0.03/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command  : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 120 THM
0.13/0.34	% Computer : n029.cluster.edu
0.13/0.34	% Model    : x86_64 x86_64
0.13/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory   : 8042.1875MB
0.13/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit : 960
0.13/0.34	% WCLimit  : 120
0.13/0.34	% DateTime : Fri Sep  5 12:53:07 EDT 2025
0.13/0.34	% CPUTime  : 
0.19/0.49	%----Proving TF0_ARI
0.37/0.56	--- Run --finite-model-find --decision=internal at 18...
0.37/0.56	% SZS status Theorem
0.37/0.56	% SZS output start Proof
0.37/0.56	(
0.37/0.56	(define @t1 () (- 1))
0.37/0.56	(define @t2 () (/ @t1 2))
0.37/0.56	(define @t3 () (@var "X" Real))
0.37/0.56	(define @t4 () (+ @t3 @t2))
0.37/0.56	(define @t5 () (to_int @t4))
0.37/0.56	(define @t6 () (/ 1 2))
0.37/0.56	(define @t7 () (+ @t3 @t6))
0.37/0.56	(define @t8 () (to_int @t7))
0.37/0.56	(define @t9 () (@list @t3))
0.37/0.56	(define @t10 () (forall @t9 (> @t8 @t5)))
0.37/0.56	(define @t11 () (not @t10))
0.37/0.56	(define @t12 () (+ -1/2 @t3))
0.37/0.56	(define @t13 () (to_int @t12))
0.37/0.56	(define @t14 () (+ 1/2 @t3))
0.37/0.56	(define @t15 () (to_int @t14))
0.37/0.56	(define @t16 () (+ @t15 (* -1 @t13)))
0.37/0.56	(define @t17 () (>= @t16 1))
0.37/0.56	(define @t18 () (+ @t13 1))
0.37/0.56	(define @t19 () (>= @t15 @t18))
0.37/0.56	(define @t20 () (* @t1 1/2))
0.37/0.56	(define @t21 () (<= @t8 @t5))
0.37/0.56	(define @t22 () (forall @t9 @t17))
0.37/0.56	(define @t23 () (@quantifiers_skolemize @t22 0))
0.37/0.56	(define @t24 () (+ 1/2 @t23))
0.37/0.56	(define @t25 () (to_int @t24))
0.37/0.56	(define @t26 () (@purify @t25))
0.37/0.56	(define @t27 () (* -1 @t26))
0.37/0.56	(define @t28 () (+ -1/2 @t23))
0.37/0.56	(define @t29 () (to_int @t28))
0.37/0.56	(define @t30 () (@purify @t29))
0.37/0.56	(define @t31 () (+ @t30 @t27))
0.37/0.56	(define @t32 () (>= @t31 0))
0.37/0.56	(define @t33 () (not @t22))
0.37/0.56	(define @t34 () (* -1 @t30))
0.37/0.56	(define @t35 () (+ @t34 @t26))
0.37/0.56	(define @t36 () (+ @t31 1))
0.37/0.56	(define @t37 () (* -1 @t29))
0.37/0.56	(define @t38 () (+ @t25 @t37))
0.37/0.56	(define @t39 () (>= @t38 1))
0.37/0.56	(define @t40 () (not @t39))
0.37/0.56	(define @t41 () (+ @t23 @t34))
0.37/0.56	(define @t42 () (+ -1/2 @t23 @t34))
0.37/0.56	(define @t43 () (+ @t34 @t23 -1/2))
0.37/0.56	(define @t44 () (+ @t28 @t34))
0.37/0.56	(define @t45 () (- @t28 @t30))
0.37/0.56	(define @t46 () (>= @t45 1/1))
0.37/0.56	(define @t47 () (>= @t41 1/2))
0.37/0.56	(define @t48 () (<= 0/1 @t45))
0.37/0.56	(define @t49 () (+ @t23 @t27))
0.37/0.56	(define @t50 () (+ 1/2 @t23 @t27))
0.37/0.56	(define @t51 () (>= @t49 1/2))
0.37/0.56	(define @t52 () (+ @t27 @t23 1/2))
0.37/0.56	(define @t53 () (+ @t24 @t27))
0.37/0.56	(define @t54 () (- @t24 @t26))
0.37/0.56	(define @t55 () (>= @t54 1/1))
0.37/0.56	(define @t56 () (<= 0/1 @t54))
0.37/0.56	(define @t57 () (not @t47))
0.37/0.56	(define @t58 () (not @t32))
0.37/0.56	(define @t59 () (not @t51))
