%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP209^3 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n007.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 08:25:24 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 : ITP209^3 : TPTP v9.2.1. Released v8.1.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n007.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 04:19:12 EDT 2026 % 0.18/0.34 % CPUTime : % 0.31/0.49 %----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 tptp.a 0) % 0.37/0.57 (declare-const tptp.a2 tptp.a) % 0.37/0.57 (declare-const tptp.c tptp.a) % 0.37/0.57 (declare-const tptp.b tptp.a) % 0.37/0.57 (declare-const tptp.f (-> tptp.a tptp.a tptp.a)) % 0.37/0.57 (define tptp.syntax_ac_operator_a () (let ((_let_1 (@var "A3" tptp.a))) (let ((_let_2 (@var "B3" tptp.a))) (let ((_let_3 (@var "F2" (-> tptp.a tptp.a tptp.a)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (_ _let_3 _let_1))) (let ((_let_6 (_ _let_5 _let_2))) (let ((_let_7 (@var "C3" tptp.a))) (lambda (@list _let_3) (and (forall (@list _let_1 _let_2 _let_7) (= (_ (_ _let_3 _let_6) _let_7) (_ _let_5 (_ _let_4 _let_7)))) (forall (@list _let_1 _let_2) (= _let_6 (_ _let_4 _let_1))))))))))))) % 0.37/0.57 (define @t1 () (@var "A" tptp.a)) % 0.37/0.57 (define @t2 () (@var "B" tptp.a)) % 0.37/0.57 (define @t3 () (_ tptp.f @t2)) % 0.37/0.57 (define @t4 () (_ tptp.f @t1)) % 0.37/0.57 (define @t5 () (_ @t4 @t2)) % 0.37/0.57 (define @t6 () (@var "C" tptp.a)) % 0.37/0.57 (define @t7 () (_ @t4 (_ @t3 @t6))) % 0.37/0.57 (define @t8 () (@list @t1 @t2 @t6)) % 0.37/0.57 (define @t9 () (@var "F" (-> tptp.a tptp.a tptp.a))) % 0.37/0.57 (define @t10 () (_ tptp.syntax_ac_operator_a @t9)) % 0.37/0.57 (define @t11 () (@var "A2" tptp.a)) % 0.37/0.57 (define @t12 () (@var "B2" tptp.a)) % 0.37/0.57 (define @t13 () (_ @t9 @t12)) % 0.37/0.57 (define @t14 () (_ @t9 @t11)) % 0.37/0.57 (define @t15 () (_ @t14 @t12)) % 0.37/0.57 (define @t16 () (@var "C2" tptp.a)) % 0.37/0.57 (define @t17 () (_ @t9 @t2)) % 0.37/0.57 (define @t18 () (_ @t9 @t1)) % 0.37/0.57 (define @t19 () (_ @t18 @t2)) % 0.37/0.57 (define @t20 () (_ (_ @t9 @t19) @t6)) % 0.37/0.57 (define @t21 () (_ @t18 (_ @t17 @t6))) % 0.37/0.57 (define @t22 () (@list @t9 @t1 @t2 @t6)) % 0.37/0.57 (define @t23 () (_ tptp.f tptp.a2)) % 0.37/0.57 (define @t24 () (_ @t23 tptp.c)) % 0.37/0.57 (define @t25 () (_ (_ tptp.f @t24) tptp.b)) % 0.37/0.57 (define @t26 () (_ @t23 tptp.b)) % 0.37/0.57 (define @t27 () (_ (_ tptp.f @t26) tptp.c)) % 0.37/0.57 (define @t28 () (= @t27 @t25)) % 0.37/0.57 (define @t29 () (not @t28)) % 0.37/0.57 (define @t30 () (@var "A3" tptp.a)) % 