%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO886^6 : 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 : n007.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 09:13:41 AM UTC 2026 % Result : Theorem 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO886^6 : TPTP v9.2.1. Released v8.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n007.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 : Wed Jun 3 01:07:56 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.38/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.57 % SZS status Theorem % 0.38/0.57 % SZS output start Proof % 0.38/0.57 ( % 0.38/0.57 (declare-sort $$unsorted 0) % 0.38/0.57 (declare-sort tptp.mworld 0) % 0.38/0.57 (declare-const tptp.mactual tptp.mworld) % 0.38/0.57 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.38/0.57 (declare-const tptp.f (-> $$unsorted tptp.mworld Bool)) % 0.38/0.57 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.38/0.57 (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)))))) % 0.38/0.57 (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))))))) % 0.38/0.57 (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))))))) % 0.38/0.57 (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))))))) % 0.38/0.57 (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))))))) % 0.38/0.57 (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)))))))) % 0.38/0.57 (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)))))))) % 0.38/0.57 (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))))))) % 0.38/0.57 (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))))))) % 0.38/0.57 (define @t1 () (@var "V" tptp.mworld)) % 0.38/0.57 (define @t2 () (@var "W" tptp.mworld)) % 0.38/0.57 (define @t3 () (_ (_ tptp.mrel @t2) @t1)) % 0.38/0.57 (define @t4 () (@list @t1)) % 0.38/0.57 (define @t5 () (@list @t2)) % 0.38/0.57 (define @t6 () (@var "__flatten_var_0" tptp.mworld)) % 0.38/0.57 (define @t7 () (@var "X" $$unsorted)) % 0.38/0.57 (define @t8 () (_ tptp.f @t7)) % 0.38/0.57 (define @t9 () (@list @t7 @t6)) % 0.38/0.57 (define @t10 () (lambda @t9 (_ @t8 @t6))) % 0.38/0.57 (define @t11 () (lambda @t9 (_ (_ tptp.mbox @t8) @t6))) % 0.38/0.57 (define @t12 () (not (_ tptp.mlocal (_ (_ tptp.mimplies (_ tptp.mforall_di @t11)) (_ tptp.mbox (_ tptp.mforall_di @t10)))))) % 0.38/0.57 (define @t13 () (@var "Phi" (-> tptp.mworld Bool))) % 0.38/0.57 (define @t14 () (lambda (@list @t13) (_ @t13 tptp.mactual))) % 0.38/0.57 (define @t15 () (@var "A" (-> tptp.mworld Bool))) % 0.38/0.57 (define @t16 () (_ @t15 @t2)) % 0.38/0.57 (define @t17 () (lambda (@list @t15 @t2) (not @t16))) % 0.38/0.57 (define @t18 () (@var "B" (-> tptp.mworld Bool))) % 0.38/0.57 (define @t19 () (_ @t18 @t2)) % 0.38/0.57 (define @t20 () (@list @t15 @t18 @t2)) % 0.38/0.57 (define @t21 () (lambda @t20 (and @t16 @t19))) % 0.38/0.57 (define @t22 () (lambda @t20 (or @t16 @t19))) % 0.38/0.57 (define @t23 () (lambda @t20 (=> @t16 @t19))) % 0.38/0.57 (define @t24 () (lambda @t20 (= @t16 @t19))) % 0.38/0.57 (define @t25 () (_ @t13 @t1)) % 0.38/0.57 (define @t26 () (forall @t4 (=> @t3 @t25))) % 0.38/0.57 (define @t27 () (@list @t13 @t2)) % 0.38/0.57 (define @t28 () (lambda @t27 @t26)) % 0.38/0.57 (define @t29 () (lambda @t27 (exists @t4 (and @t3 @t25)))) % 0.38/0.57 (define @t30 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.38/0.57 (define @t31 () (_ (_ @t30 @t7) @t2)) % 0.38/0.57 (define @t32 () (@list @t7)) % 0.38/0.57 (define @t33 () (forall @t32 @t31)) % 0.38/0.57 (define @t34 () (@list @t30 @t2)) % 0.38/0.57 (define @t35 () (lambda @t34 @t33)) % 0.38/0.57 (define @t36 () (lambda @t34 (exists @t32 @t31))) % 0.38/0.57 (define @t37 () (@var "BOUND_VARIABLE_7654" $$unsorted)) % 0.38/0.57 (define @t38 () (tptp.f @t37 @t1)) % 0.38/0.57 (define @t39 () (not (tptp.mrel tptp.mactual @t1))) % 0.38/0.57 (define @t40 () (or @t39 @t38)) % 0.38/0.57 (define @t41 () (@list @t1 @t37)) % 0.38/0.57 (define @t42 () (forall @t41 @t40)) % 0.38/0.57 (define @t43 () (tptp.f @t7 @t1)) % 0.38/0.57 (define @t44 () (@list @t7 @t1)) % 0.38/0.57 (define @t45 () (forall @t44 (or @t39 @t43))) % 0.38/0.57 (define @t46 () (tptp.mrel @t2 @t1)) % 0.38/0.57 (define @t47 () (not @t46)) % 0.38/0.57 (define @t48 () (or @t47 @t38)) % 0.38/0.57 (define @t49 () (forall @t41 @t48)) % 0.38/0.57 (define @t50 () (or @t47 @t43)) % 0.38/0.57 (define @t51 () (forall @t44 @t50)) % 0.38/0.57 (define @t52 () (lambda @t5 (=> @t51 @t49))) % 0.38/0.57 (define @t53 () (_ @t52 tptp.mactual)) % 0.38/0.57 (define @t54 () (lambda @t5 @t49)) % 0.38/0.57 (define @t55 () (_ @t54 @t2)) % 0.38/0.57 (define @t56 () (=> @t51 @t55)) % 0.38/0.57 (define @t57 () (lambda @t5 @t56)) % 0.38/0.57 (define @t58 () (@list @t18 @t2)) % 0.38/0.57 (define @t59 () (@list @t37)) % 0.38/0.57 (define @t60 () (forall @t59 @t48)) % 0.38/0.57 (define @t61 () (forall @t59 @t38)) % 0.38/0.57 (define @t62 () (or @t47 @t61)) % 0.38/0.57 (define @t63 () (forall @t32 @t43)) % 0.38/0.57 (define @t64 () (tptp.f @t7 @t2)) % 0.38/0.57 (define @t65 () (lambda @t5 (forall @t32 @t64))) % 0.38/0.57 (define @t66 () (_ @t65 @t1)) % 0.38/0.57 (define @t67 () (or @t47 @t66)) % 0.38/0.57 (define @t68 () (forall @t4 @t67)) % 0.38/0.57 (define @t69 () (lambda @t5 @t68)) % 0.38/0.57 (define @t70 () (_ @t13 @t1)) % 0.38/0.57 (define @t71 () (lambda @t27 (forall @t4 (or @t47 @t70)))) % 0.38/0.57 (define @t72 () (_ @t8 @t2)) % 0.38/0.57 (define @t73 () (_ @t10 @t7 @t2)) % 0.38/0.57 (define @t74 () (forall @t32 @t73)) % 0.38/0.57 (define @t75 () (lambda @t5 @t74)) % 0.38/0.57 (define @t76 () (_ @t30 @t7 @t2)) % 0.38/0.57 (define @t77 () (lambda @t34 (forall @t32 @t76))) % 0.38/0.57 (define @t78 () (_ @t77 @t10)) % 0.38/0.57 (define @t79 () (lambda @t5 @t51)) % 0.38/0.57 (define @t80 () (_ @t79 @t2)) % 0.38/0.57 (define @t81 () (=> @t80 @t19)) % 0.38/0.57 (define @t82 () (lambda @t58 @t81)) % 0.38/0.57 (define @t83 () (forall @t4 @t50)) % 0.38/0.57 (define @t84 () (forall @t4 (or (not (tptp.mrel @t6 @t1)) @t43))) % 0.38/0.57 (define @t85 () (lambda @t9 @t84)) % 0.38/0.57 (define @t86 () (_ @t85 @t7 @t2)) % 0.38/0.57 (define @t87 () (forall @t32 @t86)) % 0.38/0.57 (define @t88 () (lambda @t5 @t87)) % 0.38/0.57 (define @t89 () (_ @t8 @t1)) % 0.38/0.57 (define @t90 () (or @t47 @t89)) % 0.38/0.57 (define @t91 () (_ @t8 @t1)) % 0.38/0.57 (define @t92 () (or @t47 @t91)) % 0.38/0.57 (define @t93 () (forall @t4 @t92)) % 0.38/0.57 (define @t94 () (lambda @t5 @t93)) % 0.38/0.57 (define @t95 () (_ @t71 @t8)) % 0.38/0.57 (define @t96 () (lambda @t9 (_ @t95 @t6))) % 0.38/0.57 (define @t97 () (not @t3)) % 0.38/0.57 (define @t98 () (or @t97 @t25)) % 0.38/0.57 (define @t99 () (@var "BOUND_VARIABLE_7712" tptp.mworld)) % 0.38/0.57 (define @t100 () (@var "BOUND_VARIABLE_7713" $$unsorted)) % 0.38/0.57 (define @t101 () (@list @t99 @t100)) % 0.38/0.57 (define @t102 () (@list false)) % 0.38/0.57 (assume @p1 (forall @t5 (exists @t4 @t3))) % 0.38/0.57 (assume @p2 @t12) % 0.38/0.57 (assume @p3 true) % 0.38/0.57 (step @p4 (= tptp.mlocal @t14) :rule refl :args (@t14)) % 0.38/0.57 (step @p5 (= tptp.mnot @t17) :rule refl :args (@t17)) % 0.38/0.57 (step @p6 (= tptp.mand @t21) :rule refl :args (@t21)) % 0.38/0.57 (step @p7 (= tptp.mor @t22) :rule refl :args (@t22)) % 0.38/0.57 (step @p8 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.38/0.57 (step @p9 (= tptp.mequiv @t24) :rule refl :args (@t24)) % 0.38/0.57 (step @p10 (= tptp.mbox @t28) :rule refl :args (@t28)) % 0.38/0.57 (step @p11 (= tptp.mdia @t29) :rule refl :args (@t29)) % 0.38/0.57 (step @p12 (= tptp.mforall_di @t35) :rule refl :args (@t35)) % 0.38/0.57 (step @p13 (= tptp.mexists_di @t36) :rule refl :args (@t36)) % 0.38/0.57 (step @p14 :rule beta-reduce :args ((= @t53 (=> @t45 @t42)))) % 0.38/0.57 (step @p15 :rule beta-reduce :args ((= (_ @t14 @t52) @t53))) % 0.38/0.57 (step @p16 :rule trans :premises (@p15 @p14)) % 0.38/0.57 (step @p17 :rule beta-reduce :args ((= @t55 @t49))) % 0.38/0.57 (step @p18 :rule refl :args (@t51)) % 0.38/0.57 (step @p19 :rule cong :premises (@p18 @p17) :args (@t56)) % 0.38/0.57 (step @p20 :rule cong :premises (@p19) :args (@t57)) % 0.38/0.57 (step @p21 :rule beta-reduce :args ((= (_ (lambda @t58 (=> @t51 @t19)) @t54) @t57))) % 0.38/0.57 (step @p22 :rule trans :premises (@p21 @p20)) % 0.38/0.57 (step @p23 :rule quant-merge-prenex :args ((= (forall @t4 @t60) @t49))) % 0.38/0.57 (step @p24 :rule alpha_equiv :args (@t61 (@list @t37) (@list @t7))) % 0.38/0.57 (step @p25 :rule refl :args (@t47)) % 0.38/0.57 (step @p26 :rule nary_cong :premises (@p25 @p24) :args (@t62)) % 0.38/0.57 (step @p27 :rule quant-miniscope-or :args ((= @t60 @t62))) % 0.38/0.57 (step @p28 :rule trans :premises (@p27 @p26)) % 0.38/0.57 (step @p29 :rule symm :premises (@p28)) % 0.38/0.57 (step @p30 :rule cong :premises (@p29) :args ((forall @t4 (or @t47 @t63)))) % 0.38/0.57 (step @p31 :rule trans :premises (@p30 @p23)) % 0.38/0.57 (step @p32 :rule beta-reduce :args ((= @t66 @t63))) % 0.38/0.57 (step @p33 :rule refl :args (@t47)) % 0.38/0.57 (step @p34 :rule nary_cong :premises (@p33 @p32) :args (@t67)) % 0.38/0.57 (step @p35 :rule cong :premises (@p34) :args (@t68)) % 0.38/0.57 (step @p36 :rule trans :premises (@p35 @p31)) % 0.38/0.57 (step @p37 :rule cong :premises (@p36) :args (@t69)) % 0.38/0.57 (step @p38 :rule beta-reduce :args ((= (_ @t71 @t65) @t69))) % 0.38/0.57 (step @p39 :rule trans :premises (@p38 @p37)) % 0.38/0.57 (step @p40 :rule refl :args (@t64)) % 0.38/0.57 (step @p41 :rule refl :args (@t72)) % 0.38/0.57 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t72 @t64))) % 0.38/0.57 (step @p43 :rule symm :premises (@p42)) % 0.38/0.57 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 0.38/0.57 (step @p45 :rule cong :premises (@p44) :args ((forall @t32 @t72))) % 0.38/0.57 (step @p46 :rule beta-reduce :args ((= @t73 @t72))) % 0.38/0.57 (step @p47 :rule cong :premises (@p46) :args (@t74)) % 0.38/0.57 (step @p48 :rule trans :premises (@p47 @p45)) % 0.38/0.57 (step @p49 :rule cong :premises (@p48) :args (@t75)) % 0.38/0.57 (step @p50 :rule beta-reduce :args ((= @t78 @t75))) % 0.38/0.57 (step @p51 :rule trans :premises (@p50 @p49)) % 0.38/0.57 (step @p52 :rule refl :args (@t71)) % 0.38/0.57 (step @p53 :rule ho_cong :premises (@p52 @p51)) % 0.38/0.57 (step @p54 :rule trans :premises (@p53 @p39)) % 0.38/0.57 (step @p55 :rule refl :args (@t19)) % 0.38/0.57 (step @p56 :rule beta-reduce :args ((= @t80 @t51))) % 0.38/0.57 (step @p57 :rule cong :premises (@p56 @p55) :args (@t81)) % 0.38/0.57 (step @p58 :rule cong :premises (@p57) :args (@t82)) % 0.38/0.57 (step @p59 :rule beta-reduce :args ((= (_ @t23 @t79) @t82))) % 0.38/0.57 (step @p60 :rule trans :premises (@p59 @p58)) % 0.38/0.57 (step @p61 :rule quant-merge-prenex :args ((= (forall @t32 @t83) @t51))) % 0.38/0.57 (step @p62 :rule beta-reduce :args ((= @t86 @t83))) % 0.38/0.57 (step @p63 :rule cong :premises (@p62) :args (@t87)) % 0.38/0.57 (step @p64 :rule trans :premises (@p63 @p61)) % 0.38/0.57 (step @p65 :rule cong :premises (@p64) :args (@t88)) % 0.38/0.57 (step @p66 :rule beta-reduce :args ((= (_ @t77 @t85) @t88))) % 