%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO006^1 : 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 : n018.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 09:11:46 AM UTC 2026 % Result : Theorem 0.38s 0.60s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO006^1 : 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 % 0.16/0.34 % Computer : n018.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 23:51:05 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.48 %----Proving TH0 % 0.38/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.60 % SZS status Theorem % 0.38/0.60 % SZS output start Proof % 0.38/0.60 ( % 0.38/0.60 (define tptp.leibeq () (let ((_let_1 (@var "V" Bool))) (let ((_let_2 (@var "Q" (-> Bool Bool)))) (let ((_let_3 (@var "U" Bool))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ _let_2 _let_3) (_ _let_2 _let_1)))))))) % 0.38/0.60 (define @t1 () (@var "B" Bool)) % 0.38/0.60 (define @t2 () (@var "A" Bool)) % 0.38/0.60 (define @t3 () (= @t2 @t1)) % 0.38/0.60 (define @t4 () (=> (_ (_ tptp.leibeq @t2) @t1) @t3)) % 0.38/0.60 (define @t5 () (@list @t2 @t1)) % 0.38/0.60 (define @t6 () (forall @t5 @t4)) % 0.38/0.60 (define @t7 () (not @t6)) % 0.38/0.60 (define @t8 () (@var "V" Bool)) % 0.38/0.60 (define @t9 () (@var "Q" (-> Bool Bool))) % 0.38/0.60 (define @t10 () (_ @t9 @t8)) % 0.38/0.60 (define @t11 () (@var "U" Bool)) % 0.38/0.60 (define @t12 () (_ @t9 @t11)) % 0.38/0.60 (define @t13 () (@list @t9)) % 0.38/0.60 (define @t14 () (forall @t13 (=> @t12 @t10))) % 0.38/0.60 (define @t15 () (@list @t11 @t8)) % 0.38/0.60 (define @t16 () (lambda @t15 @t14)) % 0.38/0.60 (define @t17 () (_ @t9 @t1)) % 0.38/0.60 (define @t18 () (not @t1)) % 0.38/0.60 (define @t19 () (not (forall @t13 (or (not (_ @t9 @t18)) @t17)))) % 0.38/0.60 (define @t20 () (or @t19 (= @t18 @t1))) % 0.38/0.60 (define @t21 () (@list @t1)) % 0.38/0.60 (define @t22 () (not (_ @t9 @t2))) % 0.38/0.60 (define @t23 () (forall @t13 (or @t22 @t17))) % 0.38/0.60 (define @t24 () (not @t23)) % 0.38/0.60 (define @t25 () (@list @t2)) % 0.38/0.60 (define @t26 () (or @t3 @t24 @t3)) % 0.38/0.60 (define @t27 () (or @t24 @t3)) % 0.38/0.60 (define @t28 () (forall @t25 @t27)) % 0.38/0.60 (define @t29 () (forall @t21 @t28)) % 0.38/0.60 (define @t30 () (forall (@list @t1 @t2) @t27)) % 0.38/0.60 (define @t31 () (_ @t9 @t8)) % 0.38/0.60 (define @t32 () (lambda (@list @t8) (forall @t13 (or @t22 @t31)))) % 0.38/0.60 (define @t33 () (_ @t9 @t11)) % 0.38/0.60 (define @t34 () (_ (lambda @t15 (forall @t13 (or (not @t33) @t31))) @t2)) % 0.38/0.60 (define @t35 () (=> (_ @t34 @t1) @t3)) % 0.38/0.60 (define @t36 () (forall @t5 @t35)) % 0.38/0.60 (define @t37 () (not @t12)) % 0.38/0.60 (define @t38 () (or @t37 @t10)) % 0.38/0.60 (define @t39 () (forall @t21 @t19)) % 0.38/0.60 (define @t40 () (@quantifiers_skolemize @t39 0)) % 0.38/0.60 (define @t41 () (not @t40)) % 0.38/0.60 (define @t42 () (forall @t13 (or (not (_ @t9 @t41)) (_ @t9 @t40)))) % 0.38/0.60 (define @t43 () (not @t39)) % 0.38/0.60 (define @t44 () (not @t42)) % 0.38/0.60 (define @t45 () (not @t44)) % 0.38/0.60 (define @t46 () (@var "BOUND_VARIABLE_14589" Bool)) % 0.38/0.60 (define @t47 () (lambda (@list @t46) @t46)) % 0.38/0.60 (define @t48 () (_ @t47 @t40)) % 0.38/0.60 (define @t49 () (_ @t47 @t41)) % 0.38/0.60 (define @t50 () (not @t49)) % 0.38/0.60 (define @t51 () (or @t50 @t48)) % 0.38/0.60 (define @t52 () (= @t40 true)) % 0.38/0.60 (define @t53 () (not @t52)) % 0.38/0.60 (define @t54 () (@var "BOUND_VARIABLE_21689" Bool)) % 0.38/0.60 (define @t55 () (lambda (@list @t54) (ite (= @t54 true) false true))) % 0.38/0.60 (define @t56 () (_ @t55 @t40)) % 0.38/0.60 (define @t57 () (= @t41 true)) % 0.38/0.60 (define @t58 () (not @t57)) % 0.38/0.60 (define @t59 () (_ @t55 @t41)) % 0.38/0.60 (define @t60 () (not @t59)) % 0.38/0.60 (define @t61 () (or @t60 @t56)) % 0.38/0.60 (assume @p1 @t7) % 0.38/0.60 (assume @p2 true) % 0.38/0.60 (step @p3 (= tptp.leibeq @t16) :rule refl :args (@t16)) % 0.38/0.60 (step @p4 :rule aci_norm :args ((= (or @t19 false) @t19))) % 0.38/0.60 (step @p5 :rule bool-eq-nrefl :args (@t1)) % 0.38/0.60 (step @p6 :rule eq-symm :args (@t18 @t1)) % 0.38/0.60 (step @p7 :rule trans :premises (@p6 @p5)) % 0.38/0.60 (step @p8 :rule refl :args (@t19)) % 0.38/0.60 (step @p9 :rule nary_cong :premises (@p8 @p7) :args (@t20)) % 0.38/0.60 (step @p10 :rule trans :premises (@p9 @p4)) % 0.38/0.60 (step @p11 :rule cong :premises (@p10) :args ((forall @t21 @t20))) % 0.38/0.60 (step @p12 :rule quant-var-elim-eq :args ((= (forall @t25 (or (not (= @t2 @t18)) @t24 @t3)) @t20))) % 0.38/0.60 (step @p13 :rule refl :args (@t3)) % 0.38/0.60 (step @p14 :rule refl :args (@t24)) % 0.38/0.60 (step @p15 :rule bool-not-eq-elim2 :args (@t2 @t1)) % 0.38/0.60 (step @p16 :rule cong :premises (@p15) :args ((not (not @t3)))) % 0.38/0.60 (step @p17 :rule bool-double-not-elim :args (@t3)) % 0.38/0.60 (step @p18 :rule symm :premises (@p17)) % 0.38/0.60 (step @p19 :rule trans :premises (@p18 @p16)) % 0.38/0.60 (step @p20 :rule nary_cong :premises (@p19 @p14 @p13) :args (@t26)) % 0.38/0.60 (step @p21 :rule aci_norm :args ((= @t27 @t26))) % 0.38/0.60 (step @p22 :rule trans :premises (@p21 @p20)) % 0.38/0.60 (step @p23 :rule cong :premises (@p22) :args (@t28)) % 0.38/0.60 (step @p24 :rule trans :premises (@p23 @p12)) % 0.38/0.60 (step @p25 :rule cong :premises (@p24) :args (@t29)) % 0.38/0.60 (step @p26 :rule quant-merge-prenex :args ((= @t29 @t30))) % 0.38/0.60 (step @p27 :rule symm :premises (@p26)) % 0.38/0.60 (step @p28 :rule quant_var_reordering :args ((= (forall @t5 @t27) @t30))) % 0.38/0.60 (step @p29 :rule trans :premises (@p28 @p27 @p25)) % 0.38/0.60 (step @p30 :rule trans :premises (@p29 @p11)) % 0.38/0.60 (step @p31 :rule bool-impl-elim :args (@t23 @t3)) % 0.38/0.60 (step @p32 :rule cong :premises (@p31) :args ((forall @t5 (=> @t23 @t3)))) % 0.38/0.60 (step @p33 :rule trans :premises (@p32 @p30)) % 0.38/0.60 (step @p34 :rule refl :args (@t3)) % 0.38/0.60 (step @p35 :rule beta-reduce :args ((= (_ @t32 @t1) @t23))) % 0.38/0.60 (step @p36 :rule refl :args (@t1)) % 0.38/0.60 (step @p37 :rule beta-reduce :args ((= @t34 @t32))) % 0.38/0.60 (step @p38 :rule ho_cong :premises (@p37 @p36)) % 0.38/0.60 (step @p39 :rule trans :premises (@p38 @p35)) % 0.38/0.60 (step @p40 :rule cong :premises (@p39 @p34) :args (@t35)) % 0.38/0.60 (step @p41 :rule cong :premises (@p40) :args (@t36)) % 0.38/0.60 (step @p42 :rule trans :premises (@p41 @p33)) % 0.38/0.60 (step @p43 :rule cong :premises (@p42) :args ((not @t36))) % 0.38/0.60 (step @p44 :rule refl :args (@t2)) % 0.38/0.60 (step @p45 :rule refl :args (@t31)) % 0.38/0.60 (step @p46 :rule refl :args (@t10)) % 0.38/0.60 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t10 @t31))) % 0.38/0.60 (step @p48 :rule symm :premises (@p47)) % 0.38/0.60 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.38/0.60 (step @p50 :rule refl :args (@t33)) % 0.38/0.60 (step @p51 :rule refl :args (@t12)) % 0.38/0.60 (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t12 @t33))) % 0.38/0.60 (step @p53 :rule symm :premises (@p52)) % 0.38/0.60 (step @p54 :rule eq_resolve :premises (@p51 @p53)) % 0.38/0.60 (step @p55 :rule cong :premises (@p54) :args (@t37)) % 0.38/0.60 (step @p56 :rule nary_cong :premises (@p55 @p49) :args (@t38)) % 0.38/0.60 (step @p57 :rule cong :premises (@p56) :args ((forall @t13 @t38))) % 0.38/0.60 (step @p58 :rule bool-impl-elim :args (@t12 @t10)) % 0.38/0.60 (step @p59 :rule cong :premises (@p58) :args (@t14)) % 0.38/0.60 (step @p60 :rule trans :premises (@p59 @p57)) % 0.38/0.60 (step @p61 :rule cong :premises (@p60) :args (@t16)) % 0.38/0.60 (step @p62 :rule trans :premises (@p3 @p61)) % 0.38/0.60 (step @p63 :rule ho_cong :premises (@p62 @p44)) % 0.38/0.60 (step @p64 :rule ho_cong :premises (@p63 @p36)) % 0.38/0.60 (step @p65 :rule cong :premises (@p64 @p34) :args (@t4)) % 0.38/0.60 (step @p66 :rule cong :premises (@p65) :args (@t6)) % 0.38/0.60 (step @p67 :rule cong :premises (@p66) :args (@t7)) % 0.38/0.60 (step @p68 :rule trans :premises (@p67 @p43)) % 0.38/0.60 (step @p69 :rule eq_resolve :premises (@p1 @p68)) % 0.38/0.60 (step @p70 :rule refl :args (@t42)) % 0.38/0.60 (step @p71 :rule bool-double-not-elim :args (@t39)) % 0.38/0.60 (step @p72 :rule nary_cong :premises (@p71 @p70) :args ((or (not @t43) @t42))) % 0.38/0.60 (step @p73 :rule bool-double-not-elim :args (@t42)) % 0.38/0.60 (step @p74 :rule refl :args (@t43)) % 0.38/0.60 (step @p75 :rule cong :premises (@p74 @p73) :args ((=> @t43 @t45))) % 0.38/0.60 (assume-push @p131 @t43) % 0.38/0.60 (step @p77 :rule skolemize :premises (@p69)) % 0.38/0.60 (step-pop @p132 :rule scope :premises (@p77)) % 0.38/0.60 (step @p78 :rule process_scope :premises (@p132) :args (@t45)) % 0.38/0.60 (step @p80 :rule eq_resolve :premises (@p78 @p75)) % 0.38/0.60 (step @p81 :rule implies_elim :premises (@p80)) % 0.38/0.60 (step @p82 :rule eq_resolve :premises (@p81 @p72)) % 0.38/0.60 (step @p83 :rule chain_m_resolution :premises (@p82 @p69) :args (@t42 (@list true) (@list @t39))) % 0.38/0.60 (step @p84 :rule aci_norm :args ((= (or @t40 @t40) @t40))) % 0.38/0.60 (step @p85 :rule beta-reduce :args ((= @t48 @t40))) % 0.38/0.60 (step @p86 :rule bool-double-not-elim :args (@t40)) % 0.38/0.60 (step @p87 :rule beta-reduce :args ((= @t49 @t41))) % 0.38/0.60 (step @p88 :rule cong :premises (@p87) :args (@t50)) % 0.38/0.60 (step @p89 :rule trans :premises (@p88 @p86)) % 0.38/0.60 (step @p90 :rule nary_cong :premises (@p89 @p85) :args (@t51)) % 0.38/0.60 (step @p91 :rule trans :premises (@p90 @p84)) % 0.38/0.60 (step @p92 :rule cong :premises (@p70 @p91) :args ((=> @t42 @t51))) % 0.38/0.60 (assume-push @p133 @t42) % 0.38/0.60 (step @p94 :rule instantiate :premises (@p83) :args ((@list @t47))) % 0.38/0.60 (step-pop @p134 :rule scope :premises (@p94)) % 0.38/0.60 (step @p95 :rule process_scope :premises (@p134) :args (@t51)) % 0.38/0.60 (step @p97 :rule eq_resolve :premises (@p95 @p92)) % 0.38/0.60 (step @p98 :rule implies_elim :premises (@p97)) % 0.38/0.60 (step @p99 :rule reordering :premises (@p98) :args ((or @t40 @t44))) % 0.38/0.60 (step @p100 :rule chain_m_resolution :premises (@p99 @p83) :args (@t40 (@list false) (@list @t42))) % 0.38/0.60 (step @p101 :rule aci_norm :args ((= (or @t41 @t41) @t41))) % 0.38/0.60 (step @p102 :rule bool-eq-true :args (@t40)) % 0.38/0.60 (step @p103 :rule cong :premises (@p102) :args (@t53)) % 0.38/0.60 (step @p104 :rule aci_norm :args ((= (and @t53 true) @t53))) % 0.38/0.60 (step @p105 :rule ite-then-false :args (@t52 true)) % 0.38/0.60 (step @p106 :rule trans :premises (@p105 @p104)) % 0.38/0.60 (step @p107 :rule trans :premises (@p106 @p103)) % 0.38/0.60 (step @p108 :rule beta-reduce :args ((= @t56 (ite @t52 false true)))) % 0.38/0.60 (step @p109 :rule trans :premises (@p108 @p107)) % 0.38/0.60 (step @p110 :rule bool-eq-true :args (@t41)) % 0.38/0.60 (step @p111 :rule cong :premises (@p110) :args (@t58)) % 0.38/0.60 (step @p112 :rule trans :premises (@p111 @p86)) % 0.38/0.60 (step @p113 :rule aci_norm :args ((= (and @t58 true) @t58))) % 0.38/0.60 (step @p114 :rule ite-then-false :args (@t57 true)) % 0.38/0.60 (step @p115 :rule trans :premises (@p114 @p113)) % 0.38/0.60 (step @p116 :rule trans :premises (@p115 @p112)) % 0.38/0.60 (step @p117 :rule beta-reduce :args ((= @t59 (ite @t57 false true)))) % 0.38/0.60 (step @p118 :rule trans :premises (@p117 @p116)) % 0.38/0.60 (step @p119 :rule cong :premises (@p118) :args (@t60)) % 0.38/0.60 (step @p120 :rule nary_cong :premises (@p119 @p109) :args (@t61)) % 0.38/0.60 (step @p121 :rule trans :premises (@p120 @p101)) % 0.38/0.60 (step @p122 :rule cong :premises (@p70 @p121) :args ((=> @t42 @t61))) % 0.38/0.60 (assume-push @p135 @t42) % 0.38/0.60 (step @p124 :rule instantiate :premises (@p83) :args ((@list @t55))) % 0.38/0.60 (step-pop @p136 :rule scope :premises (@p124)) % 0.38/0.60 (step @p125 :rule process_scope :premises (@p136) :args (@t61)) % 0.38/0.60 (step @p127 :rule eq_resolve :premises (@p125 @p122)) % 0.38/0.60 (step @p128 :rule implies_elim :premises (@p127)) % 0.38/0.60 (step @p129 :rule reordering :premises (@p128) :args ((or @t41 @t44))) % 0.38/0.60 (step @p130 false :rule chain_m_resolution :premises (@p129 @p100 @p83) :args (false (@list false false) (@list @t40 @t42))) % 0.38/0.60 ) % 0.38/0.60 % SZS output end Proof % 0.38/0.60 % cvc5 exiting %------------------------------------------------------------------------------