%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PUZ102^5 : TPTP v9.2.1. Bugfixed v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n011.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 08:44:12 AM UTC 2026 % Result : Theorem 0.29s 0.55s % Output : Proof 0.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PUZ102^5 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n011.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 13:17:49 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.48 %----Proving TH0 % 0.29/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.29/0.55 % SZS status Theorem % 0.29/0.55 % SZS output start Proof % 0.29/0.55 ( % 0.29/0.55 (declare-sort $$unsorted 0) % 0.29/0.55 (declare-const tptp.s (-> $$unsorted $$unsorted)) % 0.29/0.55 (define tptp.cCKB_E2 () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xp" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Xu" $$unsorted))) (let ((_let_4 (@var "Xx" $$unsorted))) (lambda (@list _let_4 _let_1) (forall (@list _let_2) (=> (and (_ _let_2 _let_4) (forall (@list _let_3) (=> (_ _let_2 _let_3) (_ _let_2 (_ tptp.s (_ tptp.s _let_3)))))) (_ _let_2 _let_1))))))))) % 0.29/0.55 (define @t1 () (@var "Xx" $$unsorted)) % 0.29/0.55 (define @t2 () (_ tptp.s @t1)) % 0.29/0.55 (define @t3 () (_ tptp.s @t2)) % 0.29/0.55 (define @t4 () (@list @t1)) % 0.29/0.55 (define @t5 () (forall @t4 (_ (_ tptp.cCKB_E2 @t1) @t3))) % 0.29/0.55 (define @t6 () (not @t5)) % 0.29/0.55 (define @t7 () (@var "Xy" $$unsorted)) % 0.29/0.55 (define @t8 () (@var "Xp" (-> $$unsorted Bool))) % 0.29/0.55 (define @t9 () (_ @t8 @t7)) % 0.29/0.55 (define @t10 () (@var "Xu" $$unsorted)) % 0.29/0.55 (define @t11 () (_ tptp.s @t10)) % 0.29/0.55 (define @t12 () (_ tptp.s @t11)) % 0.29/0.55 (define @t13 () (_ @t8 @t12)) % 0.29/0.55 (define @t14 () (_ @t8 @t10)) % 0.29/0.55 (define @t15 () (@list @t10)) % 0.29/0.55 (define @t16 () (forall @t15 (=> @t14 @t13))) % 0.29/0.55 (define @t17 () (_ @t8 @t1)) % 0.29/0.55 (define @t18 () (and @t17 @t16)) % 0.29/0.55 (define @t19 () (=> @t18 @t9)) % 0.29/0.55 (define @t20 () (@list @t8)) % 0.29/0.55 (define @t21 () (forall @t20 @t19)) % 0.29/0.55 (define @t22 () (@list @t1 @t7)) % 0.29/0.55 (define @t23 () (lambda @t22 @t21)) % 0.29/0.55 (define @t24 () (tptp.s @t1)) % 0.29/0.55 (define @t25 () (tptp.s @t24)) % 0.29/0.55 (define @t26 () (tptp.s @t10)) % 0.29/0.55 (define @t27 () (tptp.s @t26)) % 0.29/0.55 (define @t28 () (_ @t8 @t27)) % 0.29/0.55 (define @t29 () (_ @t8 @t10)) % 0.29/0.55 (define @t30 () (forall @t15 (or (not @t29) @t28))) % 0.29/0.55 (define @t31 () (not @t30)) % 0.29/0.55 (define @t32 () (_ @t8 @t1)) % 0.29/0.55 (define @t33 () (not @t32)) % 0.29/0.55 (define @t34 () (or @t33 @t31 (_ @t8 @t25))) % 0.29/0.55 (define @t35 () (forall (@list @t1 @t8) @t34)) % 0.29/0.55 (define @t36 () (_ @t8 @t3)) % 0.29/0.55 (define @t37 () (or @t33 @t31 @t36)) % 0.29/0.55 (define @t38 () (forall @t20 @t37)) % 0.29/0.55 (define @t39 () (_ @t8 @t7)) % 0.29/0.55 (define @t40 () (forall @t20 (or @t33 @t31 @t39))) % 0.29/0.55 (define @t41 () (lambda (@list @t7) @t40)) % 0.29/0.55 (define @t42 () (_ (lambda @t22 @t40) @t1)) % 0.29/0.55 (define @t43 () (forall @t4 (_ @t42 @t3))) % 0.29/0.55 (define @t44 () (not @t17)) % 0.29/0.55 (define @t45 () (or @t44 @t31 @t9)) % 0.29/0.55 (define @t46 () (and @t17 @t30)) % 0.29/0.55 (define @t47 () (not @t14)) % 0.29/0.55 (define @t48 () (or @t47 @t13)) % 0.29/0.55 (define @t49 () (@quantifiers_skolemize @t35 1)) % 0.29/0.55 (define @t50 () (forall @t15 (or (not (_ @t49 @t10)) (_ @t49 @t27)))) % 0.29/0.55 (define @t51 () (@quantifiers_skolemize @t35 0)) % 0.29/0.55 (define @t52 () (_ @t49 (tptp.s (tptp.s @t51)))) % 0.29/0.55 (define @t53 () (not @t50)) % 0.29/0.55 (define @t54 () (_ @t49 @t51)) % 0.29/0.55 (define @t55 () (not @t54)) % 0.29/0.55 (define @t56 () (or @t55 @t53 @t52)) % 0.29/0.55 (define @t57 () (@list true)) % 0.29/0.55 (define @t58 () (@list @t56)) % 0.29/0.55 (define @t59 () (or @t55 @t52)) % 0.29/0.55 (define @t60 () (not @t59)) % 0.29/0.55 (assume @p1 @t6) % 0.29/0.55 (assume @p2 true) % 0.29/0.55 (step @p3 (= tptp.cCKB_E2 @t23) :rule refl :args (@t23)) % 0.29/0.55 (step @p4 :rule quant-merge-prenex :args ((= (forall @t4 (forall @t20 @t34)) @t35))) % 0.29/0.55 (step @p5 :rule refl :args ((tptp.s @t2))) % 0.29/0.55 (step @p6 :rule refl :args (@t24)) % 0.29/0.55 (step @p7 :rule cong :premises (@p6) :args (@t25)) % 0.29/0.55 (step @p8 :rule trans :premises (@p7 @p5)) % 0.29/0.55 (step @p9 :rule refl :args (tptp.s)) % 0.29/0.55 (step @p10 :rule ho_cong :premises (@p9 @p6)) % 0.29/0.55 (step @p11 :rule cong :premises (@p10 @p8) :args ((= (_ tptp.s @t24) @t25))) % 0.29/0.55 (step @p12 :rule symm :premises (@p11)) % 0.29/0.55 (step @p13 :rule refl :args (@t3)) % 0.29/0.55 (step @p14 :rule eq_resolve :premises (@p13 @p12)) % 0.29/0.55 (step @p15 :rule refl :args (@t2)) % 0.29/0.55 (step @p16 :rule cong :premises (@p15 @p6) :args ((= @t2 @t24))) % 0.29/0.55 (step @p17 :rule symm :premises (@p16)) % 0.29/0.55 (step @p18 :rule eq_resolve :premises (@p15 @p17)) % 0.29/0.55 (step @p19 :rule ho_cong :premises (@p9 @p18)) % 0.29/0.55 (step @p20 :rule trans :premises (@p19 @p14)) % 0.29/0.55 (step @p21 :rule cong :premises (@p20) :args (@t36)) % 0.29/0.55 (step @p22 :rule refl :args (@t31)) % 0.29/0.55 (step @p23 :rule refl :args (@t33)) % 0.29/0.55 (step @p24 :rule nary_cong :premises (@p23 @p22 @p21) :args (@t37)) % 0.29/0.55 (step @p25 :rule cong :premises (@p24) :args (@t38)) % 0.29/0.55 (step @p26 :rule beta-reduce :args ((= (_ @t41 @t3) @t38))) % 0.29/0.55 (step @p27 :rule trans :premises (@p26 @p25)) % 0.29/0.55 (step @p28 :rule refl :args (@t3)) % 0.29/0.55 (step @p29 :rule beta-reduce :args ((= @t42 @t41))) % 0.29/0.55 (step @p30 :rule ho_cong :premises (@p29 @p28)) % 0.29/0.55 (step @p31 :rule trans :premises (@p30 @p27)) % 0.29/0.55 (step @p32 :rule cong :premises (@p31) :args (@t43)) % 0.29/0.55 (step @p33 :rule trans :premises (@p32 @p4)) % 0.29/0.55 (step @p34 :rule cong :premises (@p33) :args ((not @t43))) % 0.29/0.55 (step @p35 :rule refl :args (@t1)) % 0.29/0.55 (step @p36 :rule refl :args (@t39)) % 0.29/0.55 (step @p37 :rule refl :args (@t9)) % 0.29/0.55 (step @p38 :rule cong :premises (@p37 @p36) :args ((= @t9 @t39))) % 0.29/0.55 (step @p39 :rule symm :premises (@p38)) % 