%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU828^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n006.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 08:53:23 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU828^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n006.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 17:54:49 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.37/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort $$unsorted 0) % 0.37/0.58 (define tptp.seteq () (let ((_let_1 (@var "U" (-> $$unsorted Bool)))) (let ((_let_2 (@var "Y" (-> (-> $$unsorted Bool) Bool)))) (let ((_let_3 (@var "X" (-> (-> $$unsorted Bool) Bool)))) (lambda (@list _let_3 _let_2) (forall (@list _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.37/0.58 (define tptp.subseteq () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (forall (@list _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.37/0.58 (define tptp.powerset () (let ((_let_1 (@var "X" (-> $$unsorted Bool)))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ (_ tptp.subseteq _let_2) _let_1))))) % 0.37/0.58 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.37/0.58 (define @t1 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.58 (define @t2 () (= @t1 tptp.emptyset)) % 0.37/0.58 (define @t3 () (@list @t1)) % 0.37/0.58 (define @t4 () (lambda @t3 @t2)) % 0.37/0.58 (define @t5 () (not (_ (_ tptp.seteq (_ tptp.powerset tptp.emptyset)) @t4))) % 0.37/0.58 (define @t6 () (@var "U" (-> $$unsorted Bool))) % 0.37/0.58 (define @t7 () (@var "Y" (-> (-> $$unsorted Bool) Bool))) % 0.37/0.58 (define @t8 () (_ @t7 @t6)) % 0.37/0.58 (define @t9 () (@var "X" (-> (-> $$unsorted Bool) Bool))) % 0.37/0.58 (define @t10 () (_ @t9 @t6)) % 0.37/0.58 (define @t11 () (= @t10 @t8)) % 0.37/0.58 (define @t12 () (@list @t6)) % 0.37/0.58 (define @t13 () (forall @t12 @t11)) % 0.37/0.58 (define @t14 () (@list @t9 @t7)) % 0.37/0.58 (define @t15 () (lambda @t14 @t13)) % 0.37/0.58 (define @t16 () (@var "U" $$unsorted)) % 0.37/0.58 (define @t17 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.58 (define @t18 () (_ @t17 @t16)) % 0.37/0.58 (define @t19 () (_ @t1 @t16)) % 0.37/0.58 (define @t20 () (@list @t16)) % 0.37/0.58 (define @t21 () (forall @t20 (=> @t19 @t18))) % 0.37/0.58 (define @t22 () (@list @t1 @t17)) % 0.37/0.58 (define @t23 () (lambda @t22 @t21)) % 0.37/0.58 (define @t24 () (lambda @t22 (_ (_ tptp.subseteq @t17) @t1))) % 0.37/0.58 (define @t25 () (@var "X" $$unsorted)) % 0.37/0.58 (define @t26 () (lambda (@list @t25) false)) % 0.37/0.58 (define @t27 () (@var "BOUND_VARIABLE_7537" $$unsorted)) % 0.37/0.58 (define @t28 () (lambda (@list @t27) false)) % 0.37/0.58 (define @t29 () (= @t6 @t28)) % 0.37/0.58 (define @t30 () (@var "BOUND_VARIABLE_7567" (-> $$unsorted Bool))) % 0.37/0.58 (define @t31 () (= @t30 @t28)) % 0.37/0.58 (define @t32 () (@list @t30)) % 0.37/0.58 (define @t33 () (lambda @t32 (ite @t31 true false))) % 0.37/0.58 (define @t34 () (_ @t33 @t6)) % 0.37/0.58 (define @t35 () (forall @t20 (not (_ @t6 @t16)))) % 0.37/0.58 (define @t36 () (forall @t12 (= @t34 @t35))) % 0.37/0.58 (define @t37 () (_ @t7 @t6)) % 0.37/0.58 (define @t38 () (@list @t7)) % 0.37/0.58 (define @t39 () (= @t1 @t26)) % 0.37/0.58 (define @t40 () (lambda @t3 @t39)) % 0.37/0.58 (define @t41 () (_ @t17 @t16)) % 0.37/0.58 (define @t42 () (not @t41)) % 0.37/0.58 (define @t43 () (@list @t17)) % 0.37/0.58 (define @t44 () (lambda @t43 (forall @t20 @t42))) % 0.37/0.58 (define @t45 () (_ @t44 @t6)) % 0.37/0.58 (define @t46 () (forall @t12 (= @t45 @t37))) % 0.37/0.58 (define @t47 () (lambda @t38 @t46)) % 0.37/0.58 (define @t48 () (_ @t9 @t6)) % 0.37/0.58 (define @t49 () (lambda @t14 (forall @t12 (= @t48 @t37)))) % 0.37/0.58 (define @t50 () (_ @t28 @t16)) % 0.37/0.58 (define @t51 () (or @t42 @t50)) % 0.37/0.58 (define @t52 () (forall @t20 @t51)) % 0.37/0.58 (define @t53 () (lambda @t43 @t52)) % 0.37/0.58 (define @t54 () (_ @t1 @t16)) % 0.37/0.58 (define @t55 () (forall @t20 (or @t42 @t54))) % 0.37/0.58 (define @t56 () (lambda @t22 @t55)) % 0.37/0.58 (define @t57 () (@var "BOUND_VARIABLE_7470" (-> $$unsorted Bool))) % 0.37/0.58 (define @t58 () (_ @t57 @t16)) % 0.37/0.58 (define @t59 () (lambda (@list @t57) (forall @t20 (or @t42 @t58)))) % 0.37/0.58 (define @t60 () (not @t54)) % 0.37/0.58 (define @t61 () (not @t19)) % 0.37/0.58 (define @t62 () (or @t61 @t18)) % 0.37/0.58 (define @t63 () (@purify @t28)) % 0.37/0.58 (define @t64 () (forall @t12 (= @t35 @t29))) % 0.37/0.58 (define @t65 () (@quantifiers_skolemize @t64 0)) % 0.37/0.58 (define @t66 () (= @t65 @t63)) % 0.37/0.58 (define @t67 () (forall @t20 (not (_ @t65 @t16)))) % 0.37/0.58 (define @t68 () (= @t67 @t66)) % 0.37/0.58 (define @t69 () (not @t68)) % 0.37/0.58 (define @t70 () (not @t64)) % 0.37/0.58 (define @t71 () (= @t28 @t65)) % 0.37/0.58 (define @t72 () (= @t67 @t71)) % 0.37/0.58 (define @t73 () (not @t72)) % 0.37/0.58 (define @t74 () (= @t67 (= @t65 @t28))) % 0.37/0.58 (define @t75 () (not @t74)) % 0.37/0.58 (define @t76 () (@list true)) % 0.37/0.58 (define @t77 () (@const 0 $$unsorted)) % 0.37/0.58 (define @t78 () (_ @t65 @t77)) % 0.37/0.58 (define @t79 () (_ @t28 @t77)) % 0.37/0.58 (define @t80 () (_ @t63 @t77)) % 0.37/0.58 (define @t81 () (= @t78 @t80)) % 0.37/0.58 (define @t82 () (not @t81)) % 0.37/0.58 (define @t83 () (or @t66 @t82)) % 0.37/0.58 (define @t84 () (not @t67)) % 0.37/0.58 (define @t85 () (_ @t65 (@quantifiers_skolemize @t67 0))) % 0.37/0.58 (define @t86 () (not (not @t85))) % 0.37/0.58 (define @t87 () (=> @t66 (= @t85 false))) % 0.37/0.58 (assume @p1 @t5) % 0.37/0.58 (assume @p2 true) % 0.37/0.58 (step @p3 (= tptp.seteq @t15) :rule refl :args (@t15)) % 0.37/0.58 (step @p4 (= tptp.subseteq @t23) :rule refl :args (@t23)) % 0.37/0.58 (step @p5 (= tptp.powerset @t24) :rule refl :args (@t24)) % 0.37/0.58 (step @p6 (= tptp.emptyset @t26) :rule refl :args (@t26)) % 0.37/0.58 (step @p7 :rule aci_norm :args ((= (or @t29 false) @t29))) % 0.37/0.58 (step @p8 :rule ite-then-true :args (@t29 false)) % 0.37/0.58 (step @p9 :rule trans :premises (@p8 @p7)) % 0.37/0.58 (step @p10 :rule beta-reduce :args ((= @t34 (ite @t29 true false)))) % 0.37/0.58 (step @p11 :rule trans :premises (@p10 @p9)) % 0.37/0.58 (step @p12 :rule refl :args (@t35)) % 0.37/0.58 (step @p13 :rule cong :premises (@p12 @p11) :args ((= @t35 @t34))) % 0.37/0.58 (step @p14 :rule eq-symm :args (@t34 @t35)) % 0.37/0.58 (step @p15 :rule trans :premises (@p14 @p13)) % 0.37/0.58 (step @p16 :rule cong :premises (@p15) :args (@t36)) % 0.37/0.58 (step @p17 :rule beta-reduce :args ((= (_ (lambda @t38 (forall @t12 (= @t37 @t35))) @t33) @t36))) % 0.37/0.58 (step @p18 :rule trans :premises (@p17 @p16)) % 0.37/0.58 (step @p19 :rule refl :args (@t33)) % 0.37/0.58 (step @p20 :rule symm :premises (@p19)) % 0.37/0.58 (step @p21 :rule aci_norm :args ((= (or @t31 false) @t31))) % 0.37/0.58 (step @p22 :rule ite-then-true :args (@t31 false)) % 0.37/0.58 (step @p23 :rule trans :premises (@p22 @p21)) % 0.37/0.58 (step @p24 :rule symm :premises (@p23)) % 0.37/0.58 (step @p25 :rule cong :premises (@p24) :args ((lambda @t32 @t31))) % 0.37/0.58 (step @p26 :rule alpha_equiv :args ((lambda @t3 (= @t1 @t28)) (@list @t1) (@list @t30))) % 0.37/0.58 (step @p27 :rule trans :premises (@p26 @p25)) % 0.37/0.58 (step @p28 :rule trans :premises (@p27 @p20)) % 0.37/0.58 (step @p29 :rule refl :args (@t28)) % 0.37/0.58 (step @p30 :rule symm :premises (@p29)) % 0.37/0.58 (step @p31 :rule alpha_equiv :args (@t26 (@list @t25) (@list @t27))) % 0.37/0.58 (step @p32 :rule trans :premises (@p31 @p30)) % 0.37/0.58 (step @p33 :rule refl :args (@t1)) % 0.37/0.58 (step @p34 :rule cong :premises (@p33 @p32) :args (@t39)) % 0.37/0.58 (step @p35 :rule cong :premises (@p34) :args (@t40)) % 0.37/0.58 (step @p36 :rule trans :premises (@p35 @p28)) % 0.37/0.58 (step @p37 :rule beta-reduce :args ((= @t45 @t35))) % 0.37/0.58 (step @p38 :rule refl :args (@t37)) % 0.37/0.58 (step @p39 :rule cong :premises (@p38 @p37) :args ((= @t37 @t45))) % 0.37/0.58 (step @p40 :rule eq-symm :args (@t45 @t37)) % 0.37/0.58 (step @p41 :rule trans :premises (@p40 @p39)) % 0.37/0.58 (step @p42 :rule cong :premises (@p41) :args (@t46)) % 0.37/0.58 (step @p43 :rule cong :premises (@p42) :args (@t47)) % 0.37/0.58 (step @p44 :rule beta-reduce :args ((= (_ @t49 @t44) @t47))) % 0.37/0.58 (step @p45 :rule trans :premises (@p44 @p43)) % 0.37/0.58 (step @p46 :rule aci_norm :args ((= (or @t42 false) @t42))) % 0.37/0.58 (step @p47 :rule beta-reduce :args ((= @t50 false))) % 0.37/0.58 (step @p48 :rule refl :args (@t42)) % 0.37/0.58 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t51)) % 0.37/0.58 (step @p50 :rule trans :premises (@p49 @p46)) % 0.37/0.58 (step @p51 :rule cong :premises (@p50) :args (@t52)) % 0.37/0.58 (step @p52 :rule cong :premises (@p51) :args (@t53)) % 0.37/0.58 (step @p53 :rule beta-reduce :args ((= (_ @t56 @t28) @t53))) % 0.37/0.58 (step @p54 :rule trans :premises (@p53 @p52)) % 0.37/0.58 (step @p55 :rule refl :args (@t56)) % 0.37/0.58 (step @p56 :rule ho_cong :premises (@p55 @p32)) % 0.37/0.58 (step @p57 :rule trans :premises (@p56 @p54)) % 0.37/0.58 (step @p58 :rule refl :args (@t49)) % 0.37/0.58 (step @p59 :rule ho_cong :premises (@p58 @p57)) % 0.37/0.58 (step @p60 :rule trans :premises (@p59 @p45)) % 0.37/0.58 (step @p61 :rule ho_cong :premises (@p60 @p36)) % 0.37/0.58 (step @p62 :rule trans :premises (@p61 @p18)) % 0.37/0.58 (step @p63 :rule