0.38/0.57 (step @p67 :rule trans :premises (@p66 @p65)) % 0.38/0.57 (step @p68 :rule beta-reduce :args ((= (_ (lambda @t5 @t83) @t6) @t84))) % 0.38/0.57 (step @p69 :rule refl :args (@t6)) % 0.38/0.57 (step @p70 :rule refl :args (@t43)) % 0.38/0.57 (step @p71 :rule refl :args (@t89)) % 0.38/0.57 (step @p72 :rule cong :premises (@p71 @p70) :args ((= @t89 @t43))) % 0.38/0.57 (step @p73 :rule symm :premises (@p72)) % 0.38/0.57 (step @p74 :rule eq_resolve :premises (@p71 @p73)) % 0.38/0.57 (step @p75 :rule nary_cong :premises (@p25 @p74) :args (@t90)) % 0.38/0.57 (step @p76 :rule cong :premises (@p75) :args ((forall @t4 @t90))) % 0.38/0.57 (step @p77 :rule refl :args (@t91)) % 0.38/0.57 (step @p78 :rule nary_cong :premises (@p33 @p77) :args (@t92)) % 0.38/0.57 (step @p79 :rule cong :premises (@p78) :args (@t93)) % 0.38/0.57 (step @p80 :rule trans :premises (@p79 @p76)) % 0.38/0.57 (step @p81 :rule cong :premises (@p80) :args (@t94)) % 0.38/0.57 (step @p82 :rule beta-reduce :args ((= @t95 @t94))) % 0.38/0.57 (step @p83 :rule trans :premises (@p82 @p81)) % 0.38/0.57 (step @p84 :rule ho_cong :premises (@p83 @p69)) % 0.38/0.57 (step @p85 :rule trans :premises (@p84 @p68)) % 0.38/0.57 (step @p86 :rule cong :premises (@p85) :args (@t96)) % 0.38/0.57 (step @p87 :rule refl :args (@t77)) % 0.38/0.57 (step @p88 :rule ho_cong :premises (@p87 @p86)) % 0.38/0.57 (step @p89 :rule trans :premises (@p88 @p67)) % 0.38/0.57 (step @p90 :rule refl :args (@t23)) % 0.38/0.57 (step @p91 :rule ho_cong :premises (@p90 @p89)) % 0.38/0.57 (step @p92 :rule trans :premises (@p91 @p60)) % 0.38/0.57 (step @p93 :rule ho_cong :premises (@p92 @p54)) % 0.38/0.57 (step @p94 :rule trans :premises (@p93 @p22)) % 0.38/0.57 (step @p95 :rule refl :args (@t14)) % 0.38/0.57 (step @p96 :rule ho_cong :premises (@p95 @p94)) % 0.38/0.57 (step @p97 :rule trans :premises (@p96 @p16)) % 0.38/0.57 (step @p98 :rule cong :premises (@p97) :args ((not (_ @t14 (_ (_ @t23 (_ @t77 @t96)) (_ @t71 @t78)))))) % 0.38/0.57 (step @p99 :rule refl :args (@t10)) % 0.38/0.57 (step @p100 :rule refl :args (@t76)) % 0.38/0.57 (step @p101 :rule refl :args (@t31)) % 0.38/0.57 (step @p102 :rule cong :premises (@p101 @p100) :args ((= @t31 @t76))) % 0.38/0.57 (step @p103 :rule symm :premises (@p102)) % 0.38/0.57 (step @p104 :rule eq_resolve :premises (@p101 @p103)) % 0.38/0.57 (step @p105 :rule cong :premises (@p104) :args (@t33)) % 0.38/0.57 (step @p106 :rule cong :premises (@p105) :args (@t35)) % 0.38/0.57 (step @p107 :rule trans :premises (@p12 @p106)) % 0.38/0.57 (step @p108 :rule ho_cong :premises (@p107 @p99)) % 0.38/0.57 (step @p109 :rule refl :args (@t70)) % 0.38/0.57 (step @p110 :rule refl :args (@t25)) % 0.38/0.57 (step @p111 :rule cong :premises (@p110 @p109) :args ((= @t25 @t70))) % 