%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NLP267^4 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n008.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 08:37:19 AM UTC 2026 % Result : Theorem 0.38s 0.59s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NLP267^4 : TPTP v9.2.1. Released v8.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n008.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 10:18:03 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.50 %----Proving TH0 % 0.38/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.59 % SZS status Theorem % 0.38/0.59 % SZS output start Proof % 0.38/0.59 ( % 0.38/0.59 (declare-sort $$unsorted 0) % 0.38/0.59 (declare-sort tptp.mworld 0) % 0.38/0.59 (declare-const tptp.mactual tptp.mworld) % 0.38/0.59 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.38/0.59 (declare-const tptp.second $$unsorted) % 0.38/0.59 (declare-const tptp.seventy $$unsorted) % 0.38/0.59 (declare-const tptp.dest (-> $$unsorted tptp.mworld Bool)) % 0.38/0.59 (declare-const tptp.paris $$unsorted) % 0.38/0.59 (declare-const tptp.class (-> $$unsorted tptp.mworld Bool)) % 0.38/0.59 (declare-const tptp.first $$unsorted) % 0.38/0.59 (declare-const tptp.price (-> $$unsorted tptp.mworld Bool)) % 0.38/0.59 (declare-const tptp.ninetyfive $$unsorted) % 0.38/0.59 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.38/0.59 (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)))))) % 0.38/0.59 (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))))))) % 0.38/0.59 (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))))))) % 0.38/0.59 (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))))))) % 0.38/0.59 (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))))))) % 0.38/0.59 (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)))))))) % 0.38/0.59 (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)))))))) % 0.38/0.59 (define @t1 () (@var "W" tptp.mworld)) % 0.38/0.59 (define @t2 () (_ tptp.mrel @t1)) % 0.38/0.59 (define @t3 () (@list @t1)) % 0.38/0.59 (define @t4 () (@var "U" tptp.mworld)) % 0.38/0.59 (define @t5 () (@var "V" tptp.mworld)) % 0.38/0.59 (define @t6 () (_ @t2 @t5)) % 0.38/0.59 (define @t7 () (_ tptp.price tptp.ninetyfive)) % 0.38/0.59 (define @t8 () (_ tptp.class tptp.first)) % 0.38/0.59 (define @t9 () (_ tptp.dest tptp.paris)) % 0.38/0.59 (define @t10 () (_ tptp.mand @t9)) % 0.38/0.59 (define @t11 () (_ tptp.price tptp.seventy)) % 0.38/0.59 (define @t12 () (_ tptp.class tptp.second)) % 0.38/0.59 (define @t13 () (not (_ tptp.mlocal (_ tptp.mbox @t11)))) % 0.38/0.59 (define @t14 () (@var "Phi" (-> tptp.mworld Bool))) % 0.38/0.59 (define @t15 () (lambda (@list @t14) (_ @t14 tptp.mactual))) % 0.38/0.59 (define @t16 () (@var "A" (-> tptp.mworld Bool))) % 0.38/0.59 (define @t17 () (_ @t16 @t1)) % 0.38/0.59 (define @t18 () (lambda (@list @t16 @t1) (not @t17))) % 