%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU775^2 : 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 : n023.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 08:53:08 AM UTC 2026 % Result : Theorem 0.34s 0.58s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU775^2 : 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 % 0.17/0.35 % Computer : n023.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 17:52:13 EDT 2026 % 0.17/0.35 % CPUTime : % 0.34/0.50 %----Proving TH0 % 0.34/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.34/0.58 % SZS status Theorem % 0.34/0.58 % SZS output start Proof % 0.34/0.58 ( % 0.34/0.58 (declare-sort $$unsorted 0) % 0.34/0.58 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.58 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.34/0.58 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.58 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.34/0.58 (declare-const tptp.dpsetconstr (-> $$unsorted $$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted)) % 0.34/0.58 (declare-const tptp.setOfPairsIsBReln1 Bool) % 0.34/0.58 (define tptp.breln () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (let ((_let_3 (@var "C" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (_ (_ tptp.subset _let_3) (_ (_ tptp.cartprod _let_2) _let_1))))))) % 0.34/0.58 (define tptp.breln1 () (let ((_let_1 (@var "R" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2 _let_1) (_ (_ (_ tptp.breln _let_2) _let_2) _let_1))))) % 0.34/0.58 (define tptp.breln1invset () (let ((_let_1 (@var "R" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "Xy" $$unsorted))) (let ((_let_4 (@var "A" $$unsorted))) (lambda (@list _let_4 _let_1) (_ (_ (_ tptp.dpsetconstr _let_4) _let_4) (lambda (@list _let_2 _let_3) (_ (_ tptp.in (_ (_ tptp.kpair _let_3) _let_2)) _let_1))))))))) % 0.34/0.58 (define @t1 () (@var "Xy" $$unsorted)) % 0.34/0.58 (define @t2 () (@var "Xx" $$unsorted)) % 0.34/0.58 (define @t3 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.34/0.58 (define @t4 () (_ (_ @t3 @t2) @t1)) % 0.34/0.58 (define @t5 () (@list @t2 @t1)) % 0.34/0.58 (define @t6 () (lambda @t5 @t4)) % 0.34/0.58 (define @t7 () (@var "A" $$unsorted)) % 0.34/0.58 (define @t8 () (_ (_ tptp.dpsetconstr @t7) @t7)) % 0.34/0.58 (define @t9 () (_ @t8 @t6)) % 0.34/0.58 (define @t10 () (_ tptp.breln1 @t7)) % 0.34/0.58 (define @t11 () (@list @t7 @t3)) % 0.34/0.58 (define @t12 () (forall @t11 (_ @t10 @t9))) % 0.34/0.58 (define @t13 () (= tptp.setOfPairsIsBReln1 @t12)) % 0.34/0.58 (define @t14 () (@var "R" $$unsorted)) % 0.34/0.58 (define @t15 () (=> (_ @t10 @t14) (_ @t10 (_ (_ tptp.breln1invset @t7) @t14)))) % 0.34/0.58 (define @t16 () (@list @t7 @t14)) % 0.34/0.58 (define @t17 () (forall @t16 @t15)) % 