%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL586^1 : TPTP v9.3.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n020.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 11:23:07 AM UTC 2026 % Result : Theorem 0.19s 0.53s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL586^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.05 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.11/0.37 % Computer : n020.cluster.edu % 0.11/0.37 % Model : x86_64 x86_64 % 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.37 % Memory : 8046.5625MB % 0.11/0.37 % OS : Linux 6.8.0-71-generic % 0.11/0.37 % CPULimit : 300 % 0.11/0.37 % WCLimit : 300 % 0.11/0.37 % DateTime : Sat Sep 5 04:45:42 UTC 2026 % 0.11/0.37 % CPUTime : % 0.11/0.44 %----Proving TH0 % 0.19/0.53 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.19/0.53 % SZS status Theorem % 0.19/0.53 % SZS output start Proof % 0.19/0.53 ( % 0.19/0.53 (declare-sort $$unsorted 0) % 0.19/0.53 (declare-sort tptp.individuals 0) % 0.19/0.53 (declare-const tptp.r (-> $$unsorted $$unsorted Bool)) % 0.19/0.53 (declare-const tptp.a (-> $$unsorted Bool)) % 0.19/0.53 (declare-const tptp.b (-> $$unsorted Bool)) % 0.19/0.53 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.19/0.53 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.19/0.53 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.19/0.53 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.19/0.53 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.19/0.53 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.19/0.53 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.19/0.53 (define tptp.mbox () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.19/0.53 (define tptp.mdia () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.19/0.53 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.19/0.53 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.19/0.53 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.19/0.53 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.19/0.53 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.19/0.53 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.19/0.53 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mimpl (_ tptp.mnot (_ (_ tptp.mdia tptp.r) tptp.a))) (_ (_ tptp.mbox tptp.r) (_ (_ tptp.mimpl tptp.a) tptp.b)))))) % 0.19/0.53 (define @t2 () (@var "X" $$unsorted)) % 0.19/0.53 (define @t3 () (@list @t2)) % 0.19/0.53 (define @t4 () (lambda @t3 false)) % 0.19/0.53 (define @t5 () (lambda @t3 true)) % 0.19/0.53 (define @t6 () (@var "U" $$unsorted)) % 0.19/0.53 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.19/0.53 (define @t8 () (_ @t7 @t6)) % 0.19/0.53 (define @t9 () (lambda (@list @t7 @t6) (not @t8))) % 0.19/0.53 (define @t10 () (@var "Y" (-> $$unsorted Bool))) % 0.19/0.53 (define @t11 () (_ @t10 @t6)) % 0.19/0.53 (define @t12 () (@list @t7 @t10 @t6)) % 0.19/0.53 (define @t13 () (lambda @t12 (or @t8 @t11))) % 0.19/0.53 (define @t14 () (lambda @t12 (and @t8 @t11))) % 0.19/0.53 (define @t15 () (@var "__flatten_var_0" $$unsorted)) % 0.19/0.53 (define @t16 () (@var "V" (-> $$unsorted Bool))) % 0.19/0.53 (define @t17 () (@var "U" (-> $$unsorted Bool))) % 0.19/0.53 (define @t18 () (@list @t17 @t16 @t15)) % 0.19/0.53 (define @t19 () (lambda @t18 (_ (_ (_ tptp.mor (_ tptp.mnot @t17)) @t16) @t15))) % 0.19/0.53 (define @t20 () (lambda @t18 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t17) @t16)) (_ (_ tptp.mimpl @t16) @t17)) @t15))) % 0.19/0.53 (define @t21 () (@var "Y" $$unsorted)) % 0.19/0.53 (define @t22 () (@var "P" (-> $$unsorted Bool))) % 0.19/0.53 (define @t23 () (_ @t22 @t21)) % 0.19/0.53 (define @t24 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.19/0.53 (define @t25 () (_ (_ @t24 @t2) @t21)) % 0.19/0.53 (define @t26 () (@list @t21)) % 0.19/0.53 (define @t27 () (forall @t26 (=> @t25 @t23))) % 0.19/0.53 (define @t28 () (@list @t24 @t22 @t2)) % 0.19/0.53 (define @t29 () (lambda @t28 @t27)) % 0.19/0.53 (define @t30 () (and @t25 @t23)) % 0.19/0.53 (define @t31 () (exists @t26 @t30)) % 0.19/0.53 (define @t32 () (lambda @t28 @t31)) % 0.19/0.53 (define @t33 () (@var "W" $$unsorted)) % 0.19/0.53 (define @t34 () (@var "X" tptp.individuals)) % 0.19/0.53 (define @t35 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.19/0.53 (define @t36 () (_ (_ @t35 @t34) @t33)) % 0.19/0.53 (define @t37 () (@list @t34)) % 0.19/0.53 (define @t38 () (@list @t35 @t33)) % 0.19/0.53 (define @t39 () (lambda @t38 (forall @t37 @t36))) % 0.19/0.53 (define @t40 () (lambda @t38 (exists @t37 @t36))) % 0.19/0.53 (define @t41 () (_ @t22 @t33)) % 0.19/0.53 (define @t42 () (@list @t33)) % 0.19/0.53 (define @t43 () (forall @t42 @t41)) % 0.19/0.53 (define @t44 () (@list @t22)) % 0.19/0.53 (define @t45 () (lambda @t44 @t43)) % 0.19/0.53 (define @t46 () (lambda @t44 (exists @t42 @t41))) % 0.19/0.53 (define @t47 () (not @t41)) % 0.19/0.53 (define @t48 () (lambda @t44 (exists @t42 @t47))) % 0.19/0.53 (define @t49 () (lambda @t44 (forall @t42 @t47))) % 0.19/0.53 (define @t50 () (@var "BOUND_VARIABLE_7865" $$unsorted)) % 0.19/0.53 (define @t51 () (tptp.b @t50)) % 0.19/0.53 (define @t52 () (not (tptp.a @t50))) % 0.19/0.53 (define @t53 () (not (tptp.r @t33 @t50))) % 0.19/0.53 (define @t54 () (tptp.a @t21)) % 0.19/0.53 (define @t55 () (not @t54)) % 0.19/0.53 (define @t56 () (not (tptp.r @t33 @t21))) % 0.19/0.53 (define @t57 () (not (forall @t26 (or @t56 @t55)))) % 0.19/0.53 (define @t58 () (or @t57 @t53 @t52 @t51)) % 0.19/0.53 (define @t59 () (or @t53 @t52 @t51)) % 0.19/0.53 (define @t60 () (or @t57 @t59)) % 0.19/0.53 (define @t61 () (@list @t33 @t50)) % 0.19/0.53 (define @t62 () (forall @t61 @t60)) % 0.19/0.53 (define @t63 () (@list @t50)) % 0.19/0.53 (define @t64 () (forall @t63 @t60)) % 0.19/0.53 (define @t65 () (forall @t63 @t59)) % 0.19/0.53 (define @t66 () (or @t57 @t65)) % 0.19/0.53 (define @t67 () (tptp.b @t21)) % 0.19/0.53 (define @t68 () (or @t57 (forall @t26 (or @t56 @t55 @t67)))) % 0.19/0.53 (define @t69 () (not (tptp.r @t15 @t21))) % 0.19/0.53 (define @t70 () (forall @t26 (or @t69 @t55 @t67))) % 0.19/0.53 (define @t71 () (forall @t26 (or @t69 @t55))) % 0.19/0.53 (define @t72 () (not @t71)) % 0.19/0.53 (define @t73 () (@list @t15)) % 0.19/0.53 (define @t74 () (lambda @t73 (or @t72 @t70))) % 0.19/0.53 (define @t75 () (_ @t74 @t33)) % 0.19/0.53 (define @t76 () (forall @t42 @t75)) % 0.19/0.53 (define @t77 () (_ @t22 @t33)) % 0.19/0.53 (define @t78 () (lambda @t44 (forall @t42 @t77))) % 0.19/0.53 (define @t79 () (not (tptp.r @t2 @t21))) % 0.19/0.53 (define @t80 () (lambda @t3 (forall @t26 (or @t79 @t55 @t67)))) % 0.19/0.53 (define @t81 () (_ @t80 @t15)) % 0.19/0.53 (define @t82 () (or @t72 @t81)) % 0.19/0.53 (define @t83 () (lambda @t73 @t82)) % 0.19/0.53 (define @t84 () (_ @t16 @t15)) % 0.19/0.53 (define @t85 () (@list @t16 @t15)) % 0.19/0.53 (define @t86 () (_ tptp.b @t21)) % 0.19/0.53 (define @t87 () (_ tptp.a @t21)) % 0.19/0.53 (define @t88 () (not @t87)) % 0.19/0.53 (define @t89 () (or @t79 @t88 @t86)) % 0.19/0.53 (define @t90 () (or @t88 @t86)) % 0.19/0.53 (define @t91 () (not (_ tptp.a @t15))) % 0.19/0.53 (define @t92 () (lambda @t73 (or @t91 (_ tptp.b @t15)))) % 0.19/0.53 (define @t93 () (_ @t92 @t21)) % 0.19/0.53 (define @t94 () (or @t79 @t93)) % 0.19/0.53 (define @t95 () (forall @t26 @t94)) % 0.19/0.53 (define @t96 () (lambda @t3 @t95)) % 0.19/0.53 (define @t97 () (_ @t22 @t21)) % 0.19/0.53 (define @t98 () (@list @t22 @t2)) % 0.19/0.53 (define @t99 () (lambda @t98 (forall @t26 (or @t79 @t97)))) % 0.19/0.53 (define @t100 () (lambda @t85 (or @t91 @t84))) % 0.19/0.53 (define @t101 () (or (not (_ @t17 @t15)) @t84)) % 0.19/0.53 (define @t102 () (lambda @t18 @t101)) % 0.19/0.53 (define @t103 () (_ @t102 tptp.a)) % 0.19/0.53 (define @t104 () (_ @t24 @t2 @t21)) % 0.19/0.53 (define @t105 () (not @t104)) % 0.19/0.53 (define @t106 () (_ (lambda @t28 (forall @t26 (or @t105 @t97))) tptp.r)) % 0.19/0.53 (define @t107 () (forall @t26 (or (not (tptp.r @t6 @t21)) @t55))) % 0.19/0.53 (define @t108 () (@list @t6)) % 0.19/0.53 (define @t109 () (lambda @t108 @t107)) % 0.19/0.53 (define @t110 () (_ @t109 @t15)) % 0.19/0.53 (define @t111 () (not @t110)) % 0.19/0.53 (define @t112 () (or @t111 @t84)) % 0.19/0.53 (define @t113 () (lambda @t85 @t112)) % 0.19/0.53 (define @t114 () (lambda @t3 (not (forall @t26 (or @t79 @t55))))) % 0.19/0.53 (define @t115 () (_ @t114 @t6)) % 0.19/0.53 (define @t116 () (not @t115)) % 0.19/0.53 (define @t117 () (lambda @t108 @t116)) % 0.19/0.53 (define @t118 () (not @t97)) % 0.19/0.53 (define @t119 () (lambda @t98 (not (forall @t26 (or @t79 @t118))))) % 0.19/0.53 (define @t120 () (_ (lambda @t28 (not (forall @t26 (or @t105 @t118)))) tptp.r)) % 0.19/0.53 (define @t121 () (not (_ @t17 @t6))) % 0.19/0.53 (define @t122 () (lambda @t108 (or @t121 (_ @t16 @t6)))) % 0.19/0.53 (define @t123 () (@list @t10 @t6)) % 0.19/0.53 (define @t124 () (lambda @t108 @t121)) % 0.19/0.53 (define @t125 () (_ @t124 @t6)) % 0.19/0.53 (define @t126 () (or @t125 @t11)) % 0.19/0.53 (define @t127 () (lambda @t123 @t126)) % 0.19/0.53 (define @t128 () (not @t25)) % 0.19/0.53 (define @t129 () (or @t128 @t23)) % 0.19/0.53 (define @t130 () (not @t23)) % 0.19/0.53 (define @t131 () (or @t128 @t130)) % 0.19/0.53 (define @t132 () (forall @t26 (not @t30))) % 0.19/0.53 (define @t133 () (not @t132)) % 0.19/0.53 (define @t134 () (forall @t61 @t58)) % 0.19/0.53 (define @t135 () (@quantifiers_skolemize @t134 0)) % 0.19/0.53 (define @t136 () (forall @t26 (or (not (tptp.r @t135 @t21)) @t55))) % 0.19/0.53 (define @t137 () (@quantifiers_skolemize @t134 1)) % 0.19/0.53 (define @t138 () (tptp.a @t137)) % 0.19/0.53 (define @t139 () (not @t138)) % 0.19/0.53 (define @t140 () (tptp.r @t135 @t137)) % 0.19/0.53 (define @t141 () (not @t140)) % 0.19/0.53 (define @t142 () (not @t136)) % 0.19/0.53 (define @t143 () (or @t142 @t141 @t139 (tptp.b @t137))) % 0.19/0.53 (define @t144 () (@list true)) % 0.19/0.53 (define @t145 () (@list @t143)) % 0.19/0.53 (define @t146 () (or @t141 @t139)) % 0.19/0.53 (define @t147 () (not @t146)) % 0.19/0.53 (assume @p1 @t1) % 0.19/0.53 (assume @p2 true) % 0.19/0.53 (step @p3 (= tptp.mfalse @t4) :rule refl :args (@t4)) % 0.19/0.53 (step @p4 (= tptp.mtrue @t5) :rule refl :args (@t5)) % 0.19/0.53 (step @p5 (= tptp.mnot @t9) :rule refl :args (@t9)) % 0.19/0.53 (step @p6 (= tptp.mor @t13) :rule refl :args (@t13)) % 0.19/0.53 (step @p7 (= tptp.mand @t14) :rule refl :args (@t14)) % 0.19/0.53 (step @p8 (= tptp.mimpl @t19) :rule refl :args (@t19)) % 0.19/0.53 (step @p9 (= tptp.miff @t20) :rule refl :args (@t20)) % 0.19/0.53 (step @p10 (= tptp.mbox @t29) :rule refl :args (@t29)) % 0.19/0.53 (step @p11 (= tptp.mdia @t32) :rule refl :args (@t32)) % 0.19/0.53 (step @p12 (= tptp.mall @t39) :rule refl :args (@t39)) % 0.19/0.53 (step @p13 (= tptp.mexists @t40) :rule refl :args (@t40)) % 0.19/0.53 (step @p14 (= tptp.mvalid @t45) :rule refl :args (@t45)) % 0.19/0.53 (step @p15 (= tptp.msatisfiable @t46) :rule refl :args (@t46)) % 0.19/0.53 (step @p16 (= tptp.mcountersatisfiable @t48) :rule refl :args (@t48)) % 0.19/0.53 (step @p17 (= tptp.minvalid @t49) :rule refl :args (@t49)) % 0.19/0.53 (step @p18 :rule aci_norm :args ((= @t60 @t58))) % 0.19/0.53 (step @p19 :rule cong :premises (@p18) :args (@t62)) % 0.19/0.53 (step @p20 :rule quant-merge-prenex :args ((= (forall @t42 @t64) @t62))) % 0.19/0.53 (step @p21 :rule alpha_equiv :args (@t65 (@list @t50) (@list @t21))) % 0.19/0.53 (step @p22 :rule refl :args (@t57)) % 0.19/0.53 (step @p23 :rule nary_cong :premises (@p22 @p21) :args (@t66)) % 0.19/0.53 (step @p24 :rule quant-miniscope-or :args ((= @t64 @t66))) % 0.19/0.53 (step @p25 :rule trans :premises (@p24 @p23)) % 0.19/0.53 (step @p26 :rule symm :premises (@p25)) % 0.19/0.53 (step @p27 :rule cong :premises (@p26) :args ((forall @t42 @t68))) % 0.19/0.53 (step @p28 :rule trans :premises (@p27 @p20)) % 0.19/0.53 (step @p29 :rule trans :premises (@p28 @p19)) % 0.19/0.53 (step @p30 :rule beta-reduce :args ((= @t75 @t68))) % 