0.07/0.11	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command  : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM
0.13/0.33	% Computer : n029.cluster.edu
0.13/0.33	% Model    : x86_64 x86_64
0.13/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory   : 8042.1875MB
0.13/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit : 1920
0.13/0.33	% WCLimit  : 240
0.13/0.33	% DateTime : Sat Sep  6 01:27:37 EDT 2025
0.13/0.33	% CPUTime  : 
0.19/0.48	%----Proving TH0
0.46/0.69	--- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 72s...
0.46/0.69	% SZS status Theorem
0.46/0.69	% SZS output start Proof
0.46/0.69	(
0.46/0.69	(declare-type tptp.beverage ())
0.46/0.69	(declare-type tptp.syrup ())
0.46/0.69	(declare-const tptp.mix (-> tptp.beverage tptp.syrup tptp.beverage))
0.46/0.69	(declare-const tptp.heat (-> tptp.beverage tptp.beverage))
0.46/0.69	(declare-const tptp.hot (-> tptp.beverage Bool))
0.46/0.69	(declare-const tptp.coffee tptp.beverage)
0.46/0.69	(define tptp.cold_mixture () (let ((_let_1 (@var "S" tptp.syrup))) (let ((_let_2 (@var "B" tptp.beverage))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mix _let_2) _let_1)))))
0.46/0.69	(define tptp.hot_mixture () (let ((_let_1 (@var "S" tptp.syrup))) (let ((_let_2 (@var "B" tptp.beverage))) (lambda (@list _let_2 _let_1) (_ tptp.heat (_ (_ tptp.mix _let_2) _let_1))))))
0.46/0.69	(define @t1 () (@var "B" tptp.beverage))
0.46/0.69	(define @t2 () (@var "S" tptp.syrup))
0.46/0.69	(define @t3 () (@var "Mixture" (-> tptp.beverage tptp.syrup tptp.beverage)))
0.46/0.69	(define @t4 () (_ (_ @t3 tptp.coffee) @t2))
0.46/0.69	(define @t5 () (_ tptp.hot @t1))
0.46/0.69	(define @t6 () (and @t5 (= @t4 @t1)))
0.46/0.69	(define @t7 () (@list @t1))
0.46/0.69	(define @t8 () (exists @t7 @t6))
0.46/0.69	(define @t9 () (@list @t2))
0.46/0.69	(define @t10 () (forall @t9 @t8))
0.46/0.69	(define @t11 () (@list @t3))
0.46/0.69	(define @t12 () (exists @t11 @t10))
0.46/0.69	(define @t13 () (not @t12))
0.46/0.69	(define @t14 () (_ tptp.heat @t1))
0.46/0.69	(define @t15 () (_ tptp.hot @t14))
0.46/0.69	(define @t16 () (forall @t7 @t15))
0.46/0.69	(define @t17 () (_ (_ tptp.mix @t1) @t2))
0.46/0.69	(define @t18 () (@list @t1 @t2))
0.46/0.69	(define @t19 () (lambda @t18 @t17))
0.46/0.69	(define @t20 () (lambda @t18 (_ tptp.heat @t17)))
0.46/0.69	(define @t21 () (tptp.heat @t1))
0.46/0.69	(define @t22 () (tptp.hot @t21))
0.46/0.69	(define @t23 () (_ @t3 tptp.coffee @t2))
0.46/0.69	(define @t24 () (tptp.hot @t23))
0.46/0.69	(define @t25 () (forall @t9 @t24))
0.46/0.69	(define @t26 () (forall @t11 (not @t25)))
0.46/0.69	(define @t27 () (not @t24))
0.46/0.69	(define @t28 () (not (= @t23 @t23)))
0.46/0.69	(define @t29 () (or @t27 @t28))
0.46/0.69	(define @t30 () (not (= @t1 @t23)))
0.46/0.69	(define @t31 () (tptp.hot @t1))
0.46/0.69	(define @t32 () (not @t31))
0.46/0.69	(define @t33 () (or @t30 @t32 @t30))
0.46/0.69	(define @t34 () (or @t32 @t30))
0.46/0.69	(define @t35 () (= @t1 @t4))
0.46/0.69	(define @t36 () (not @t35))
0.46/0.69	(define @t37 () (not @t5))
0.46/0.69	(define @t38 () (or @t37 @t36))
0.46/0.69	(define @t39 () (and @t5 @t35))
0.46/0.69	(define @t40 () (forall @t7 (not @t39)))
