%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO892^15 : 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 : n005.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 09:13:43 AM UTC 2026 % Result : Theorem 0.39s 0.59s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO892^15 : TPTP v9.2.1. Released v8.1.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n005.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Wed Jun 3 01:08:48 EDT 2026 % 0.16/0.35 % CPUTime : % 0.32/0.51 %----Proving TH0 % 0.39/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.59 % SZS status Theorem % 0.39/0.59 % SZS output start Proof % 0.39/0.59 ( % 0.39/0.59 (declare-sort $$unsorted 0) % 0.39/0.59 (declare-sort tptp.mworld 0) % 0.39/0.59 (declare-const tptp.mactual tptp.mworld) % 0.39/0.59 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.39/0.59 (declare-const tptp.eiw_di (-> $$unsorted tptp.mworld Bool)) % 0.39/0.59 (declare-const tptp.f (-> $$unsorted tptp.mworld Bool)) % 0.39/0.59 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.39/0.59 (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)))))) % 0.39/0.59 (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))))))) % 0.39/0.59 (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))))))) % 0.39/0.59 (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))))))) % 0.39/0.59 (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))))))) % 0.39/0.59 (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)))))))) % 0.39/0.59 (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)))))))) % 0.39/0.59 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.39/0.59 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (and (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.39/0.59 (define @t1 () (@var "V" tptp.mworld)) % 0.39/0.59 (define @t2 () (@var "W" tptp.mworld)) % 0.39/0.59 (define @t3 () (_ (_ tptp.mrel @t2) @t1)) % 0.39/0.59 (define @t4 () (@list @t1)) % 0.39/0.59 (define @t5 () (@list @t2)) % 0.39/0.59 (define @t6 () (@var "X" $$unsorted)) % 0.39/0.59 (define @t7 () (_ tptp.eiw_di @t6)) % 0.39/0.59 (define @t8 () (_ @t7 @t2)) % 0.39/0.59 (define @t9 () (@list @t6)) % 0.39/0.59 (define @t10 () (_ @t7 @t1)) % 0.39/0.59 (define @t11 () (and @t8 @t3)) % 0.39/0.59 (define @t12 () (@list @t2 @t1 @t6)) % 0.39/0.59 (define @t13 () (forall @t12 (=> @t11 @t10))) % 0.39/0.59 (define @t14 () (@var "__flatten_var_0" tptp.mworld)) % 0.39/0.59 (define @t15 () (_ tptp.f @t6)) % 0.39/0.59 (define @t16 () (@list @t6 @t14)) % 0.39/0.59 (define @t17 () (lambda @t16 (_ (_ tptp.mdia @t15) @t14))) % 0.39/0.59 (define @t18 () (lambda @t16 (_ @t15 @t14))) % 0.39/0.59 (define @t19 () (not (_ tptp.mlocal (_ (_ tptp.mimplies (_ tptp.mdia (_ tptp.mforall_di @t18))) (_ tptp.mforall_di @t17))))) % 0.39/0.59 (define @t20 () (@var "Phi" (-> tptp.mworld Bool))) % 0.39/0.59 (define @t21 () (lambda (@list @t20) (_ @t20 tptp.mactual))) % 0.39/0.59 (define @t22 () (@var "A" (-> tptp.mworld Bool))) % 0.39/0.59 (define @t23 () (_ @t22 @t2)) % 0.39/0.59 (define @t24 () (lambda (@list @t22 @t2) (not @t23))) % 0.39/0.59 (define @t25 () (@var "B" (-> tptp.mworld Bool))) % 0.39/0.59 (define @t26 () (_ @t25 @t2)) % 0.39/0.59 (define @t27 () (@list @t22 @t25 @t2)) % 0.39/0.59 (define @t28 () (lambda @t27 (and @t23 @t26))) % 0.39/0.59 (define @t29 () (lambda @t27 (or @t23 @t26))) % 0.39/0.59 (define @t30 () (lambda @t27 (=> @t23 @t26))) % 0.39/0.59 (define @t31 () (lambda @t27 (= @t23 @t26))) % 0.39/0.59 (define @t32 () (_ @t20 @t1)) % 0.39/0.59 (define @t33 () (@list @t20 @t2)) % 0.39/0.59 (define @t34 () (lambda @t33 (forall @t4 (=> @t3 @t32)))) % 0.39/0.59 (define @t35 () (and @t3 @t32)) % 0.39/0.59 (define @t36 () (exists @t4 @t35)) % 0.39/0.59 (define @t37 () (lambda @t33 @t36)) % 0.39/0.59 (define @t38 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.39/0.59 (define @t39 () (_ (_ @t38 @t6) @t2)) % 0.39/0.59 (define @t40 () (forall @t9 (=> @t8 @t39))) % 0.39/0.59 (define @t41 () (@list @t38 @t2)) % 0.39/0.59 (define @t42 () (lambda @t41 @t40)) % 0.39/0.59 (define @t43 () (lambda @t41 (exists @t9 (and @t8 @t39)))) % 0.39/0.59 (define @t44 () (tptp.f @t6 @t1)) % 0.39/0.59 (define @t45 () (not @t44)) % 0.39/0.59 (define @t46 () (not (tptp.mrel tptp.mactual @t1))) % 0.39/0.59 (define @t47 () (forall @t9 (or (not (tptp.eiw_di @t6 tptp.mactual)) (not (forall @t4 (or @t46 @t45)))))) % 0.39/0.59 (define @t48 () (tptp.eiw_di @t6 @t1)) % 0.39/0.59 (define @t49 () (forall @t9 (or (not @t48) @t44))) % 0.39/0.59 (define @t50 () (not @t49)) % 0.39/0.59 (define @t51 () (forall @t4 (or @t46 @t50))) % 0.39/0.59 (define @t52 () (tptp.mrel @t2 @t1)) % 0.39/0.59 (define @t53 () (not @t52)) % 0.39/0.59 (define @t54 () (not (forall @t4 (or @t53 @t45)))) % 0.39/0.59 (define @t55 () (tptp.eiw_di @t6 @t2)) % 0.39/0.59 (define @t56 () (not @t55)) % 0.39/0.59 (define @t57 () (forall @t9 (or @t56 @t54))) % 0.39/0.59 (define @t58 () (not (forall @t4 (or @t53 @t50)))) % 0.39/0.59 (define @t59 () (lambda @t5 (=> @t58 @t57))) % 0.39/0.59 (define @t60 () (_ @t59 tptp.mactual)) % 0.39/0.59 (define @t61 () (lambda @t5 @t57)) % 0.39/0.59 (define @t62 () (_ @t61 @t2)) % 0.39/0.59 (define @t63 () (=> @t58 @t62)) % 0.39/0.59 (define @t64 () (lambda @t5 @t63)) % 0.39/0.59 (define @t65 () (@list @t25 @t2)) % 0.39/0.59 (define @t66 () (not (forall @t4 (or (not (tptp.mrel @t14 @t1)) @t45)))) % 0.39/0.59 (define @t67 () (lambda @t16 @t66)) % 0.39/0.59 (define @t68 () (_ @t67 @t6 @t2)) % 0.39/0.59 (define @t69 () (or @t56 @t68)) % 0.39/0.59 (define @t70 () (forall @t9 @t69)) % 0.39/0.59 (define @t71 () (lambda @t5 @t70)) % 0.39/0.59 (define @t72 () (_ @t38 @t6 @t2)) % 0.39/0.59 (define @t73 () (lambda @t41 (forall @t9 (or @t56 @t72)))) % 0.39/0.59 (define @t74 () (_ @t15 @t1)) % 0.39/0.59 (define @t75 () (not @t74)) % 0.39/0.59 (define @t76 () (or @t53 @t75)) % 