0.37/0.56	(define @t60 () (< @t49 1/2))
0.37/0.56	(define @t61 () (* -1 0))
0.37/0.56	(define @t62 () (* -1/1 1/2))
0.37/0.56	(define @t63 () (+ 1/2 @t62 @t61))
0.37/0.56	(define @t64 () (* 0 @t23))
0.37/0.56	(define @t65 () (* 0 @t26))
0.37/0.56	(define @t66 () (+ @t65 @t30 @t34 @t64))
0.37/0.56	(define @t67 () (+ @t49 (* -1/1 @t41) (* -1 @t31)))
0.37/0.56	(define @t68 () (>= @t67 @t63))
0.37/0.56	(assume @p1 @t11)
0.37/0.56	(assume @p2 true)
0.37/0.56	(step @p3 :rule bool-double-not-elim :args (@t17))
0.37/0.56	(step @p4 :rule arith_poly_norm :args ((= (* -1 (- @t15 @t18)) (* -1 (- @t16 1)))))
0.37/0.56	(step @p5 :rule arith_poly_norm_rel :premises (@p4) :args ((= @t19 @t17)))
0.37/0.56	(step @p6 :rule cong :premises (@p5) :args ((not @t19)))
0.37/0.56	(step @p7 :rule arith-leq-norm :args (@t15 @t13))
0.37/0.56	(step @p8 :rule trans :premises (@p7 @p6))
0.37/0.56	(step @p9 :rule arith_poly_norm :args ((= (+ @t3 -1/2) @t12)))
0.37/0.56	(step @p10 :rule evaluate :args ((* -1 1/2)))
0.37/0.56	(step @p11 :rule refl :args (1/2))
0.37/0.56	(step @p12 :rule evaluate :args (@t1))
0.37/0.56	(step @p13 :rule nary_cong :premises (@p12 @p11) :args (@t20))
0.37/0.56	(step @p14 :rule trans :premises (@p13 @p10))
0.37/0.56	(step @p15 :rule evaluate :args (@t20))
0.37/0.56	(step @p16 :rule symm :premises (@p15))
0.37/0.56	(step @p17 :rule evaluate :args (@t2))
0.37/0.56	(step @p18 :rule trans :premises (@p17 @p16))
0.37/0.56	(step @p19 :rule trans :premises (@p18 @p14))
0.37/0.56	(step @p20 :rule refl :args (@t3))
0.37/0.56	(step @p21 :rule nary_cong :premises (@p20 @p19) :args (@t4))
0.37/0.56	(step @p22 :rule trans :premises (@p21 @p9))
0.37/0.56	(step @p23 :rule cong :premises (@p22) :args (@t5))
0.37/0.56	(step @p24 :rule arith_poly_norm :args ((= (+ @t3 1/2) @t14)))
0.37/0.56	(step @p25 :rule evaluate :args (@t6))
0.37/0.56	(step @p26 :rule nary_cong :premises (@p20 @p25) :args (@t7))
0.37/0.56	(step @p27 :rule trans :premises (@p26 @p24))
0.37/0.56	(step @p28 :rule cong :premises (@p27) :args (@t8))
0.37/0.56	(step @p29 :rule cong :premises (@p28 @p23) :args (@t21))
0.37/0.56	(step @p30 :rule trans :premises (@p29 @p8))
0.37/0.56	(step @p31 :rule cong :premises (@p30) :args ((not @t21)))
0.37/0.56	(step @p32 :rule trans :premises (@p31 @p3))
0.37/0.56	(step @p33 :rule arith-elim-leq :args (@t8 @t5))
0.37/0.56	(step @p34 :rule symm :premises (@p33))
0.37/0.56	(step @p35 :rule cong :premises (@p34) :args ((not (>= @t5 @t8))))
0.37/0.56	(step @p36 :rule arith-elim-gt :args (@t8 @t5))
0.37/0.56	(step @p37 :rule trans :premises (@p36 @p35))
0.37/0.56	(step @p38 :rule trans :premises (@p37 @p32))
0.37/0.56	(step @p39 :rule cong :premises (@p38) :args (@t10))
0.37/0.56	(step @p40 :rule cong :premises (@p39) :args (@t11))
0.37/0.56	(step @p41 :rule eq_resolve :premises (@p1 @p40))
0.37/0.56	(step @p42 :rule refl :args (@t32))
0.37/0.56	(step @p43 :rule bool-double-not-elim :args (@t22))
0.37/0.56	(step @p44 :rule nary_cong :premises (@p43 @p42) :args ((or (not @t33) @t32)))
0.37/0.56	(step @p45 :rule bool-double-not-elim :args (@t32))