0.34/0.58 (define @t18 () (=> tptp.setOfPairsIsBReln1 @t17)) % 0.34/0.58 (define @t19 () (not @t18)) % 0.34/0.58 (define @t20 () (@var "B" $$unsorted)) % 0.34/0.58 (define @t21 () (_ tptp.cartprod @t7)) % 0.34/0.58 (define @t22 () (@var "C" $$unsorted)) % 0.34/0.58 (define @t23 () (_ tptp.subset @t22)) % 0.34/0.58 (define @t24 () (_ @t23 (_ @t21 @t20))) % 0.34/0.58 (define @t25 () (lambda (@list @t7 @t20 @t22) @t24)) % 0.34/0.58 (define @t26 () (lambda @t16 (_ (_ (_ tptp.breln @t7) @t7) @t14))) % 0.34/0.58 (define @t27 () (_ (_ tptp.kpair @t1) @t2)) % 0.34/0.58 (define @t28 () (_ (_ tptp.in @t27) @t14)) % 0.34/0.58 (define @t29 () (lambda @t5 @t28)) % 0.34/0.58 (define @t30 () (_ @t8 @t29)) % 0.34/0.58 (define @t31 () (lambda @t16 @t30)) % 0.34/0.58 (define @t32 () (tptp.cartprod @t7 @t7)) % 0.34/0.58 (define @t33 () (tptp.kpair @t1 @t2)) % 0.34/0.58 (define @t34 () (tptp.in @t33 @t14)) % 0.34/0.58 (define @t35 () (lambda @t5 @t34)) % 0.34/0.58 (define @t36 () (tptp.dpsetconstr @t7 @t7 @t35)) % 0.34/0.58 (define @t37 () (tptp.subset @t36 @t32)) % 0.34/0.58 (define @t38 () (tptp.subset @t14 @t32)) % 0.34/0.58 (define @t39 () (forall @t16 (or (not @t38) @t37))) % 0.34/0.58 (define @t40 () (_ @t3 @t2 @t1)) % 0.34/0.58 (define @t41 () (lambda @t5 @t40)) % 0.34/0.58 (define @t42 () (tptp.dpsetconstr @t7 @t7 @t41)) % 0.34/0.58 (define @t43 () (tptp.subset @t42 @t32)) % 0.34/0.58 (define @t44 () (_ @t21 @t7)) % 0.34/0.58 (define @t45 () (_ (_ tptp.subset @t9) @t44)) % 0.34/0.58 (define @t46 () (_ tptp.subset @t14)) % 0.34/0.58 (define @t47 () (_ @t46 @t44)) % 0.34/0.58 (define @t48 () (@list @t14)) % 0.34/0.58 (define @t49 () (lambda @t48 @t47)) % 0.34/0.58 (define @t50 () (_ (lambda @t16 @t47) @t7)) % 0.34/0.58 (define @t51 () (forall @t11 (_ @t50 @t9))) % 0.34/0.58 (define @t52 () (lambda (@list @t22) (_ @t23 @t44))) % 0.34/0.58 (define @t53 () (lambda (@list @t20 @t22) @t24)) % 0.34/0.58 (define @t54 () (=> tptp.setOfPairsIsBReln1 @t39)) % 0.34/0.58 (define @t55 () (_ (_ tptp.subset @t30) @t44)) % 0.34/0.58 (define @t56 () (not @t47)) % 0.34/0.58 (define @t57 () (or @t56 @t55)) % 0.34/0.58 (define @t58 () (lambda @t48 @t30)) % 0.34/0.58 (define @t59 () (_ @t31 @t7)) % 0.34/0.58 (define @t60 () (=> (_ @t50 @t14) (_ @t50 (_ @t59 @t14)))) % 0.34/0.58 (define @t61 () (forall @t16 @t60)) % 0.34/0.58 (define @t62 () (=> tptp.setOfPairsIsBReln1 @t61)) % 0.34/0.58 (define @t63 () (@quantifiers_skolemize @t39 0)) % 0.34/0.58 (define @t64 () (tptp.cartprod @t63 @t63)) % 0.34/0.58 (define @t65 () (@quantifiers_skolemize @t39 1)) % 0.34/0.58 (define @t66 () (lambda @t5 (tptp.in @t33 @t65))) % 0.34/0.58 (define @t67 () (@purify @t66)) % 0.34/0.58 (define @t68 () (tptp.subset (tptp.dpsetconstr @t63 @t63 @t67) @t64)) % 