0.07/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command  : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM
0.13/0.35	% Computer : n031.cluster.edu
0.13/0.35	% Model    : x86_64 x86_64
0.13/0.35	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory   : 8042.1875MB
0.13/0.35	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit : 1920
0.13/0.35	% WCLimit  : 240
0.13/0.35	% DateTime : Fri Sep  5 21:25:52 EDT 2025
0.13/0.35	% CPUTime  : 
0.20/0.51	%----Proving TH0
1.29/1.49	--- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 72s...
1.29/1.49	% SZS status Theorem
1.29/1.49	% SZS output start Proof
1.29/1.49	(
1.29/1.49	(declare-type tptp.a ())
1.29/1.49	(define @t1 () (@var "Xf" (-> tptp.a Bool)))
1.29/1.49	(define @t2 () (@var "Xj" tptp.a))
1.29/1.49	(define @t3 () (@var "Xg" (-> tptp.a tptp.a Bool)))
1.29/1.49	(define @t4 () (_ @t3 @t2))
1.29/1.49	(define @t5 () (= (= @t4 @t1) (= @t1 @t1)))
1.29/1.49	(define @t6 () (@list @t2))
1.29/1.49	(define @t7 () (exists @t6 @t5))
1.29/1.49	(define @t8 () (@list @t1))
1.29/1.49	(define @t9 () (forall @t8 @t7))
1.29/1.49	(define @t10 () (@list @t3))
1.29/1.49	(define @t11 () (exists @t10 @t9))
1.29/1.49	(define @t12 () (= @t1 @t4))
1.29/1.49	(define @t13 () (not (forall @t6 (not @t12))))
1.29/1.49	(define @t14 () (forall @t8 @t13))
1.29/1.49	(define @t15 () (forall @t10 (not @t14)))
1.29/1.49	(define @t16 () (not @t15))
1.29/1.49	(define @t17 () (@quantifiers_skolemize @t15 0))
1.29/1.49	(define @t18 () (_ @t17 @t2))
1.29/1.49	(define @t19 () (forall @t8 (not (forall @t6 (not (= @t1 @t18))))))
1.29/1.49	(define @t20 () (not (not @t19)))
1.29/1.49	(define @t21 () (@list true))
1.29/1.49	(define @t22 () (@var "BOUND_VARIABLE_14274" tptp.a))
1.29/1.50	(define @t23 () (not (_ @t17 @t22 @t22)))
1.29/1.50	(define @t24 () (@list @t22))
1.29/1.50	(define @t25 () (lambda @t24 @t23))
1.29/1.50	(define @t26 () (not (= @t25 @t18)))
1.29/1.50	(define @t27 () (forall @t6 @t26))
1.29/1.50	(define @t28 () (not @t27))
1.29/1.50	(define @t29 () (@purify @t25))
1.29/1.50	(define @t30 () (forall @t6 (not (= @t18 @t25))))
1.29/1.50	(define @t31 () (@quantifiers_skolemize @t30 0))
1.29/1.50	(define @t32 () (_ @t17 @t31))
1.29/1.50	(define @t33 () (= @t32 @t29))
1.29/1.50	(define @t34 () (not @t30))
1.29/1.50	(define @t35 () (= @t25 @t32))
1.29/1.50	(define @t36 () (= @t32 @t25))
1.29/1.50	(define @t37 () (not (not @t36)))
1.29/1.50	(define @t38 () (_ @t29 @t22))
1.29/1.50	(define @t39 () (_ @t25 @t22))
1.29/1.50	(define @t40 () (= @t38 @t39))
1.29/1.50	(define @t41 () (forall @t24 @t40))
1.29/1.50	(define @t42 () (_ @t29 @t31))
1.29/1.50	(define @t43 () (_ @t17 @t31 @t31))
1.29/1.50	(define @t44 () (not @t43))
1.29/1.50	(define @t45 () (= @t44 @t42))
1.29/1.50	(define @t46 () (not @t45))
1.29/1.50	(define @t47 () (not @t44))
1.29/1.50	(define @t48 () (not @t42))
1.29/1.50	(define @t49 () (not @t33))
1.29/1.50	(define @t50 () (and @t42 @t44 @t33))
1.29/1.50	(define @t51 () (and @t48 @t43 @t33))
1.29/1.50	(assume @p1 (not (not @t11)))
1.29/1.50	(assume @p2 true)
1.29/1.50	(step @p3 :rule exists-elim :args ((= (exists @t10 @t14) @t16)))
1.29/1.50	(step @p4 :rule exists-elim :args ((= (exists @t6 @t12) @t13)))
1.29/1.50	(step @p5 :rule bool-eq-true :args (@t12))
1.29/1.50	(step @p6 :rule eq-refl :args (@t1))
1.29/1.50	(step @p7 :rule eq-symm :args (@t4 @t1))