0.29/0.55 (step @p40 :rule eq_resolve :premises (@p37 @p39)) % 0.29/0.55 (step @p41 :rule refl :args (@t32)) % 0.29/0.55 (step @p42 :rule refl :args (@t17)) % 0.29/0.55 (step @p43 :rule cong :premises (@p42 @p41) :args ((= @t17 @t32))) % 0.29/0.55 (step @p44 :rule symm :premises (@p43)) % 0.29/0.55 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 0.29/0.55 (step @p46 :rule cong :premises (@p45) :args (@t44)) % 0.29/0.55 (step @p47 :rule nary_cong :premises (@p46 @p22 @p40) :args (@t45)) % 0.29/0.55 (step @p48 :rule cong :premises (@p47) :args ((forall @t20 @t45))) % 0.29/0.55 (step @p49 :rule aci_norm :args ((= (or (or @t44 @t31) @t9) @t45))) % 0.29/0.55 (step @p50 :rule bool-and-de-morgan :args (@t17 @t30 true)) % 0.29/0.55 (step @p51 :rule nary_cong :premises (@p50 @p37) :args ((or (not @t46) @t9))) % 0.29/0.55 (step @p52 :rule trans :premises (@p51 @p49)) % 0.29/0.55 (step @p53 :rule bool-impl-elim :args (@t46 @t9)) % 0.29/0.55 (step @p54 :rule trans :premises (@p53 @p52)) % 0.29/0.55 (step @p55 :rule cong :premises (@p54) :args ((forall @t20 (=> @t46 @t9)))) % 0.29/0.55 (step @p56 :rule trans :premises (@p55 @p48)) % 0.29/0.55 (step @p57 :rule refl :args (@t9)) % 0.29/0.55 (step @p58 :rule refl :args ((_ @t8 @t12))) % 0.29/0.55 (step @p59 :rule refl :args ((tptp.s @t11))) % 0.29/0.55 (step @p60 :rule refl :args (@t26)) % 0.29/0.55 (step @p61 :rule cong :premises (@p60) :args (@t27)) % 0.29/0.55 (step @p62 :rule trans :premises (@p61 @p59)) % 0.29/0.55 (step @p63 :rule cong :premises (@p62) :args (@t28)) % 0.29/0.55 (step @p64 :rule trans :premises (@p63 @p58)) % 0.29/0.55 (step @p65 :rule refl :args (@t8)) % 0.29/0.55 (step @p66 :rule ho_cong :premises (@p65 @p62)) % 0.29/0.55 (step @p67 :rule cong :premises (@p66 @p64) :args ((= (_ @t8 @t27) @t28))) % 0.29/0.55 (step @p68 :rule symm :premises (@p67)) % 0.29/0.55 (step @p69 :rule refl :args (@t13)) % 0.29/0.55 (step @p70 :rule eq_resolve :premises (@p69 @p68)) % 0.29/0.55 (step @p71 :rule ho_cong :premises (@p9 @p60)) % 0.29/0.55 (step @p72 :rule cong :premises (@p71 @p62) :args ((= (_ tptp.s @t26) @t27))) % 0.29/0.55 (step @p73 :rule symm :premises (@p72)) % 0.29/0.55 (step @p74 :rule refl :args (@t12)) % 0.29/0.55 (step @p75 :rule eq_resolve :premises (@p74 @p73)) % 0.29/0.55 (step @p76 :rule refl :args (@t11)) % 0.29/0.55 (step @p77 :rule cong :premises (@p76 @p60) :args ((= @t11 @t26))) % 0.29/0.55 (step @p78 :rule symm :premises (@p77)) % 0.29/0.55 (step @p79 :rule eq_resolve :premises (@p76 @p78)) % 0.29/0.55 (step @p80 :rule ho_cong :premises (@p9 @p79)) % 0.29/0.55 (step @p81 :rule trans :premises (@p80 @p75)) % 0.29/0.55 (step @p82 :rule ho_cong :premises (@p65 @p81)) % 0.29/0.55 (step @p83 :rule trans :premises (@p82 @p70)) % 0.29/0.55 (step @p84 :rule refl :args (@t29)) % 0.29/0.55 (step @p85 :rule refl :args (@t14)) % 0.29/0.55 (step @p86 :rule cong :premises (@p85 @p84) :args ((= @t14 @t29))) % 0.29/0.55 (step @p87 :rule symm :premises (@p86)) % 0.29/0.55 (step @p88 :rule eq_resolve :premises (@p85 @p87)) % 0.29/0.55 (step @p89 :rule cong :premises (@p88) :args (@t47)) % 0.29/0.55 (step @p90 :rule nary_cong :premises (@p89 @p83) :args (@t48)) % 0.29/0.55 (step @p91 :rule cong :premises (@p90) :args ((forall @t15 @t48))) % 0.29/0.55 (step @p92 :rule bool-impl-elim :args (@t14 @t13)) % 0.29/0.55 (step @p93 :rule cong :premises (@p92) :args (@t16)) % 0.29/0.55 (step @p94 :rule trans :premises (@p93 @p91)) % 0.29/0.55 (step @p95 :rule refl :args (@t17)) % 0.29/0.55 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t18)) % 0.29/0.55 (step @p97 :rule cong :premises (@p96 @p57) :args (@t19)) % 0.29/0.55 (step @p98 :rule cong :premises (@p97) :args (@t21)) % 0.29/0.55 (step @p99 :rule trans :premises (@p98 @p56)) % 0.29/0.55 (step @p100 :rule cong :premises (@p99) :args (@t23)) % 0.29/0.55 (step @p101 :rule trans :premises (@p3 @p100)) % 0.29/0.55 (step @p102 :rule ho_cong :premises (@p101 @p35)) % 0.29/0.55 (step @p103 :rule ho_cong :premises (@p102 @p28)) % 0.29/0.55 (step @p104 :rule cong :premises (@p103) :args (@t5)) % 0.29/0.55 (step @p105 :rule cong :premises (@p104) :args (@t6)) % 0.29/0.55 (step @p106 :rule trans :premises (@p105 @p34)) % 0.29/0.55 (step @p107 :rule eq_resolve :premises (@p1 @p106)) % 0.29/0.55 (step @p108 :rule skolemize :premises (@p107)) % 0.29/0.55 (step @p109 :rule bool-double-not-elim :args (@t50)) % 0.29/0.55 (step @p110 :rule refl :args (@t56)) % 0.29/0.55 (step @p111 :rule nary_cong :premises (@p110 @p109) :args ((or @t56 (not @t53)))) % 0.29/0.55 (step @p112 :rule cnf_or_neg :args (@t56 1)) % 0.29/0.55 (step @p113 :rule eq_resolve :premises (@p112 @p111)) % 0.29/0.55 (step @p114 :rule reordering :premises (@p113) :args ((or @t50 @t56))) % 0.29/0.55 (step @p115 :rule chain_m_resolution :premises (@p114 @p108) :args (@t50 @t57 @t58)) % 0.29/0.55 (step @p116 :rule cnf_or_neg :args (@t56 2)) % 0.29/0.55 (step @p117 :rule chain_m_resolution :premises (@p116 @p108) :args ((not @t52) @t57 @t58)) % 0.29/0.55 (step @p118 :rule bool-double-not-elim :args (@t54)) % 0.29/0.55 (step @p119 :rule nary_cong :premises (@p110 @p118) :args ((or @t56 (not @t55)))) % 0.29/0.55 (step @p120 :rule cnf_or_neg :args (@t56 0)) % 0.29/0.55 (step @p121 :rule eq_resolve :premises (@p120 @p119)) % 0.29/0.55 (step @p122 :rule reordering :premises (@p121) :args ((or @t54 @t56))) % 0.29/0.55 (step @p123 :rule chain_m_resolution :premises (@p122 @p108) :args (@t54 @t57 @t58)) % 0.29/0.55 (step @p124 :rule cnf_or_pos :args (@t59)) % 0.29/0.55 (step @p125 :rule reordering :premises (@p124) :args ((or @t55 @t52 @t60))) % 0.29/0.55 (step @p126 :rule chain_m_resolution :premises (@p125 @p123 @p117) :args (@t60 (@list false true) (@list @t54 @t52))) % 0.29/0.55 (assume-push @p133 @t50) % 0.29/0.55 (step @p128 :rule instantiate :premises (@p115) :args ((@list @t51))) % 0.29/0.55 (step-pop @p134 :rule scope :premises (@p128)) % 0.29/0.55 (step @p129 :rule process_scope :premises (@p134) :args (@t59)) % 0.29/0.55 (step @p131 :rule implies_elim :premises (@p129)) % 0.29/0.55 (step @p132 false :rule chain_m_resolution :premises (@p131 @p126 @p115) :args (false (@list true false) (@list @t59 @t50))) % 0.29/0.55 ) % 0.29/0.55 % SZS output end Proof % 0.29/0.55 % cvc5 exiting %------------------------------------------------------------------------------