0.38/0.59 (define @t19 () (@var "B" (-> tptp.mworld Bool))) % 0.38/0.59 (define @t20 () (_ @t19 @t1)) % 0.38/0.59 (define @t21 () (@list @t16 @t19 @t1)) % 0.38/0.59 (define @t22 () (lambda @t21 (and @t17 @t20))) % 0.38/0.59 (define @t23 () (lambda @t21 (or @t17 @t20))) % 0.38/0.59 (define @t24 () (lambda @t21 (=> @t17 @t20))) % 0.38/0.59 (define @t25 () (lambda @t21 (= @t17 @t20))) % 0.38/0.59 (define @t26 () (_ @t14 @t5)) % 0.38/0.59 (define @t27 () (@list @t5)) % 0.38/0.59 (define @t28 () (forall @t27 (=> @t6 @t26))) % 0.38/0.59 (define @t29 () (@list @t14 @t1)) % 0.38/0.59 (define @t30 () (lambda @t29 @t28)) % 0.38/0.59 (define @t31 () (lambda @t29 (exists @t27 (and @t6 @t26)))) % 0.38/0.59 (define @t32 () (tptp.price tptp.seventy @t5)) % 0.38/0.59 (define @t33 () (not (tptp.mrel tptp.mactual @t5))) % 0.38/0.59 (define @t34 () (forall @t27 (or @t33 @t32))) % 0.38/0.59 (define @t35 () (tptp.mrel @t1 @t5)) % 0.38/0.59 (define @t36 () (not @t35)) % 0.38/0.59 (define @t37 () (lambda @t3 (forall @t27 (or @t36 @t32)))) % 0.38/0.59 (define @t38 () (_ @t37 tptp.mactual)) % 0.38/0.59 (define @t39 () (_ @t11 @t5)) % 0.38/0.59 (define @t40 () (or @t36 @t39)) % 0.38/0.59 (define @t41 () (_ @t11 @t5)) % 0.38/0.59 (define @t42 () (or @t36 @t41)) % 0.38/0.59 (define @t43 () (forall @t27 @t42)) % 0.38/0.59 (define @t44 () (lambda @t3 @t43)) % 0.38/0.59 (define @t45 () (_ @t14 @t5)) % 0.38/0.59 (define @t46 () (lambda @t29 (forall @t27 (or @t36 @t45)))) % 0.38/0.59 (define @t47 () (_ @t46 @t11)) % 0.38/0.59 (define @t48 () (not @t6)) % 0.38/0.59 (define @t49 () (or @t48 @t26)) % 0.38/0.59 (define @t50 () (@quantifiers_skolemize @t34 0)) % 0.38/0.59 (define @t51 () (tptp.mrel tptp.mactual @t50)) % 0.38/0.59 (define @t52 () (tptp.price tptp.seventy @t50)) % 0.38/0.59 (define @t53 () (not @t51)) % 0.38/0.59 (define @t54 () (or @t53 @t52)) % 0.38/0.59 (define @t55 () (@list true)) % 0.38/0.59 (define @t56 () (@list @t54)) % 0.38/0.59 (define @t57 () (tptp.class tptp.second @t5)) % 0.38/0.59 (define @t58 () (not @t57)) % 0.38/0.59 (define @t59 () (tptp.dest tptp.paris @t5)) % 0.38/0.59 (define @t60 () (not @t59)) % 0.38/0.59 (define @t61 () (lambda @t3 (forall @t27 (or @t36 @t60 @t58 @t32)))) % 0.38/0.59 (define @t62 () (_ @t61 tptp.mactual)) % 0.38/0.59 (define @t63 () (_ @t12 @t5)) % 0.38/0.59 (define @t64 () (not @t63)) % 0.38/0.59 (define @t65 () (_ @t9 @t5)) % 0.38/0.59 (define @t66 () (not @t65)) % 0.38/0.59 (define @t67 () (or @t36 @t66 @t64 @t39)) % 0.38/0.59 (define @t68 () (or @t66 @t64 @t39)) % 0.38/0.59 (define @t69 () (and @t65 @t63)) % 0.38/0.59 (define @t70 () (=> @t69 @t39)) % 0.38/0.59 (define @t71 () (or @t36 @t70)) % 0.38/0.59 (define @t72 () (_ @t9 @t1)) % 0.38/0.59 (define @t73 () (and @t72 (_ @t12 @t1))) % 0.38/0.59 (define @t74 () (lambda @t3 (=> @t73 (_ @t11 @t1)))) % 0.38/0.59 (define @t75 () (_ @t74 @t5)) % 0.38/0.59 (define @t76 () (or @t36 @t75)) % 0.38/0.59 (define @t77 () (forall @t27 @t76)) % 0.38/0.59 (define @t78 () (lambda @t3 @t77)) % 0.38/0.59 (define @t79 () (@list @t19 @t1)) % 0.38/0.59 (define @t80 () (lambda @t3 @t73)) % 0.38/0.59 (define @t81 () (_ @t80 @t1)) % 0.38/0.59 (define @t82 () (=> @t81 @t20)) % 0.38/0.59 (define @t83 () (lambda @t79 @t82)) % 0.38/0.59 (define @t84 () (lambda @t79 (and @t72 @t20))) % 0.38/0.59 (define @t85 () (@list @t50)) % 0.38/0.59 (define @t86 () (lambda @t3 (forall @t27 (or @t36 @t59)))) % 0.38/0.59 (define @t87 () (_ @t86 tptp.mactual)) % 0.38/0.59 (define @t88 () (or @t36 @t65)) % 0.38/0.59 (define @t89 () (_ @t9 @t5)) % 0.38/0.59 (define @t90 () (or @t36 @t89)) % 0.38/0.59 (define @t91 () (forall @t27 @t90)) % 0.38/0.59 (define @t92 () (lambda @t3 @t91)) % 0.38/0.59 (define @t93 () (tptp.dest tptp.paris @t50)) % 0.38/0.59 (define @t94 () (or @t53 @t93)) % 0.38/0.59 (define @t95 () (@list false false)) % 0.38/0.59 (define @t96 () (lambda @t3 (forall @t27 (or @t36 @t57)))) % 0.38/0.59 (define @t97 () (_ @t96 tptp.mactual)) % 0.38/0.59 (define @t98 () (or @t36 @t63)) % 0.38/0.59 (define @t99 () (_ @t12 @t5)) % 0.38/0.59 (define @t100 () (or @t36 @t99)) % 0.38/0.59 (define @t101 () (forall @t27 @t100)) % 0.38/0.59 (define @t102 () (lambda @t3 @t101)) % 0.38/0.59 (define @t103 () (tptp.class tptp.second @t50)) % 0.38/0.59 (define @t104 () (or @t53 @t103)) % 0.38/0.59 (define @t105 () (not @t103)) % 0.38/0.59 (define @t106 () (not @t93)) % 0.38/0.59 (define @t107 () (or @t53 @t106 @t105 @t52)) % 0.38/0.59 (assume @p1 (forall @t3 (_ @t2 @t1))) % 0.38/0.59 (assume @p2 (forall (@list @t1 @t5 @t4) (=> (and @t6 (_ (_ tptp.mrel @t5) @t4)) (_ @t2 @t4)))) % 0.38/0.59 (assume @p3 (_ tptp.mlocal (_ tptp.mbox (_ (_ tptp.mimplies (_ @t10 @t8)) @t7)))) % 0.38/0.59 (assume @p4 (_ tptp.mlocal (_ tptp.mbox (_ (_ tptp.mimplies (_ @t10 @t12)) @t11)))) % 0.38/0.59 (assume @p5 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mnot (_ (_ tptp.mand @t8) @t12))))) % 0.38/0.59 (assume @p6 (_ tptp.mlocal (_ tptp.mbox (_ tptp.mnot (_ (_ tptp.mand @t7) @t11))))) % 0.38/0.59 (assume @p7 (_ tptp.mlocal (_ tptp.mbox @t9))) % 0.38/0.59 (assume @p8 (_ tptp.mlocal (_ tptp.mbox @t12))) % 0.38/0.59 (assume @p9 @t13) % 0.38/0.59 (assume @p10 true) % 0.38/0.59 (step @p11 (= tptp.mlocal @t15) :rule refl :args (@t15)) % 0.38/0.59 (step @p12 (= tptp.mnot @t18) :rule refl :args (@t18)) % 0.38/0.59 (step @p13 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.38/0.59 (step @p14 (= tptp.mor @t23) :rule refl :args (@t23)) % 0.38/0.59 (step @p15 (= tptp.mimplies @t24) :rule refl :args (@t24)) % 0.38/0.59 (step @p16 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.38/0.59 (step @p17 (= tptp.mbox @t30) :rule refl :args (@t30)) % 0.38/0.59 (step @p18 (= tptp.mdia @t31) :rule refl :args (@t31)) % 0.38/0.59 (step @p19 :rule beta-reduce :args ((= @t38 @t34))) % 0.38/0.59 (step @p20 :rule beta-reduce :args ((= (_ @t15 @t37) @t38))) % 0.38/0.59 (step @p21 :rule trans :premises (@p20 @p19)) % 0.38/0.59 (step @p22 :rule refl :args (@t32)) % 0.38/0.59 (step @p23 :rule refl :args (@t39)) % 0.38/0.59 (step @p24 :rule cong :premises (@p23 @p22) :args ((= @t39 @t32))) % 0.38/0.59 (step @p25 :rule symm :premises (@p24)) % 0.38/0.59 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 0.38/0.59 (step @p27 :rule refl :args (@t36)) % 0.38/0.59 (step @p28 :rule nary_cong :premises (@p27 @p26) :args (@t40)) % 0.38/0.59 (step @p29 :rule cong :premises (@p28) :args ((forall @t27 @t40))) % 0.38/0.59 (step @p30 :rule refl :args (@t41)) % 0.38/0.59 (step @p31 :rule refl :args (@t36)) % 0.38/0.59 (step @p32 :rule nary_cong :premises (@p31 @p30) :args (@t42)) % 0.38/0.59 (step @p33 :rule cong :premises (@p32) :args (@t43)) % 0.38/0.59 (step @p34 :rule trans :premises (@p33 @p29)) % 0.38/0.59 (step @p35 :rule cong :premises (@p34) :args (@t44)) % 0.38/0.59 (step @p36 :rule beta-reduce :args ((= @t47 @t44))) % 0.38/0.59 (step @p37 :rule trans :premises (@p36 @p35)) % 0.38/0.59 (step @p38 :rule refl :args (@t15)) % 0.38/0.59 (step @p39 :rule ho_cong :premises (@p38 @p37)) % 0.38/0.59 (step @p40 :rule trans :premises (@p39 @p21)) % 0.38/0.59 (step @p41 :rule cong :premises (@p40) :args ((not (_ @t15 @t47)))) % 0.38/0.59 (step @p42 :rule refl :args (@t11)) % 0.38/0.59 (step @p43 :rule refl :args (@t45)) % 0.38/0.59 (step @p44 :rule refl :args (@t26)) % 0.38/0.59 (step @p45 :rule cong :premises (@p44 @p43) :args ((= @t26 @t45))) % 0.38/0.59 (step @p46 :rule symm :premises (@p45)) % 0.38/0.59 (step @p47 :rule eq_resolve :premises (@p44 @p46)) % 0.38/0.59 (step @p48 :rule refl :args (@t35)) % 0.38/0.59 (step @p49 :rule refl :args (@t6)) % 0.38/0.59 (step @p50 :rule cong :premises (@p49 @p48) :args ((= @t6 @t35))) % 0.38/0.59 (step @p51 :rule symm :premises (@p50)) % 0.38/0.59 (step @p52 :rule eq_resolve :premises (@p49 @p51)) % 0.38/0.59 (step @p53 :rule cong :premises (@p52) :args (@t48)) % 0.38/0.59 (step @p54 :rule nary_cong :premises (@p53 @p47) :args (@t49)) % 0.38/0.59 (step @p55 :rule cong :premises (@p54) :args ((forall @t27 @t49))) % 0.38/0.59 (step @p56 :rule bool-impl-elim :args (@t6 @t26)) % 0.38/0.59 (step @p57 :rule cong :premises (@p56) :args (@t28)) % 0.38/0.59 (step @p58 :rule trans :premises (@p57 @p55)) % 0.38/0.59 (step @p59 :rule cong :premises (@p58) :args (@t30)) % 0.38/0.59 (step @p60 :rule trans :premises (@p17 @p59)) % 0.38/0.59 (step @p61 :rule ho_cong :premises (@p60 @p42)) % 0.38/0.59 (step @p62 :rule ho_cong :premises (@p11 @p61)) % 0.38/0.59 (step @p63 :rule cong :premises (@p62) :args (@t13)) % 0.38/0.59 (step @p64 :rule trans :premises (@p63 @p41)) % 0.38/0.59 (step @p65 :rule eq_resolve :premises (@p9 @p64)) % 0.38/0.59 (step @p66 :rule skolemize :premises (@p65)) % 0.38/0.59 (step @p67 :rule bool-double-not-elim :args (@t51)) % 0.38/0.59 (step @p68 :rule refl :args (@t54)) % 0.38/0.59 (step @p69 :rule nary_cong :premises (@p68 @p67) :args ((or @t54 (not @t53)))) % 0.38/0.59 (step @p70 :rule cnf_or_neg :args (@t54 0)) % 0.38/0.59 (step @p71 :rule eq_resolve :premises (@p70 @p69)) % 0.38/0.59 (step @p72 :rule reordering :premises (@p71) :args ((or @t51 @t54))) % 0.38/0.59 (step @p73 :rule chain_m_resolution :premises (@p72 @p66) :args (@t51 @t55 @t56)) % 0.38/0.59 (step @p74 :rule cnf_or_neg :args (@t54 1)) % 0.38/0.59 (step @p75 :rule chain_m_resolution :premises (@p74 @p66) :args ((not @t52) @t55 @t56)) % 0.38/0.59 (step @p76 :rule beta-reduce :args ((= @t62 (forall @t27 (or @t33 @t60 @t58 @t32))))) % 0.38/0.59 (step @p77 :rule beta-reduce :args ((= (_ @t15 @t61) @t62))) % 0.38/0.59 (step @p78 :rule trans :premises (@p77 @p76)) % 0.38/0.59 (step @p79 :rule refl :args (@t57)) % 0.38/0.59 (step @p80 :rule refl :args (@t63)) % 0.38/0.59 (step @p81 :rule cong :premises (@p80 @p79) :args ((= @t63 @t57))) % 0.38/0.59 (step @p82 :rule symm :premises (@p81)) % 0.38/0.59 (step @p83 :rule eq_resolve :premises (@p80 @p82)) % 0.38/0.59 (step @p84 :rule cong :premises (@p83) :args (@t64)) % 0.38/0.59 (step @p85 :rule refl :args (@t59)) % 0.38/0.59 (step @p86 :rule refl :args (@t65)) % 0.38/0.59 (step @p87 :rule cong :premises (@p86 @p85) :args ((= @t65 @t59))) % 0.38/0.59 (step @p88 :rule symm :premises (@p87)) % 0.38/0.59 (step @p89 :rule eq_resolve :premises (@p86 @p88)) % 0.38/0.59 (step @p90 :rule cong :premises (@p89) :args (@t66)) % 0.38/0.59 (step @p91 :rule nary_cong :premises (@p27 @p90 @p84 @p26) :args (@t67)) % 0.38/0.59 (step @p92 :rule cong :premises (@p91) :args ((forall @t27 @t67))) % 0.38/0.59 (step @p93 :rule aci_norm :args ((= (or @t36 @t68) @t67))) % 0.38/0.59 (step @p94 :rule aci_norm :args ((= (or (or @t66 @t64) @t39) @t68))) % 0.38/0.59 (step @p95 :rule bool-and-de-morgan :args (@t65 @t63 true)) % 0.38/0.59 (step @p96 :rule nary_cong :premises (@p95 @p23) :args ((or (not @t69) @t39))) % 0.38/0.59 (step @p97 :rule trans :premises (@p96 @p94)) % 0.38/0.59 (step @p98 :rule bool-impl-elim :args (@t69 @t39)) % 0.38/0.59 (step @p99 :rule trans :premises (@p98 @p97)) % 0.38/0.59 (step @p100 :rule nary_cong :premises (@p27 @p99) :args (@t71)) % 0.38/0.59 (step @p101 :rule trans :premises (@p100 @p93)) % 0.38/0.59 (step @p102 :rule cong :premises (@p101) :args ((forall @t27 @t71))) % 0.38/0.59 (step @p103 :rule trans :premises (@p102 @p92)) % 0.38/0.59 (step @p104 :rule beta-reduce :args ((= @t75 @t70))) % 0.38/0.59 (step @p105 :rule nary_cong :premises (@p31 @p104) :args (@t76)) % 0.38/0.59 (step @p106 :rule cong :premises (@p105) :args (@t77)) % 0.38/0.59 (step @p107 :rule trans :premises (@p106 @p103)) % 0.38/0.59 (step @p108 :rule cong :premises (@p107) :args (@t78)) % 