%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO033^1 : 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 : n020.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 09:11:49 AM UTC 2026 % Result : Theorem 2.84s 3.07s % Output : Proof 2.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYO033^1 : 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 % 0.17/0.35 % Computer : n020.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 23:52:10 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.50 %----Proving TH0 % 2.84/3.07 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 2.84/3.07 % SZS status Theorem % 2.84/3.07 % SZS output start Proof % 2.84/3.07 ( % 2.84/3.07 (declare-sort $$unsorted 0) % 2.84/3.07 (define @t1 () (@var "X" $$unsorted)) % 2.84/3.07 (define @t2 () (@var "P" (-> $$unsorted Bool))) % 2.84/3.07 (define @t3 () (_ @t2 @t1)) % 2.84/3.07 (define @t4 () (@list @t1)) % 2.84/3.07 (define @t5 () (forall @t4 @t3)) % 2.84/3.07 (define @t6 () (@var "Q" (-> (-> $$unsorted Bool) Bool))) % 2.84/3.07 (define @t7 () (_ @t6 @t2)) % 2.84/3.07 (define @t8 () (= @t7 @t5)) % 2.84/3.07 (define @t9 () (@list @t2)) % 2.84/3.07 (define @t10 () (forall @t9 @t8)) % 2.84/3.07 (define @t11 () (@list @t6)) % 2.84/3.07 (define @t12 () (exists @t11 @t10)) % 2.84/3.07 (define @t13 () (not @t12)) % 2.84/3.07 (define @t14 () (_ @t6 @t2)) % 2.84/3.07 (define @t15 () (_ @t2 @t1)) % 2.84/3.07 (define @t16 () (forall @t4 @t15)) % 2.84/3.07 (define @t17 () (forall @t9 (= @t16 @t14))) % 2.84/3.07 (define @t18 () (forall @t11 (not @t17))) % 2.84/3.07 (define @t19 () (= @t7 @t16)) % 2.84/3.07 (define @t20 () (lambda (@list (@var "BOUND_VARIABLE_35757" $$unsorted)) true)) % 2.84/3.07 (define @t21 () (@var "BOUND_VARIABLE_35815" (-> $$unsorted Bool))) % 2.84/3.07 (define @t22 () (lambda (@list @t21) (= @t20 @t21))) % 2.84/3.07 (define @t23 () (_ @t22 @t2)) % 2.84/3.07 (define @t24 () (= @t16 @t23)) % 2.84/3.07 (define @t25 () (forall @t9 @t24)) % 2.84/3.07 (define @t26 () (not @t25)) % 2.84/3.07 (define @t27 () (forall @t9 (= @t16 (= @t2 @t20)))) % 2.84/3.07 (define @t28 () (not @t27)) % 2.84/3.07 (define @t29 () (@quantifiers_skolemize @t27 0)) % 2.84/3.07 (define @t30 () (@purify @t20)) % 2.84/3.07 (define @t31 () (= @t30 @t29)) % 2.84/3.07 (define @t32 () (forall @t4 (_ @t29 @t1))) % 2.84/3.07 (define @t33 () (= @t32 @t31)) % 2.84/3.07 (define @t34 () (not @t33)) % 2.84/3.07 (define @t35 () (= @t20 @t29)) % 2.84/3.07 (define @t36 () (= @t32 @t35)) % 2.84/3.07 (define @t37 () (not @t36)) % 2.84/3.07 (define @t38 () (= @t32 (= @t29 @t20))) % 2.84/3.07 (define @t39 () (not @t38)) % 2.84/3.07 (define @t40 () (@list true)) % 2.84/3.07 (define @t41 () (@const 0 $$unsorted)) % 2.84/3.07 (define @t42 () (_ @t29 @t41)) % 2.84/3.07 (define @t43 () (_ @t30 @t41)) % 2.84/3.07 (define @t44 () (= @t43 @t42)) % 2.84/3.07 (define @t45 () (not @t44)) % 2.84/3.07 (define @t46 () (or @t31 @t45)) % 2.84/3.07 (define @t47 () (not @t32)) % 2.84/3.07 (define @t48 () (_ @t29 (@quantifiers_skolemize @t32 0))) % 2.84/3.07 (define @t49 () (not @t48)) % 2.84/3.07 (define @t50 () (=> (= @t29 @t30) (= @t48 true))) % 2.84/3.07 (assume @p1 @t13) % 2.84/3.07 (assume @p2 true) % 2.84/3.07 (step @p3 :rule bool-double-not-elim :args (@t18)) % 2.84/3.07 (step @p4 :rule exists-elim :args ((= (exists @t11 @t17) (not @t18)))) % 2.84/3.07 (step @p5 :rule eq-symm :args (@t14 @t16)) % 2.84/3.07 (step @p6 :rule cong :premises (@p5) :args ((forall @t9 (= @t14 @t16)))) % 2.84/3.07 (step @p7 :rule refl :args (@t16)) % 2.84/3.07 (step @p8 :rule refl :args (@t14)) % 2.84/3.07 (step @p9 :rule refl :args (@t7)) % 2.84/3.07 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t7 @t14))) % 2.84/3.07 (step @p11 :rule symm :premises (@p10)) % 2.84/3.07 (step @p12 :rule eq_resolve :premises (@p9 @p11)) % 2.84/3.07 (step @p13 :rule cong :premises (@p12 @p7) :args (@t19)) % 2.84/3.07 (step @p14 :rule cong :premises (@p13) :args ((forall @t9 @t19))) % 2.84/3.07 (step @p15 :rule trans :premises (@p14 @p6)) % 2.84/3.07 (step @p16 :rule refl :args (@t15)) % 2.84/3.07 (step @p17 :rule refl :args (@t3)) % 2.84/3.07 (step @p18 :rule cong :premises (@p17 @p16) :args ((= @t3 @t15))) % 2.84/3.07 (step @p19 :rule symm :premises (@p18)) % 2.84/3.07 (step @p20 :rule eq_resolve :premises (@p17 @p19)) % 2.84/3.07 (step @p21 :rule cong :premises (@p20) :args (@t5)) % 2.84/3.07 (step @p22 :rule refl :args (@t7)) % 2.84/3.07 (step @p23 :rule cong :premises (@p22 @p21) :args (@t8)) % 2.84/3.07 (step @p24 :rule cong :premises (@p23) :args (@t10)) % 2.84/3.07 (step @p25 :rule trans :premises (@p24 @p15)) % 2.84/3.07 (step @p26 :rule cong :premises (@p25) :args (@t12)) % 2.84/3.07 (step @p27 :rule trans :premises (@p26 @p4)) % 2.84/3.07 (step @p28 :rule cong :premises (@p27) :args (@t13)) % 2.84/3.07 (step @p29 :rule trans :premises (@p28 @p3)) % 2.84/3.07 (step @p30 :rule eq_resolve :premises (@p1 @p29)) % 2.84/3.07 (step @p31 :rule eq-symm :args (@t20 @t2)) % 2.84/3.07 (step @p32 :rule beta-reduce :args ((= @t23 (= @t20 @t2)))) % 2.84/3.07 (step @p33 :rule trans :premises (@p32 @p31)) % 2.84/3.07 (step @p34 :rule refl :args (@t16)) % 2.84/3.07 (step @p35 :rule cong :premises (@p34 @p33) :args (@t24)) % 2.84/3.07 (step @p36 :rule cong :premises (@p35) :args (@t25)) % 2.84/3.07 (step @p37 :rule cong :premises (@p36) :args (@t26)) % 2.84/3.07 (step @p38 :rule refl :args (@t18)) % 2.84/3.07 (step @p39 :rule cong :premises (@p38 @p37) :args ((=> @t18 @t26))) % 2.84/3.07 (assume-push @p124 @t18) % 2.84/3.07 (step @p41 :rule instantiate :premises (@p30) :args ((@list @t22))) % 2.84/3.07 (step-pop @p125 :rule scope :premises (@p41)) % 2.84/3.07 (step @p42 :rule process_scope :premises (@p125) :args (@t26)) % 2.84/3.07 (step @p44 :rule eq_resolve :premises (@p42 @p39)) % 2.84/3.07 (step @p45 :rule implies_elim :premises (@p44)) % 2.84/3.07 (step @p46 :rule chain_m_resolution :premises (@p45 @p30) :args (@t28 (@list false) (@list @t18))) % 2.84/3.07 (step @p47 :rule refl :args (@t34)) % 2.84/3.07 (step @p48 :rule bool-double-not-elim :args (@t27)) % 2.84/3.07 (step @p49 :rule nary_cong :premises (@p48 @p47) :args ((or (not @t28) @t34))) % 2.84/3.07 (step @p50 :rule refl :args (@t29)) % 2.84/3.07 (step @p51 :rule eq-refl :args (@t20)) % 2.84/3.07 (step @p52 :rule refl :args (@t20)) % 2.84/3.07 (step @p53 :rule symm :premises (@p52)) % 2.84/3.07 (step @p54 :rule refl :args (@t20)) % 2.84/3.07 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t20 @t20))) % 2.84/3.07 (step @p56 :rule trans :premises (@p55 @p51)) % 2.84/3.07 (step @p57 :rule skolem_intro :args (@t30)) % 2.84/3.07 (step @p58 :rule cong :premises (@p54 @p57) :args ((= @t20 @t30))) % 2.84/3.07 (step @p59 :rule trans :premises (@p58 @p56)) % 2.84/3.07 (step @p60 :rule true_elim :premises (@p59)) % 2.84/3.07 (step @p61 :rule cong :premises (@p60 @p50) :args (@t35)) % 2.84/3.07 (step @p62 :rule refl :args (@t32)) % 2.84/3.07 (step @p63 :rule cong :premises (@p62 @p61) :args (@t36)) % 2.84/3.07 (step @p64 :rule cong :premises (@p63) :args (@t37)) % 2.84/3.07 (step @p65 :rule refl :args (@t28)) % 2.84/3.07 (step @p66 :rule cong :premises (@p65 @p64) :args ((=> @t28 @t37))) % 2.84/3.07 (step @p67 :rule eq-symm :args (@t29 @t20)) % 2.84/3.07 (step @p68 :rule cong :premises (@p62 @p67) :args (@t38)) % 2.84/3.07 (step @p69 :rule cong :premises (@p68) :args (@t39)) % 2.84/3.07 (step @p70 :rule cong :premises (@p65 @p69) :args ((=> @t28 @t39))) % 2.84/3.07 (step @p71 :rule trans :premises (@p70 @p66)) % 2.84/3.07 (assume-push @p126 @t28) % 2.84/3.07 (step @p73 :rule skolemize :premises (@p46)) % 2.84/3.07 (step-pop @p127 :rule scope :premises (@p73)) % 2.84/3.07 (step @p74 :rule process_scope :premises (@p127) :args (@t39)) % 2.84/3.07 (step @p76 :rule eq_resolve :premises (@p74 @p71)) % 2.84/3.07 (step @p77 :rule implies_elim :premises (@p76)) % 2.84/3.07 (step @p78 :rule eq_resolve :premises (@p77 @p49)) % 2.84/3.07 (step @p79 :rule chain_m_resolution :premises (@p78 @p46) :args (@t34 @t40 (@list @t27))) % 2.84/3.07 (step @p80 :rule cnf_equiv_neg2 :args (@t33)) % 2.84/3.07 (step @p81 :rule bool-eq-true :args (@t42)) % 2.84/3.07 (step @p82 :rule eq-symm :args (true @t42)) % 2.84/3.07 (step @p83 :rule trans :premises (@p82 @p81)) % 2.84/3.07 (step @p84 :rule refl :args (@t42)) % 2.84/3.07 (step @p85 :rule beta-reduce :args ((= (_ @t20 @t41) true))) % 2.84/3.07 (step @p86 :rule refl :args (@t41)) % 2.84/3.07 (step @p87 :rule ho_cong :premises (@p57 @p86)) % 2.84/3.07 (step @p88 :rule bool-eq-true :args (@t43)) % 2.84/3.07 (step @p89 :rule trans :premises (@p88 @p87 @p85)) % 2.84/3.07 (step @p90 :rule true_elim :premises (@p89)) % 2.84/3.07 (step @p91 :rule cong :premises (@p90 @p84) :args (@t44)) % 2.84/3.07 (step @p92 :rule trans :premises (@p91 @p83)) % 2.84/3.07 (step @p93 :rule cong :premises (@p92) :args (@t45)) % 2.84/3.07 (step @p94 :rule refl :args (@t31)) % 2.84/3.07 (step @p95 :rule nary_cong :premises (@p94 @p93) :args (@t46)) % 2.84/3.07 ; WARNING: add trust step for TRUST % 2.84/3.07 ; trust TRUST THEORY_LEMMA % 2.84/3.07 (step @p96 :rule trust :premises () :args (@t46)) % 2.84/3.07 (step @p97 :rule eq_resolve :premises (@p96 @p95)) % 2.84/3.07 (assume-push @p128 @t32) % 2.84/3.07 (step @p99 :rule instantiate :premises (@p128) :args ((@list @t41))) % 2.84/3.07 (step-pop @p129 :rule scope :premises (@p99)) % 2.84/3.07 (step @p100 :rule process_scope :premises (@p129) :args (@t42)) % 2.84/3.07 (step @p102 :rule implies_elim :premises (@p100)) % 2.84/3.07 (step @p103 :rule chain_m_resolution :premises (@p102 @p97 @p80 @p79) :args (@t47 (@list true true true) (@list @t42 @t31 @t33))) % 2.84/3.07 (step @p104 :rule cnf_equiv_neg1 :args (@t33)) % 2.84/3.07 (step @p105 :rule reordering :premises (@p104) :args ((or @t32 @t31 @t33))) % 2.84/3.07 (step @p106 :rule chain_m_resolution :premises (@p105 @p103 @p79) :args (@t31 (@list true true) (@list @t32 @t33))) % 2.84/3.07 (step @p107 :rule refl :args (@t49)) % 2.84/3.07 (step @p108 :rule bool-double-not-elim :args (@t32)) % 2.84/3.07 (step @p109 :rule nary_cong :premises (@p108 @p107) :args ((or (not @t47) @t49))) % 2.84/3.07 (assume-push @p130 @t47) % 2.84/3.07 (step @p111 :rule skolemize :premises (@p130)) % 2.84/3.07 (step-pop @p131 :rule scope :premises (@p111)) % 2.84/3.07 (step @p112 :rule process_scope :premises (@p131) :args (@t49)) % 2.84/3.07 (step @p114 :rule implies_elim :premises (@p112)) % 2.84/3.07 (step @p115 :rule eq_resolve :premises (@p114 @p109)) % 2.84/3.07 (step @p116 :rule chain_m_resolution :premises (@p115 @p103) :args (@t49 @t40 (@list @t32))) % 2.84/3.07 (step @p117 :rule bool-eq-true :args (@t48)) % 2.84/3.07 (step @p118 :rule eq-symm :args (@t29 @t30)) % 2.84/3.07 (step @p119 :rule cong :premises (@p118 @p117) :args (@t50)) % 2.84/3.07 ; trust TRUST THEORY_LEMMA % 2.84/3.07 (step @p120 :rule trust :premises () :args (@t50)) % 2.84/3.07 (step @p121 :rule eq_resolve :premises (@p120 @p119)) % 2.84/3.07 (step @p122 :rule implies_elim :premises (@p121)) % 2.84/3.07 (step @p123 false :rule chain_m_resolution :premises (@p122 @p116 @p106) :args (false (@list true false) (@list @t48 @t31))) % 2.84/3.07 ) % 2.84/3.07 % SZS output end Proof % 2.84/3.07 % cvc5 exiting %------------------------------------------------------------------------------