0.46/0.69	(define @t41 () (not @t40))
0.46/0.69	(define @t42 () (tptp.heat tptp.coffee))
0.46/0.69	(define @t43 () (tptp.hot @t42))
0.46/0.69	(define @t44 () (@var "BOUND_VARIABLE_34949" tptp.beverage))
0.46/0.69	(define @t45 () (lambda (@list @t44 (@var "BOUND_VARIABLE_34950" tptp.syrup)) (tptp.heat @t44)))
0.46/0.69	(define @t46 () (_ @t45 tptp.coffee @t2))
0.46/0.69	(define @t47 () (tptp.hot @t46))
0.46/0.69	(define @t48 () (forall @t9 @t47))
0.46/0.69	(define @t49 () (not @t48))
0.46/0.69	(define @t50 () (forall @t7 @t22))
0.46/0.69	(assume @p1 @t13)
0.46/0.69	(assume @p2 @t16)
0.46/0.69	(assume @p3 true)
0.46/0.69	(step @p4 (= tptp.cold_mixture @t19) :rule refl :args (@t19))
0.46/0.69	(step @p5 (= tptp.hot_mixture @t20) :rule refl :args (@t20))
0.46/0.69	(step @p6 :rule refl :args ((tptp.hot @t14)))
0.46/0.69	(step @p7 :rule refl :args (@t21))
0.46/0.69	(step @p8 :rule cong :premises (@p7) :args (@t22))
0.46/0.69	(step @p9 :rule trans :premises (@p8 @p6))
0.46/0.69	(step @p10 :rule refl :args (tptp.hot))
0.46/0.69	(step @p11 :rule ho_cong :premises (@p10 @p7))
0.46/0.69	(step @p12 :rule cong :premises (@p11 @p9) :args ((= (_ tptp.hot @t21) @t22)))
0.46/0.69	(step @p13 :rule symm :premises (@p12))
0.46/0.69	(step @p14 :rule refl :args (@t15))
0.46/0.69	(step @p15 :rule eq_resolve :premises (@p14 @p13))
0.46/0.69	(step @p16 :rule refl :args (@t14))
0.46/0.69	(step @p17 :rule cong :premises (@p16 @p7) :args ((= @t14 @t21)))
0.46/0.69	(step @p18 :rule symm :premises (@p17))
0.46/0.69	(step @p19 :rule eq_resolve :premises (@p16 @p18))
0.46/0.69	(step @p20 :rule ho_cong :premises (@p10 @p19))
0.46/0.69	(step @p21 :rule trans :premises (@p20 @p15))
0.46/0.69	(step @p22 :rule cong :premises (@p21) :args (@t16))
0.46/0.69	(step @p23 :rule eq_resolve :premises (@p2 @p22))
0.46/0.69	(step @p24 :rule bool-double-not-elim :args (@t26))
0.46/0.69	(step @p25 :rule exists-elim :args ((= (exists @t11 @t25) (not @t26))))
0.46/0.69	(step @p26 :rule bool-double-not-elim :args (@t24))
0.46/0.69	(step @p27 :rule aci_norm :args ((= (or @t27 false) @t27)))
0.46/0.69	(step @p28 :rule evaluate :args ((not true)))
0.46/0.69	(step @p29 :rule eq-refl :args (@t23))
0.46/0.69	(step @p30 :rule cong :premises (@p29) :args (@t28))
0.46/0.70	(step @p31 :rule trans :premises (@p30 @p28))
0.46/0.70	(step @p32 :rule refl :args (@t27))
0.46/0.70	(step @p33 :rule nary_cong :premises (@p32 @p31) :args (@t29))
0.46/0.70	(step @p34 :rule trans :premises (@p33 @p27))
0.46/0.70	(step @p35 :rule quant-var-elim-eq :args ((= (forall @t7 @t33) @t29)))
0.46/0.70	(step @p36 :rule aci_norm :args ((= @t34 @t33)))
0.46/0.70	(step @p37 :rule cong :premises (@p36) :args ((forall @t7 @t34)))
0.46/0.70	(step @p38 :rule trans :premises (@p37 @p35))
0.46/0.70	(step @p39 :rule trans :premises (@p38 @p34))
0.46/0.70	(step @p40 :rule refl :args (@t23))
0.46/0.70	(step @p41 :rule refl :args (@t4))
0.46/0.70	(step @p42 :rule cong :premises (@p41 @p40) :args ((= @t4 @t23)))
0.46/0.70	(step @p43 :rule symm :premises (@p42))
0.46/0.70	(step @p44 :rule eq_resolve :premises (@p41 @p43))
0.46/0.70	(step @p45 :rule refl :args (@t1))
0.46/0.70	(step @p46 :rule cong :premises (@p45 @p44) :args (@t35))