0.38/0.59 (step @p109 :rule beta-reduce :args ((= (_ @t46 @t74) @t78))) % 0.38/0.59 (step @p110 :rule trans :premises (@p109 @p108)) % 0.38/0.59 (step @p111 :rule beta-reduce :args ((= (_ (lambda @t79 (=> @t73 @t20)) @t11) @t74))) % 0.38/0.59 (step @p112 :rule refl :args (@t20)) % 0.38/0.59 (step @p113 :rule beta-reduce :args ((= @t81 @t73))) % 0.38/0.59 (step @p114 :rule cong :premises (@p113 @p112) :args (@t82)) % 0.38/0.59 (step @p115 :rule cong :premises (@p114) :args (@t83)) % 0.38/0.59 (step @p116 :rule beta-reduce :args ((= (_ @t24 @t80) @t83))) % 0.38/0.59 (step @p117 :rule trans :premises (@p116 @p115)) % 0.38/0.59 (step @p118 :rule beta-reduce :args ((= (_ @t84 @t12) @t80))) % 0.38/0.59 (step @p119 :rule refl :args (@t12)) % 0.38/0.59 (step @p120 :rule beta-reduce :args ((= (_ @t22 @t9) @t84))) % 0.38/0.59 (step @p121 :rule ho_cong :premises (@p120 @p119)) % 0.38/0.59 (step @p122 :rule trans :premises (@p121 @p118)) % 0.38/0.59 (step @p123 :rule refl :args (@t24)) % 0.38/0.59 (step @p124 :rule ho_cong :premises (@p123 @p122)) % 0.38/0.59 (step @p125 :rule trans :premises (@p124 @p117)) % 0.38/0.59 (step @p126 :rule ho_cong :premises (@p125 @p42)) % 0.38/0.59 (step @p127 :rule trans :premises (@p126 @p111)) % 0.38/0.59 (step @p128 :rule refl :args (@t46)) % 0.38/0.59 (step @p129 :rule ho_cong :premises (@p128 @p127)) % 0.38/0.59 (step @p130 :rule trans :premises (@p129 @p110)) % 0.38/0.59 (step @p131 :rule ho_cong :premises (@p38 @p130)) % 0.38/0.59 (step @p132 :rule trans :premises (@p131 @p78)) % 0.38/0.59 (step @p133 :rule refl :args (@t9)) % 0.38/0.59 (step @p134 :rule ho_cong :premises (@p13 @p133)) % 0.38/0.59 (step @p135 :rule ho_cong :premises (@p134 @p119)) % 0.38/0.59 (step @p136 :rule ho_cong :premises (@p15 @p135)) % 0.38/0.59 (step @p137 :rule ho_cong :premises (@p136 @p42)) % 0.38/0.59 (step @p138 :rule ho_cong :premises (@p60 @p137)) % 0.38/0.59 (step @p139 :rule ho_cong :premises (@p11 @p138)) % 0.38/0.59 (step @p140 :rule trans :premises (@p139 @p132)) % 0.38/0.59 (step @p141 :rule eq_resolve :premises (@p4 @p140)) % 0.38/0.59 (step @p142 :rule instantiate :premises (@p141) :args (@t85)) % 0.38/0.59 (step @p143 :rule beta-reduce :args ((= @t87 (forall @t27 (or @t33 @t59))))) % 0.38/0.59 (step @p144 :rule beta-reduce :args ((= (_ @t15 @t86) @t87))) % 0.38/0.59 (step @p145 :rule trans :premises (@p144 @p143)) % 0.38/0.59 (step @p146 :rule nary_cong :premises (@p27 @p89) :args (@t88)) % 0.38/0.59 (step @p147 :rule cong :premises (@p146) :args ((forall @t27 @t88))) % 0.38/0.59 (step @p148 :rule refl :args (@t89)) % 0.38/0.59 (step @p149 :rule nary_cong :premises (@p31 @p148) :args (@t90)) % 0.38/0.59 (step @p150 :rule cong :premises (@p149) :args (@t91)) % 0.38/0.59 (step @p151 :rule trans :premises (@p150 @p147)) % 0.38/0.59 (step @p152 :rule cong :premises (@p151) :args (@t92)) % 0.38/0.59 (step @p153 :rule