0.34/0.58 (define @t69 () (not (tptp.subset @t65 @t64))) % 0.34/0.58 (define @t70 () (or @t69 @t68)) % 0.34/0.58 (define @t71 () (not @t70)) % 0.34/0.58 (define @t72 () (not @t39)) % 0.34/0.58 (define @t73 () (tptp.dpsetconstr @t63 @t63 @t66)) % 0.34/0.58 (define @t74 () (tptp.subset @t73 @t64)) % 0.34/0.58 (define @t75 () (or @t69 @t74)) % 0.34/0.58 (define @t76 () (not @t75)) % 0.34/0.58 (define @t77 () (@list true)) % 0.34/0.58 (define @t78 () (forall @t11 (tptp.subset (tptp.dpsetconstr @t7 @t7 @t3) @t32))) % 0.34/0.58 (assume @p1 @t13) % 0.34/0.58 (assume @p2 @t19) % 0.34/0.58 (assume @p3 true) % 0.34/0.58 (step @p4 (= tptp.breln @t25) :rule refl :args (@t25)) % 0.34/0.58 (step @p5 (= tptp.breln1 @t26) :rule refl :args (@t26)) % 0.34/0.58 (step @p6 (= tptp.breln1invset @t31) :rule refl :args (@t31)) % 0.34/0.58 (step @p7 :rule refl :args (@t39)) % 0.34/0.58 (step @p8 :rule refl :args (@t32)) % 0.34/0.58 (step @p9 :rule lambda-elim :args ((= @t41 @t3))) % 0.34/0.58 (step @p10 :rule refl :args (@t7)) % 0.34/0.58 (step @p11 :rule cong :premises (@p10 @p10 @p9) :args (@t42)) % 0.34/0.58 (step @p12 :rule cong :premises (@p11 @p8) :args (@t43)) % 0.34/0.58 (step @p13 :rule cong :premises (@p12) :args ((forall @t11 @t43))) % 0.34/0.58 (step @p14 :rule refl :args ((tptp.subset @t9 @t44))) % 0.34/0.58 (step @p15 :rule refl :args (@t32)) % 0.34/0.58 (step @p16 :rule refl :args ((tptp.dpsetconstr @t7 @t7 @t6))) % 0.34/0.58 (step @p17 :rule refl :args (@t40)) % 0.34/0.58 (step @p18 :rule cong :premises (@p17) :args (@t41)) % 0.34/0.58 (step @p19 :rule refl :args (@t7)) % 0.34/0.58 (step @p20 :rule cong :premises (@p19 @p19 @p18) :args (@t42)) % 0.34/0.58 (step @p21 :rule trans :premises (@p20 @p16)) % 0.34/0.58 (step @p22 :rule cong :premises (@p21 @p15) :args (@t43)) % 0.34/0.58 (step @p23 :rule trans :premises (@p22 @p14)) % 0.34/0.58 (step @p24 :rule refl :args (tptp.subset)) % 0.34/0.58 (step @p25 :rule ho_cong :premises (@p24 @p21)) % 0.34/0.58 (step @p26 :rule ho_cong :premises (@p25 @p15)) % 0.34/0.58 (step @p27 :rule cong :premises (@p26 @p23) :args ((= (_ (_ tptp.subset @t42) @t32) @t43))) % 0.34/0.58 (step @p28 :rule symm :premises (@p27)) % 0.34/0.58 (step @p29 :rule refl :args (@t45)) % 0.34/0.58 (step @p30 :rule eq_resolve :premises (@p29 @p28)) % 0.34/0.58 (step @p31 :rule refl :args (@t44)) % 0.34/0.58 (step @p32 :rule cong :premises (@p31 @p15) :args ((= @t44 @t32))) % 0.34/0.58 (step @p33 :rule symm :premises (@p32)) % 0.34/0.58 (step @p34 :rule eq_resolve :premises (@p31 @p33)) % 0.34/0.58 (step @p35 :rule refl :args (@t8)) % 0.34/0.58 (step @p36 :rule ho_cong :premises (@p35 @p18)) % 0.34/0.58 (step @p37 :rule cong :premises (@p36 @p21) :args ((= (_ @t8 @t41) @t42))) % 0.34/0.58 (step @p38 :rule symm :premises (@p37)) % 0.34/0.58 (step @p39 :rule refl :args (@t9)) % 0.34/0.58 (step @p40 :rule eq_resolve :premises (@p39 @p38)) % 0.34/0.58 (step @p41 :rule refl :args (@t4)) % 0.34/0.58 (step @p42 :rule cong :premises (@p41 @p17) :args ((= @t4 @t40))) % 0.34/0.58 (step @p43 :rule symm :premises (@p42)) % 0.34/0.58 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 0.34/0.58 (step @p45 :rule cong :premises (@p44) :args (@t6)) % 0.34/0.58 (step @p46 :rule ho_cong :premises (@p35 @p45)) % 0.34/0.58 (step @p47 :rule trans :premises (@p46 @p40)) % 0.34/0.58 (step @p48 :rule ho_cong :premises (@p24 @p47)) % 0.34/0.58 (step @p49 :rule ho_cong :premises (@p48 @p34)) % 0.34/0.58 (step @p50 :rule trans :premises (@p49 @p30)) % 0.34/0.58 (step @p51 :rule cong :premises (@p50) :args ((forall @t11 @t45))) % 0.34/0.58 (step @p52 :rule trans :premises (@p51 @p13)) % 0.34/0.58 (step @p53 :rule beta-reduce :args ((= (_ @t49 @t9) @t45))) % 0.34/0.58 (step @p54 :rule refl :args (@t9)) % 0.34/0.58 (step @p55 :rule beta-reduce :args ((= @t50 @t49))) % 0.34/0.58 (step @p56 :rule ho_cong :premises (@p55 @p54)) % 0.34/0.58 (step @p57 :rule trans :premises (@p56 @p53)) % 0.34/0.58 (step @p58 :rule cong :premises (@p57) :args (@t51)) % 0.34/0.58 (step @p59 :rule trans :premises (@p58 @p52)) % 0.34/0.58 (step @p60 :rule refl :args (tptp.setOfPairsIsBReln1)) % 0.34/0.58 (step @p61 :rule cong :premises (@p60 @p59) :args ((= tptp.setOfPairsIsBReln1 @t51))) % 0.34/0.58 (step @p62 :rule beta-reduce :args ((= (_ @t52 @t14) @t47))) % 0.34/0.58 (step @p63 :rule refl :args (@t14)) % 0.34/0.58 (step @p64 :rule beta-reduce :args ((= (_ @t53 @t7) @t52))) % 0.34/0.58 (step @p65 :rule beta-reduce :args ((= (_ @t25 @t7) @t53))) % 0.34/0.58 (step @p66 :rule ho_cong :premises (@p65 @p10)) % 0.34/0.58 (step @p67 :rule trans :premises (@p66 @p64)) % 0.34/0.58 (step @p68 :rule ho_cong :premises (@p67 @p63)) % 0.34/0.58 (step @p69 :rule trans :premises (@p68 @p62)) % 0.34/0.58 (step @p70 :rule ho_cong :premises (@p4 @p10)) % 0.34/0.58 (step @p71 :rule ho_cong :premises (@p70 @p10)) % 0.34/0.58 (step @p72 :rule ho_cong :premises (@p71 @p63)) % 0.34/0.58 (step @p73 :rule trans :premises (@p72 @p69)) % 0.34/0.58 (step @p74 :rule cong :premises (@p73) :args (@t26)) % 0.34/0.58 (step @p75 :rule trans :premises (@p5 @p74)) % 0.34/0.58 (step @p76 :rule ho_cong :premises (@p75 @p10)) % 0.34/0.58 (step @p77 :rule ho_cong :premises (@p76 @p54)) % 0.34/0.58 (step @p78 :rule cong :premises (@p77) :args (@t12)) % 0.34/0.58 (step @p79 :rule cong :premises (@p60 @p78) :args (@t13)) % 0.34/0.58 (step @p80 :rule trans :premises (@p79 @p61)) % 0.34/0.58 (step @p81 :rule eq_resolve :premises (@p1 @p80)) % 0.34/0.58 (step @p82 :rule cong :premises (@p81 @p7) :args (@t54)) % 0.34/0.58 (step @p83 :rule cong :premises (@p82) :args ((not @t54))) % 0.34/0.58 (step @p84 :rule refl :args ((tptp.subset @t30 @t44))) % 0.34/0.58 (step @p85 :rule refl :args ((tptp.dpsetconstr @t7 @t7 @t29))) % 0.34/0.58 (step @p86 :rule refl :args ((tptp.in @t27 @t14))) % 0.34/0.58 (step @p87 :rule refl :args (@t14)) % 0.34/0.58 (step @p88 :rule refl :args (@t33)) % 0.34/0.58 (step @p89 :rule cong :premises (@p88 @p87) :args (@t34)) % 0.34/0.58 (step @p90 :rule trans :premises (@p89 @p86)) % 0.34/0.58 (step @p91 :rule cong :premises (@p90) :args (@t35)) % 0.34/0.58 (step @p92 :rule cong :premises (@p19 @p19 @p91) :args (@t36)) % 0.34/0.58 (step @p93 :rule trans :premises (@p92 @p85)) % 0.34/0.58 (step @p94 :rule cong :premises (@p93 @p15) :args (@t37)) % 0.34/0.58 (step @p95 :rule trans :premises (@p94 @p84)) % 0.34/0.58 (step @p96 :rule ho_cong :premises (@p24 @p93)) % 0.34/0.58 (step @p97 :rule ho_cong :premises (@p96 @p15)) % 0.34/0.58 (step @p98 :rule cong :premises (@p97 @p95) :args ((= (_ (_ tptp.subset @t36) @t32) @t37))) % 0.34/0.58 (step @p99 :rule symm :premises (@p98)) % 0.34/0.58 (step @p100 :rule refl :args (@t55)) % 0.34/0.58 (step @p101 :rule eq_resolve :premises (@p100 @p99)) % 0.34/0.58 (step @p102 :rule ho_cong :premises (@p35 @p91)) % 0.34/0.58 (step @p103 :rule cong :premises (@p102 @p93) :args ((= (_ @t8 @t35) @t36))) % 0.34/0.58 (step @p104 :rule symm :premises (@p103)) % 0.34/0.58 (step @p105 :rule refl :args (@t30)) % 0.34/0.58 (step @p106 :rule eq_resolve :premises (@p105 @p104)) % 0.34/0.58 (step @p107 :rule refl :args (tptp.in)) % 0.34/0.58 (step @p108 :rule ho_cong :premises (@p107 @p88)) % 0.34/0.58 (step @p109 :rule ho_cong :premises (@p108 @p87)) % 0.34/0.58 (step @p110 :rule cong :premises (@p109 @p90) :args ((= (_ (_ tptp.in @t33) @t14) @t34))) % 0.34/0.58 (step @p111 :rule symm :premises (@p110)) % 0.34/0.58 (step @p112 :rule refl :args (@t28)) % 0.34/0.58 (step @p113 :rule eq_resolve :premises (@p112 @p111)) % 0.34/0.58 (step @p114 :rule refl :args (@t27)) % 0.34/0.58 (step @p115 :rule cong :premises (@p114 @p88) :args ((= @t27 @t33))) % 0.34/0.58 (step @p116 :rule symm :premises (@p115)) % 0.34/0.58 (step @p117 :rule eq_resolve :premises (@p114 @p116)) % 0.34/0.58 (step @p118 :rule ho_cong :premises (@p107 @p117)) % 0.34/0.58 (step @p119 :rule ho_cong :premises (@p118 @p87)) % 0.34/0.58 (step @p120 :rule trans :premises (@p119 @p113)) % 0.34/0.58 (step @p121 :rule cong :premises (@p120) :args (@t29)) % 0.34/0.58 (step @p122 :rule ho_cong :premises (@p35 @p121)) % 0.34/0.58 (step @p123 :rule trans :premises (@p122 @p106)) % 0.34/0.58 (step @p124 :rule ho_cong :premises (@p24 @p123)) % 0.34/0.58 (step @p125 :rule ho_cong :premises (@p124 @p34)) % 0.34/0.58 (step @p126 :rule trans :premises (@p125 @p101)) % 0.34/0.58 (step @p127 :rule refl :args ((tptp.subset @t14 @t44))) % 0.34/0.58 (step @p128 :rule cong :premises (@p87 @p15) :args (@t38)) % 0.34/0.58 (step @p129 :rule trans :premises (@p128 @p127)) % 0.34/0.58 (step @p130 :rule refl :args (@t46)) % 0.34/0.58 (step @p131 :rule ho_cong :premises (@p130 @p15)) % 0.34/0.58 (step @p132 :rule cong :premises (@p131 @p129) :args ((= (_ @t46 @t32) @t38))) % 0.34/0.58 (step @p133 :rule symm :premises (@p132)) % 0.34/0.58 (step @p134 :rule refl :args (@t47)) % 0.34/0.58 (step @p135 :rule eq_resolve :premises (@p134 @p133)) % 0.34/0.58 (step @p136 :rule ho_cong :premises (@p130 @p34)) % 0.34/0.58 (step @p137 :rule trans :premises (@p136 @p135)) % 0.34/0.58 (step @p138 :rule cong :premises (@p137) :args (@t56)) % 0.34/0.58 (step @p139 :rule nary_cong :premises (@p138 @p126) :args (@t57)) % 0.34/0.58 (step @p140 :rule cong :premises (@p139) :args ((forall @t16 @t57))) % 0.34/0.58 (step @p141 :rule bool-impl-elim :args (@t47 @t55)) % 0.34/0.58 (step @p142 :rule cong :premises (@p141) :args ((forall @t16 (=> @t47 @t55)))) % 0.34/0.58 (step @p143 :rule trans :premises (@p142 @p140)) % 0.34/0.58 (step @p144 :rule beta-reduce :args ((= (_ @t49 @t30) @t55))) % 0.34/0.58 (step @p145 :rule beta-reduce :args ((= (_ @t58 @t14) @t30))) % 0.34/0.58 (step @p146 :rule beta-reduce :args ((= @t59 @t58))) % 0.34/0.58 (step @p147 :rule ho_cong :premises (@p146 @p63)) % 0.34/0.58 (step @p148 :rule trans :premises (@p147 @p145)) % 0.34/0.58 (step @p149 :rule ho_cong :premises (@p55 @p148)) % 0.34/0.58 (step @p150 :rule trans :premises (@p149 @p144)) % 0.34/0.58 (step @p151 :rule beta-reduce :args ((= (_ @t49 @t14) @t47))) % 0.34/0.58 (step @p152 :rule ho_cong :premises (@p55 @p63)) % 0.34/0.58 (step @p153 :rule trans :premises (@p152 @p151)) % 0.34/0.58 (step @p154 :rule cong :premises (@p153 @p150) :args (@t60)) % 0.34/0.58 (step @p155 :rule cong :premises (@p154) :args (@t61)) % 0.34/0.58 (step @p156 :rule trans :premises (@p155 @p143)) % 0.34/0.58 (step @p157 :rule cong :premises (@p60 @p156) :args (@t62)) % 0.34/0.58 (step @p158 :rule cong :premises (@p157) :args ((not @t62))) % 0.34/0.58 (step @p159 :rule ho_cong :premises (@p6 @p10)) % 0.34/0.58 (step @p160 :rule ho_cong :premises (@p159 @p63)) % 0.34/0.58 (step @p161 :rule ho_cong :premises (@p76 @p160)) % 0.34/0.58 (step @p162 :rule ho_cong :premises (@p76 @p63)) % 0.34/0.58 (step @p163 :rule cong :premises (@p162 @p161) :args (@t15)) % 0.34/0.58 (step @p164 :rule cong :premises (@p163) :args (@t17)) % 0.34/0.58 (step @p165 :rule cong :premises (@p60 @p164) :args (@t18)) % 0.34/0.58 (step @p166 :rule cong :premises (@p165) :args (@t19)) % 0.34/0.58 (step @p167 :rule trans :premises (@p166 @p158)) % 0.34/0.58 (step @p168 :rule trans :premises (@p167 @p83)) % 0.34/0.58 (step @p169 :rule eq_resolve :premises (@p2 @p168)) % 0.34/0.58 (step @p170 :rule not_implies_elim1 :premises (@p169)) % 0.34/0.58 (step @p171 :rule not_implies_elim2 :premises (@p169)) % 0.34/0.58 (step @p172 :rule refl :args (@t71)) % 0.34/0.58 (step @p173 :rule bool-double-not-elim :args (@t39)) % 0.34/0.58 (step @p174 :rule nary_cong :premises (@p173 @p172) :args ((or (not @t72) @t71))) % 0.34/0.58 (step @p175 :rule refl :args (@t64)) % 0.34/0.58 (step @p176 :rule eq-refl :args (@t66)) % 0.34/0.58 (step @p177 :rule skolem_intro :args (@t67)) % 0.34/0.58 (step @p178 :rule refl :args (@t66)) % 0.34/0.58 (step @p179 :rule cong :premises (@p178 @p177) :args ((= @t66 @t67))) % 0.34/0.58 (step @p180 :rule trans :premises (@p179 @p176)) % 0.34/0.58 (step @p181 :rule true_elim :premises (@p180)) % 0.34/0.58 (step @p182 :rule refl :args (@t63)) % 0.34/0.58 (step @p183 :rule cong :premises (@p182 @p182 @p181) :args (@t73)) % 0.34/0.58 (step @p184 :rule cong :premises (@p183 @p175) :args (@t74)) % 0.34/0.58 (step @p185 :rule refl :args (@t69)) % 0.34/0.58 (step @p186 :rule nary_cong :premises (@p185 @p184) :args (@t75)) % 0.34/0.58 (step @p187 :rule cong :premises (@p186) :args (@t76)) % 0.34/0.58 (step @p188 :rule refl :args (@t72)) % 0.34/0.58 (step @p189 :rule cong :premises (@p188 @p187) :args ((=> @t72 @t76))) % 0.34/0.58 (assume-push @p206 @t72) % 0.34/0.58 (step @p191 :rule skolemize :premises (@p171)) % 0.34/0.58 (step-pop @p207 :rule scope :premises (@p191)) % 0.34/0.58 (step @p192 :rule process_scope :premises (@p207) :args (@t76)) % 0.34/0.58 (step @p194 :rule eq_resolve :premises (@p192 @p189)) % 0.34/0.58 (step @p195 :rule implies_elim :premises (@p194)) % 0.34/0.58 (step @p196 :rule eq_resolve :premises (@p195 @p174)) % 0.34/0.58 (step @p197 :rule chain_m_resolution :premises (@p196 @p171) :args (@t71 @t77 (@list @t39))) % 0.34/0.58 (step @p198 :rule cnf_or_neg :args (@t70 1)) % 0.34/0.58 (step @p199 :rule chain_m_resolution :premises (@p198 @p197) :args ((not @t68) @t77 (@list @t70))) % 0.34/0.58 (assume-push @p208 @t78) % 0.34/0.58 (step @p201 :rule instantiate :premises (@p170) :args ((@list @t63 @t67))) % 0.34/0.58 (step-pop @p209 :rule scope :premises (@p201)) % 0.34/0.58 (step @p202 :rule process_scope :premises (@p209) :args (@t68)) % 0.34/0.58 (step @p204 :rule implies_elim :premises (@p202)) % 0.34/0.58 (step @p205 false :rule chain_m_resolution :premises (@p204 @p199 @p170) :args (false (@list true false) (@list @t68 @t78))) % 0.34/0.58 ) % 0.34/0.58 % SZS output end Proof % 0.34/0.58 % cvc5 exiting %------------------------------------------------------------------------------