%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM713^1 : 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 : n017.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 08:40:28 AM UTC 2026 % Result : Theorem 0.45s 0.69s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM713^1 : TPTP v9.2.1. Released v3.7.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n017.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 12:02:31 EDT 2026 % 0.17/0.34 % CPUTime : % 0.26/0.48 %----Proving TH0 % 0.45/0.69 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.45/0.69 % SZS status Theorem % 0.45/0.69 % SZS output start Proof % 0.45/0.69 ( % 0.45/0.69 (declare-sort tptp.nat 0) % 0.45/0.69 (declare-const tptp.z tptp.nat) % 0.45/0.69 (declare-const tptp.ts (-> tptp.nat tptp.nat tptp.nat)) % 0.45/0.69 (declare-const tptp.x tptp.nat) % 0.45/0.69 (declare-const tptp.pl (-> tptp.nat tptp.nat tptp.nat)) % 0.45/0.69 (declare-const tptp.y tptp.nat) % 0.45/0.69 (define @t1 () (@var "Xx_0" tptp.nat)) % 0.45/0.69 (define @t2 () (_ (_ tptp.pl tptp.y) @t1)) % 0.45/0.69 (define @t3 () (= tptp.x @t2)) % 0.45/0.69 (define @t4 () (not @t3)) % 0.45/0.69 (define @t5 () (@list @t1)) % 0.45/0.69 (define @t6 () (forall @t5 @t4)) % 0.45/0.69 (define @t7 () (not @t6)) % 0.45/0.69 (define @t8 () (@var "Xa" Bool)) % 0.45/0.69 (define @t9 () (@var "Xx" tptp.nat)) % 0.45/0.69 (define @t10 () (@var "Xy" tptp.nat)) % 0.45/0.69 (define @t11 () (_ (_ tptp.ts @t10) @t9)) % 0.45/0.69 (define @t12 () (_ tptp.ts @t9)) % 0.45/0.69 (define @t13 () (_ @t12 @t10)) % 0.45/0.69 (define @t14 () (= @t13 @t11)) % 0.45/0.69 (define @t15 () (forall (@list @t9 @t10) @t14)) % 0.45/0.69 (define @t16 () (@var "Xz" tptp.nat)) % 0.45/0.69 (define @t17 () (_ @t12 @t16)) % 0.45/0.69 (define @t18 () (_ (_ tptp.pl @t13) @t17)) % 0.45/0.69 (define @t19 () (_ (_ tptp.pl @t10) @t16)) % 0.45/0.69 (define @t20 () (_ @t12 @t19)) % 0.45/0.69 (define @t21 () (= @t20 @t18)) % 0.45/0.69 (define @t22 () (forall (@list @t9 @t10 @t16) @t21)) % 0.45/0.69 (define @t23 () (_ (_ tptp.ts tptp.y) tptp.z)) % 0.45/0.69 (define @t24 () (_ (_ tptp.pl @t23) @t1)) % 0.45/0.69 (define @t25 () (_ (_ tptp.ts tptp.x) tptp.z)) % 0.45/0.69 (define @t26 () (= @t25 @t24)) % 0.45/0.69 (define @t27 () (not @t26)) % 0.45/0.69 (define @t28 () (forall @t5 @t27)) % 0.45/0.69 (define @t29 () (tptp.ts tptp.y tptp.z)) % 0.45/0.69 (define @t30 () (tptp.pl @t29 @t1)) % 0.45/0.69 (define @t31 () (tptp.ts tptp.x tptp.z)) % 0.45/0.69 (define @t32 () (tptp.pl tptp.y @t1)) % 0.45/0.69 (define @t33 () (forall @t5 (not (= tptp.x @t32)))) % 0.45/0.69 (define @t34 () (@quantifiers_skolemize @t33 0)) % 0.45/0.69 (define @t35 () (tptp.ts tptp.z @t34)) % 0.45/0.69 (define @t36 () (tptp.ts @t10 @t9)) % 0.45/0.69 (define @t37 () (tptp.ts @t9 @t10)) % 0.45/0.69 (define @t38 () (tptp.ts @t9 @t16)) % 0.45/0.69 (define @t39 () (tptp.pl @t37 @t38)) % 0.45/0.69 (define @t40 () (tptp.pl @t10 @t16)) % 0.45/0.69 (define @t41 () (tptp.ts @t9 @t40)) % 0.45/0.69 (define @t42 () (= tptp.x (tptp.pl tptp.y @t34))) % 0.45/0.69 (define @t43 () (not @t33)) % 0.45/0.69 (define @t44 () (not (not @t42))) % 0.45/0.69 (define @t45 () (forall @t5 (not (= @t31 @t30)))) % 0.45/0.69 (define @t46 () (= @t31 (tptp.pl @t29 @t35))) % 0.45/0.69 (assume @p1 @t7) % 0.45/0.69 (assume @p2 (forall (@list @t8) (=> (not (not @t8)) @t8))) % 0.45/0.69 (assume @p3 @t15) % 0.45/0.69 (assume @p4 @t22) % 0.45/0.69 (assume @p5 (not (not @t28))) % 0.45/0.69 (assume @p6 true) % 0.45/0.69 (step @p7 :rule refl :args ((tptp.pl @t23 @t1))) % 0.45/0.69 (step @p8 :rule refl :args (@t1)) % 0.45/0.69 (step @p9 :rule refl :args (@t29)) % 0.45/0.69 (step @p10 :rule cong :premises (@p9 @p8) :args (@t30)) % 0.45/0.69 (step @p11 :rule trans :premises (@p10 @p7)) % 0.45/0.69 (step @p12 :rule refl :args (tptp.pl)) % 0.45/0.69 (step @p13 :rule ho_cong :premises (@p12 @p9)) % 0.45/0.69 (step @p14 :rule ho_cong :premises (@p13 @p8)) % 0.45/0.69 (step @p15 :rule cong :premises (@p14 @p11) :args ((= (_ (_ tptp.pl @t29) @t1) @t30))) % 0.45/0.69 (step @p16 :rule symm :premises (@p15)) % 0.45/0.69 (step @p17 :rule refl :args (@t24)) % 0.45/0.69 (step @p18 :rule eq_resolve :premises (@p17 @p16)) % 0.45/0.69 (step @p19 :rule refl :args (@t23)) % 0.45/0.69 (step @p20 :rule cong :premises (@p19 @p9) :args ((= @t23 @t29))) % 0.45/0.69 (step @p21 :rule symm :premises (@p20)) % 0.45/0.69 (step @p22 :rule eq_resolve :premises (@p19 @p21)) % 0.45/0.69 (step @p23 :rule ho_cong :premises (@p12 @p22)) % 0.45/0.69 (step @p24 :rule ho_cong :premises (@p23 @p8)) % 0.45/0.69 (step @p25 :rule trans :premises (@p24 @p18)) % 0.45/0.69 (step @p26 :rule refl :args (@t31)) % 0.45/0.69 (step @p27 :rule refl :args (@t25)) % 0.45/0.69 (step @p28 :rule cong :premises (@p27 @p26) :args ((= @t25 @t31))) % 0.45/0.69 (step @p29 :rule symm :premises (@p28)) % 0.45/0.69 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 0.45/0.69 (step @p31 :rule cong :premises (@p30 @p25) :args (@t26)) % 0.45/0.69 (step @p32 :rule cong :premises (@p31) :args (@t27)) % 0.45/0.69 (step @p33 :rule cong :premises (@p32) :args (@t28)) % 0.45/0.69 (step @p34 :rule bool-double-not-elim :args (@t28)) % 0.45/0.69 (step @p35 :rule trans :premises (@p34 @p33)) % 0.45/0.69 (step @p36 :rule eq_resolve :premises (@p5 @p35)) % 0.45/0.69 (step @p37 :rule refl :args (@t35)) % 0.45/0.69 (step @p38 :rule refl :args (@t36)) % 0.45/0.69 (step @p39 :rule refl :args (@t11)) % 0.45/0.69 (step @p40 :rule cong :premises (@p39 @p38) :args ((= @t11 @t36))) % 0.45/0.69 (step @p41 :rule symm :premises (@p40)) % 0.45/0.69 (step @p42 :rule eq_resolve :premises (@p39 @p41)) % 0.45/0.69 (step @p43 :rule refl :args (@t37)) % 0.45/0.69 (step @p44 :rule refl :args (@t13)) % 0.45/0.69 (step @p45 :rule cong :premises (@p44 @p43) :args ((= @t13 @t37))) % 0.45/0.69 (step @p46 :rule symm :premises (@p45)) % 0.45/0.69 (step @p47 :rule eq_resolve :premises (@p44 @p46)) % 0.45/0.69 (step @p48 :rule cong :premises (@p47 @p42) :args (@t14)) % 0.45/0.69 (step @p49 :rule cong :premises (@p48) :args (@t15)) % 0.45/0.69 (step @p50 :rule eq_resolve :premises (@p3 @p49)) % 0.45/0.69 (step @p51 :rule instantiate :premises (@p50) :args ((@list tptp.y tptp.z))) % 0.45/0.69 (step @p52 :rule symm :premises (@p51)) % 0.45/0.69 (step @p53 :rule cong :premises (@p52 @p37) :args ((tptp.pl (tptp.ts tptp.z tptp.y) @t35))) % 0.45/0.69 (step @p54 :rule refl :args ((tptp.pl @t13 @t17))) % 0.45/0.69 (step @p55 :rule refl :args (@t38)) % 0.45/0.69 (step @p56 :rule cong :premises (@p43 @p55) :args (@t39)) % 0.45/0.69 (step @p57 :rule trans :premises (@p56 @p54)) % 0.45/0.69 (step @p58 :rule ho_cong :premises (@p12 @p43)) % 0.45/0.69 (step @p59 :rule ho_cong :premises (@p58 @p55)) % 0.45/0.69 (step @p60 :rule cong :premises (@p59 @p57) :args ((= (_ (_ tptp.pl @t37) @t38) @t39))) % 0.45/0.69 (step @p61 :rule symm :premises (@p60)) % 0.45/0.69 (step @p62 :rule refl :args (@t18)) % 0.45/0.69 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 0.45/0.69 (step @p64 :rule refl :args (@t17)) % 0.45/0.69 (step @p65 :rule cong :premises (@p64 @p55) :args ((= @t17 @t38))) % 0.45/0.69 (step @p66 :rule symm :premises (@p65)) % 0.45/0.69 (step @p67 :rule eq_resolve :premises (@p64 @p66)) % 0.45/0.69 (step @p68 :rule ho_cong :premises (@p12 @p47)) % 0.45/0.69 (step @p69 :rule ho_cong :premises (@p68 @p67)) % 0.45/0.69 (step @p70 :rule trans :premises (@p69 @p63)) % 0.45/0.69 (step @p71 :rule refl :args ((tptp.ts @t9 @t19))) % 0.45/0.69 (step @p72 :rule refl :args (@t40)) % 0.45/0.69 (step @p73 :rule refl :args (@t9)) % 0.45/0.69 (step @p74 :rule cong :premises (@p73 @p72) :args (@t41)) % 0.45/0.69 (step @p75 :rule trans :premises (@p74 @p71)) % 0.45/0.69 (step @p76 :rule refl :args (@t12)) % 0.45/0.69 (step @p77 :rule ho_cong :premises (@p76 @p72)) % 0.45/0.69 (step @p78 :rule cong :premises (@p77 @p75) :args ((= (_ @t12 @t40) @t41))) % 0.45/0.69 (step @p79 :rule symm :premises (@p78)) % 0.45/0.69 (step @p80 :rule refl :args (@t20)) % 0.45/0.69 (step @p81 :rule eq_resolve :premises (@p80 @p79)) % 0.45/0.69 (step @p82 :rule refl :args (@t19)) % 0.45/0.69 (step @p83 :rule cong :premises (@p82 @p72) :args ((= @t19 @t40))) % 0.45/0.69 (step @p84 :rule symm :premises (@p83)) % 0.45/0.69 (step @p85 :rule eq_resolve :premises (@p82 @p84)) % 0.45/0.69 (step @p86 :rule ho_cong :premises (@p76 @p85)) % 0.45/0.69 (step @p87 :rule trans :premises (@p86 @p81)) % 0.45/0.69 (step @p88 :rule cong :premises (@p87 @p70) :args (@t21)) % 0.45/0.69 (step @p89 :rule cong :premises (@p88) :args (@t22)) % 0.45/0.69 (step @p90 :rule eq_resolve :premises (@p4 @p89)) % 0.45/0.69 (step @p91 :rule instantiate :premises (@p90) :args ((@list tptp.z tptp.y @t34))) % 0.45/0.69 (step @p92 :rule refl :args (@t32)) % 0.45/0.69 (step @p93 :rule refl :args (@t2)) % 0.45/0.69 (step @p94 :rule cong :premises (@p93 @p92) :args ((= @t2 @t32))) % 0.45/0.69 (step @p95 :rule symm :premises (@p94)) % 0.45/0.69 (step @p96 :rule eq_resolve :premises (@p93 @p95)) % 0.45/0.69 (step @p97 :rule refl :args (tptp.x)) % 0.45/0.69 (step @p98 :rule cong :premises (@p97 @p96) :args (@t3)) % 0.45/0.69 (step @p99 :rule cong :premises (@p98) :args (@t4)) % 0.45/0.69 (step @p100 :rule cong :premises (@p99) :args (@t6)) % 0.45/0.69 (step @p101 :rule cong :premises (@p100) :args (@t7)) % 0.45/0.69 (step @p102 :rule eq_resolve :premises (@p1 @p101)) % 0.45/0.69 (step @p103 :rule refl :args (@t42)) % 0.45/0.69 (step @p104 :rule bool-double-not-elim :args (@t33)) % 0.45/0.69 (step @p105 :rule nary_cong :premises (@p104 @p103) :args ((or (not @t43) @t42))) % 0.45/0.69 (step @p106 :rule bool-double-not-elim :args (@t42)) % 0.45/0.69 (step @p107 :rule refl :args (@t43)) % 0.45/0.69 (step @p108 :rule cong :premises (@p107 @p106) :args ((=> @t43 @t44))) % 0.45/0.69 (assume-push @p127 @t43) % 0.45/0.69 (step @p110 :rule skolemize :premises (@p102)) % 0.45/0.69 (step-pop @p128 :rule scope :premises (@p110)) % 0.45/0.69 (step @p111 :rule process_scope :premises (@p128) :args (@t44)) % 0.45/0.69 (step @p113 :rule eq_resolve :premises (@p111 @p108)) % 0.45/0.69 (step @p114 :rule implies_elim :premises (@p113)) % 0.45/0.69 (step @p115 :rule eq_resolve :premises (@p114 @p105)) % 0.45/0.69 (step @p116 :rule chain_m_resolution :premises (@p115 @p102) :args (@t42 (@list true) (@list @t33))) % 0.45/0.69 (step @p117 :rule refl :args (tptp.z)) % 0.45/0.69 (step @p118 :rule cong :premises (@p117 @p116) :args ((tptp.ts tptp.z tptp.x))) % 0.45/0.69 (step @p119 :rule instantiate :premises (@p50) :args ((@list tptp.x tptp.z))) % 0.45/0.69 (step @p120 :rule trans :premises (@p119 @p118 @p91 @p53)) % 0.45/0.69 (assume-push @p129 @t45) % 0.45/0.69 (step @p122 :rule instantiate :premises (@p36) :args ((@list @t35))) % 0.45/0.69 (step-pop @p130 :rule scope :premises (@p122)) % 0.45/0.69 (step @p123 :rule process_scope :premises (@p130) :args ((not @t46))) % 0.45/0.69 (step @p125 :rule implies_elim :premises (@p123)) % 0.45/0.69 (step @p126 false :rule chain_m_resolution :premises (@p125 @p120 @p36) :args (false (@list false false) (@list @t46 @t45))) % 0.45/0.69 ) % 0.45/0.69 % SZS output end Proof % 0.45/0.69 % cvc5 exiting %------------------------------------------------------------------------------