%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV232^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n015.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 08:55:38 AM UTC 2026 % Result : Theorem 120.88s 151.36s % Output : Proof 120.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV232^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n015.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 18:21:34 EDT 2026 % 0.15/0.34 % CPUTime : % 0.31/0.48 %----Proving TH0 % 120.88/151.36 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 120.88/151.36 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 120.88/151.36 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 120.88/151.36 --- Run --ho-elim --full-saturate-quant at 18s... % 120.88/151.36 % SZS status Theorem % 120.88/151.36 % SZS output start Proof % 120.88/151.36 ( % 120.88/151.36 (declare-sort $$unsorted 0) % 120.88/151.36 (declare-const tptp.c0 (-> (-> $$unsorted Bool) Bool)) % 120.88/151.36 (declare-const tptp.cS (-> (-> (-> $$unsorted Bool) Bool) (-> $$unsorted Bool) Bool)) % 120.88/151.36 (define @t1 () (@var "Xx" (-> (-> $$unsorted Bool) Bool))) % 120.88/151.36 (define @t2 () (@var "S0" (-> (-> (-> $$unsorted Bool) Bool) Bool))) % 120.88/151.36 (define @t3 () (_ @t2 @t1)) % 120.88/151.36 (define @t4 () (@var "X" (-> (-> $$unsorted Bool) Bool))) % 120.88/151.36 (define @t5 () (_ tptp.cS @t4)) % 120.88/151.36 (define @t6 () (_ @t2 @t5)) % 120.88/151.36 (define @t7 () (_ @t2 @t4)) % 120.88/151.36 (define @t8 () (@list @t4)) % 120.88/151.36 (define @t9 () (forall @t8 (=> @t7 @t6))) % 120.88/151.36 (define @t10 () (_ @t2 tptp.c0)) % 120.88/151.36 (define @t11 () (and @t10 @t9)) % 120.88/151.36 (define @t12 () (=> @t11 @t3)) % 120.88/151.36 (define @t13 () (@list @t2)) % 120.88/151.36 (define @t14 () (forall @t13 @t12)) % 120.88/151.36 (define @t15 () (@list @t1)) % 120.88/151.36 (define @t16 () (lambda @t15 @t14)) % 120.88/151.36 (define @t17 () (@var "N" (-> (-> $$unsorted Bool) Bool))) % 120.88/151.36 (define @t18 () (@var "P" (-> (-> (-> $$unsorted Bool) Bool) Bool))) % 120.88/151.36 (define @t19 () (_ @t18 @t17)) % 120.88/151.36 (define @t20 () (_ @t18 @t5)) % 120.88/151.36 (define @t21 () (_ @t18 @t4)) % 120.88/151.36 (define @t22 () (forall @t8 (=> @t21 @t20))) % 120.88/151.36 (define @t23 () (_ @t18 tptp.c0)) % 120.88/151.36 (define @t24 () (and @t23 @t22)) % 120.88/151.36 (define @t25 () (=> @t24 @t19)) % 120.88/151.36 (define @t26 () (@list @t18)) % 120.88/151.36 (define @t27 () (forall @t26 @t25)) % 120.88/151.36 (define @t28 () (@list @t17)) % 120.88/151.36 (define @t29 () (lambda @t28 @t27)) % 120.88/151.36 (define @t30 () (= @t29 @t16)) % 120.88/151.36 (define @t31 () (not @t30)) % 120.88/151.36 (define @t32 () (@var "BOUND_VARIABLE_7542" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)))) % 120.88/151.36 (define @t33 () (@var "BOUND_VARIABLE_7547" (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)))) % 