cong :premises (@p62) :args ((not (_ (_ @t49 (_ @t56 @t26)) @t40)))) % 0.37/0.58 (step @p64 :rule cong :premises (@p33 @p6) :args (@t2)) % 0.37/0.58 (step @p65 :rule cong :premises (@p64) :args (@t4)) % 0.37/0.58 (step @p66 :rule beta-reduce :args ((= (_ @t59 @t1) @t55))) % 0.37/0.58 (step @p67 :rule beta-reduce :args ((= (_ (lambda (@list @t1 @t57) (forall @t20 (or @t60 @t58))) @t17) @t59))) % 0.37/0.58 (step @p68 :rule refl :args (@t17)) % 0.37/0.58 (step @p69 :rule alpha_equiv :args ((lambda @t22 (forall @t20 (or @t60 @t41))) (@list @t17) (@list @t57))) % 0.37/0.58 (step @p70 :rule ho_cong :premises (@p69 @p68)) % 0.37/0.58 (step @p71 :rule trans :premises (@p70 @p67)) % 0.37/0.58 (step @p72 :rule ho_cong :premises (@p71 @p33)) % 0.37/0.58 (step @p73 :rule trans :premises (@p72 @p66)) % 0.37/0.58 (step @p74 :rule refl :args (@t17)) % 0.37/0.58 (step @p75 :rule refl :args (@t41)) % 0.37/0.58 (step @p76 :rule refl :args (@t18)) % 0.37/0.58 (step @p77 :rule cong :premises (@p76 @p75) :args ((= @t18 @t41))) % 0.37/0.58 (step @p78 :rule symm :premises (@p77)) % 0.37/0.58 (step @p79 :rule eq_resolve :premises (@p76 @p78)) % 0.37/0.58 (step @p80 :rule refl :args (@t54)) % 0.37/0.58 (step @p81 :rule refl :args (@t19)) % 0.37/0.58 (step @p82 :rule cong :premises (@p81 @p80) :args ((= @t19 @t54))) % 0.37/0.58 (step @p83 :rule symm :premises (@p82)) % 0.37/0.58 (step @p84 :rule eq_resolve :premises (@p81 @p83)) % 0.37/0.58 (step @p85 :rule cong :premises (@p84) :args (@t61)) % 0.37/0.58 (step @p86 :rule nary_cong :premises (@p85 @p79) :args (@t62)) % 0.37/0.58 (step @p87 :rule cong :premises (@p86) :args ((forall @t20 @t62))) % 0.37/0.58 (step @p88 :rule bool-impl-elim :args (@t19 @t18)) % 0.37/0.58 (step @p89 :rule cong :premises (@p88) :args (@t21)) % 0.37/0.58 (step @p90 :rule trans :premises (@p89 @p87)) % 0.37/0.58 (step @p91 :rule cong :premises (@p90) :args (@t23)) % 0.37/0.58 (step @p92 :rule trans :premises (@p4 @p91)) % 0.37/0.58 (step @p93 :rule ho_cong :premises (@p92 @p74)) % 0.37/0.58 (step @p94 :rule ho_cong :premises (@p93 @p33)) % 0.37/0.58 (step @p95 :rule trans :premises (@p94 @p73)) % 0.37/0.58 (step @p96 :rule cong :premises (@p95) :args (@t24)) % 0.37/0.58 (step @p97 :rule trans :premises (@p5 @p96)) % 0.37/0.58 (step @p98 :rule ho_cong :premises (@p97 @p6)) % 0.37/0.58 (step @p99 :rule refl :args (@t37)) % 0.37/0.58 (step @p100 :rule refl :args (@t8)) % 0.37/0.58 (step @p101 :rule cong :premises (@p100 @p99) :args ((= @t8 @t37))) % 0.37/0.58 (step @p102 :rule symm :premises (@p101)) % 0.37/0.58 (step @p103 :rule eq_resolve :premises (@p100 @p102)) % 0.37/0.58 (step @p104 :rule refl :args (@t48)) % 0.37/0.58 (step @p105 :rule refl :args (@t10)) % 0.37/0.58 (step @p106 :rule cong :premises (@p105 @p104) :args ((= @t10 @t48))) % 0.37/0.58 (step @p107 :rule symm :premises (@p106)) % 0.37/0.58 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 0.37/0.58 (step @p109 :rule cong :premises (@p108 @p103) :args (@t11)) % 0.37/0.58 (step @p110 :rule cong :premises (@p109) :args (@t13)) % 0.37/0.58 (step @p111 :rule cong :premises (@p110) :args (@t15)) % 0.37/0.58 (step @p112 :rule