0.37/0.56	(step @p46 :rule arith_poly_norm :args ((= (* -1 (- 0 @t36)) (* -1 (- @t35 1)))))
0.37/0.56	(step @p47 :rule arith_poly_norm_rel :premises (@p46) :args ((= (>= 0 @t36) (>= @t35 1))))
0.37/0.56	(step @p48 :rule arith-geq-tighten :args (@t31 0))
0.37/0.56	(step @p49 :rule trans :premises (@p48 @p47))
0.37/0.56	(step @p50 :rule symm :premises (@p49))
0.37/0.56	(step @p51 :rule refl :args (1))
0.37/0.56	(step @p52 :rule arith_poly_norm :args ((= (+ @t26 @t34) @t35)))
0.37/0.56	(step @p53 :rule arith_reduction :args (@t29))
0.37/0.56	(step @p54 :rule and_elim :premises (@p53) :args (0))
0.37/0.56	(step @p55 :rule refl :args (-1))
0.37/0.56	(step @p56 :rule nary_cong :premises (@p55 @p54) :args (@t37))
0.37/0.56	(step @p57 :rule arith_reduction :args (@t25))
0.37/0.56	(step @p58 :rule and_elim :premises (@p57) :args (0))
0.37/0.56	(step @p59 :rule nary_cong :premises (@p58 @p56) :args (@t38))
0.37/0.56	(step @p60 :rule trans :premises (@p59 @p52))
0.37/0.56	(step @p61 :rule cong :premises (@p60 @p51) :args (@t39))
0.37/0.56	(step @p62 :rule trans :premises (@p61 @p50))
0.37/0.56	(step @p63 :rule cong :premises (@p62) :args (@t40))
0.37/0.56	(step @p64 :rule trans :premises (@p63 @p45))
0.37/0.56	(step @p65 :rule refl :args (@t33))
0.37/0.56	(step @p66 :rule cong :premises (@p65 @p64) :args ((=> @t33 @t40)))
0.37/0.56	(assume-push @p184 @t33)
0.37/0.56	(step @p68 :rule skolemize :premises (@p41))
0.37/0.56	(step-pop @p184 :rule scope :premises (@p68))
0.37/0.56	(step @p69 :rule process_scope :premises (@p184) :args (@t40))
0.37/0.56	(step @p71 :rule eq_resolve :premises (@p69 @p66))
0.37/0.56	(step @p72 :rule implies_elim :premises (@p71))
0.37/0.56	(step @p73 :rule eq_resolve :premises (@p72 @p44))
0.37/0.56	(step @p74 :rule chain_resolution :premises (@p73 @p41) :args ((@list true) (@list @t22)))
0.37/0.56	(step @p75 :rule arith_poly_norm :args ((= (* -3/2 (- @t42 1/1)) (* -3/2 (- @t41 3/2)))))
0.37/0.56	(step @p76 :rule arith_poly_norm_rel :premises (@p75) :args ((= (>= @t42 1/1) (>= @t41 3/2))))
0.37/0.56	(step @p77 :rule refl :args (1/1))
0.37/0.56	(step @p78 :rule arith_poly_norm :args ((= @t43 @t42)))
0.37/0.56	(step @p79 :rule arith_poly_norm :args ((= @t44 @t43)))
0.37/0.56	(step @p80 :rule trans :premises (@p79 @p78))
0.37/0.56	(step @p81 :rule arith_poly_norm :args ((= @t45 @t44)))
0.37/0.56	(step @p82 :rule trans :premises (@p81 @p80))
0.37/0.56	(step @p83 :rule cong :premises (@p82 @p77) :args (@t46))
0.37/0.56	(step @p84 :rule trans :premises (@p83 @p76))
0.37/0.56	(step @p85 :rule cong :premises (@p84) :args ((not @t46)))
0.37/0.56	(step @p86 :rule arith-elim-lt :args (@t45 1/1))
0.37/0.56	(step @p87 :rule trans :premises (@p86 @p85))
0.37/0.56	(step @p88 :rule arith_poly_norm :args ((= (* -1/2 (- @t42 0/1)) (* -1/2 (- @t41 1/2)))))
0.37/0.56	(step @p89 :rule arith_poly_norm_rel :premises (@p88) :args ((= (>= @t42 0/1) @t47)))
0.37/0.56	(step @p90 :rule arith-elim-leq :args (0/1 @t42))
0.37/0.56	(step @p91 :rule trans :premises (@p90 @p89))