120.88/151.36 (define @t34 () (@const 0 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool))) % 120.88/151.36 (define @t35 () (@var "BOUND_VARIABLE_7549" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)))) % 120.88/151.36 (define @t36 () (@const 1 (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) (@ho-elim-sort (-> $$unsorted Bool)) Bool)))) % 120.88/151.36 (define @t37 () (@const 2 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) (@ho-elim-sort (-> $$unsorted Bool)) Bool)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool))))) % 120.88/151.36 (define @t38 () (_ @t37 @t36 @t35)) % 120.88/151.36 (define @t39 () (@list @t35)) % 120.88/151.36 (define @t40 () (not (forall @t39 (or (not (_ @t34 @t33 @t35)) (_ @t34 @t33 @t38))))) % 120.88/151.36 (define @t41 () (@const 3 (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)))) % 120.88/151.36 (define @t42 () (not (_ @t34 @t33 @t41))) % 120.88/151.36 (define @t43 () (@list @t33)) % 120.88/151.36 (define @t44 () (forall @t43 (or @t42 @t40 (_ @t34 @t33 @t32)))) % 120.88/151.36 (define @t45 () (@const 4 (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)))) % 120.88/151.36 (define @t46 () (_ @t34 @t45 @t32)) % 120.88/151.36 (define @t47 () (forall (@list @t32) (= @t44 @t46))) % 120.88/151.36 (define @t48 () (@var "BOUND_VARIABLE_7504" (-> (-> $$unsorted Bool) Bool))) % 120.88/151.36 (define @t49 () (@const 5 (-> (-> (-> $$unsorted Bool) Bool) Bool))) % 120.88/151.36 (define @t50 () (_ @t2 @t5)) % 120.88/151.36 (define @t51 () (_ @t2 @t4)) % 120.88/151.36 (define @t52 () (forall @t8 (or (not @t51) @t50))) % 120.88/151.36 (define @t53 () (not @t52)) % 120.88/151.36 (define @t54 () (_ @t2 tptp.c0)) % 120.88/151.36 (define @t55 () (not @t54)) % 120.88/151.36 (define @t56 () (forall (@list @t48) (= (forall @t13 (or @t55 @t53 (_ @t2 @t48))) (_ @t49 @t48)))) % 120.88/151.36 (define @t57 () (@var "z" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)))) % 120.88/151.36 (define @t58 () (@const 6 (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)))) % 120.88/151.36 (define @t59 () (@list @t57)) % 120.88/151.36 (define @t60 () (forall @t59 (= (_ @t34 @t45 @t57) (_ @t34 @t58 @t57)))) % 120.88/151.36 (define @t61 () (@quantifiers_skolemize @t60 0)) % 120.88/151.36 (define @t62 () (@list @t61)) % 120.88/151.36 (define @t63 () (@var "y" (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)))) % 120.88/151.36 (define @t64 () (@var "x" (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)))) % 120.88/151.36 (define @t65 () (forall (@list @t64 @t63) (or (not (forall @t59 (= (_ @t34 @t64 @t57) (_ @t34 @t63 @t57)))) (= @t64 @t63)))) % 120.88/151.36 (define @t66 () (not @t60)) % 120.88/151.36 (define @t67 () (= @t45 @t58)) % 120.88/151.36 (define @t68 () (or @t66 @t67)) % 120.88/151.36 (define @t69 () (= @t58 @t45)) % 120.88/151.36 (define @t70 () (or @t66 @t69)) % 120.88/151.36 (define @t71 () (not @t67)) % 