (step @p303 :rule trans :premises (@p302 @p298)) % 0.37/0.65 (step @p304 :rule eq_resolve :premises (@p18 @p303)) % 0.37/0.65 (step @p305 :rule skolemize :premises (@p304)) % 0.37/0.65 (step @p306 :rule cnf_equiv_pos2 :args (@t196)) % 0.37/0.65 (step @p307 :rule reordering :premises (@p306) :args ((or @t195 @t197 (not @t196)))) % 0.37/0.65 (step @p308 :rule chain_m_resolution :premises (@p307 @p305 @p265) :args (@t197 @t198 (@list @t195 @t196))) % 0.37/0.65 (step @p309 :rule skolemize :premises (@p308)) % 0.37/0.65 (step @p310 :rule aci_norm :args ((= @t201 @t200))) % 0.37/0.65 (step @p311 :rule refl :args (@t202)) % 0.37/0.65 (step @p312 :rule cong :premises (@p311 @p310) :args (@t203)) % 0.37/0.65 (step @p313 :rule refl :args (@t78)) % 0.37/0.65 (step @p314 :rule cong :premises (@p313 @p312) :args ((=> @t78 @t203))) % 0.37/0.65 (assume-push @p322 @t78) % 0.37/0.65 (step @p316 :rule instantiate :premises (@p161) :args ((@list @t183 @t183 @t199))) % 0.37/0.65 (step-pop @p323 :rule scope :premises (@p316)) % 0.37/0.65 (step @p317 :rule process_scope :premises (@p323) :args (@t203)) % 0.37/0.65 (step @p319 :rule eq_resolve :premises (@p317 @p314)) % 0.37/0.65 (step @p320 :rule implies_elim :premises (@p319)) % 0.37/0.65 (step @p321 false :rule chain_m_resolution :premises (@p320 @p309 @p161) :args (false @t198 (@list (= @t202 @t200) @t78))) % 0.37/0.65 ) % 0.37/0.65 % SZS output end Proof % 0.37/0.65 % cvc5 exiting %------------------------------------------------------------------------------