%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU771^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n028.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 08:53:07 AM UTC 2026 % Result : Theorem 0.37s 0.57s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU771^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n028.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 17:51:20 EDT 2026 % 0.18/0.35 % CPUTime : % 0.27/0.50 %----Proving TH0 % 0.37/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.57 % SZS status Theorem % 0.37/0.57 % SZS output start Proof % 0.37/0.57 ( % 0.37/0.57 (declare-sort $$unsorted 0) % 0.37/0.57 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.setOfPairsIsBReln Bool) % 0.37/0.57 (declare-const tptp.dpsetconstr (-> $$unsorted $$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted)) % 0.37/0.57 (define tptp.breln () (let ((_let_1 (@var "B" $$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))))))) % 0.37/0.57 (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))))) % 0.37/0.57 (define @t1 () (@var "Xy" $$unsorted)) % 0.37/0.57 (define @t2 () (@var "Xx" $$unsorted)) % 0.37/0.57 (define @t3 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.37/0.57 (define @t4 () (_ (_ @t3 @t2) @t1)) % 0.37/0.57 (define @t5 () (@list @t2 @t1)) % 0.37/0.57 (define @t6 () (lambda @t5 @t4)) % 0.37/0.57 (define @t7 () (@var "B" $$unsorted)) % 0.37/0.57 (define @t8 () (@var "A" $$unsorted)) % 0.37/0.57 (define @t9 () (_ tptp.dpsetconstr @t8)) % 0.37/0.57 (define @t10 () (_ @t9 @t7)) % 0.37/0.57 (define @t11 () (_ @t10 @t6)) % 0.37/0.57 (define @t12 () (_ tptp.breln @t8)) % 0.37/0.57 (define @t13 () (@list @t8 @t7 @t3)) % 0.37/0.57 (define @t14 () (forall @t13 (_ (_ @t12 @t7) @t11))) % 0.37/0.57 (define @t15 () (= tptp.setOfPairsIsBReln @t14)) % 0.37/0.57 (define @t16 () (_ @t9 @t8)) % 0.37/0.57 (define @t17 () (_ @t16 @t6)) % 0.37/0.57 (define @t18 () (@list @t8 @t3)) % 0.37/0.57 (define @t19 () (forall @t18 (_ (_ tptp.breln1 @t8) @t17))) % 0.37/0.57 (define @t20 () (=> tptp.setOfPairsIsBReln @t19)) % 0.37/0.57 (define @t21 () (not @t20)) % 0.37/0.57 (define @t22 () (_ tptp.cartprod @t8)) % 0.37/0.57 (define @t23 () (_ @t22 @t7)) % 0.37/0.57 (define @t24 () (@var "C" $$unsorted)) % 0.37/0.57 (define @t25 () (_ tptp.subset @t24)) % 0.37/0.57 (define @t26 () (_ @t25 @t23)) % 0.37/0.57 (define @t27 () (lambda (@list @t8 @t7 @t24) @t26)) % 0.37/0.57 (define @t28 () (@var "R" $$unsorted)) % 0.37/0.57 (define @t29 () (@list @t8 @t28)) % 0.37/0.57 (define @t30 () (lambda @t29 (_ (_ @t12 @t8) @t28))) % 0.37/0.57 (define @t31 () (tptp.cartprod @t8 @t8)) % 0.37/0.57 (define @t32 () (forall @t18 (tptp.subset (tptp.dpsetconstr @t8 @t8 @t3) @t31))) % 0.37/0.57 (define @t33 () (tptp.cartprod @t8 @t7)) % 0.37/0.57 (define @t34 () (_ @t3 @t2 @t1)) % 0.37/0.57 (define @t35 () (lambda @t5 @t34)) % 0.37/0.57 (define @t36 () (tptp.dpsetconstr @t8 @t7 @t35)) % 0.37/0.57 (define @t37 () (tptp.subset @t36 @t33)) % 0.37/0.57 (define @t38 () (_ (_ tptp.subset @t11) @t23)) % 0.37/0.57 (define @t39 () (@list @t24)) % 0.37/0.57 (define @t40 () (lambda @t39 @t26)) % 0.37/0.57 (define @t41 () (lambda (@list @t7 @t24) @t26)) % 0.37/0.57 (define @t42 () (_ @t27 @t8)) % 0.37/0.57 (define @t43 () (forall @t13 (_ (_ @t42 @t7) @t11))) % 0.37/0.57 (define @t44 () (=> tptp.setOfPairsIsBReln @t32)) % 0.37/0.57 (define @t45 () (tptp.dpsetconstr @t8 @t8 @t35)) % 0.37/0.57 (define @t46 () (tptp.subset @t45 @t31)) % 0.37/0.57 (define @t47 () (_ @t22 @t8)) % 0.37/0.57 (define @t48 () (_ (_ tptp.subset @t17) @t47)) % 0.37/0.57 (define @t49 () (_ (_ tptp.subset @t28) @t47)) % 0.37/0.57 (define @t50 () (lambda (@list @t28) @t49)) % 0.37/0.57 (define @t51 () (_ (lambda @t29 @t49) @t8)) % 0.37/0.57 (define @t52 () (forall @t18 (_ @t51 @t17))) % 0.37/0.57 (define @t53 () (=> tptp.setOfPairsIsBReln @t52)) % 0.37/0.57 (define @t54 () (lambda @t39 (_ @t25 @t47))) % 0.37/0.57 (define @t55 () (forall @t13 (tptp.subset (tptp.dpsetconstr @t8 @t7 @t3) @t33))) % 0.37/0.57 (define @t56 () (@quantifiers_skolemize @t32 1)) % 0.37/0.57 (define @t57 () (@quantifiers_skolemize @t32 0)) % 0.37/0.57 (define @t58 () (tptp.subset (tptp.dpsetconstr @t57 @t57 @t56) (tptp.cartprod @t57 @t57))) % 0.37/0.57 (assume @p1 @t15) % 0.37/0.57 (assume @p2 @t21) % 0.37/0.57 (assume @p3 true) % 0.37/0.57 (step @p4 (= tptp.breln @t27) :rule refl :args (@t27)) % 0.37/0.57 (step @p5 (= tptp.breln1 @t30) :rule refl :args (@t30)) % 0.37/0.57 (step @p6 :rule refl :args (@t32)) % 0.37/0.57 (step @p7 :rule refl :args (@t33)) % 0.37/0.57 (step @p8 :rule lambda-elim :args ((= @t35 @t3))) % 0.37/0.57 (step @p9 :rule refl :args (@t7)) % 0.37/0.57 (step @p10 :rule refl :args (@t8)) % 0.37/0.57 (step @p11 :rule cong :premises (@p10 @p9 @p8) :args (@t36)) % 0.37/0.57 (step @p12 :rule cong :premises (@p11 @p7) :args (@t37)) % 0.37/0.57 (step @p13 :rule cong :premises (@p12) :args ((forall @t13 @t37))) % 0.37/0.57 (step @p14 :rule refl :args ((tptp.subset @t11 @t23))) % 0.37/0.57 (step @p15 :rule refl :args (@t33)) % 0.37/0.57 (step @p16 :rule refl :args ((tptp.dpsetconstr @t8 @t7 @t6))) % 0.37/0.57 (step @p17 :rule refl :args (@t34)) % 0.37/0.57 (step @p18 :rule cong :premises (@p17) :args (@t35)) % 0.37/0.57 (step @p19 :rule refl :args (@t7)) % 0.37/0.57 (step @p20 :rule refl :args (@t8)) % 0.37/0.57 (step @p21 :rule cong :premises (@p20 @p19 @p18) :args (@t36)) % 0.37/0.57 (step @p22 :rule trans :premises (@p21 @p16)) % 0.37/0.57 (step @p23 :rule cong :premises (@p22 @p15) :args (@t37)) % 0.37/0.57 (step @p24 :rule trans :premises (@p23 @p14)) % 0.37/0.57 (step @p25 :rule refl :args (tptp.subset)) % 0.37/0.57 (step @p26 :rule ho_cong :premises (@p25 @p22)) % 0.37/0.57 (step @p27 :rule ho_cong :premises (@p26 @p15)) % 0.37/0.57 (step @p28 :rule cong :premises (@p27 @p24) :args ((= (_ (_ tptp.subset @t36) @t33) @t37))) % 0.37/0.57 (step @p29 :rule symm :premises (@p28)) % 0.37/0.57 (step @p30 :rule refl :args (@t38)) % 0.37/0.57 (step @p31 :rule eq_resolve :premises (@p30 @p29)) % 0.37/0.57 (step @p32 :rule refl :args (@t23)) % 0.37/0.57 (step @p33 :rule cong :premises (@p32 @p15) :args ((= @t23 @t33))) % 0.37/0.57 (step @p34 :rule symm :premises (@p33)) % 0.37/0.57 (step @p35 :rule eq_resolve :premises (@p32 @p34)) % 0.37/0.57 (step @p36 :rule refl :args (@t10)) % 0.37/0.57 (step @p37 :rule ho_cong :premises (@p36 @p18)) % 0.37/0.57 (step @p38 :rule cong :premises (@p37 @p22) :args ((= (_ @t10 @t35) @t36))) % 0.37/0.57 (step @p39 :rule symm :premises (@p38)) % 0.37/0.57 (step @p40 :rule refl :args (@t11)) % 0.37/0.57 (step @p41 :rule eq_resolve :premises (@p40 @p39)) % 0.37/0.57 (step @p42 :rule refl :args (@t4)) % 0.37/0.57 (step @p43 :rule cong :premises (@p42 @p17) :args ((= @t4 @t34))) % 0.37/0.57 (step @p44 :rule symm :premises (@p43)) % 0.37/0.57 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 0.37/0.57 (step @p46 :rule cong :premises (@p45) :args (@t6)) % 0.37/0.57 (step @p47 :rule ho_cong :premises (@p36 @p46)) % 0.37/0.57 (step @p48 :rule trans :premises (@p47 @p41)) % 0.37/0.57 (step @p49 :rule ho_cong :premises (@p25 @p48)) % 0.37/0.57 (step @p50 :rule ho_cong :premises (@p49 @p35)) % 0.37/0.57 (step @p51 :rule trans :premises (@p50 @p31)) % 0.37/0.57 (step @p52 :rule cong :premises (@p51) :args ((forall @t13 @t38))) % 0.37/0.57 (step @p53 :rule trans :premises (@p52 @p13)) % 0.37/0.57 (step @p54 :rule beta-reduce :args ((= (_ @t40 @t11) @t38))) % 0.37/0.57 (step @p55 :rule refl :args (@t11)) % 0.37/0.57 (step @p56 :rule beta-reduce :args ((= (_ @t41 @t7) @t40))) % 0.37/0.57 (step @p57 :rule beta-reduce :args ((= @t42 @t41))) % 0.37/0.57 (step @p58 :rule ho_cong :premises (@p57 @p9)) % 0.37/0.57 (step @p59 :rule trans :premises (@p58 @p56)) % 0.37/0.57 (step @p60 :rule ho_cong :premises (@p59 @p55)) % 0.37/0.57 (step @p61 :rule trans :premises (@p60 @p54)) % 0.37/0.57 (step @p62 :rule cong :premises (@p61) :args (@t43)) % 0.37/0.57 (step @p63 :rule trans :premises (@p62 @p53)) % 0.37/0.57 (step @p64 :rule refl :args (tptp.setOfPairsIsBReln)) % 0.37/0.57 (step @p65 :rule cong :premises (@p64 @p63) :args ((= tptp.setOfPairsIsBReln @t43))) % 0.37/0.57 (step @p66 :rule ho_cong :premises (@p4 @p10)) % 0.37/0.57 (step @p67 :rule ho_cong :premises (@p66 @p9)) % 0.37/0.57 (step @p68 :rule ho_cong :premises (@p67 @p55)) % 0.37/0.57 (step @p69 :rule cong :premises (@p68) :args (@t14)) % 0.37/0.57 (step @p70 :rule cong :premises (@p64 @p69) :args (@t15)) % 0.37/0.57 (step @p71 :rule trans :premises (@p70 @p65)) % 0.37/0.57 (step @p72 :rule eq_resolve :premises (@p1 @p71)) % 0.37/0.57 (step @p73 :rule cong :premises (@p72 @p6) :args (@t44)) % 0.37/0.57 (step @p74 :rule cong :premises (@p73) :args ((not @t44))) % 0.37/0.57 (step @p75 :rule refl :args (@t31)) % 0.37/0.57 (step @p76 :rule cong :premises (@p10 @p10 @p8) :args (@t45)) % 0.37/0.57 (step @p77 :rule cong :premises (@p76 @p75) :args (@t46)) % 0.37/0.57 (step @p78 :rule cong :premises (@p77) :args ((forall @t18 @t46))) % 0.37/0.57 (step @p79 :rule refl :args ((tptp.subset @t17 @t47))) % 0.37/0.57 (step @p80 :rule refl :args (@t31)) % 0.37/0.57 (step @p81 :rule refl :args ((tptp.dpsetconstr @t8 @t8 @t6))) % 0.37/0.57 (step @p82 :rule cong :premises (@p20 @p20 @p18) :args (@t45)) % 0.37/0.57 (step @p83 :rule trans :premises (@p82 @p81)) % 0.37/0.57 (step @p84 :rule cong :premises (@p83 @p80) :args (@t46)) % 0.37/0.57 (step @p85 :rule trans :premises (@p84 @p79)) % 0.37/0.57 (step @p86 :rule ho_cong :premises (@p25 @p83)) % 0.37/0.57 (step @p87 :rule ho_cong :premises (@p86 @p80)) % 0.37/0.57 (step @p88 :rule cong :premises (@p87 @p85) :args ((= (_ (_ tptp.subset @t45) @t31) @t46))) % 0.37/0.57 (step @p89 :rule symm :premises (@p88)) % 0.37/0.57 (step @p90 :rule refl :args (@t48)) % 0.37/0.57 (step @p91 :rule eq_resolve :premises (@p90 @p89)) % 0.37/0.57 (step @p92 :rule refl :args (@t47)) % 0.37/0.57 (step @p93 :rule cong :premises (@p92 @p80) :args ((= @t47 @t31))) % 0.37/0.57 (step @p94 :rule symm :premises (@p93)) % 0.37/0.57 (step @p95 :rule eq_resolve :premises (@p92 @p94)) % 0.37/0.57 (step @p96 :rule refl :args (@t16)) % 0.37/0.57 (step @p97 :rule ho_cong :premises (@p96 @p18)) % 0.37/0.57 (step @p98 :rule cong :premises (@p97 @p83) :args ((= (_ @t16 @t35) @t45))) % 0.37/0.57 (step @p99 :rule symm :premises (@p98)) % 0.37/0.57 (step @p100 :rule refl :args (@t17)) % 0.37/0.57 (step @p101 :rule eq_resolve :premises (@p100 @p99)) % 0.37/0.57 (step @p102 :rule ho_cong :premises (@p96 @p46)) % 0.37/0.57 (step @p103 :rule trans :premises (@p102 @p101)) % 0.37/0.57 (step @p104 :rule ho_cong :premises (@p25 @p103)) % 0.37/0.57 (step @p105 :rule ho_cong :premises (@p104 @p95)) % 0.37/0.57 (step @p106 :rule trans :premises (@p105 @p91)) % 0.37/0.57 (step @p107 :rule cong :premises (@p106) :args ((forall @t18 @t48))) % 0.37/0.57 (step @p108 :rule trans :premises (@p107 @p78)) % 0.37/0.57 (step @p109 :rule beta-reduce :args ((= (_ @t50 @t17) @t48))) % 0.37/0.57 (step @p110 :rule refl :args (@t17)) % 0.37/0.57 (step @p111 :rule beta-reduce :args ((= @t51 @t50))) % 0.37/0.57 (step @p112 :rule ho_cong :premises (@p111 @p110)) % 0.37/0.57 (step @p113 :rule trans :premises (@p112 @p109)) % 0.37/0.57 (step @p114 :rule cong :premises (@p113) :args (@t52)) % 0.37/0.57 (step @p115 :rule trans :premises (@p114 @p108)) % 0.37/0.57 (step @p116 :rule cong :premises (@p64 @p115) :args (@t53)) % 0.37/0.57 (step @p117 :rule cong :premises (@p116) :args ((not @t53))) % 0.37/0.57 (step @p118 :rule beta-reduce :args ((= (_ @t54 @t28) @t49))) % 0.37/0.57 (step @p119 :rule refl :args (@t28)) % 0.37/0.57 (step @p120 :rule beta-reduce :args ((= (_ @t41 @t8) @t54))) % 0.37/0.57 (step @p121 :rule ho_cong :premises (@p57 @p10)) % 0.37/0.57 (step @p122 :rule trans :premises (@p121 @p120)) % 0.37/0.57 (step @p123 :rule ho_cong :premises (@p122 @p119)) % 0.37/0.57 (step @p124 :rule trans :premises (@p123 @p118)) % 0.37/0.57 (step @p125 :rule ho_cong :premises (@p66 @p10)) % 0.37/0.57 (step @p126 :rule ho_cong :premises (@p125 @p119)) % 0.37/0.57 (step @p127 :rule trans :premises (@p126 @p124)) % 0.37/0.57 (step @p128 :rule cong :premises (@p127) :args (@t30)) % 0.37/0.57 (step @p129 :rule trans :premises (@p5 @p128)) % 0.37/0.57 (step @p130 :rule ho_cong :premises (@p129 @p10)) % 0.37/0.57 (step @p131 :rule ho_cong :premises (@p130 @p110)) % 0.37/0.57 (step @p132 :rule cong :premises (@p131) :args (@t19)) % 0.37/0.57 (step @p133 :rule cong :premises (@p64 @p132) :args (@t20)) % 0.37/0.57 (step @p134 :rule cong :premises (@p133) :args (@t21)) % 0.37/0.57 (step @p135 :rule trans :premises (@p134 @p117)) % 0.37/0.57 (step @p136 :rule trans :premises (@p135 @p74)) % 0.37/0.57 (step @p137 :rule eq_resolve :premises (@p2 @p136)) % 0.37/0.57 (step @p138 :rule not_implies_elim1 :premises (@p137)) % 0.37/0.57 (step @p139 :rule not_implies_elim2 :premises (@p137)) % 0.37/0.57 (step @p140 :rule skolemize :premises (@p139)) % 0.37/0.57 (assume-push @p147 @t55) % 0.37/0.57 (step @p142 :rule instantiate :premises (@p138) :args ((@list @t57 @t57 @t56))) % 0.37/0.57 (step-pop @p148 :rule scope :premises (@p142)) % 0.37/0.57 (step @p143 :rule process_scope :premises (@p148) :args (@t58)) % 0.37/0.57 (step @p145 :rule implies_elim :premises (@p143)) % 0.37/0.57 (step @p146 false :rule chain_m_resolution :premises (@p145 @p140 @p138) :args (false (@list true false) (@list @t58 @t55))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------