0.39/0.59 (define @t77 () (_ @t15 @t1)) % 0.39/0.59 (define @t78 () (not @t77)) % 0.39/0.59 (define @t79 () (or @t53 @t78)) % 0.39/0.59 (define @t80 () (forall @t4 @t79)) % 0.39/0.59 (define @t81 () (not @t80)) % 0.39/0.59 (define @t82 () (lambda @t5 @t81)) % 0.39/0.59 (define @t83 () (_ @t20 @t1)) % 0.39/0.59 (define @t84 () (lambda @t33 (not (forall @t4 (or @t53 (not @t83)))))) % 0.39/0.59 (define @t85 () (_ @t84 @t15)) % 0.39/0.59 (define @t86 () (lambda @t16 (_ @t85 @t14))) % 0.39/0.59 (define @t87 () (lambda @t5 @t58)) % 0.39/0.59 (define @t88 () (_ @t87 @t2)) % 0.39/0.59 (define @t89 () (=> @t88 @t26)) % 0.39/0.59 (define @t90 () (lambda @t65 @t89)) % 0.39/0.59 (define @t91 () (tptp.f @t6 @t2)) % 0.39/0.59 (define @t92 () (lambda @t5 (forall @t9 (or @t56 @t91)))) % 0.39/0.59 (define @t93 () (_ @t92 @t1)) % 0.39/0.59 (define @t94 () (not @t93)) % 0.39/0.59 (define @t95 () (or @t53 @t94)) % 0.39/0.59 (define @t96 () (forall @t4 @t95)) % 0.39/0.59 (define @t97 () (not @t96)) % 0.39/0.59 (define @t98 () (lambda @t5 @t97)) % 0.39/0.59 (define @t99 () (_ @t15 @t2)) % 0.39/0.59 (define @t100 () (or @t56 @t99)) % 0.39/0.59 (define @t101 () (_ @t18 @t6 @t2)) % 0.39/0.59 (define @t102 () (or @t56 @t101)) % 0.39/0.59 (define @t103 () (forall @t9 @t102)) % 0.39/0.59 (define @t104 () (lambda @t5 @t103)) % 0.39/0.59 (define @t105 () (_ @t73 @t18)) % 0.39/0.59 (define @t106 () (not @t32)) % 0.39/0.59 (define @t107 () (not @t3)) % 0.39/0.59 (define @t108 () (or @t107 @t106)) % 0.39/0.59 (define @t109 () (forall @t4 (not @t35))) % 0.39/0.59 (define @t110 () (not @t109)) % 0.39/0.59 (define @t111 () (not @t8)) % 0.39/0.59 (define @t112 () (or @t111 @t39)) % 0.39/0.59 (define @t113 () (@quantifiers_skolemize @t51 0)) % 0.39/0.59 (define @t114 () (forall @t9 (or (not (tptp.eiw_di @t6 @t113)) (tptp.f @t6 @t113)))) % 0.39/0.59 (define @t115 () (not @t114)) % 0.39/0.59 (define @t116 () (tptp.mrel tptp.mactual @t113)) % 0.39/0.59 (define @t117 () (not @t116)) % 0.39/0.59 (define @t118 () (or @t117 @t115)) % 0.39/0.59 (define @t119 () (@list true)) % 0.39/0.59 (define @t120 () (@list @t118)) % 0.39/0.59 (define @t121 () (or @t111 @t107 @t10)) % 0.39/0.59 (define @t122 () (@quantifiers_skolemize @t47 0)) % 0.39/0.59 (define @t123 () (tptp.eiw_di @t122 tptp.mactual)) % 0.39/0.59 (define @t124 () (forall @t4 (or @t46 (not (tptp.f @t122 @t1))))) % 0.39/0.59 (define @t125 () (not @t124)) % 0.39/0.59 (define @t126 () (not @t123)) % 0.39/0.59 (define @t127 () (or @t126 @t125)) % 0.39/0.59 (define @t128 () (@list @t127)) % 0.39/0.59 (define @t129 () (tptp.eiw_di @t122 @t113)) % 0.39/0.59 (define @t130 () (or @t126 @t117 @t129)) % 0.39/0.59 (define @t131 () (tptp.f @t122 @t113)) % 0.39/0.59 (define @t132 () (not @t131)) % 0.39/0.59 (define @t133 () (or @t117 @t132)) % 0.39/0.59 (define @t134 () (not @t129)) % 0.39/0.59 (define @t135 () (or @t134 @t131)) % 0.39/0.59 (define @t136 () (not @t135)) % 