0.37/0.56	(step @p92 :rule refl :args (0/1))
0.37/0.56	(step @p93 :rule cong :premises (@p92 @p82) :args (@t48))
0.37/0.56	(step @p94 :rule trans :premises (@p93 @p91))
0.37/0.56	(step @p95 :rule nary_cong :premises (@p94 @p87) :args ((and @t48 (< @t45 1/1))))
0.37/0.56	(step @p96 :rule and_elim :premises (@p53) :args (1))
0.37/0.56	(step @p97 :rule eq_resolve :premises (@p96 @p95))
0.37/0.56	(step @p98 :rule and_elim :premises (@p97) :args (0))
0.37/0.56	(step @p99 :rule arith_poly_norm :args ((= (* -1/2 (- @t50 1/1)) (* -1/2 (- @t49 1/2)))))
0.37/0.56	(step @p100 :rule arith_poly_norm_rel :premises (@p99) :args ((= (>= @t50 1/1) @t51)))
0.37/0.56	(step @p101 :rule arith_poly_norm :args ((= @t52 @t50)))
0.37/0.56	(step @p102 :rule arith_poly_norm :args ((= @t53 @t52)))
0.37/0.56	(step @p103 :rule trans :premises (@p102 @p101))
0.37/0.56	(step @p104 :rule arith_poly_norm :args ((= @t54 @t53)))
0.37/0.56	(step @p105 :rule trans :premises (@p104 @p103))
0.37/0.56	(step @p106 :rule cong :premises (@p105 @p77) :args (@t55))
0.37/0.56	(step @p107 :rule trans :premises (@p106 @p100))
0.37/0.56	(step @p108 :rule cong :premises (@p107) :args ((not @t55)))
0.37/0.56	(step @p109 :rule arith-elim-lt :args (@t54 1/1))
0.37/0.56	(step @p110 :rule trans :premises (@p109 @p108))
0.37/0.56	(step @p111 :rule arith_poly_norm :args ((= (* 1/2 (- @t50 0/1)) (* 1/2 (- @t49 -1/2)))))
0.39/0.57	(step @p112 :rule arith_poly_norm_rel :premises (@p111) :args ((= (>= @t50 0/1) (>= @t49 -1/2))))
0.39/0.57	(step @p113 :rule arith-elim-leq :args (0/1 @t50))
0.39/0.57	(step @p114 :rule trans :premises (@p113 @p112))
0.39/0.57	(step @p115 :rule cong :premises (@p92 @p105) :args (@t56))
0.39/0.57	(step @p116 :rule trans :premises (@p115 @p114))
0.39/0.57	(step @p117 :rule nary_cong :premises (@p116 @p110) :args ((and @t56 (< @t54 1/1))))
0.39/0.57	(step @p118 :rule and_elim :premises (@p57) :args (1))
0.39/0.57	(step @p119 :rule eq_resolve :premises (@p118 @p117))
0.39/0.57	(step @p120 :rule and_elim :premises (@p119) :args (1))
0.39/0.57	(step @p121 :rule bool-double-not-elim :args (@t51))
0.39/0.57	(step @p122 :rule refl :args (@t57))
0.39/0.57	(step @p123 :rule refl :args (@t58))
0.39/0.57	(step @p124 :rule nary_cong :premises (@p123 @p122 @p121) :args ((or @t58 @t57 (not @t59))))
0.39/0.57	(assume-push @p186 @t32)
0.39/0.57	(assume-push @p187 @t47)
0.39/0.57	(assume-push @p188 @t59)
0.39/0.57	(step @p128 :rule arith-elim-lt :args (@t49 1/2))
0.39/0.57	(step @p129 :rule cong :premises (@p128) :args ((not @t60)))
0.39/0.57	(step @p130 :rule trans :premises (@p129 @p121))
0.39/0.57	(step @p131 :rule symm :premises (@p130))
0.39/0.57	(assume-push @p189 @t60)
0.39/0.57	(step @p133 :rule evaluate :args ((not true)))
0.39/0.57	(step @p134 :rule evaluate :args ((>= 0/1 0/1)))
0.39/0.57	(step @p135 :rule evaluate :args ((+ 1/2 -1/2 0)))
0.39/0.57	(step @p136 :rule evaluate :args (@t61))
0.39/0.57	(step @p137 :rule evaluate :args (@t62))
0.39/0.57	(step @p138 :rule nary_cong :premises (@p11 @p137 @p136) :args (@t63))