120.88/151.36 (define @t72 () (@const 7 (-> (-> (-> $$unsorted Bool) Bool) Bool))) % 120.88/151.36 (define @t73 () (not (= @t72 @t49))) % 120.88/151.36 (define @t74 () (_ @t2 @t1)) % 120.88/151.36 (define @t75 () (_ @t18 @t17)) % 120.88/151.36 (define @t76 () (_ @t18 @t5)) % 120.88/151.36 (define @t77 () (_ @t18 @t4)) % 120.88/151.36 (define @t78 () (forall @t8 (or (not @t77) @t76))) % 120.88/151.36 (define @t79 () (not @t78)) % 120.88/151.36 (define @t80 () (_ @t18 tptp.c0)) % 120.88/151.36 (define @t81 () (not @t80)) % 120.88/151.36 (define @t82 () (not @t10)) % 120.88/151.36 (define @t83 () (or @t82 @t53 @t3)) % 120.88/151.36 (define @t84 () (and @t10 @t52)) % 120.88/151.36 (define @t85 () (not @t7)) % 120.88/151.36 (define @t86 () (or @t85 @t6)) % 120.88/151.36 (define @t87 () (not @t23)) % 120.88/151.36 (define @t88 () (or @t87 @t79 @t19)) % 120.88/151.36 (define @t89 () (and @t23 @t78)) % 120.88/151.36 (define @t90 () (not @t21)) % 120.88/151.36 (define @t91 () (or @t90 @t20)) % 120.88/151.36 (define @t92 () (@list true false)) % 120.88/151.36 (define @t93 () (_ @t34 @t58 @t61)) % 120.88/151.36 (define @t94 () (_ @t34 @t45 @t61)) % 120.88/151.36 (define @t95 () (= @t94 @t93)) % 120.88/151.36 (define @t96 () (forall @t43 (or @t42 @t40 (_ @t34 @t33 @t61)))) % 120.88/151.36 (define @t97 () (= @t94 @t96)) % 120.88/151.36 (define @t98 () (not @t97)) % 120.88/151.36 (define @t99 () (not @t94)) % 120.88/151.36 (define @t100 () (@var "BOUND_VARIABLE_7577" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)))) % 120.88/151.36 (define @t101 () (@var "BOUND_VARIABLE_7580" (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)))) % 120.88/151.36 (define @t102 () (not (forall @t39 (or (not (_ @t34 @t101 @t35)) (_ @t34 @t101 @t38))))) % 120.88/151.36 (define @t103 () (not (_ @t34 @t101 @t41))) % 120.88/151.36 (define @t104 () (@list @t101)) % 120.88/151.36 (define @t105 () (forall @t104 (or @t103 @t102 (_ @t34 @t101 @t100)))) % 120.88/151.36 (define @t106 () (_ @t34 @t58 @t100)) % 120.88/151.36 (define @t107 () (forall (@list @t100) (= @t105 @t106))) % 120.88/151.36 (define @t108 () (@var "BOUND_VARIABLE_7512" (-> (-> $$unsorted Bool) Bool))) % 120.88/151.36 (define @t109 () (forall (@list @t108) (= (forall @t26 (or @t81 @t79 (_ @t18 @t108))) (_ @t72 @t108)))) % 120.88/151.36 (define @t110 () (forall @t104 (or @t103 @t102 (_ @t34 @t101 @t61)))) % 120.88/151.36 (define @t111 () (= @t93 @t110)) % 120.88/151.36 (define @t112 () (not @t111)) % 120.88/151.36 (define @t113 () (@var "BOUND_VARIABLE_8452" (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)))) % 120.88/151.36 (define @t114 () (@var "BOUND_VARIABLE_8453" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)))) % 120.88/151.36 (define @t115 () (@list @t113 @t114)) % 120.88/151.36 (define @t116 () (not @t96)) % 120.88/151.36 (assume @p1 @t31) % 120.88/151.36 (assume @p2 true) % 120.88/151.36 (step @p3 :rule eq-symm :args (@t44 @t46)) % 