1.29/1.50	(step @p8 :rule cong :premises (@p7 @p6) :args (@t5))
1.29/1.50	(step @p9 :rule trans :premises (@p8 @p5))
1.29/1.50	(step @p10 :rule cong :premises (@p9) :args (@t7))
1.29/1.50	(step @p11 :rule trans :premises (@p10 @p4))
1.29/1.50	(step @p12 :rule cong :premises (@p11) :args (@t9))
1.29/1.50	(step @p13 :rule cong :premises (@p12) :args (@t11))
1.29/1.50	(step @p14 :rule trans :premises (@p13 @p3))
1.29/1.50	(step @p15 :rule bool-double-not-elim :args (@t11))
1.29/1.50	(step @p16 :rule trans :premises (@p15 @p14))
1.29/1.50	(step @p17 :rule eq_resolve :premises (@p1 @p16))
1.29/1.50	(step @p18 :rule refl :args (@t19))
1.29/1.50	(step @p19 :rule bool-double-not-elim :args (@t15))
1.29/1.50	(step @p20 :rule nary_cong :premises (@p19 @p18) :args ((or (not @t16) @t19)))
1.29/1.50	(step @p21 :rule bool-double-not-elim :args (@t19))
1.29/1.50	(step @p22 :rule refl :args (@t16))
1.29/1.50	(step @p23 :rule cong :premises (@p22 @p21) :args ((=> @t16 @t20)))
1.29/1.50	(assume-push @p166 @t16)
1.29/1.50	(step @p25 :rule skolemize :premises (@p17))
1.29/1.50	(step-pop @p166 :rule scope :premises (@p25))
1.29/1.50	(step @p26 :rule process_scope :premises (@p166) :args (@t20))
1.29/1.50	(step @p28 :rule eq_resolve :premises (@p26 @p23))
1.29/1.50	(step @p29 :rule implies_elim :premises (@p28))
1.29/1.50	(step @p30 :rule eq_resolve :premises (@p29 @p20))
1.29/1.50	(step @p31 :rule chain_resolution :premises (@p30 @p17) :args (@t21 (@list @t15)))
1.29/1.50	(step @p32 :rule eq-symm :args (@t25 @t18))
1.29/1.50	(step @p33 :rule cong :premises (@p32) :args (@t26))
1.29/1.50	(step @p34 :rule cong :premises (@p33) :args (@t27))
1.29/1.50	(step @p35 :rule cong :premises (@p34) :args (@t28))
1.29/1.50	(step @p36 :rule cong :premises (@p18 @p35) :args ((=> @t19 @t28)))
1.29/1.50	(assume-push @p168 @t19)
1.29/1.50	(step @p38 :rule instantiate :premises (@p31) :args ((@list @t25)))
1.29/1.50	(step-pop @p168 :rule scope :premises (@p38))
1.29/1.50	(step @p39 :rule process_scope :premises (@p168) :args (@t28))
1.29/1.50	(step @p41 :rule eq_resolve :premises (@p39 @p36))
1.29/1.50	(step @p42 :rule implies_elim :premises (@p41))
1.29/1.50	(step @p43 :rule chain_resolution :premises (@p42 @p31) :args ((@list false) (@list @t19)))
1.29/1.50	(step @p44 :rule refl :args (@t33))
1.29/1.50	(step @p45 :rule bool-double-not-elim :args (@t30))
1.29/1.50	(step @p46 :rule nary_cong :premises (@p45 @p44) :args ((or (not @t34) @t33)))
1.29/1.50	(step @p47 :rule eq-symm :args (@t29 @t32))
1.29/1.50	(step @p48 :rule refl :args (@t32))
1.29/1.50	(step @p49 :rule eq-refl :args (@t25))
1.29/1.50	(step @p50 :rule skolem_intro :args (@t29))
1.29/1.50	(step @p51 :rule refl :args (@t25))
1.29/1.50	(step @p52 :rule cong :premises (@p51 @p50) :args ((= @t25 @t29)))
1.29/1.50	(step @p53 :rule trans :premises (@p52 @p49))
1.29/1.50	(step @p54 :rule true_elim :premises (@p53))
1.29/1.50	(step @p55 :rule cong :premises (@p54 @p48) :args (@t35))
1.29/1.50	(step @p56 :rule trans :premises (@p55 @p47))
1.29/1.50	(step @p57 :rule refl :args (@t34))
1.29/1.50	(step @p58 :rule cong :premises (@p57 @p56) :args ((=> @t34 @t35)))
1.29/1.50	(step @p59 :rule eq-symm :args (@t32 @t25))
1.29/1.50	(step @p60 :rule bool-double-not-elim :args (@t36))
1.29/1.50	(step @p61 :rule trans :premises (@p60 @p59))