0.39/0.57	(step @p139 :rule trans :premises (@p138 @p135))
0.39/0.57	(step @p140 :rule arith_poly_norm :args ((= (+ 0 @t30 @t34 0/1) 0/1)))
0.39/0.57	(step @p141 :rule arith_poly_norm :args ((= @t64 0/1)))
0.39/0.57	(step @p142 :rule refl :args (@t34))
0.39/0.57	(step @p143 :rule refl :args (@t30))
0.39/0.57	(step @p144 :rule arith_poly_norm :args ((= @t65 0)))
0.39/0.57	(step @p145 :rule nary_cong :premises (@p144 @p143 @p142 @p141) :args (@t66))
0.39/0.57	(step @p146 :rule trans :premises (@p145 @p140))
0.39/0.57	(step @p147 :rule arith_poly_norm :args ((= @t67 @t66)))
0.39/0.57	(step @p148 :rule trans :premises (@p147 @p146))
0.39/0.57	(step @p149 :rule cong :premises (@p148 @p139) :args (@t68))
0.39/0.57	(step @p150 :rule trans :premises (@p149 @p134))
0.39/0.57	(step @p151 :rule cong :premises (@p150) :args ((not @t68)))
0.39/0.57	(step @p152 :rule trans :premises (@p151 @p133))
0.39/0.57	(step @p153 :rule arith-elim-lt :args (@t67 @t63))
0.39/0.57	(step @p154 :rule trans :premises (@p153 @p152))
0.39/0.57	(step @p155 :rule arith_mult_neg :args (-1 @t32))
0.39/0.57	(step @p156 :rule evaluate :args ((< -1 0)))
0.39/0.57	(step @p157 :rule true_elim :premises (@p156))
0.39/0.57	(step @p158 :rule and_intro :premises (@p157 @p74))
0.39/0.57	(step @p159 :rule modus_ponens :premises (@p158 @p155))
0.39/0.57	(step @p160 :rule arith_mult_neg :args (-1/1 @t47))
0.39/0.57	(step @p161 :rule evaluate :args ((< -1/1 0/1)))
0.39/0.57	(step @p162 :rule true_elim :premises (@p161))
0.39/0.57	(step @p163 :rule and_intro :premises (@p162 @p98))
0.39/0.57	(step @p164 :rule modus_ponens :premises (@p163 @p160))
0.39/0.57	(step @p165 :rule symm :premises (@p128))
0.39/0.57	(step @p166 :rule and_elim :premises (@p119) :args (1))
0.39/0.57	(step @p167 :rule eq_resolve :premises (@p166 @p165))
0.39/0.57	(step @p168 :rule arith_sum_ub :premises (@p167 @p164 @p159))
0.39/0.57	(step @p169 false :rule eq_resolve :premises (@p168 @p154))
0.39/0.57	(step-pop @p189 :rule scope :premises (@p169))
0.39/0.57	(step @p170 :rule process_scope :premises (@p189) :args (false))
0.39/0.57	(step @p172 :rule eq_resolve :premises (@p170 @p130))
0.39/0.57	(step @p173 :rule eq_resolve :premises (@p172 @p131))
0.39/0.57	(step @p165 :rule symm :premises (@p128))
0.39/0.57	(step @p174 :rule eq_resolve :premises (@p120 @p165))
0.39/0.57	(step @p175 false :rule contra :premises (@p174 @p173))
0.39/0.57	(step-pop @p190 :rule scope :premises (@p175))
0.39/0.57	(step-pop @p191 :rule scope :premises (@p190))
0.39/0.57	(step-pop @p192 :rule scope :premises (@p191))
0.39/0.57	(step @p176 :rule process_scope :premises (@p192) :args (false))
0.39/0.57	(step @p180 :rule not_and :premises (@p176))
0.39/0.57	(step @p181 :rule eq_resolve :premises (@p180 @p124))
0.39/0.57	(step @p182 :rule reordering :premises (@p181) :args ((or @t58 @t51 @t57)))
0.39/0.57	(step @p183 false :rule chain_resolution :premises (@p182 @p120 @p98 @p74) :args ((@list true false false) (@list @t51 @t47 @t32)))
0.39/0.57	)
0.39/0.57	% SZS output end Proof
0.39/0.57	% cvc5 exiting
0.39/0.57	EOF