0.37/0.57 (define @t31 () (@var "B3" tptp.a)) % 0.37/0.57 (define @t32 () (@var "F2" (-> tptp.a tptp.a tptp.a))) % 0.37/0.57 (define @t33 () (_ @t32 @t31)) % 0.37/0.57 (define @t34 () (_ @t33 @t30)) % 0.37/0.57 (define @t35 () (_ @t32 @t30)) % 0.37/0.57 (define @t36 () (_ @t35 @t31)) % 0.37/0.57 (define @t37 () (= @t36 @t34)) % 0.37/0.57 (define @t38 () (@list @t30 @t31)) % 0.37/0.57 (define @t39 () (forall @t38 @t37)) % 0.37/0.57 (define @t40 () (@var "C3" tptp.a)) % 0.37/0.57 (define @t41 () (_ @t33 @t40)) % 0.37/0.57 (define @t42 () (_ @t35 @t41)) % 0.37/0.57 (define @t43 () (_ (_ @t32 @t36) @t40)) % 0.37/0.57 (define @t44 () (= @t43 @t42)) % 0.37/0.57 (define @t45 () (@list @t30 @t31 @t40)) % 0.37/0.57 (define @t46 () (forall @t45 @t44)) % 0.37/0.57 (define @t47 () (and @t46 @t39)) % 0.37/0.57 (define @t48 () (@list @t32)) % 0.37/0.57 (define @t49 () (lambda @t48 @t47)) % 0.37/0.57 (define @t50 () (tptp.f @t30 @t31)) % 0.37/0.57 (define @t51 () (forall @t45 (= (tptp.f @t50 @t40) (tptp.f @t30 (tptp.f @t31 @t40))))) % 0.37/0.57 (define @t52 () (_ @t32 @t31 @t30)) % 0.37/0.57 (define @t53 () (_ @t32 @t30 @t31)) % 0.37/0.57 (define @t54 () (_ @t32 @t31 @t40)) % 0.37/0.57 (define @t55 () (_ @t32 @t30 @t54)) % 0.37/0.57 (define @t56 () (_ @t32 @t53 @t40)) % 0.37/0.57 (define @t57 () (tptp.f (tptp.f tptp.c tptp.a2) tptp.b)) % 0.37/0.57 (define @t58 () (tptp.f tptp.a2 tptp.b)) % 0.37/0.57 (define @t59 () (tptp.f tptp.c @t58)) % 0.37/0.57 (define @t60 () (= @t59 @t57)) % 0.37/0.57 (define @t61 () (= @t57 @t59)) % 0.37/0.57 (define @t62 () (tptp.f @t58 tptp.c)) % 0.37/0.57 (define @t63 () (tptp.f tptp.a2 tptp.c)) % 0.37/0.57 (define @t64 () (tptp.f @t63 tptp.b)) % 0.37/0.57 (assume @p1 (_ tptp.syntax_ac_operator_a tptp.f)) % 0.37/0.57 (assume @p2 (forall (@list @t1 @t2) (= @t5 (_ @t3 @t1)))) % 0.37/0.57 (assume @p3 (forall @t8 (= @t7 (_ @t3 (_ @t4 @t6))))) % 0.37/0.57 (assume @p4 (forall @t8 (= (_ (_ tptp.f @t5) @t6) @t7))) % 0.37/0.57 (assume @p5 (forall (@list @t9) (=> (forall (@list @t11 @t12 @t16) (= (_ (_ @t9 @t15) @t16) (_ @t14 (_ @t13 @t16)))) (=> (forall (@list @t11 @t12) (= @t15 (_ @t13 @t11))) @t10)))) % 0.37/0.57 (assume @p6 (forall (@list @t9 @t1 @t2) (=> @t10 (= @t19 (_ @t17 @t1))))) % 0.37/0.57 (assume @p7 (forall @t22 (=> @t10 (= @t21 @t20)))) % 0.37/0.57 (assume @p8 (forall @t22 (=> @t10 (= @t20 @t21)))) % 0.37/0.57 (assume @p9 (forall @t22 (=> @t10 (= @t21 (_ @t17 (_ @t18 @t6)))))) % 0.37/0.57 (assume @p10 @t29) % 0.37/0.57 (assume @p11 true) % 0.37/0.57 (step @p12 (= tptp.syntax_ac_operator_a @t49) :rule refl :args (@t49)) % 0.37/0.57 (step @p13 :rule beta-reduce :args ((= (_ (lambda @t48 (and (forall @t45 (= @t56 @t55)) (forall @t38 (= @t53 @t52)))) tptp.f) (and @t51 (forall @t38 (= @t50 (tptp.f @t31 @t30))))))) % 0.37/0.57 (step @p14 :rule refl :args (tptp.f)) % 0.37/0.57 (step @p15 :rule refl :args (@t52)) % 0.37/0.57 (step @p16 :rule refl :args (@t34)) % 0.37/0.57 (step @p17 :rule cong :premises (@p16 @p15) :args ((= @t34 @t52))) % 0.37/0.57 (step @p18 :rule symm :premises (@p17)) % 0.37/0.57 (step @p19 :rule eq_resolve :premises (@p16 @p18)) % 0.37/0.57 (step @p20 :rule refl :args (@t53)) % 0.37/0.57 (step @p21 :rule refl :args (@t36)) % 0.37/0.57 (step @p22 :rule cong :premises (@p21 @p20) :args ((= @t36 @t53))) % 0.37/0.57 (step @p23 :rule symm :premises (@p22)) % 0.37/0.57 (step @p24 :rule eq_resolve :premises (@p21 @p23)) % 0.37/0.57 (step @p25 :rule cong :premises (@p24 @p19) :args (@t37)) % 0.37/0.57 (step @p26 :rule cong :premises (@p25) :args (@t39)) % 0.37/0.57 (step @p27 :rule refl :args ((_ @t32 @t30 @t41))) % 0.37/0.57 (step @p28 :rule refl :args (@t54)) % 0.37/0.57 (step @p29 :rule refl :args (@t30)) % 0.37/0.57 (step @p30 :rule cong :premises (@p29 @p28) :args (@t55)) % 0.37/0.57 (step @p31 :rule trans :premises (@p30 @p27)) % 0.37/0.57 (step @p32 :rule refl :args (@t35)) % 0.37/0.57 (step @p33 :rule ho_cong :premises (@p32 @p28)) % 0.37/0.57 (step @p34 :rule cong :premises (@p33 @p31) :args ((= (_ @t35 @t54) @t55))) % 0.37/0.57 (step @p35 :rule symm :premises (@p34)) % 0.37/0.57 (step @p36 :rule refl :args (@t42)) % 0.37/0.57 (step @p37 :rule eq_resolve :premises (@p36 @p35)) % 0.37/0.57 (step @p38 :rule refl :args (@t41)) % 0.37/0.57 (step @p39 :rule cong :premises (@p38 @p28) :args ((= @t41 @t54))) % 0.37/0.57 (step @p40 :rule symm :premises (@p39)) % 0.37/0.57 (step @p41 :rule eq_resolve :premises (@p38 @p40)) % 0.37/0.57 (step @p42 :rule ho_cong :premises (@p32 @p41)) % 0.37/0.57 (step @p43 :rule trans :premises (@p42 @p37)) % 0.37/0.57 (step @p44 :rule refl :args ((_ @t32 @t36 @t40))) % 0.37/0.57 (step @p45 :rule refl :args (@t40)) % 0.37/0.57 (step @p46 :rule cong :premises (@p20 @p45) :args (@t56)) % 0.37/0.57 (step @p47 :rule trans :premises (@p46 @p44)) % 0.37/0.57 (step @p48 :rule refl :args (@t32)) % 0.37/0.57 (step @p49 :rule ho_cong :premises (@p48 @p20)) % 0.37/0.57 (step @p50 :rule ho_cong :premises (@p49 @p45)) % 0.37/0.57 (step @p51 :rule cong :premises (@p50 @p47) :args ((= (_ (_ @t32 @t53) @t40) @t56))) % 0.37/0.57 (step @p52 :rule symm :premises (@p51)) % 0.37/0.57 (step @p53 :rule refl :args (@t43)) % 0.37/0.57 (step @p54 :rule eq_resolve :premises (@p53 @p52)) % 0.37/0.57 (step @p55 :rule ho_cong :premises (@p48 @p24)) % 