0.46/0.70	(step @p47 :rule cong :premises (@p46) :args (@t36))
0.46/0.70	(step @p48 :rule refl :args (@t31))
0.46/0.70	(step @p49 :rule refl :args (@t5))
0.46/0.70	(step @p50 :rule cong :premises (@p49 @p48) :args ((= @t5 @t31)))
0.46/0.70	(step @p51 :rule symm :premises (@p50))
0.46/0.70	(step @p52 :rule eq_resolve :premises (@p49 @p51))
0.46/0.70	(step @p53 :rule cong :premises (@p52) :args (@t37))
0.46/0.70	(step @p54 :rule nary_cong :premises (@p53 @p47) :args (@t38))
0.46/0.70	(step @p55 :rule cong :premises (@p54) :args ((forall @t7 @t38)))
0.46/0.70	(step @p56 :rule trans :premises (@p55 @p39))
0.46/0.70	(step @p57 :rule bool-and-de-morgan :args (@t5 @t35 true))
0.46/0.70	(step @p58 :rule cong :premises (@p57) :args (@t40))
0.46/0.70	(step @p59 :rule trans :premises (@p58 @p56))
0.46/0.70	(step @p60 :rule cong :premises (@p59) :args (@t41))
0.46/0.70	(step @p61 :rule trans :premises (@p60 @p26))
0.46/0.70	(step @p62 :rule exists-elim :args ((= (exists @t7 @t39) @t41)))
0.46/0.70	(step @p63 :rule trans :premises (@p62 @p61))
0.46/0.70	(step @p64 :rule eq-symm :args (@t4 @t1))
0.46/0.70	(step @p65 :rule refl :args (@t5))
0.46/0.70	(step @p66 :rule nary_cong :premises (@p65 @p64) :args (@t6))
0.46/0.70	(step @p67 :rule cong :premises (@p66) :args (@t8))
0.46/0.70	(step @p68 :rule trans :premises (@p67 @p63))
0.46/0.70	(step @p69 :rule cong :premises (@p68) :args (@t10))
0.46/0.70	(step @p70 :rule cong :premises (@p69) :args (@t12))
0.46/0.70	(step @p71 :rule trans :premises (@p70 @p25))
0.46/0.70	(step @p72 :rule cong :premises (@p71) :args (@t13))
0.46/0.70	(step @p73 :rule trans :premises (@p72 @p24))
0.46/0.70	(step @p74 :rule eq_resolve :premises (@p1 @p73))
0.46/0.70	(step @p75 :rule quant-unused-vars :args ((= (forall @t9 @t43) @t43)))
0.46/0.70	(step @p76 :rule beta-reduce :args ((= @t46 @t42)))
0.46/0.70	(step @p77 :rule cong :premises (@p76) :args (@t47))
0.46/0.70	(step @p78 :rule cong :premises (@p77) :args (@t48))
0.46/0.70	(step @p79 :rule trans :premises (@p78 @p75))
0.46/0.70	(step @p80 :rule cong :premises (@p79) :args (@t49))
0.46/0.70	(step @p81 :rule refl :args (@t26))
0.46/0.70	(step @p82 :rule cong :premises (@p81 @p80) :args ((=> @t26 @t49)))
0.46/0.70	(assume-push @p96 @t26)
0.46/0.70	(step @p84 :rule instantiate :premises (@p74) :args ((@list @t45)))
0.46/0.70	(step-pop @p96 :rule scope :premises (@p84))
0.46/0.70	(step @p85 :rule process_scope :premises (@p96) :args (@t49))
0.46/0.70	(step @p87 :rule eq_resolve :premises (@p85 @p82))
0.46/0.70	(step @p88 :rule implies_elim :premises (@p87))
0.46/0.70	(step @p89 :rule chain_resolution :premises (@p88 @p74) :args ((@list false) (@list @t26)))
0.46/0.70	(assume-push @p98 @t50)
0.46/0.70	(step @p91 :rule instantiate :premises (@p23) :args ((@list tptp.coffee)))
0.46/0.70	(step-pop @p98 :rule scope :premises (@p91))
0.46/0.70	(step @p92 :rule process_scope :premises (@p98) :args (@t43))
0.46/0.70	(step @p94 :rule implies_elim :premises (@p92))
0.46/0.70	(step @p95 false :rule chain_resolution :premises (@p94 @p89 @p23) :args ((@list true false) (@list @t43 @t50)))
0.46/0.70	)
0.46/0.70	% SZS output end Proof
0.46/0.70	% cvc5 exiting
0.56/0.70	EOF