120.88/151.36 (step @p4 :rule cong :premises (@p3) :args (@t47)) % 120.88/151.36 ; WARNING: add trust step for TRUST % 120.88/151.36 ; trust TRUST PREPROCESS_HO_ELIM % 120.88/151.36 (step @p5 :rule trust :premises () :args ((= @t56 @t47))) % 120.88/151.36 (step @p6 :rule trans :premises (@p5 @p4)) % 120.88/151.36 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 120.88/151.36 (step @p7 :rule trust :premises () :args (@t56)) % 120.88/151.36 (step @p8 :rule eq_resolve :premises (@p7 @p6)) % 120.88/151.36 (step @p9 :rule instantiate :premises (@p8) :args (@t62)) % 120.88/151.36 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 120.88/151.36 (step @p10 :rule trust :premises () :args (@t65)) % 120.88/151.36 (step @p11 :rule eq-symm :args (@t45 @t58)) % 120.88/151.36 (step @p12 :rule refl :args (@t66)) % 120.88/151.36 (step @p13 :rule nary_cong :premises (@p12 @p11) :args (@t68)) % 120.88/151.36 (step @p14 :rule refl :args (@t65)) % 120.88/151.36 (step @p15 :rule cong :premises (@p14 @p13) :args ((=> @t65 @t68))) % 120.88/151.36 (assume-push @p155 @t65) % 120.88/151.36 (step @p17 :rule instantiate :premises (@p10) :args ((@list @t45 @t58))) % 120.88/151.36 (step-pop @p156 :rule scope :premises (@p17)) % 120.88/151.36 (step @p18 :rule process_scope :premises (@p156) :args (@t68)) % 120.88/151.36 (step @p20 :rule eq_resolve :premises (@p18 @p15)) % 120.88/151.36 (step @p21 :rule implies_elim :premises (@p20)) % 120.88/151.36 (step @p22 :rule chain_m_resolution :premises (@p21 @p10) :args (@t70 (@list false) (@list @t65))) % 120.88/151.36 (step @p23 :rule cong :premises (@p11) :args (@t71)) % 120.88/151.36 ; trust TRUST PREPROCESS_HO_ELIM % 120.88/151.36 (step @p24 :rule trust :premises () :args ((= (not (= @t49 @t72)) @t71))) % 120.88/151.36 (step @p25 :rule eq-symm :args (@t72 @t49)) % 120.88/151.36 (step @p26 :rule cong :premises (@p25) :args (@t73)) % 120.88/151.36 ; trust TRUST PREPROCESS_HO_ELIM % 120.88/151.36 (step @p27 :rule trust :premises () :args ((= (not (= (lambda @t28 (forall @t26 (or @t81 @t79 @t75))) (lambda @t15 (forall @t13 (or @t55 @t53 @t74))))) @t73))) % 120.88/151.36 (step @p28 :rule refl :args (@t74)) % 120.88/151.36 (step @p29 :rule refl :args (@t3)) % 120.88/151.36 (step @p30 :rule cong :premises (@p29 @p28) :args ((= @t3 @t74))) % 120.88/151.36 (step @p31 :rule symm :premises (@p30)) % 120.88/151.36 (step @p32 :rule eq_resolve :premises (@p29 @p31)) % 120.88/151.36 (step @p33 :rule refl :args (@t53)) % 120.88/151.36 (step @p34 :rule refl :args (@t54)) % 120.88/151.36 (step @p35 :rule refl :args (@t10)) % 120.88/151.36 (step @p36 :rule cong :premises (@p35 @p34) :args ((= @t10 @t54))) % 120.88/151.36 (step @p37 :rule symm :premises (@p36)) % 120.88/151.36 (step @p38 :rule eq_resolve :premises (@p35 @p37)) % 120.88/151.36 (step @p39 :rule cong :premises (@p38) :args (@t82)) % 120.88/151.36 (step @p40 :rule nary_cong :premises (@p39 @p33 @p32) :args (@t83)) % 120.88/151.36 (step @p41 :rule cong :premises (@p40) :args ((forall @t13 @t83))) % 120.88/151.36 (step @p42 :rule aci_norm :args ((= (or (or @t82 @t53) @t3) @t83))) % 120.88/151.36 (step @p43 :rule bool-and-de-morgan :args (@t10 @t52 true)) % 120.88/151.36 (step @p44 :rule nary_cong :premises (@p43 @p29) :args ((or (not @t84) @t3))) % 120.88/151.36 (step @p45 :rule trans :premises (@p44 @p42)) % 120.88/151.36 (step @p46 :rule bool-impl-elim :args (@t84 @t3)) % 120.88/151.36 (step @p47 :rule trans :premises (@p46 @p45)) % 120.88/151.36 (step @p48 :rule cong :premises (@p47) :args ((forall @t13 (=> @t84 @t3)))) % 120.88/151.36 (step @p49 :rule trans :premises (@p48 @p41)) % 120.88/151.36 (step @p50 :rule refl :args (@t3)) % 120.88/151.36 (step @p51 :rule refl :args (@t50)) % 120.88/151.36 (step @p52 :rule refl :args (@t6)) % 120.88/151.36 (step @p53 :rule cong :premises (@p52 @p51) :args ((= @t6 @t50))) % 120.88/151.36 (step @p54 :rule symm :premises (@p53)) % 120.88/151.36 (step @p55 :rule eq_resolve :premises (@p52 @p54)) % 120.88/151.36 (step @p56 :rule refl :args (@t51)) % 120.88/151.36 (step @p57 :rule refl :args (@t7)) % 120.88/151.36 (step @p58 :rule cong :premises (@p57 @p56) :args ((= @t7 @t51))) % 120.88/151.36 (step @p59 :rule symm :premises (@p58)) % 120.88/151.36 (step @p60 :rule eq_resolve :premises (@p57 @p59)) % 120.88/151.36 (step @p61 :rule cong :premises (@p60) :args (@t85)) % 120.88/151.36 (step @p62 :rule nary_cong :premises (@p61 @p55) :args (@t86)) % 120.88/151.36 (step @p63 :rule cong :premises (@p62) :args ((forall @t8 @t86))) % 120.88/151.36 (step @p64 :rule bool-impl-elim :args (@t7 @t6)) % 120.88/151.36 (step @p65 :rule cong :premises (@p64) :args (@t9)) % 120.88/151.36 (step @p66 :rule trans :premises (@p65 @p63)) % 120.88/151.36 (step @p67 :rule refl :args (@t10)) % 120.88/151.36 (step @p68 :rule nary_cong :premises (@p67 @p66) :args (@t11)) % 120.88/151.36 (step @p69 :rule cong :premises (@p68 @p50) :args (@t12)) % 120.88/151.36 (step @p70 :rule cong :premises (@p69) :args (@t14)) % 120.88/151.36 (step @p71 :rule trans :premises (@p70 @p49)) % 120.88/151.36 (step @p72 :rule cong :premises (@p71) :args (@t16)) % 120.88/151.36 (step @p73 :rule refl :args (@t75)) % 120.88/151.36 (step @p74 :rule refl :args (@t19)) % 120.88/151.36 (step @p75 :rule cong :premises (@p74 @p73) :args ((= @t19 @t75))) % 120.88/151.36 (step @p76 :rule symm :premises (@p75)) % 120.88/151.36 (step @p77 :rule eq_resolve :premises (@p74 @p76)) % 120.88/151.36 (step @p78 :rule refl :args (@t79)) % 120.88/151.36 (step @p79 :rule refl :args (@t80)) % 120.88/151.36 (step @p80 :rule refl :args (@t23)) % 120.88/151.36 (step @p81 :rule cong :premises (@p80 @p79) :args ((= @t23 @t80))) % 120.88/151.36 (step @p82 :rule symm :premises (@p81)) % 120.88/151.36 (step @p83 :rule eq_resolve :premises (@p80 @p82)) % 120.88/151.36 (step @p84 :rule cong :premises (@p83) :args (@t87)) % 120.88/151.36 (step @p85 :rule nary_cong :premises (@p84 @p78 @p77) :args (@t88)) % 120.88/151.36 (step @p86 :rule cong :premises (@p85) :args ((forall @t26 @t88))) % 120.88/151.36 (step @p87 :rule aci_norm :args ((= (or (or @t87 @t79) @t19) @t88))) % 120.88/151.36 (step @p88 :rule bool-and-de-morgan :args (@t23 @t78 true)) % 120.88/151.36 (step @p89 :rule nary_cong :premises (@p88 @p74) :args ((or (not @t89) @t19))) % 120.88/151.36 (step @p90 :rule trans :premises (@p89 @p87)) % 120.88/151.36 (step @p91 :rule bool-impl-elim :args (@t89 @t19)) % 120.88/151.36 (step @p92 :rule trans :premises (@p91 @p90)) % 120.88/151.36 (step @p93 :rule cong :premises (@p92) :args ((forall @t26 (=> @t89 @t19)))) % 120.88/151.36 (step @p94 :rule trans :premises (@p93 @p86)) % 120.88/151.36 (step @p95 :rule refl :args (@t19)) % 120.88/151.36 (step @p96 :rule refl :args (@t76)) % 120.88/151.36 (step @p97 :rule refl :args (@t20)) % 120.88/151.36 (step @p98 :rule cong :premises (@p97 @p96) :args ((= @t20 @t76))) % 120.88/151.36 (step @p99 :rule symm :premises (@p98)) % 120.88/151.36 (step @p100 :rule eq_resolve :premises (@p97 @p99)) % 120.88/151.36 (step @p101 :rule refl :args (@t77)) % 120.88/151.36 (step @p102 :rule refl :args (@t21)) % 120.88/151.36 (step @p103 :rule cong :premises (@p102 @p101) :args ((= @t21 @t77))) % 120.88/151.36 (step @p104 :rule symm :premises (@p103)) % 120.88/151.36 (step @p105 :rule eq_resolve :premises (@p102 @p104)) % 120.88/151.36 (step @p106 :rule cong :premises (@p105) :args (@t90)) % 120.88/151.36 (step @p107 :rule nary_cong :premises (@p106 @p100) :args (@t91)) % 120.88/151.36 (step @p108 :rule cong :premises (@p107) :args ((forall @t8 @t91))) % 120.88/151.36 (step @p109 :rule bool-impl-elim :args (@t21 @t20)) % 120.88/151.36 (step @p110 :rule cong :premises (@p109) :args (@t22)) % 120.88/151.36 (step @p111 :rule trans :premises (@p110 @p108)) % 120.88/151.36 (step @p112 :rule refl :args (@t23)) % 120.88/151.36 (step @p113 :rule nary_cong :premises (@p112 @p111) :args (@t24)) % 120.88/151.36 (step @p114 :rule cong :premises (@p113 @p95) :args (@t25)) % 120.88/151.36 (step @p115 :rule cong :premises (@p114) :args (@t27)) % 120.88/151.36 (step @p116 :rule trans :premises (@p115 @p94)) % 120.88/151.36 (step @p117 :rule cong :premises (@p116) :args (@t29)) % 120.88/151.36 (step @p118 :rule cong :premises (@p117 @p72) :args (@t30)) % 120.88/151.36 (step @p119 :rule cong :premises (@p118) :args (@t31)) % 120.88/151.36 (step @p120 :rule trans :premises (@p119 @p27 @p26 @p24 @p23)) % 120.88/151.36 (step @p121 :rule eq_resolve :premises (@p1 @p120)) % 120.88/151.36 (step @p122 :rule cnf_or_pos :args (@t70)) % 120.88/151.36 (step @p123 :rule reordering :premises (@p122) :args ((or @t69 @t66 (not @t70)))) % 120.88/151.36 (step @p124 :rule chain_m_resolution :premises (@p123 @p121 @p22) :args (@t66 @t92 (@list @t69 @t70))) % 120.88/151.36 (step @p125 :rule skolemize :premises (@p124)) % 120.88/151.36 (step @p126 :rule