0.19/0.53 (step @p31 :rule cong :premises (@p30) :args (@t76)) % 0.19/0.53 (step @p32 :rule trans :premises (@p31 @p29)) % 0.19/0.53 (step @p33 :rule beta-reduce :args ((= (_ @t78 @t74) @t76))) % 0.19/0.53 (step @p34 :rule trans :premises (@p33 @p32)) % 0.19/0.53 (step @p35 :rule beta-reduce :args ((= @t81 @t70))) % 0.19/0.53 (step @p36 :rule refl :args (@t72)) % 0.19/0.53 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t82)) % 0.19/0.53 (step @p38 :rule cong :premises (@p37) :args (@t83)) % 0.19/0.53 (step @p39 :rule beta-reduce :args ((= (_ (lambda @t85 (or @t72 @t84)) @t80) @t83))) % 0.19/0.53 (step @p40 :rule trans :premises (@p39 @p38)) % 0.19/0.53 (step @p41 :rule refl :args (@t67)) % 0.19/0.53 (step @p42 :rule refl :args (@t86)) % 0.19/0.53 (step @p43 :rule cong :premises (@p42 @p41) :args ((= @t86 @t67))) % 0.19/0.53 (step @p44 :rule symm :premises (@p43)) % 0.19/0.53 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 0.19/0.53 (step @p46 :rule refl :args (@t54)) % 0.19/0.53 (step @p47 :rule refl :args (@t87)) % 0.19/0.53 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t87 @t54))) % 0.19/0.53 (step @p49 :rule symm :premises (@p48)) % 0.19/0.53 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 0.19/0.53 (step @p51 :rule cong :premises (@p50) :args (@t88)) % 0.19/0.53 (step @p52 :rule refl :args (@t79)) % 0.19/0.53 (step @p53 :rule nary_cong :premises (@p52 @p51 @p45) :args (@t89)) % 0.19/0.53 (step @p54 :rule cong :premises (@p53) :args ((forall @t26 @t89))) % 0.19/0.53 (step @p55 :rule aci_norm :args ((= (or @t79 @t90) @t89))) % 0.19/0.53 (step @p56 :rule beta-reduce :args ((= @t93 @t90))) % 0.19/0.53 (step @p57 :rule refl :args (@t79)) % 0.19/0.53 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t94)) % 0.19/0.53 (step @p59 :rule trans :premises (@p58 @p55)) % 0.19/0.53 (step @p60 :rule cong :premises (@p59) :args (@t95)) % 0.19/0.53 (step @p61 :rule trans :premises (@p60 @p54)) % 0.19/0.53 (step @p62 :rule cong :premises (@p61) :args (@t96)) % 0.19/0.53 (step @p63 :rule beta-reduce :args ((= (_ @t99 @t92) @t96))) % 0.19/0.53 (step @p64 :rule trans :premises (@p63 @p62)) % 0.19/0.53 (step @p65 :rule beta-reduce :args ((= (_ @t100 tptp.b) @t92))) % 0.19/0.53 (step @p66 :rule refl :args (tptp.b)) % 0.19/0.53 (step @p67 :rule beta-reduce :args ((= @t103 @t100))) % 0.19/0.53 (step @p68 :rule ho_cong :premises (@p67 @p66)) % 0.19/0.53 (step @p69 :rule trans :premises (@p68 @p65)) % 0.19/0.53 (step @p70 :rule beta-reduce :args ((= @t106 @t99))) % 0.19/0.53 (step @p71 :rule ho_cong :premises (@p70 @p69)) % 0.19/0.53 (step @p72 :rule trans :premises (@p71 @p64)) % 0.19/0.53 (step @p73 :rule refl :args (@t84)) % 0.19/0.53 (step @p74 :rule beta-reduce :args ((= @t110 @t71))) % 0.19/0.53 (step @p75 :rule cong :premises (@p74) :args (@t111)) % 0.19/0.53 (step @p76 :rule nary_cong :premises (@p75 @p73) :args (@t112)) % 0.19/0.53 (step @p77 :rule cong :premises (@p76) :args (@t113)) % 0.19/0.53 (step @p78 :rule