0.37/0.57 (step @p56 :rule ho_cong :premises (@p55 @p45)) % 0.37/0.57 (step @p57 :rule trans :premises (@p56 @p54)) % 0.37/0.57 (step @p58 :rule cong :premises (@p57 @p43) :args (@t44)) % 0.37/0.57 (step @p59 :rule cong :premises (@p58) :args (@t46)) % 0.37/0.57 (step @p60 :rule nary_cong :premises (@p59 @p26) :args (@t47)) % 0.37/0.57 (step @p61 :rule cong :premises (@p60) :args (@t49)) % 0.37/0.57 (step @p62 :rule trans :premises (@p12 @p61)) % 0.37/0.57 (step @p63 :rule ho_cong :premises (@p62 @p14)) % 0.37/0.57 (step @p64 :rule trans :premises (@p63 @p13)) % 0.37/0.57 (step @p65 :rule eq_resolve :premises (@p1 @p64)) % 0.37/0.57 (step @p66 :rule and_elim :premises (@p65) :args (0)) % 0.37/0.57 (step @p67 :rule bool-eq-false :args (@t60)) % 0.37/0.57 (step @p68 :rule symm :premises (@p67)) % 0.37/0.57 (step @p69 :rule eq-symm :args (@t57 @t59)) % 0.37/0.57 (step @p70 :rule cong :premises (@p69) :args ((not @t61))) % 0.37/0.57 (step @p71 :rule bool-eq-false :args (@t61)) % 0.37/0.57 (step @p72 :rule trans :premises (@p71 @p70)) % 0.37/0.57 (step @p73 :rule trans :premises (@p72 @p68)) % 0.37/0.57 (step @p74 :rule eq-symm :args (@t62 @t64)) % 0.37/0.57 (step @p75 :rule refl :args ((tptp.f @t24 tptp.b))) % 0.37/0.57 (step @p76 :rule refl :args (tptp.b)) % 0.37/0.57 (step @p77 :rule refl :args (@t63)) % 0.37/0.57 (step @p78 :rule cong :premises (@p77 @p76) :args (@t64)) % 0.37/0.57 (step @p79 :rule trans :premises (@p78 @p75)) % 0.37/0.57 (step @p80 :rule refl :args (tptp.f)) % 0.37/0.57 (step @p81 :rule ho_cong :premises (@p80 @p77)) % 0.37/0.57 (step @p82 :rule ho_cong :premises (@p81 @p76)) % 0.37/0.57 (step @p83 :rule cong :premises (@p82 @p79) :args ((= (_ (_ tptp.f @t63) tptp.b) @t64))) % 0.37/0.57 (step @p84 :rule symm :premises (@p83)) % 0.37/0.57 (step @p85 :rule refl :args (@t25)) % 0.37/0.57 (step @p86 :rule eq_resolve :premises (@p85 @p84)) % 0.37/0.57 (step @p87 :rule refl :args (tptp.b)) % 0.37/0.57 (step @p88 :rule refl :args (@t24)) % 0.37/0.57 (step @p89 :rule cong :premises (@p88 @p77) :args ((= @t24 @t63))) % 0.37/0.57 (step @p90 :rule symm :premises (@p89)) % 0.37/0.57 (step @p91 :rule eq_resolve :premises (@p88 @p90)) % 0.37/0.57 (step @p92 :rule ho_cong :premises (@p14 @p91)) % 0.37/0.57 (step @p93 :rule ho_cong :premises (@p92 @p87)) % 0.37/0.57 (step @p94 :rule trans :premises (@p93 @p86)) % 0.37/0.57 (step @p95 :rule refl :args ((tptp.f @t26 tptp.c))) % 0.37/0.57 (step @p96 :rule refl :args (tptp.c)) % 0.37/0.57 (step @p97 :rule refl :args (@t58)) % 0.37/0.57 (step @p98 :rule cong :premises (@p97 @p96) :args (@t62)) % 0.37/0.57 (step @p99 :rule trans :premises (@p98 @p95)) % 0.37/0.57 (step @p100 :rule ho_cong :premises (@p80 @p97)) % 0.37/0.57 (step @p101 :rule ho_cong :premises (@p100 @p96)) % 0.37/0.57 (step @p102 :rule cong :premises (@p101 @p99) :args ((= (_ (_ tptp.f @t58) tptp.c) @t62))) % 0.37/0.57 (step @p103 :rule symm :premises (@p102)) % 0.37/0.57 (step @p104 :rule refl :args (@t27)) % 0.37/0.57 (step @p105 :rule eq_resolve :premises (@p104 @p103)) % 0.37/0.57 (step @p106 :rule refl :args (tptp.c)) % 0.37/0.57 (step @p107 :rule refl :args (@t26)) % 0.37/0.57 (step @p108 :rule cong :premises (@p107 @p97) :args ((= @t26 @t58))) % 0.37/0.57 (step @p109 :rule symm :premises (@p108)) % 0.37/0.57 (step @p110 :rule eq_resolve :premises (@p107 @p109)) % 0.37/0.57 (step @p111 :rule ho_cong :premises (@p14 @p110)) % 0.37/0.57 (step @p112 :rule ho_cong :premises (@p111 @p106)) % 0.37/0.57 (step @p113 :rule trans :premises (@p112 @p105)) % 0.37/0.57 (step @p114 :rule cong :premises (@p113 @p94) :args (@t28)) % 0.37/0.57 (step @p115 :rule trans :premises (@p114 @p74)) % 0.37/0.57 (step @p116 :rule cong :premises (@p115) :args (@t29)) % 0.37/0.57 (step @p117 :rule eq_resolve :premises (@p10 @p116)) % 0.37/0.57 (step @p118 :rule false_intro :premises (@p117)) % 0.37/0.57 (step @p119 :rule and_elim :premises (@p65) :args (1)) % 0.37/0.57 (step @p120 :rule instantiate :premises (@p119) :args ((@list @t58 tptp.c))) % 0.37/0.57 (step @p121 :rule symm :premises (@p120)) % 0.37/0.57 (step @p122 :rule instantiate :premises (@p119) :args ((@list tptp.a2 tptp.c))) % 0.37/0.57 (step @p123 :rule symm :premises (@p122)) % 0.37/0.57 (step @p124 :rule cong :premises (@p123 @p87) :args (@t57)) % 0.37/0.57 (step @p125 :rule cong :premises (@p124 @p121) :args (@t61)) % 0.37/0.57 (step @p126 :rule trans :premises (@p125 @p118)) % 0.37/0.57 (step @p127 :rule eq_resolve :premises (@p126 @p73)) % 0.37/0.57 (step @p128 :rule false_elim :premises (@p127)) % 0.37/0.57 (step @p129 :rule refl :args (@t51)) % 0.37/0.57 (step @p130 :rule cong :premises (@p129 @p69) :args ((=> @t51 @t61))) % 0.37/0.57 (assume-push @p138 @t51) % 0.37/0.57 (step @p132 :rule instantiate :premises (@p66) :args ((@list tptp.c tptp.a2 tptp.b))) % 0.37/0.57 (step-pop @p139 :rule scope :premises (@p132)) % 0.37/0.57 (step @p133 :rule process_scope :premises (@p139) :args (@t61)) % 0.37/0.57 (step @p135 :rule eq_resolve :premises (@p133 @p130)) % 0.37/0.57 (step @p136 :rule implies_elim :premises (@p135)) % 0.37/0.57 (step @p137 false :rule chain_m_resolution :premises (@p136 @p128 @p66) :args (false (@list true false) (@list @t60 @t51))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------