beta-reduce :args ((= (_ @t46 @t9) @t92))) % 0.38/0.59 (step @p154 :rule trans :premises (@p153 @p152)) % 0.38/0.59 (step @p155 :rule ho_cong :premises (@p38 @p154)) % 0.38/0.59 (step @p156 :rule trans :premises (@p155 @p145)) % 0.38/0.59 (step @p157 :rule ho_cong :premises (@p60 @p133)) % 0.38/0.59 (step @p158 :rule ho_cong :premises (@p11 @p157)) % 0.38/0.59 (step @p159 :rule trans :premises (@p158 @p156)) % 0.38/0.59 (step @p160 :rule eq_resolve :premises (@p7 @p159)) % 0.38/0.59 (step @p161 :rule instantiate :premises (@p160) :args (@t85)) % 0.38/0.59 (step @p162 :rule cnf_or_pos :args (@t94)) % 0.38/0.59 (step @p163 :rule reordering :premises (@p162) :args ((or @t53 @t93 (not @t94)))) % 0.38/0.59 (step @p164 :rule chain_m_resolution :premises (@p163 @p73 @p161) :args (@t93 @t95 (@list @t51 @t94))) % 0.38/0.59 (step @p165 :rule beta-reduce :args ((= @t97 (forall @t27 (or @t33 @t57))))) % 0.38/0.59 (step @p166 :rule beta-reduce :args ((= (_ @t15 @t96) @t97))) % 0.38/0.59 (step @p167 :rule trans :premises (@p166 @p165)) % 0.38/0.59 (step @p168 :rule nary_cong :premises (@p27 @p83) :args (@t98)) % 0.38/0.59 (step @p169 :rule cong :premises (@p168) :args ((forall @t27 @t98))) % 0.38/0.59 (step @p170 :rule refl :args (@t99)) % 0.38/0.59 (step @p171 :rule nary_cong :premises (@p31 @p170) :args (@t100)) % 0.38/0.59 (step @p172 :rule cong :premises (@p171) :args (@t101)) % 0.38/0.59 (step @p173 :rule trans :premises (@p172 @p169)) % 0.38/0.59 (step @p174 :rule cong :premises (@p173) :args (@t102)) % 0.38/0.59 (step @p175 :rule beta-reduce :args ((= (_ @t46 @t12) @t102))) % 0.38/0.59 (step @p176 :rule trans :premises (@p175 @p174)) % 0.38/0.59 (step @p177 :rule ho_cong :premises (@p38 @p176)) % 0.38/0.59 (step @p178 :rule trans :premises (@p177 @p167)) % 0.38/0.59 (step @p179 :rule ho_cong :premises (@p60 @p119)) % 0.38/0.59 (step @p180 :rule ho_cong :premises (@p11 @p179)) % 0.38/0.59 (step @p181 :rule trans :premises (@p180 @p178)) % 0.38/0.59 (step @p182 :rule eq_resolve :premises (@p8 @p181)) % 0.38/0.59 (step @p183 :rule instantiate :premises (@p182) :args (@t85)) % 0.38/0.59 (step @p184 :rule cnf_or_pos :args (@t104)) % 0.38/0.59 (step @p185 :rule reordering :premises (@p184) :args ((or @t53 @t103 (not @t104)))) % 0.38/0.59 (step @p186 :rule chain_m_resolution :premises (@p185 @p73 @p183) :args (@t103 @t95 (@list @t51 @t104))) % 0.38/0.59 (step @p187 :rule cnf_or_pos :args (@t107)) % 0.38/0.59 (step @p188 :rule reordering :premises (@p187) :args ((or @t53 @t52 @t106 @t105 (not @t107)))) % 0.38/0.59 (step @p189 false :rule chain_m_resolution :premises (@p188 @p186 @p164 @p142 @p75 @p73) :args (false (@list false false false true false) (@list @t103 @t93 @t107 @t52 @t51))) % 0.38/0.59 ) % 0.38/0.59 % SZS output end Proof % 0.38/0.59 % cvc5 exiting %------------------------------------------------------------------------------