trans :premises (@p3 @p111)) % 0.37/0.58 (step @p113 :rule ho_cong :premises (@p112 @p98)) % 0.37/0.58 (step @p114 :rule ho_cong :premises (@p113 @p65)) % 0.37/0.58 (step @p115 :rule cong :premises (@p114) :args (@t5)) % 0.37/0.58 (step @p116 :rule trans :premises (@p115 @p63)) % 0.37/0.58 (step @p117 :rule eq_resolve :premises (@p1 @p116)) % 0.37/0.58 (step @p118 :rule refl :args (@t69)) % 0.37/0.58 (step @p119 :rule bool-double-not-elim :args (@t64)) % 0.37/0.58 (step @p120 :rule nary_cong :premises (@p119 @p118) :args ((or (not @t70) @t69))) % 0.37/0.58 (step @p121 :rule eq-symm :args (@t63 @t65)) % 0.37/0.58 (step @p122 :rule refl :args (@t65)) % 0.37/0.58 (step @p123 :rule eq-refl :args (@t28)) % 0.37/0.58 (step @p124 :rule refl :args (@t28)) % 0.37/0.58 (step @p125 :rule cong :premises (@p124 @p30) :args ((= @t28 @t28))) % 0.37/0.58 (step @p126 :rule trans :premises (@p125 @p123)) % 0.37/0.58 (step @p127 :rule skolem_intro :args (@t63)) % 0.37/0.58 (step @p128 :rule cong :premises (@p124 @p127) :args ((= @t28 @t63))) % 0.37/0.58 (step @p129 :rule trans :premises (@p128 @p126)) % 0.37/0.58 (step @p130 :rule true_elim :premises (@p129)) % 0.37/0.58 (step @p131 :rule cong :premises (@p130 @p122) :args (@t71)) % 0.37/0.58 (step @p132 :rule trans :premises (@p131 @p121)) % 0.37/0.58 (step @p133 :rule refl :args (@t67)) % 0.37/0.58 (step @p134 :rule cong :premises (@p133 @p132) :args (@t72)) % 0.37/0.58 (step @p135 :rule cong :premises (@p134) :args (@t73)) % 0.37/0.58 (step @p136 :rule refl :args (@t70)) % 0.37/0.58 (step @p137 :rule cong :premises (@p136 @p135) :args ((=> @t70 @t73))) % 0.37/0.58 (step @p138 :rule eq-symm :args (@t65 @t28)) % 0.37/0.58 (step @p139 :rule cong :premises (@p133 @p138) :args (@t74)) % 0.37/0.58 (step @p140 :rule cong :premises (@p139) :args (@t75)) % 0.37/0.58 (step @p141 :rule cong :premises (@p136 @p140) :args ((=> @t70 @t75))) % 0.37/0.58 (step @p142 :rule trans :premises (@p141 @p137)) % 0.37/0.58 (assume-push @p202 @t70) % 0.37/0.58 (step @p144 :rule skolemize :premises (@p117)) % 0.37/0.58 (step-pop @p203 :rule scope :premises (@p144)) % 0.37/0.58 (step @p145 :rule process_scope :premises (@p203) :args (@t75)) % 0.37/0.58 (step @p147 :rule eq_resolve :premises (@p145 @p142)) % 0.37/0.58 (step @p148 :rule implies_elim :premises (@p147)) % 0.37/0.58 (step @p149 :rule eq_resolve :premises (@p148 @p120)) % 0.37/0.58 (step @p150 :rule chain_m_resolution :premises (@p149 @p117) :args (@t69 @t76 (@list @t64))) % 0.37/0.58 (step @p151 :rule cnf_equiv_neg2 :args (@t68)) % 0.37/0.58 (step @p152 :rule bool-double-not-elim :args (@t78)) % 0.37/0.58 (step @p153 :rule bool-eq-false :args (@t78)) % 0.37/0.58 (step @p154 :rule evaluate :args ((not false))) % 0.37/0.58 (step @p155 :rule beta-reduce :args ((= @t79 false))) % 0.37/0.59 (step @p156 :rule cong :premises (@p155) :args ((not @t79))) % 0.37/0.59 (step @p157 :rule trans :premises (@p156 @p154)) % 0.37/0.59 (step @p158 :rule refl :args (@t77)) % 0.37/0.59 (step @p159 :rule ho_cong :premises (@p127 @p158)) % 0.37/0.59 (step @p160 :rule cong :premises (@p159) :args ((not @t80))) % 0.37/0.59 (step @p161 :rule