1.29/1.50	(step @p62 :rule cong :premises (@p57 @p61) :args ((=> @t34 @t37)))
1.29/1.50	(step @p63 :rule trans :premises (@p62 @p58))
1.29/1.50	(assume-push @p170 @t34)
1.29/1.50	(step @p65 :rule skolemize :premises (@p43))
1.29/1.50	(step-pop @p170 :rule scope :premises (@p65))
1.29/1.50	(step @p66 :rule process_scope :premises (@p170) :args (@t37))
1.29/1.50	(step @p68 :rule eq_resolve :premises (@p66 @p63))
1.29/1.50	(step @p69 :rule implies_elim :premises (@p68))
1.29/1.50	(step @p70 :rule eq_resolve :premises (@p69 @p46))
1.29/1.50	(step @p71 :rule chain_resolution :premises (@p70 @p43) :args (@t21 (@list @t30)))
1.29/1.50	(step @p72 :rule eq-symm :args (@t38 @t23))
1.29/1.50	(step @p73 :rule beta-reduce :args ((= @t39 @t23)))
1.29/1.50	(step @p74 :rule refl :args (@t38))
1.29/1.50	(step @p75 :rule cong :premises (@p74 @p73) :args (@t40))
1.29/1.50	(step @p76 :rule trans :premises (@p75 @p72))
1.29/1.50	(step @p77 :rule cong :premises (@p76) :args (@t41))
1.29/1.50	(step @p78 :rule quant-unused-vars :args ((= (forall @t24 true) true)))
1.29/1.50	(step @p79 :rule eq-refl :args (@t39))
1.29/1.50	(step @p80 :rule cong :premises (@p79) :args ((forall @t24 (= @t39 @t39))))
1.29/1.50	(step @p81 :rule trans :premises (@p80 @p78))
1.29/1.50	(step @p82 :rule refl :args (@t39))
1.29/1.50	(step @p83 :rule refl :args (@t22))
1.29/1.50	(step @p84 :rule ho_cong :premises (@p50 @p83))
1.29/1.50	(step @p85 :rule cong :premises (@p84 @p82) :args (@t40))
1.29/1.50	(step @p86 :rule cong :premises (@p85) :args (@t41))
1.29/1.50	(step @p87 :rule trans :premises (@p86 @p81))
1.29/1.50	(step @p88 :rule true_elim :premises (@p87))
1.29/1.50	(step @p89 :rule eq_resolve :premises (@p88 @p77))
1.29/1.50	(step @p90 :rule instantiate :premises (@p89) :args ((@list @t31)))
1.29/1.50	(step @p91 :rule refl :args (@t42))
1.29/1.50	(step @p92 :rule bool-double-not-elim :args (@t43))
1.29/1.50	(step @p93 :rule refl :args (@t46))
1.29/1.50	(step @p94 :rule nary_cong :premises (@p93 @p92 @p91) :args ((or @t46 @t47 @t42)))
1.29/1.50	(step @p95 :rule cnf_equiv_pos1 :args (@t45))
1.29/1.50	(step @p96 :rule eq_resolve :premises (@p95 @p94))
1.29/1.50	(step @p97 :rule reordering :premises (@p96) :args ((or @t43 @t42 @t46)))
1.29/1.50	(step @p98 :rule refl :args (@t48))
1.29/1.50	(step @p99 :rule refl :args (@t49))
1.29/1.50	(step @p100 :rule nary_cong :premises (@p99 @p92 @p98) :args ((or @t49 @t47 @t48)))
1.29/1.50	(assume-push @p172 @t42)
1.29/1.50	(assume-push @p173 @t44)
1.29/1.50	(assume-push @p174 @t33)
1.29/1.50	(step @p104 :rule evaluate :args ((= true false)))
1.29/1.50	(step @p105 :rule false_intro :premises (@p173))
1.29/1.50	(step @p106 :rule refl :args (@t43))
1.29/1.50	(step @p107 :rule symm :premises (@p106))
1.29/1.50	(step @p108 :rule refl :args (@t31))
1.29/1.50	(step @p109 :rule symm :premises (@p71))
1.29/1.50	(step @p110 :rule ho_cong :premises (@p109 @p108))
1.29/1.50	(step @p111 :rule refl :args (@t42))
1.29/1.50	(step @p112 :rule true_intro :premises (@p172))
1.29/1.50	(step @p113 :rule symm :premises (@p112))
1.29/1.50	(step @p114 :rule trans :premises (@p113 @p111 @p110 @p107 @p105))
1.29/1.50	(step @p115 false :rule eq_resolve :premises (@p114 @p104))
1.29/1.50	(step-pop @p174 :rule scope :premises (@p115))
1.29/1.50	(step-pop @p175 :rule scope :premises (@p174))
1.29/1.50	(step-pop @p176 :rule scope :premises (@p175))
