%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO517^1 : TPTP v9.2.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n016.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 09:13:02 AM UTC 2026 % Result : Theorem 0.63s 0.80s % Output : Proof 0.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO517^1 : TPTP v9.2.1. Released v4.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n016.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 : Wed Jun 3 00:19:24 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.63/0.80 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.63/0.80 % SZS status Theorem % 0.63/0.80 % SZS output start Proof % 0.63/0.80 ( % 0.63/0.80 (declare-sort $$unsorted 0) % 0.63/0.80 (define @t1 () (@var "P" (-> $$unsorted Bool))) % 0.63/0.80 (define @t2 () (@var "D" (-> (-> $$unsorted Bool) $$unsorted))) % 0.63/0.80 (define @t3 () (_ @t2 @t1)) % 0.63/0.80 (define @t4 () (_ @t1 @t3)) % 0.63/0.80 (define @t5 () (@var "Y" $$unsorted)) % 0.63/0.80 (define @t6 () (@var "X" $$unsorted)) % 0.63/0.80 (define @t7 () (= @t6 @t5)) % 0.63/0.80 (define @t8 () (_ @t1 @t5)) % 0.63/0.80 (define @t9 () (@list @t5)) % 0.63/0.80 (define @t10 () (forall @t9 (=> @t8 @t7))) % 0.63/0.80 (define @t11 () (_ @t1 @t6)) % 0.63/0.80 (define @t12 () (and @t11 @t10)) % 0.63/0.80 (define @t13 () (@list @t6)) % 0.63/0.80 (define @t14 () (exists @t13 @t12)) % 0.63/0.80 (define @t15 () (=> @t14 @t4)) % 0.63/0.80 (define @t16 () (@list @t1)) % 0.63/0.80 (define @t17 () (forall @t16 @t15)) % 0.63/0.80 (define @t18 () (@list @t2)) % 0.63/0.80 (define @t19 () (exists @t18 @t17)) % 0.63/0.80 (define @t20 () (not @t19)) % 0.63/0.80 (define @t21 () (@var "BOUND_VARIABLE_7459" $$unsorted)) % 0.63/0.80 (define @t22 () (_ @t1 @t5)) % 0.63/0.80 (define @t23 () (not @t22)) % 0.63/0.80 (define @t24 () (not (forall @t9 (or @t23 (= @t5 @t21))))) % 0.63/0.80 (define @t25 () (not (_ @t1 @t21))) % 0.63/0.80 (define @t26 () (_ @t2 @t1)) % 0.63/0.80 (define @t27 () (_ @t1 @t26)) % 0.63/0.80 (define @t28 () (@list @t1 @t21)) % 0.63/0.80 (define @t29 () (forall @t28 (or @t27 @t25 @t24))) % 0.63/0.80 (define @t30 () (forall @t18 (not @t29))) % 0.63/0.80 (define @t31 () (or @t23 (= @t21 @t5))) % 0.63/0.80 (define @t32 () (forall @t9 @t31)) % 0.63/0.80 (define @t33 () (not @t32)) % 0.63/0.80 (define @t34 () (or @t27 @t25 @t33)) % 0.63/0.80 (define @t35 () (or @t25 @t33)) % 0.63/0.80 (define @t36 () (or @t35 @t27)) % 0.63/0.80 (define @t37 () (forall @t28 @t36)) % 0.63/0.80 (define @t38 () (@list @t21)) % 0.63/0.80 (define @t39 () (forall @t38 @t36)) % 0.63/0.80 (define @t40 () (forall @t38 @t35)) % 0.63/0.80 (define @t41 () (or @t40 @t27)) % 0.63/0.80 (define @t42 () (forall @t9 (or @t23 @t7))) % 0.63/0.80 (define @t43 () (not @t42)) % 0.63/0.80 (define @t44 () (_ @t1 @t6)) % 0.63/0.80 (define @t45 () (forall @t13 (or (not @t44) @t43))) % 0.63/0.80 (define @t46 () (or @t45 @t4)) % 0.63/0.80 (define @t47 () (not @t45)) % 0.63/0.80 (define @t48 () (not @t11)) % 0.63/0.80 (define @t49 () (or @t48 @t43)) % 0.63/0.80 (define @t50 () (and @t11 @t42)) % 0.63/0.80 (define @t51 () (forall @t13 (not @t50))) % 0.63/0.80 (define @t52 () (not @t51)) % 0.63/0.80 (define @t53 () (not @t8)) % 0.63/0.80 (define @t54 () (or @t53 @t7)) % 0.63/0.80 (define @t55 () (@const 0 (-> (-> $$unsorted Bool) $$unsorted))) % 0.63/0.80 (define @t56 () (_ @t55 @t1)) % 0.63/0.80 (define @t57 () (@var "BOUND_VARIABLE_21559" (-> $$unsorted Bool))) % 0.63/0.80 (define @t58 () (_ @t55 @t57)) % 0.63/0.80 (define @t59 () (@list @t57)) % 0.63/0.80 (define @t60 () (lambda @t59 @t58)) % 0.63/0.80 (define @t61 () (_ @t60 @t1)) % 0.63/0.80 (define @t62 () (_ @t1 @t61)) % 0.63/0.80 (define @t63 () (or @t62 @t25 @t24)) % 0.63/0.80 (define @t64 () (forall @t28 @t63)) % 0.63/0.80 (define @t65 () (not @t64)) % 0.63/0.80 (define @t66 () (forall @t28 (or (_ @t1 @t56) @t25 @t24))) % 0.63/0.80 (define @t67 () (@quantifiers_skolemize @t66 1)) % 0.63/0.80 (define @t68 () (@quantifiers_skolemize @t66 0)) % 0.63/0.80 (define @t69 () (_ @t68 @t67)) % 0.63/0.80 (define @t70 () (not @t69)) % 0.63/0.80 (define @t71 () (_ @t68 (_ @t55 @t68))) % 0.63/0.80 (define @t72 () (or @t71 @t70 (not (forall @t9 (or (not (_ @t68 @t5)) (= @t5 @t67)))))) % 0.63/0.80 (define @t73 () (@list true)) % 0.63/0.80 (define @t74 () (@list @t72)) % 0.63/0.80 (define @t75 () (@var "x" $$unsorted)) % 0.63/0.80 (define @t76 () (@list @t75)) % 0.63/0.80 (define @t77 () (forall @t76 (not (_ @t68 @t75)))) % 0.63/0.80 (define @t78 () (or @t77 @t71)) % 0.63/0.80 (assume @p1 @t20) % 0.63/0.80 (assume @p2 true) % 0.63/0.80 (step @p3 :rule bool-double-not-elim :args (@t30)) % 0.63/0.80 (step @p4 :rule exists-elim :args ((= (exists @t18 @t29) (not @t30)))) % 0.63/0.80 (step @p5 :rule eq-symm :args (@t21 @t5)) % 0.63/0.80 (step @p6 :rule refl :args (@t23)) % 0.63/0.80 (step @p7 :rule nary_cong :premises (@p6 @p5) :args (@t31)) % 0.63/0.80 (step @p8 :rule cong :premises (@p7) :args (@t32)) % 0.63/0.80 (step @p9 :rule cong :premises (@p8) :args (@t33)) % 0.63/0.80 (step @p10 :rule refl :args (@t25)) % 0.63/0.80 (step @p11 :rule refl :args (@t27)) % 0.63/0.80 (step @p12 :rule nary_cong :premises (@p11 @p10 @p9) :args (@t34)) % 0.63/0.80 (step @p13 :rule aci_norm :args ((= @t36 @t34))) % 0.63/0.80 (step @p14 :rule trans :premises (@p13 @p12)) % 0.63/0.80 (step @p15 :rule cong :premises (@p14) :args (@t37)) % 0.63/0.80 (step @p16 :rule quant-merge-prenex :args ((= (forall @t16 @t39) @t37))) % 0.63/0.80 (step @p17 :rule refl :args (@t27)) % 0.63/0.80 (step @p18 :rule alpha_equiv :args (@t40 (@list @t21) (@list @t6))) % 0.63/0.80 (step @p19 :rule nary_cong :premises (@p18 @p17) :args (@t41)) % 0.63/0.80 (step @p20 :rule quant-miniscope-or :args ((= @t39 @t41))) % 0.63/0.80 (step @p21 :rule trans :premises (@p20 @p19)) % 0.63/0.80 (step @p22 :rule symm :premises (@p21)) % 0.63/0.80 (step @p23 :rule cong :premises (@p22) :args ((forall @t16 (or @t45 @t27)))) % 0.63/0.80 (step @p24 :rule trans :premises (@p23 @p16)) % 0.63/0.80 (step @p25 :rule trans :premises (@p24 @p15)) % 0.63/0.80 (step @p26 :rule refl :args ((_ @t1 @t3))) % 0.63/0.80 (step @p27 :rule refl :args (@t26)) % 0.63/0.80 (step @p28 :rule cong :premises (@p27) :args (@t27)) % 0.63/0.80 (step @p29 :rule trans :premises (@p28 @p26)) % 0.63/0.80 (step @p30 :rule refl :args (@t1)) % 0.63/0.80 (step @p31 :rule ho_cong :premises (@p30 @p27)) % 0.63/0.80 (step @p32 :rule cong :premises (@p31 @p29) :args ((= (_ @t1 @t26) @t27))) % 0.63/0.80 (step @p33 :rule symm :premises (@p32)) % 0.63/0.80 (step @p34 :rule refl :args (@t4)) % 0.63/0.80 (step @p35 :rule eq_resolve :premises (@p34 @p33)) % 0.63/0.80 (step @p36 :rule refl :args (@t3)) % 0.63/0.80 (step @p37 :rule cong :premises (@p36 @p27) :args ((= @t3 @t26))) % 0.63/0.80 (step @p38 :rule symm :premises (@p37)) % 0.63/0.80 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 0.63/0.80 (step @p40 :rule ho_cong :premises (@p30 @p39)) % 0.63/0.80 (step @p41 :rule trans :premises (@p40 @p35)) % 0.63/0.80 (step @p42 :rule refl :args (@t45)) % 0.63/0.80 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t46)) % 0.63/0.80 (step @p44 :rule cong :premises (@p43) :args ((forall @t16 @t46))) % 0.63/0.80 (step @p45 :rule trans :premises (@p44 @p25)) % 0.63/0.80 (step @p46 :rule bool-double-not-elim :args (@t45)) % 0.63/0.80 (step @p47 :rule nary_cong :premises (@p46 @p34) :args ((or (not @t47) @t4))) % 0.63/0.80 (step @p48 :rule bool-impl-elim :args (@t47 @t4)) % 0.63/0.80 (step @p49 :rule trans :premises (@p48 @p47)) % 0.63/0.80 (step @p50 :rule cong :premises (@p49) :args ((forall @t16 (=> @t47 @t4)))) % 0.63/0.80 (step @p51 :rule trans :premises (@p50 @p45)) % 0.63/0.80 (step @p52 :rule refl :args (@t4)) % 0.63/0.80 (step @p53 :rule refl :args (@t43)) % 0.63/0.80 (step @p54 :rule refl :args (@t44)) % 0.63/0.80 (step @p55 :rule refl :args (@t11)) % 0.63/0.80 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t11 @t44))) % 0.63/0.80 (step @p57 :rule symm :premises (@p56)) % 0.63/0.80 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 0.63/0.80 (step @p59 :rule cong :premises (@p58) :args (@t48)) % 0.63/0.80 (step @p60 :rule nary_cong :premises (@p59 @p53) :args (@t49)) % 0.63/0.80 (step @p61 :rule cong :premises (@p60) :args ((forall @t13 @t49))) % 0.63/0.80 (step @p62 :rule bool-and-de-morgan :args (@t11 @t42 true)) % 0.63/0.80 (step @p63 :rule cong :premises (@p62) :args (@t51)) % 0.63/0.80 (step @p64 :rule trans :premises (@p63 @p61)) % 0.63/0.80 (step @p65 :rule cong :premises (@p64) :args (@t52)) % 0.63/0.80 (step @p66 :rule exists-elim :args ((= (exists @t13 @t50) @t52))) % 0.63/0.80 (step @p67 :rule trans :premises (@p66 @p65)) % 0.63/0.80 (step @p68 :rule refl :args (@t7)) % 0.63/0.80 (step @p69 :rule refl :args (@t22)) % 0.63/0.80 (step @p70 :rule refl :args (@t8)) % 0.63/0.80 (step @p71 :rule cong :premises (@p70 @p69) :args ((= @t8 @t22))) % 0.63/0.80 (step @p72 :rule symm :premises (@p71)) % 0.63/0.80 (step @p73 :rule eq_resolve :premises (@p70 @p72)) % 0.63/0.80 (step @p74 :rule cong :premises (@p73) :args (@t53)) % 0.63/0.80 (step @p75 :rule nary_cong :premises (@p74 @p68) :args (@t54)) % 0.63/0.80 (step @p76 :rule cong :premises (@p75) :args ((forall @t9 @t54))) % 0.63/0.80 (step @p77 :rule bool-impl-elim :args (@t8 @t7)) % 0.63/0.80 (step @p78 :rule cong :premises (@p77) :args (@t10)) % 0.63/0.80 (step @p79 :rule trans :premises (@p78 @p76)) % 0.63/0.80 (step @p80 :rule refl :args (@t11)) % 0.63/0.80 (step @p81 :rule nary_cong :premises (@p80 @p79) :args (@t12)) % 0.63/0.80 (step @p82 :rule cong :premises (@p81) :args (@t14)) % 0.63/0.80 (step @p83 :rule trans :premises (@p82 @p67)) % 0.63/0.80 (step @p84 :rule cong :premises (@p83 @p52) :args (@t15)) % 0.63/0.80 (step @p85 :rule cong :premises (@p84) :args (@t17)) % 0.63/0.80 (step @p86 :rule trans :premises (@p85 @p51)) % 0.63/0.80 (step @p87 :rule