0.39/0.59 (define @t137 () (@list true false)) % 0.39/0.59 (assume @p1 (forall @t5 (exists @t4 @t3))) % 0.39/0.59 (assume @p2 (forall @t5 (exists @t9 @t8))) % 0.39/0.59 (assume @p3 @t13) % 0.39/0.59 (assume @p4 @t19) % 0.39/0.59 (assume @p5 true) % 0.39/0.59 (step @p6 (= tptp.mlocal @t21) :rule refl :args (@t21)) % 0.39/0.59 (step @p7 (= tptp.mnot @t24) :rule refl :args (@t24)) % 0.39/0.59 (step @p8 (= tptp.mand @t28) :rule refl :args (@t28)) % 0.39/0.59 (step @p9 (= tptp.mor @t29) :rule refl :args (@t29)) % 0.39/0.59 (step @p10 (= tptp.mimplies @t30) :rule refl :args (@t30)) % 0.39/0.59 (step @p11 (= tptp.mequiv @t31) :rule refl :args (@t31)) % 0.39/0.59 (step @p12 (= tptp.mbox @t34) :rule refl :args (@t34)) % 0.39/0.59 (step @p13 (= tptp.mdia @t37) :rule refl :args (@t37)) % 0.39/0.59 (step @p14 (= tptp.mforall_di @t42) :rule refl :args (@t42)) % 0.39/0.59 (step @p15 (= tptp.mexists_di @t43) :rule refl :args (@t43)) % 0.39/0.59 (step @p16 :rule beta-reduce :args ((= @t60 (=> (not @t51) @t47)))) % 0.39/0.59 (step @p17 :rule beta-reduce :args ((= (_ @t21 @t59) @t60))) % 0.39/0.59 (step @p18 :rule trans :premises (@p17 @p16)) % 0.39/0.59 (step @p19 :rule beta-reduce :args ((= @t62 @t57))) % 0.39/0.59 (step @p20 :rule refl :args (@t58)) % 0.39/0.59 (step @p21 :rule cong :premises (@p20 @p19) :args (@t63)) % 0.39/0.59 (step @p22 :rule cong :premises (@p21) :args (@t64)) % 0.39/0.59 (step @p23 :rule beta-reduce :args ((= (_ (lambda @t65 (=> @t58 @t26)) @t61) @t64))) % 0.39/0.59 (step @p24 :rule trans :premises (@p23 @p22)) % 0.39/0.59 (step @p25 :rule beta-reduce :args ((= @t68 @t54))) % 0.39/0.59 (step @p26 :rule refl :args (@t56)) % 0.39/0.59 (step @p27 :rule nary_cong :premises (@p26 @p25) :args (@t69)) % 0.39/0.59 (step @p28 :rule cong :premises (@p27) :args (@t70)) % 0.39/0.59 (step @p29 :rule cong :premises (@p28) :args (@t71)) % 0.39/0.59 (step @p30 :rule beta-reduce :args ((= (_ @t73 @t67) @t71))) % 0.39/0.59 (step @p31 :rule trans :premises (@p30 @p29)) % 0.39/0.59 (step @p32 :rule beta-reduce :args ((= (_ (lambda @t5 @t54) @t14) @t66))) % 0.39/0.59 (step @p33 :rule refl :args (@t14)) % 0.39/0.59 (step @p34 :rule refl :args (@t44)) % 0.39/0.59 (step @p35 :rule refl :args (@t74)) % 0.39/0.59 (step @p36 :rule cong :premises (@p35 @p34) :args ((= @t74 @t44))) % 0.39/0.59 (step @p37 :rule symm :premises (@p36)) % 0.39/0.59 (step @p38 :rule eq_resolve :premises (@p35 @p37)) % 0.39/0.59 (step @p39 :rule cong :premises (@p38) :args (@t75)) % 0.39/0.59 (step @p40 :rule refl :args (@t53)) % 0.39/0.59 (step @p41 :rule nary_cong :premises (@p40 @p39) :args (@t76)) % 0.39/0.59 (step @p42 :rule cong :premises (@p41) :args ((forall @t4 @t76))) % 0.39/0.59 (step @p43 :rule refl :args (@t77)) % 0.39/0.59 (step @p44 :rule cong :premises (@p43) :args (@t78)) % 0.39/0.59 (step @p45 :rule refl :args (@t53)) % 0.39/0.59 (step @p46 :rule nary_cong :premises (@p45 @p44) :args (@t79)) % 0.39/0.59 (step @p47 :rule cong :premises (@p46) :args (@t80)) % 0.39/0.59 (step @p48 :rule trans :premises (@p47 @p42)) % 0.39/0.59 (step @p49 :rule cong :premises (@p48) :args (@t81)) % 0.39/0.59 (step @p50 :rule cong :premises (@p49) :args (@t82)) % 0.39/0.59 (step @p51 :rule beta-reduce :args ((= @t85 @t82))) % 0.39/0.59 (step @p52 :rule trans :premises (@p51 @p50)) % 0.39/0.59 (step @p53 :rule ho_cong :premises (@p52 @p33)) % 0.39/0.59 (step @p54 :rule trans :premises (@p53 @p32)) % 0.39/0.59 (step @p55 :rule cong :premises (@p54) :args (@t86)) % 0.39/0.59 (step @p56 :rule refl :args (@t73)) % 0.39/0.59 (step @p57 :rule ho_cong :premises (@p56 @p55)) % 0.39/0.59 (step @p58 :rule trans :premises (@p57 @p31)) % 0.39/0.59 (step @p59 :rule refl :args (@t26)) % 0.39/0.59 (step @p60 :rule beta-reduce :args ((= @t88 @t58))) % 0.39/0.59 (step @p61 :rule cong :premises (@p60 @p59) :args (@t89)) % 0.39/0.59 (step @p62 :rule cong :premises (@p61) :args (@t90)) % 0.39/0.59 (step @p63 :rule beta-reduce :args ((= (_ @t30 @t87) @t90))) % 0.39/0.59 (step @p64 :rule trans :premises (@p63 @p62)) % 0.39/0.59 (step @p65 :rule beta-reduce :args ((= @t93 @t49))) % 0.39/0.59 (step @p66 :rule cong :premises (@p65) :args (@t94)) % 0.39/0.59 (step @p67 :rule nary_cong :premises (@p45 @p66) :args (@t95)) % 0.39/0.59 (step @p68 :rule cong :premises (@p67) :args (@t96)) % 0.39/0.59 (step @p69 :rule cong :premises (@p68) :args (@t97)) % 0.39/0.59 (step @p70 :rule cong :premises (@p69) :args (@t98)) % 0.39/0.59 (step @p71 :rule beta-reduce :args ((= (_ @t84 @t92) @t98))) % 0.39/0.59 (step @p72 :rule trans :premises (@p71 @p70)) % 0.39/0.59 (step @p73 :rule refl :args (@t91)) % 0.39/0.59 (step @p74 :rule refl :args (@t99)) % 0.39/0.59 (step @p75 :rule cong :premises (@p74 @p73) :args ((= @t99 @t91))) % 0.39/0.59 (step @p76 :rule symm :premises (@p75)) % 0.39/0.59 (step @p77 :rule eq_resolve :premises (@p74 @p76)) % 0.39/0.59 (step @p78 :rule refl :args (@t56)) % 0.39/0.59 (step @p79 :rule nary_cong :premises (@p78 @p77) :args (@t100)) % 0.39/0.59 (step @p80 :rule cong :premises (@p79) :args ((forall @t9 @t100))) % 0.39/0.59 (step @p81 :rule beta-reduce :args ((= @t101 @t99))) % 0.39/0.59 (step @p82 :rule nary_cong :premises (@p26 @p81) :args (@t102)) % 0.39/0.59 (step @p83 :rule cong :premises (@p82) :args (@t103)) % 0.39/0.59 (step @p84 :rule trans :premises (@p83 @p80)) % 0.39/0.59 (step @p85 :rule cong :premises (@p84) :args (@t104)) % 0.39/0.59 (step @p86 :rule beta-reduce :args ((= @t105 @t104))) % 0.39/0.59 (step @p87 :rule trans :premises (@p86 @p85)) % 0.39/0.59 (step @p88 :rule refl :args (@t84)) % 0.39/0.59 (step @p89 :rule ho_cong :premises (@p88 @p87)) % 0.39/0.59 (step @p90 :rule trans :premises (@p89 @p72)) % 0.39/0.59 (step @p91 :rule refl :args (@t30)) % 0.39/0.59 (step @p92 :rule ho_cong :premises (@p91 @p90)) % 0.39/0.59 (step @p93 :rule trans :premises (@p92 @p64)) % 0.39/0.59 (step @p94 :rule ho_cong :premises (@p93 @p58)) % 0.39/0.59 (step @p95 :rule trans :premises (@p94 @p24)) % 0.39/0.59 (step @p96 :rule refl :args (@t21)) % 0.39/0.59 (step @p97 :rule ho_cong :premises (@p96 @p95)) % 0.39/0.59 (step @p98 :rule trans :premises (@p97 @p18)) % 0.39/0.59 (step @p99 :rule cong :premises (@p98) :args ((not (_ @t21 (_ (_ @t30 (_ @t84 @t105)) (_ @t73 @t86)))))) % 0.39/0.59 (step @p100 :rule refl :args (@t15)) % 0.39/0.59 (step @p101 :rule refl :args (@t83)) % 0.39/0.59 (step @p102 :rule refl :args (@t32)) % 0.39/0.59 (step @p103 :rule cong :premises (@p102 @p101) :args ((= @t32 @t83))) % 0.39/0.59 (step @p104 :rule symm :premises (@p103)) % 0.39/0.59 (step @p105 :rule eq_resolve :premises (@p102 @p104)) % 0.39/0.59 (step @p106 :rule cong :premises (@p105) :args (@t106)) % 0.39/0.59 (step @p107 :rule refl :args (@t52)) % 0.39/0.59 (step @p108 :rule refl :args (@t3)) % 0.39/0.59 (step @p109 :rule cong :premises (@p108 @p107) :args ((= @t3 @t52))) % 0.39/0.59 (step @p110 :rule symm :premises (@p109)) % 0.39/0.59 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 0.39/0.59 (step @p112 :rule cong :premises (@p111) :args (@t107)) % 0.39/0.59 (step @p113 :rule nary_cong :premises (@p112 @p106) :args (@t108)) % 0.39/0.59 (step @p114 :rule cong :premises (@p113) :args ((forall @t4 @t108))) % 0.39/0.59 (step @p115 :rule bool-and-de-morgan :args (@t3 @t32 true)) % 0.39/0.59 (step @p116 :rule cong :premises (@p115) :args (@t109)) % 0.39/0.59 (step @p117 :rule trans :premises (@p116 @p114)) % 0.39/0.59 (step @p118 :rule cong :premises (@p117) :args (@t110)) % 0.39/0.59 (step @p119 :rule exists-elim :args ((= @t36 @t110))) % 0.39/0.59 (step @p120 :rule trans :premises (@p119 @p118)) % 0.39/0.59 (step @p121 :rule cong :premises (@p120) :args (@t37)) % 0.39/0.59 (step @p122 :rule trans :premises (@p13 @p121)) % 0.39/0.59 (step @p123 :rule ho_cong :premises (@p122 @p100)) % 0.39/0.59 (step @p124 :rule ho_cong :premises (@p123 @p33)) % 0.39/0.59 (step @p125 :rule cong :premises (@p124) :args (@t17)) % 0.39/0.59 (step @p126 :rule refl :args (@t72)) % 0.39/0.59 (step @p127 :rule refl :args (@t39)) % 0.39/0.59 (step @p128 :rule cong :premises (@p127 @p126) :args ((= @t39 @t72))) % 0.39/0.59 (step @p129 :rule symm :premises (@p128)) % 0.39/0.59 (step @p130 :rule eq_resolve :premises (@p127 @p129)) % 0.39/0.59 (step @p131 :rule refl :args (@t55)) % 0.39/0.59 (step @p132 :rule refl :args (@t8)) % 0.39/0.59 (step @p133 :rule cong :premises (@p132 @p131) :args ((= @t8 @t55))) % 0.39/0.59 (step @p134 :rule symm :premises (@p133)) % 0.39/0.59 (step @p135 :rule eq_resolve :premises (@p132 @p134)) % 0.39/0.59 (step @p136 :rule cong :premises (@p135) :args (@t111)) % 0.39/0.59 (step @p137 :rule nary_cong :premises (@p136 @p130) :args (@t112)) % 0.39/0.59 (step @p138 :rule cong :premises (@p137) :args ((forall @t9 @t112))) % 0.39/0.59 (step @p139 :rule bool-impl-elim :args (@t8 @t39)) % 