1.29/1.50	(step @p116 :rule process_scope :premises (@p176) :args (false))
1.29/1.50	(assume-push @p178 @t33)
1.29/1.50	(assume-push @p179 @t44)
1.29/1.50	(assume-push @p180 @t42)
1.29/1.50	(step @p123 :rule and_intro :premises (@p180 @p179 @p71))
1.29/1.50	(step-pop @p180 :rule scope :premises (@p123))
1.29/1.50	(step-pop @p181 :rule scope :premises (@p180))
1.29/1.50	(step-pop @p182 :rule scope :premises (@p181))
1.29/1.50	(step @p124 :rule process_scope :premises (@p182) :args (@t50))
1.29/1.50	(step @p128 :rule implies_elim :premises (@p124))
1.29/1.50	(step @p129 :rule resolution :premises (@p128 @p116) :args (true @t50))
1.29/1.50	(step @p130 :rule not_and :premises (@p129))
1.29/1.50	(step @p131 :rule eq_resolve :premises (@p130 @p100))
1.29/1.50	(step @p132 :rule chain_resolution :premises (@p131 @p71 @p97 @p90) :args ((@list false false false) (@list @t33 @t42 @t45)))
1.29/1.50	(step @p133 :rule factoring :premises (@p132))
1.29/1.50	(step @p134 :rule cnf_equiv_pos2 :args (@t45))
1.29/1.50	(step @p135 :rule reordering :premises (@p134) :args ((or @t44 @t48 @t46)))
1.29/1.50	(step @p136 :rule chain_resolution :premises (@p135 @p133 @p90) :args ((@list false false) (@list @t43 @t45)))
1.29/1.50	(step @p137 :rule bool-double-not-elim :args (@t42))
1.29/1.50	(step @p138 :rule refl :args (@t44))
1.29/1.50	(step @p139 :rule nary_cong :premises (@p99 @p138 @p137) :args ((or @t49 @t44 (not @t48))))
1.29/1.50	(assume-push @p184 @t48)
1.29/1.50	(assume-push @p185 @t43)
1.29/1.50	(assume-push @p186 @t33)
1.29/1.50	(step @p143 :rule evaluate :args ((= false true)))
1.29/1.50	(step @p144 :rule true_intro :premises (@p185))
1.29/1.50	(step @p106 :rule refl :args (@t43))
1.29/1.50	(step @p107 :rule symm :premises (@p106))
1.29/1.50	(step @p108 :rule refl :args (@t31))
1.29/1.50	(step @p109 :rule symm :premises (@p71))
1.29/1.50	(step @p110 :rule ho_cong :premises (@p109 @p108))
1.29/1.50	(step @p111 :rule refl :args (@t42))
1.29/1.50	(step @p145 :rule false_intro :premises (@p184))
1.29/1.50	(step @p146 :rule symm :premises (@p145))
1.29/1.50	(step @p147 :rule trans :premises (@p146 @p111 @p110 @p107 @p144))
1.29/1.50	(step @p148 false :rule eq_resolve :premises (@p147 @p143))
1.29/1.50	(step-pop @p186 :rule scope :premises (@p148))
1.29/1.50	(step-pop @p187 :rule scope :premises (@p186))
1.29/1.50	(step-pop @p188 :rule scope :premises (@p187))
1.29/1.50	(step @p149 :rule process_scope :premises (@p188) :args (false))
1.29/1.50	(assume-push @p190 @t33)
1.29/1.50	(assume-push @p191 @t43)
1.29/1.50	(assume-push @p192 @t48)
1.29/1.50	(step @p156 :rule and_intro :premises (@p192 @p191 @p71))
1.29/1.50	(step-pop @p192 :rule scope :premises (@p156))
1.29/1.50	(step-pop @p193 :rule scope :premises (@p192))
1.29/1.50	(step-pop @p194 :rule scope :premises (@p193))
1.29/1.50	(step @p157 :rule process_scope :premises (@p194) :args (@t51))
1.29/1.50	(step @p161 :rule implies_elim :premises (@p157))
1.29/1.50	(step @p162 :rule resolution :premises (@p161 @p149) :args (true @t51))
1.29/1.50	(step @p163 :rule not_and :premises (@p162))
1.29/1.50	(step @p164 :rule eq_resolve :premises (@p163 @p139))
1.29/1.50	(step @p165 false :rule chain_resolution :premises (@p164 @p136 @p133 @p71) :args ((@list true false false) (@list @t42 @t43 @t33)))
1.29/1.50	)
1.29/1.50	% SZS output end Proof
1.29/1.50	% cvc5 exiting
1.29/1.50	EOF