cong :premises (@p86) :args (@t19)) % 0.63/0.80 (step @p88 :rule trans :premises (@p87 @p4)) % 0.63/0.80 (step @p89 :rule cong :premises (@p88) :args (@t20)) % 0.63/0.80 (step @p90 :rule trans :premises (@p89 @p3)) % 0.63/0.80 (step @p91 :rule eq_resolve :premises (@p1 @p90)) % 0.63/0.80 (step @p92 :rule refl :args (@t24)) % 0.63/0.80 (step @p93 :rule beta-reduce :args ((= @t61 @t56))) % 0.63/0.80 (step @p94 :rule cong :premises (@p93) :args (@t62)) % 0.63/0.80 (step @p95 :rule nary_cong :premises (@p94 @p10 @p92) :args (@t63)) % 0.63/0.80 (step @p96 :rule cong :premises (@p95) :args (@t64)) % 0.63/0.80 (step @p97 :rule cong :premises (@p96) :args (@t65)) % 0.63/0.80 (step @p98 :rule refl :args (@t30)) % 0.63/0.80 (step @p99 :rule cong :premises (@p98 @p97) :args ((=> @t30 @t65))) % 0.63/0.80 (assume-push @p129 @t30) % 0.63/0.80 (step @p101 :rule instantiate :premises (@p91) :args ((@list @t60))) % 0.63/0.80 (step-pop @p130 :rule scope :premises (@p101)) % 0.63/0.80 (step @p102 :rule process_scope :premises (@p130) :args (@t65)) % 0.63/0.80 (step @p104 :rule eq_resolve :premises (@p102 @p99)) % 0.63/0.80 (step @p105 :rule implies_elim :premises (@p104)) % 0.63/0.80 (step @p106 :rule chain_m_resolution :premises (@p105 @p91) :args ((not @t66) (@list false) (@list @t30))) % 0.63/0.80 (step @p107 :rule skolemize :premises (@p106)) % 0.63/0.80 (step @p108 :rule bool-double-not-elim :args (@t69)) % 0.63/0.80 (step @p109 :rule refl :args (@t72)) % 0.63/0.80 (step @p110 :rule nary_cong :premises (@p109 @p108) :args ((or @t72 (not @t70)))) % 0.63/0.80 (step @p111 :rule cnf_or_neg :args (@t72 1)) % 0.63/0.80 (step @p112 :rule eq_resolve :premises (@p111 @p110)) % 0.63/0.80 (step @p113 :rule reordering :premises (@p112) :args ((or @t69 @t72))) % 0.63/0.80 (step @p114 :rule chain_m_resolution :premises (@p113 @p107) :args (@t69 @t73 @t74)) % 0.63/0.80 ; WARNING: add trust step for TRUST % 0.63/0.80 ; trust TRUST THEORY_LEMMA % 0.63/0.80 (step @p115 :rule trust :premises () :args ((forall @t59 (or (forall @t76 (not (_ @t57 @t75))) (_ @t57 @t58))))) % 0.63/0.80 (step @p116 :rule instantiate :premises (@p115) :args ((@list @t68))) % 0.63/0.80 (step @p117 :rule cnf_or_neg :args (@t72 0)) % 0.63/0.80 (step @p118 :rule chain_m_resolution :premises (@p117 @p107) :args ((not @t71) @t73 @t74)) % 0.63/0.80 (step @p119 :rule cnf_or_pos :args (@t78)) % 0.63/0.80 (step @p120 :rule reordering :premises (@p119) :args ((or @t71 @t77 (not @t78)))) % 0.63/0.80 (step @p121 :rule chain_m_resolution :premises (@p120 @p118 @p116) :args (@t77 (@list true false) (@list @t71 @t78))) % 0.63/0.80 (assume-push @p131 @t77) % 0.63/0.80 (step @p123 :rule instantiate :premises (@p121) :args ((@list @t67))) % 0.63/0.80 (step-pop @p132 :rule scope :premises (@p123)) % 0.63/0.80 (step @p124 :rule process_scope :premises (@p132) :args (@t70)) % 0.63/0.80 (step @p126 :rule implies_elim :premises (@p124)) % 0.63/0.80 (step @p127 :rule reordering :premises (@p126) :args ((or @t70 (not @t77)))) % 0.63/0.80 (step @p128 false :rule chain_m_resolution :premises (@p127 @p121 @p114) :args (false (@list false false) (@list @t77 @t69))) % 0.63/0.80 ) % 0.63/0.80 % SZS output end Proof % 0.63/0.80 % cvc5 exiting %------------------------------------------------------------------------------