bool-eq-false :args (@t80)) % 0.37/0.59 (step @p162 :rule trans :premises (@p161 @p160 @p157)) % 0.37/0.59 (step @p163 :rule true_elim :premises (@p162)) % 0.37/0.59 (step @p164 :rule refl :args (@t78)) % 0.37/0.59 (step @p165 :rule cong :premises (@p164 @p163) :args (@t81)) % 0.37/0.59 (step @p166 :rule trans :premises (@p165 @p153)) % 0.37/0.59 (step @p167 :rule cong :premises (@p166) :args (@t82)) % 0.37/0.59 (step @p168 :rule trans :premises (@p167 @p152)) % 0.37/0.59 (step @p169 :rule refl :args (@t66)) % 0.37/0.59 (step @p170 :rule nary_cong :premises (@p169 @p168) :args (@t83)) % 0.37/0.59 ; WARNING: add trust step for TRUST % 0.37/0.59 ; trust TRUST THEORY_LEMMA % 0.37/0.59 (step @p171 :rule trust :premises () :args (@t83)) % 0.37/0.59 (step @p172 :rule eq_resolve :premises (@p171 @p170)) % 0.37/0.59 (assume-push @p204 @t67) % 0.37/0.59 (step @p174 :rule instantiate :premises (@p204) :args ((@list @t77))) % 0.37/0.59 (step-pop @p205 :rule scope :premises (@p174)) % 0.37/0.59 (step @p175 :rule process_scope :premises (@p205) :args ((not @t78))) % 0.37/0.59 (step @p177 :rule implies_elim :premises (@p175)) % 0.37/0.59 (step @p178 :rule chain_m_resolution :premises (@p177 @p172 @p151 @p150) :args (@t84 (@list false true true) (@list @t78 @t66 @t68))) % 0.37/0.59 (step @p179 :rule cnf_equiv_neg1 :args (@t68)) % 0.37/0.59 (step @p180 :rule reordering :premises (@p179) :args ((or @t67 @t66 @t68))) % 0.37/0.59 (step @p181 :rule chain_m_resolution :premises (@p180 @p178 @p150) :args (@t66 (@list true true) (@list @t67 @t68))) % 0.37/0.59 (step @p182 :rule refl :args (@t85)) % 0.37/0.59 (step @p183 :rule bool-double-not-elim :args (@t67)) % 0.37/0.59 (step @p184 :rule nary_cong :premises (@p183 @p182) :args ((or (not @t84) @t85))) % 0.37/0.59 (step @p185 :rule bool-double-not-elim :args (@t85)) % 0.37/0.59 (step @p186 :rule refl :args (@t84)) % 0.37/0.59 (step @p187 :rule cong :premises (@p186 @p185) :args ((=> @t84 @t86))) % 0.37/0.59 (assume-push @p206 @t84) % 0.37/0.59 (step @p189 :rule skolemize :premises (@p206)) % 0.37/0.59 (step-pop @p207 :rule scope :premises (@p189)) % 0.37/0.59 (step @p190 :rule process_scope :premises (@p207) :args (@t86)) % 0.37/0.59 (step @p192 :rule eq_resolve :premises (@p190 @p187)) % 0.37/0.59 (step @p193 :rule implies_elim :premises (@p192)) % 0.37/0.59 (step @p194 :rule eq_resolve :premises (@p193 @p184)) % 0.37/0.59 (step @p195 :rule chain_m_resolution :premises (@p194 @p178) :args (@t85 @t76 (@list @t67))) % 0.37/0.59 (step @p196 :rule bool-eq-false :args (@t85)) % 0.37/0.59 (step @p197 :rule cong :premises (@p169 @p196) :args (@t87)) % 0.37/0.59 ; trust TRUST THEORY_LEMMA % 0.37/0.59 (step @p198 :rule trust :premises () :args (@t87)) % 0.37/0.59 (step @p199 :rule eq_resolve :premises (@p198 @p197)) % 0.37/0.59 (step @p200 :rule implies_elim :premises (@p199)) % 0.37/0.59 (step @p201 false :rule chain_m_resolution :premises (@p200 @p195 @p181) :args (false (@list false false) (@list @t85 @t66))) % 0.37/0.59 ) % 0.37/0.59 % SZS output end Proof % 0.37/0.59 % cvc5 exiting %------------------------------------------------------------------------------