0.39/0.59 (step @p140 :rule cong :premises (@p139) :args (@t40)) % 0.39/0.59 (step @p141 :rule trans :premises (@p140 @p138)) % 0.39/0.59 (step @p142 :rule cong :premises (@p141) :args (@t42)) % 0.39/0.59 (step @p143 :rule trans :premises (@p14 @p142)) % 0.39/0.59 (step @p144 :rule ho_cong :premises (@p143 @p125)) % 0.39/0.59 (step @p145 :rule refl :args (@t18)) % 0.39/0.59 (step @p146 :rule ho_cong :premises (@p143 @p145)) % 0.39/0.59 (step @p147 :rule ho_cong :premises (@p122 @p146)) % 0.39/0.59 (step @p148 :rule ho_cong :premises (@p10 @p147)) % 0.39/0.59 (step @p149 :rule ho_cong :premises (@p148 @p144)) % 0.39/0.59 (step @p150 :rule ho_cong :premises (@p6 @p149)) % 0.39/0.59 (step @p151 :rule cong :premises (@p150) :args (@t19)) % 0.39/0.59 (step @p152 :rule trans :premises (@p151 @p99)) % 0.39/0.59 (step @p153 :rule eq_resolve :premises (@p4 @p152)) % 0.39/0.59 (step @p154 :rule not_implies_elim1 :premises (@p153)) % 0.39/0.59 (step @p155 :rule skolemize :premises (@p154)) % 0.39/0.59 (step @p156 :rule bool-double-not-elim :args (@t114)) % 0.39/0.59 (step @p157 :rule refl :args (@t118)) % 0.39/0.59 (step @p158 :rule nary_cong :premises (@p157 @p156) :args ((or @t118 (not @t115)))) % 0.39/0.59 (step @p159 :rule cnf_or_neg :args (@t118 1)) % 0.39/0.59 (step @p160 :rule eq_resolve :premises (@p159 @p158)) % 0.39/0.59 (step @p161 :rule reordering :premises (@p160) :args ((or @t114 @t118))) % 0.39/0.59 (step @p162 :rule chain_m_resolution :premises (@p161 @p155) :args (@t114 @t119 @t120)) % 0.39/0.59 (step @p163 :rule refl :args (@t48)) % 0.39/0.59 (step @p164 :rule refl :args (@t10)) % 0.39/0.59 (step @p165 :rule cong :premises (@p164 @p163) :args ((= @t10 @t48))) % 0.39/0.59 (step @p166 :rule symm :premises (@p165)) % 0.39/0.59 (step @p167 :rule eq_resolve :premises (@p164 @p166)) % 0.39/0.59 (step @p168 :rule nary_cong :premises (@p136 @p112 @p167) :args (@t121)) % 0.39/0.59 (step @p169 :rule cong :premises (@p168) :args ((forall @t12 @t121))) % 0.39/0.59 (step @p170 :rule aci_norm :args ((= (or (or @t111 @t107) @t10) @t121))) % 0.39/0.59 (step @p171 :rule bool-and-de-morgan :args (@t8 @t3 true)) % 0.39/0.59 (step @p172 :rule nary_cong :premises (@p171 @p164) :args ((or (not @t11) @t10))) % 0.39/0.59 (step @p173 :rule trans :premises (@p172 @p170)) % 0.39/0.59 (step @p174 :rule bool-impl-elim :args (@t11 @t10)) % 0.39/0.59 (step @p175 :rule trans :premises (@p174 @p173)) % 0.39/0.59 (step @p176 :rule cong :premises (@p175) :args (@t13)) % 0.39/0.59 (step @p177 :rule trans :premises (@p176 @p169)) % 0.39/0.59 (step @p178 :rule eq_resolve :premises (@p3 @p177)) % 0.39/0.59 (step @p179 :rule instantiate :premises (@p178) :args ((@list tptp.mactual @t113 @t122))) % 0.39/0.59 (step @p180 :rule not_implies_elim2 :premises (@p153)) % 0.39/0.59 (step @p181 :rule skolemize :premises (@p180)) % 0.39/0.59 (step @p182 :rule bool-double-not-elim :args (@t123)) % 0.39/0.59 (step @p183 :rule refl :args (@t127)) % 0.39/0.59 (step @p184 :rule nary_cong :premises (@p183 @p182) :args ((or @t127 (not @t126)))) % 0.39/0.59 (step @p185 :rule cnf_or_neg :args (@t127 0)) % 0.39/0.59 (step @p186 :rule eq_resolve :premises (@p185 @p184)) % 0.39/0.59 (step @p187 :rule reordering :premises (@p186) :args ((or @t123 @t127))) % 0.39/0.59 (step @p188 :rule chain_m_resolution :premises (@p187 @p181) :args (@t123 @t119 @t128)) % 0.39/0.59 (step @p189 :rule bool-double-not-elim :args (@t116)) % 0.39/0.59 (step @p190 :rule nary_cong :premises (@p157 @p189) :args ((or @t118 (not @t117)))) % 0.39/0.59 (step @p191 :rule cnf_or_neg :args (@t118 0)) % 0.39/0.59 (step @p192 :rule eq_resolve :premises (@p191 @p190)) % 0.39/0.59 (step @p193 :rule reordering :premises (@p192) :args ((or @t116 @t118))) % 0.39/0.59 (step @p194 :rule chain_m_resolution :premises (@p193 @p155) :args (@t116 @t119 @t120)) % 0.39/0.59 (step @p195 :rule cnf_or_pos :args (@t130)) % 0.39/0.59 (step @p196 :rule reordering :premises (@p195) :args ((or @t117 @t126 @t129 (not @t130)))) % 0.39/0.59 (step @p197 :rule chain_m_resolution :premises (@p196 @p194 @p188 @p179) :args (@t129 (@list false false false) (@list @t116 @t123 @t130))) % 0.39/0.59 (step @p198 :rule bool-double-not-elim :args (@t124)) % 0.39/0.59 (step @p199 :rule nary_cong :premises (@p183 @p198) :args ((or @t127 (not @t125)))) % 0.39/0.59 (step @p200 :rule cnf_or_neg :args (@t127 1)) % 0.39/0.59 (step @p201 :rule eq_resolve :premises (@p200 @p199)) % 0.39/0.59 (step @p202 :rule reordering :premises (@p201) :args ((or @t124 @t127))) % 0.39/0.59 (step @p203 :rule chain_m_resolution :premises (@p202 @p181) :args (@t124 @t119 @t128)) % 0.39/0.59 (step @p204 :rule instantiate :premises (@p203) :args ((@list @t113))) % 0.39/0.59 (step @p205 :rule cnf_or_pos :args (@t133)) % 0.39/0.59 (step @p206 :rule reordering :premises (@p205) :args ((or @t117 @t132 (not @t133)))) % 0.39/0.59 (step @p207 :rule chain_m_resolution :premises (@p206 @p194 @p204) :args (@t132 (@list false false) (@list @t116 @t133))) % 0.39/0.59 (step @p208 :rule cnf_or_pos :args (@t135)) % 0.39/0.59 (step @p209 :rule reordering :premises (@p208) :args ((or @t131 @t134 @t136))) % 0.39/0.59 (step @p210 :rule chain_m_resolution :premises (@p209 @p207 @p197) :args (@t136 @t137 (@list @t131 @t129))) % 0.39/0.59 (assume-push @p217 @t114) % 0.39/0.59 (step @p212 :rule instantiate :premises (@p162) :args ((@list @t122))) % 0.39/0.59 (step-pop @p218 :rule scope :premises (@p212)) % 0.39/0.59 (step @p213 :rule process_scope :premises (@p218) :args (@t135)) % 0.39/0.59 (step @p215 :rule implies_elim :premises (@p213)) % 0.39/0.59 (step @p216 false :rule chain_m_resolution :premises (@p215 @p210 @p162) :args (false @t137 (@list @t135 @t114))) % 0.39/0.59 ) % 0.39/0.59 % SZS output end Proof % 0.39/0.59 % cvc5 exiting %------------------------------------------------------------------------------