cnf_equiv_neg2 :args (@t95)) % 120.88/151.36 (step @p127 :rule cnf_equiv_pos1 :args (@t97)) % 120.88/151.36 (step @p128 :rule reordering :premises (@p127) :args ((or @t99 @t96 @t98))) % 120.88/151.36 (step @p129 :rule eq-symm :args (@t105 @t106)) % 120.88/151.36 (step @p130 :rule cong :premises (@p129) :args (@t107)) % 120.88/151.36 ; trust TRUST PREPROCESS_HO_ELIM % 120.88/151.36 (step @p131 :rule trust :premises () :args ((= @t109 @t107))) % 120.88/151.36 (step @p132 :rule trans :premises (@p131 @p130)) % 120.88/151.36 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 120.88/151.36 (step @p133 :rule trust :premises () :args (@t109)) % 120.88/151.36 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 120.88/151.36 (step @p135 :rule instantiate :premises (@p134) :args (@t62)) % 120.88/151.36 (step @p136 :rule cnf_equiv_pos2 :args (@t111)) % 120.88/151.36 (step @p137 :rule reordering :premises (@p136) :args ((or @t93 (not @t110) @t112))) % 120.88/151.36 (step @p138 :rule alpha_equiv :args ((forall (@list @t113) (or (not (_ @t34 @t113 @t41)) (not (forall (@list @t114) (or (not (_ @t34 @t113 @t114)) (_ @t34 @t113 (_ @t37 @t36 @t114))))) (_ @t34 @t113 @t61))) @t115 (@list @t101 @t35))) % 120.88/151.36 (step @p139 :rule alpha_equiv :args (@t96 (@list @t33 @t35) @t115)) % 120.88/151.36 (step @p140 :rule trans :premises (@p139 @p138)) % 120.88/151.36 (step @p141 :rule equiv_elim1 :premises (@p140)) % 120.88/151.36 (step @p142 :rule reordering :premises (@p141) :args ((or @t110 @t116))) % 120.88/151.36 (step @p143 :rule chain_m_resolution :premises (@p142 @p137 @p135 @p128 @p9 @p126 @p125) :args (@t99 (@list true false false false true true) (@list @t110 @t111 @t96 @t97 @t93 @t95))) % 120.88/151.36 (step @p144 :rule cnf_equiv_pos2 :args (@t97)) % 120.88/151.36 (step @p145 :rule reordering :premises (@p144) :args ((or @t94 @t116 @t98))) % 120.88/151.36 (step @p146 :rule chain_m_resolution :premises (@p145 @p143 @p9) :args (@t116 @t92 (@list @t94 @t97))) % 120.88/151.36 (step @p147 :rule cnf_equiv_neg1 :args (@t95)) % 120.88/151.36 (step @p148 :rule reordering :premises (@p147) :args ((or @t94 @t93 @t95))) % 120.88/151.36 (step @p149 :rule chain_m_resolution :premises (@p148 @p143 @p125) :args (@t93 (@list true true) (@list @t94 @t95))) % 120.88/151.36 (step @p150 :rule cnf_equiv_pos1 :args (@t111)) % 120.88/151.36 (step @p151 :rule reordering :premises (@p150) :args ((or (not @t93) @t110 @t112))) % 120.88/151.36 (step @p152 :rule chain_m_resolution :premises (@p151 @p149 @p135) :args (@t110 (@list false false) (@list @t93 @t111))) % 120.88/151.36 (step @p153 :rule equiv_elim2 :premises (@p140)) % 120.88/151.36 (step @p154 false :rule chain_m_resolution :premises (@p153 @p152 @p146) :args (false (@list false true) (@list @t110 @t96))) % 120.88/151.36 ) % 120.88/151.36 % SZS output end Proof % 120.88/151.36 % cvc5 exiting %------------------------------------------------------------------------------