0.38/0.57 (step @p112 :rule symm :premises (@p111)) % 0.38/0.57 (step @p113 :rule eq_resolve :premises (@p110 @p112)) % 0.38/0.57 (step @p114 :rule refl :args (@t46)) % 0.38/0.57 (step @p115 :rule refl :args (@t3)) % 0.38/0.57 (step @p116 :rule cong :premises (@p115 @p114) :args ((= @t3 @t46))) % 0.38/0.57 (step @p117 :rule symm :premises (@p116)) % 0.38/0.57 (step @p118 :rule eq_resolve :premises (@p115 @p117)) % 0.38/0.57 (step @p119 :rule cong :premises (@p118) :args (@t97)) % 0.38/0.57 (step @p120 :rule nary_cong :premises (@p119 @p113) :args (@t98)) % 0.38/0.57 (step @p121 :rule cong :premises (@p120) :args ((forall @t4 @t98))) % 0.38/0.57 (step @p122 :rule bool-impl-elim :args (@t3 @t25)) % 0.38/0.57 (step @p123 :rule cong :premises (@p122) :args (@t26)) % 0.38/0.57 (step @p124 :rule trans :premises (@p123 @p121)) % 0.38/0.57 (step @p125 :rule cong :premises (@p124) :args (@t28)) % 0.38/0.57 (step @p126 :rule trans :premises (@p10 @p125)) % 0.38/0.57 (step @p127 :rule ho_cong :premises (@p126 @p108)) % 0.38/0.57 (step @p128 :rule refl :args (@t8)) % 0.38/0.57 (step @p129 :rule ho_cong :premises (@p126 @p128)) % 0.38/0.57 (step @p130 :rule ho_cong :premises (@p129 @p69)) % 0.38/0.57 (step @p131 :rule cong :premises (@p130) :args (@t11)) % 0.38/0.57 (step @p132 :rule ho_cong :premises (@p107 @p131)) % 0.38/0.57 (step @p133 :rule ho_cong :premises (@p8 @p132)) % 0.38/0.57 (step @p134 :rule ho_cong :premises (@p133 @p127)) % 0.38/0.57 (step @p135 :rule ho_cong :premises (@p4 @p134)) % 0.38/0.57 (step @p136 :rule cong :premises (@p135) :args (@t12)) % 0.38/0.57 (step @p137 :rule trans :premises (@p136 @p98)) % 0.38/0.57 (step @p138 :rule eq_resolve :premises (@p2 @p137)) % 0.38/0.57 (step @p139 :rule not_implies_elim1 :premises (@p138)) % 0.38/0.57 (step @p140 :rule quant_var_reordering :args ((= (forall (@list @t37 @t1) @t40) @t42))) % 0.38/0.57 (step @p141 :rule alpha_equiv :args ((forall (@list @t100 @t99) (or (not (tptp.mrel tptp.mactual @t99)) (tptp.f @t100 @t99))) @t101 (@list @t1 @t37))) % 0.38/0.57 (step @p142 :rule alpha_equiv :args (@t45 (@list @t1 @t7) @t101)) % 0.38/0.57 (step @p143 :rule trans :premises (@p142 @p141 @p140)) % 0.38/0.57 (step @p144 :rule equiv_elim1 :premises (@p143)) % 0.38/0.57 (step @p145 :rule reordering :premises (@p144) :args ((or @t42 (not @t45)))) % 0.38/0.57 (step @p146 :rule chain_m_resolution :premises (@p145 @p139) :args (@t42 @t102 (@list @t45))) % 0.38/0.57 (step @p147 :rule not_implies_elim2 :premises (@p138)) % 0.38/0.57 (step @p148 false :rule chain_m_resolution :premises (@p147 @p146) :args (false @t102 (@list @t42))) % 0.38/0.57 ) % 0.38/0.57 % SZS output end Proof % 0.38/0.57 % cvc5 exiting %------------------------------------------------------------------------------