beta-reduce :args ((= (_ @t102 @t109) @t113))) % 0.19/0.53 (step @p79 :rule trans :premises (@p78 @p77)) % 0.19/0.53 (step @p80 :rule bool-double-not-elim :args (@t107)) % 0.19/0.53 (step @p81 :rule beta-reduce :args ((= @t115 (not @t107)))) % 0.19/0.53 (step @p82 :rule cong :premises (@p81) :args (@t116)) % 0.19/0.53 (step @p83 :rule trans :premises (@p82 @p80)) % 0.19/0.53 (step @p84 :rule cong :premises (@p83) :args (@t117)) % 0.19/0.53 (step @p85 :rule beta-reduce :args ((= (_ @t9 @t114) @t117))) % 0.19/0.53 (step @p86 :rule trans :premises (@p85 @p84)) % 0.19/0.53 (step @p87 :rule beta-reduce :args ((= (_ @t119 tptp.a) @t114))) % 0.19/0.53 (step @p88 :rule refl :args (tptp.a)) % 0.19/0.53 (step @p89 :rule beta-reduce :args ((= @t120 @t119))) % 0.19/0.53 (step @p90 :rule ho_cong :premises (@p89 @p88)) % 0.19/0.53 (step @p91 :rule trans :premises (@p90 @p87)) % 0.19/0.53 (step @p92 :rule refl :args (@t9)) % 0.19/0.53 (step @p93 :rule ho_cong :premises (@p92 @p91)) % 0.19/0.53 (step @p94 :rule trans :premises (@p93 @p86)) % 0.19/0.53 (step @p95 :rule refl :args (@t102)) % 0.19/0.53 (step @p96 :rule ho_cong :premises (@p95 @p94)) % 0.19/0.53 (step @p97 :rule trans :premises (@p96 @p79)) % 0.19/0.53 (step @p98 :rule ho_cong :premises (@p97 @p72)) % 0.19/0.53 (step @p99 :rule trans :premises (@p98 @p40)) % 0.19/0.53 (step @p100 :rule refl :args (@t78)) % 0.19/0.53 (step @p101 :rule ho_cong :premises (@p100 @p99)) % 0.19/0.53 (step @p102 :rule trans :premises (@p101 @p34)) % 0.19/0.53 (step @p103 :rule cong :premises (@p102) :args ((not (_ @t78 (_ (_ @t102 (_ @t9 (_ @t120 tptp.a))) (_ @t106 (_ @t103 tptp.b))))))) % 0.19/0.53 (step @p104 :rule beta-reduce :args ((= (_ @t122 @t15) @t101))) % 0.19/0.53 (step @p105 :rule refl :args (@t15)) % 0.19/0.53 (step @p106 :rule beta-reduce :args ((= (_ (lambda @t123 (or @t121 @t11)) @t16) @t122))) % 0.19/0.53 (step @p107 :rule refl :args (@t16)) % 0.19/0.53 (step @p108 :rule refl :args (@t11)) % 0.19/0.53 (step @p109 :rule beta-reduce :args ((= @t125 @t121))) % 0.19/0.53 (step @p110 :rule nary_cong :premises (@p109 @p108) :args (@t126)) % 0.19/0.53 (step @p111 :rule cong :premises (@p110) :args (@t127)) % 0.19/0.53 (step @p112 :rule beta-reduce :args ((= (_ @t13 @t124) @t127))) % 0.19/0.53 (step @p113 :rule trans :premises (@p112 @p111)) % 0.19/0.53 (step @p114 :rule beta-reduce :args ((= (_ @t9 @t17) @t124))) % 0.19/0.53 (step @p115 :rule refl :args (@t13)) % 0.19/0.53 (step @p116 :rule ho_cong :premises (@p115 @p114)) % 0.19/0.53 (step @p117 :rule trans :premises (@p116 @p113)) % 0.19/0.53 (step @p118 :rule ho_cong :premises (@p117 @p107)) % 0.19/0.53 (step @p119 :rule trans :premises (@p118 @p106)) % 0.19/0.53 (step @p120 :rule ho_cong :premises (@p119 @p105)) % 0.19/0.53 (step @p121 :rule trans :premises (@p120 @p104)) % 0.19/0.53 (step @p122 :rule refl :args (@t17)) % 0.19/0.53 (step @p123 :rule ho_cong :premises (@p5 @p122)) % 0.19/0.53 (step @p124 :rule ho_cong :premises (@p6 @p123)) % 0.19/0.53 (step @p125 :rule ho_cong :premises (@p124 @p107)) % 0.19/0.53 (step @p126 :rule ho_cong :premises (@p125 @p105)) % 0.19/0.53 (step @p127 :rule trans :premises (@p126 @p121)) % 0.19/0.53 (step @p128 :rule cong :premises (@p127) :args (@t19)) % 0.19/0.53 (step @p129 :rule trans :premises (@p8 @p128)) % 0.19/0.53 (step @p130 :rule ho_cong :premises (@p129 @p88)) % 0.19/0.53 (step @p131 :rule ho_cong :premises (@p130 @p66)) % 0.19/0.53 (step @p132 :rule refl :args (tptp.r)) % 0.19/0.53 (step @p133 :rule refl :args (@t97)) % 0.19/0.53 (step @p134 :rule refl :args (@t23)) % 0.19/0.53 (step @p135 :rule cong :premises (@p134 @p133) :args ((= @t23 @t97))) % 0.19/0.53 (step @p136 :rule symm :premises (@p135)) % 0.19/0.53 (step @p137 :rule eq_resolve :premises (@p134 @p136)) % 0.19/0.53 (step @p138 :rule refl :args (@t104)) % 0.19/0.53 (step @p139 :rule refl :args (@t25)) % 0.19/0.53 (step @p140 :rule cong :premises (@p139 @p138) :args ((= @t25 @t104))) % 0.19/0.53 (step @p141 :rule symm :premises (@p140)) % 0.19/0.53 (step @p142 :rule eq_resolve :premises (@p139 @p141)) % 0.19/0.53 (step @p143 :rule cong :premises (@p142) :args (@t128)) % 0.19/0.53 (step @p144 :rule nary_cong :premises (@p143 @p137) :args (@t129)) % 0.19/0.53 (step @p145 :rule cong :premises (@p144) :args ((forall @t26 @t129))) % 0.19/0.53 (step @p146 :rule bool-impl-elim :args (@t25 @t23)) % 0.19/0.53 (step @p147 :rule cong :premises (@p146) :args (@t27)) % 0.19/0.53 (step @p148 :rule trans :premises (@p147 @p145)) % 0.19/0.53 (step @p149 :rule cong :premises (@p148) :args (@t29)) % 0.19/0.53 (step @p150 :rule trans :premises (@p10 @p149)) % 0.19/0.53 (step @p151 :rule ho_cong :premises (@p150 @p132)) % 0.19/0.53 (step @p152 :rule ho_cong :premises (@p151 @p131)) % 0.19/0.53 (step @p153 :rule cong :premises (@p137) :args (@t130)) % 0.19/0.53 (step @p154 :rule nary_cong :premises (@p143 @p153) :args (@t131)) % 0.19/0.53 (step @p155 :rule cong :premises (@p154) :args ((forall @t26 @t131))) % 0.19/0.53 (step @p156 :rule bool-and-de-morgan :args (@t25 @t23 true)) % 0.19/0.53 (step @p157 :rule cong :premises (@p156) :args (@t132)) % 0.19/0.53 (step @p158 :rule trans :premises (@p157 @p155)) % 0.19/0.53 (step @p159 :rule cong :premises (@p158) :args (@t133)) % 0.19/0.53 (step @p160 :rule exists-elim :args ((= @t31 @t133))) % 0.19/0.53 (step @p161 :rule trans :premises (@p160 @p159)) % 0.19/0.53 (step @p162 :rule cong :premises (@p161) :args (@t32)) % 0.19/0.53 (step @p163 :rule trans :premises (@p11 @p162)) % 0.19/0.53 (step @p164 :rule ho_cong :premises (@p163 @p132)) % 0.19/0.53 (step @p165 :rule ho_cong :premises (@p164 @p88)) % 0.19/0.53 (step @p166 :rule ho_cong :premises (@p5 @p165)) % 0.19/0.53 (step @p167 :rule ho_cong :premises (@p129 @p166)) % 0.19/0.53 (step @p168 :rule ho_cong :premises (@p167 @p152)) % 0.19/0.53 (step @p169 :rule refl :args (@t77)) % 0.19/0.53 (step @p170 :rule refl :args (@t41)) % 0.19/0.53 (step @p171 :rule cong :premises (@p170 @p169) :args ((= @t41 @t77))) % 0.19/0.53 (step @p172 :rule symm :premises (@p171)) % 0.19/0.53 (step @p173 :rule eq_resolve :premises (@p170 @p172)) % 0.19/0.53 (step @p174 :rule cong :premises (@p173) :args (@t43)) % 0.19/0.53 (step @p175 :rule cong :premises (@p174) :args (@t45)) % 0.19/0.53 (step @p176 :rule trans :premises (@p14 @p175)) % 0.19/0.53 (step @p177 :rule ho_cong :premises (@p176 @p168)) % 0.19/0.53 (step @p178 :rule cong :premises (@p177) :args (@t1)) % 0.19/0.53 (step @p179 :rule trans :premises (@p178 @p103)) % 0.19/0.53 (step @p180 :rule eq_resolve :premises (@p1 @p179)) % 0.19/0.53 (step @p181 :rule skolemize :premises (@p180)) % 0.19/0.53 (step @p182 :rule bool-double-not-elim :args (@t136)) % 0.19/0.53 (step @p183 :rule refl :args (@t143)) % 0.19/0.53 (step @p184 :rule nary_cong :premises (@p183 @p182) :args ((or @t143 (not @t142)))) % 0.19/0.53 (step @p185 :rule cnf_or_neg :args (@t143 0)) % 0.19/0.53 (step @p186 :rule eq_resolve :premises (@p185 @p184)) % 0.19/0.53 (step @p187 :rule reordering :premises (@p186) :args ((or @t136 @t143))) % 0.19/0.53 (step @p188 :rule chain_m_resolution :premises (@p187 @p181) :args (@t136 @t144 @t145)) % 0.19/0.53 (step @p189 :rule bool-double-not-elim :args (@t138)) % 0.19/0.53 (step @p190 :rule nary_cong :premises (@p183 @p189) :args ((or @t143 (not @t139)))) % 0.19/0.53 (step @p191 :rule cnf_or_neg :args (@t143 2)) % 0.19/0.53 (step @p192 :rule eq_resolve :premises (@p191 @p190)) % 0.19/0.53 (step @p193 :rule reordering :premises (@p192) :args ((or @t138 @t143))) % 0.19/0.53 (step @p194 :rule chain_m_resolution :premises (@p193 @p181) :args (@t138 @t144 @t145)) % 0.19/0.53 (step @p195 :rule bool-double-not-elim :args (@t140)) % 0.19/0.53 (step @p196 :rule nary_cong :premises (@p183 @p195) :args ((or @t143 (not @t141)))) % 0.19/0.53 (step @p197 :rule cnf_or_neg :args (@t143 1)) % 0.19/0.53 (step @p198 :rule eq_resolve :premises (@p197 @p196)) % 0.19/0.53 (step @p199 :rule reordering :premises (@p198) :args ((or @t140 @t143))) % 0.19/0.53 (step @p200 :rule chain_m_resolution :premises (@p199 @p181) :args (@t140 @t144 @t145)) % 0.19/0.53 (step @p201 :rule cnf_or_pos :args (@t146)) % 0.19/0.53 (step @p202 :rule reordering :premises (@p201) :args ((or @t141 @t139 @t147))) % 0.19/0.53 (step @p203 :rule chain_m_resolution :premises (@p202 @p200 @p194) :args (@t147 (@list false false) (@list @t140 @t138))) % 0.19/0.53 (assume-push @p210 @t136) % 0.19/0.53 (step @p205 :rule instantiate :premises (@p188) :args ((@list @t137))) % 0.19/0.53 (step-pop @p211 :rule scope :premises (@p205)) % 0.19/0.53 (step @p206 :rule process_scope :premises (@p211) :args (@t146)) % 0.19/0.53 (step @p208 :rule implies_elim :premises (@p206)) % 0.19/0.53 (step @p209 false :rule chain_m_resolution :premises (@p208 @p203 @p188) :args (false (@list true false) (@list @t146 @t136))) % 0.19/0.53 ) % 0.19/0.53 % SZS output end Proof % 0.19/0.54 % cvc5 exiting %------------------------------------------------------------------------------