%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ARI724_1 : TPTP v9.2.1. Released v6.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n015.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 08:08:12 AM UTC 2026 % Result : Theorem 0.33s 0.57s % Output : Proof 0.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ARI724_1 : TPTP v9.2.1. Released v6.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n015.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 02:32:49 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.50 %----Proving TF0_ARI % 0.33/0.57 --- Run --finite-model-find --decision=internal at 45... % 0.33/0.57 % SZS status Theorem % 0.33/0.57 % SZS output start Proof % 0.33/0.57 ( % 0.33/0.57 (define @t1 () (@var "X" Real)) % 0.33/0.57 (define @t2 () (to_int @t1)) % 0.33/0.57 (define @t3 () (* 2/1 (to_real @t2))) % 0.33/0.57 (define @t4 () (to_int (* 2/1 @t1))) % 0.33/0.57 (define @t5 () (to_real @t4)) % 0.33/0.57 (define @t6 () (>= @t5 @t3)) % 0.33/0.57 (define @t7 () (@list @t1)) % 0.33/0.57 (define @t8 () (forall @t7 @t6)) % 0.33/0.57 (define @t9 () (not @t8)) % 0.33/0.57 (define @t10 () (* 2 @t2)) % 0.33/0.57 (define @t11 () (to_real @t10)) % 0.33/0.57 (define @t12 () (+ @t10 (* -1 @t4))) % 0.33/0.57 (define @t13 () (+ @t12 1)) % 0.33/0.57 (define @t14 () (forall @t7 (not (>= @t12 1)))) % 0.33/0.57 (define @t15 () (@quantifiers_skolemize @t14 0)) % 0.33/0.57 (define @t16 () (to_int @t15)) % 0.33/0.57 (define @t17 () (@purify @t16)) % 0.33/0.57 (define @t18 () (* 2/1 @t15)) % 0.33/0.57 (define @t19 () (to_int @t18)) % 0.33/0.57 (define @t20 () (@purify @t19)) % 0.33/0.57 (define @t21 () (+ @t20 (* -2 @t17))) % 0.33/0.57 (define @t22 () (>= @t21 0)) % 0.33/0.57 (define @t23 () (not @t22)) % 0.33/0.57 (define @t24 () (not @t14)) % 0.33/0.57 (define @t25 () (* 2 @t17)) % 0.33/0.57 (define @t26 () (* -1 @t20)) % 0.33/0.57 (define @t27 () (+ @t26 @t25)) % 0.33/0.57 (define @t28 () (+ @t21 1)) % 0.33/0.57 (define @t29 () (* -1 @t19)) % 0.33/0.57 (define @t30 () (* 2 @t16)) % 0.33/0.57 (define @t31 () (+ @t30 @t29)) % 0.33/0.57 (define @t32 () (>= @t31 1)) % 0.33/0.57 (define @t33 () (not (not @t32))) % 0.33/0.57 (define @t34 () (to_real @t20)) % 0.33/0.57 (define @t35 () (* -1/2 @t34)) % 0.33/0.57 (define @t36 () (+ @t15 @t35)) % 0.33/0.57 (define @t37 () (to_real @t26)) % 0.33/0.57 (define @t38 () (+ @t18 @t37)) % 0.33/0.57 (define @t39 () (>= @t36 1/2)) % 0.33/0.57 (define @t40 () (* -1/1 @t34)) % 0.33/0.57 (define @t41 () (+ @t18 @t40)) % 0.33/0.57 (define @t42 () (- @t18 @t34)) % 0.33/0.57 (define @t43 () (>= @t42 1/1)) % 0.33/0.57 (define @t44 () (<= 0/1 @t42)) % 0.33/0.57 (define @t45 () (to_real (* -1 @t17))) % 0.33/0.57 (define @t46 () (to_real @t17)) % 0.33/0.57 (define @t47 () (* -1/1 @t46)) % 0.33/0.57 (define @t48 () (+ @t15 @t47)) % 0.33/0.57 (define @t49 () (- @t15 @t46)) % 0.33/0.57 (define @t50 () (>= @t49 1/1)) % 0.33/0.57 (define @t51 () (+ @t15 @t45)) % 0.33/0.57 (define @t52 () (<= 0/1 @t49)) % 0.33/0.57 (define @t53 () (>= @t51 0/1)) % 0.33/0.57 (define @t54 () (not @t53)) % 0.33/0.57 (define @t55 () (not @t39)) % 0.33/0.57 (define @t56 () (* 1/2 -1/1)) % 0.33/0.57 (define @t57 () (* -1/1 0/1)) % 0.33/0.57 (define @t58 () (+ @t57 @t56 1/2)) % 0.33/0.57 (define @t59 () (* 1/2 @t34)) % 0.33/0.57 (define @t60 () (* 0/1 @t15)) % 0.33/0.57 (define @t61 () (+ @t46 @t35 @t45 @t59 @t60)) % 0.33/0.57 (define @t62 () (to_real @t21)) % 0.33/0.57 (define @t63 () (* 1/2 @t62)) % 0.33/0.57 (define @t64 () (+ (* -1/1 @t51) @t63 @t36)) % 0.33/0.57 (define @t65 () (>= @t64 @t58)) % 0.33/0.57 (define @t66 () (> 1/2 0/1)) % 0.33/0.57 (define @t67 () (<= @t21 -1)) % 0.33/0.57 (define @t68 () (to_real -1)) % 0.33/0.57 (define @t69 () (<= @t62 @t68)) % 0.33/0.57 (define @t70 () (and @t55 @t23 @t53)) % 0.33/0.57 (assume @p1 @t9) % 0.33/0.57 (assume @p2 true) % 0.33/0.57 (step @p3 :rule arith_poly_norm :args ((= (* 1/1 (to_real (- 1 @t13))) (* 1/1 (- @t5 @t11))))) % 0.33/0.57 (step @p4 :rule arith_poly_norm_rel :premises (@p3) :args ((= (>= 1 @t13) (>= @t5 @t11)))) % 0.33/0.57 (step @p5 :rule arith-geq-tighten :args (@t12 1)) % 0.33/0.57 (step @p6 :rule trans :premises (@p5 @p4)) % 0.33/0.57 (step @p7 :rule symm :premises (@p6)) % 0.33/0.57 (step @p8 :rule arith_poly_norm :args ((= @t3 @t11))) % 0.33/0.57 (step @p9 :rule refl :args (@t5)) % 0.33/0.57 (step @p10 :rule cong :premises (@p9 @p8) :args (@t6)) % 0.33/0.57 (step @p11 :rule trans :premises (@p10 @p7)) % 0.33/0.57 (step @p12 :rule cong :premises (@p11) :args (@t8)) % 0.33/0.57 (step @p13 :rule cong :premises (@p12) :args (@t9)) % 0.33/0.57 (step @p14 :rule eq_resolve :premises (@p1 @p13)) % 0.33/0.57 (step @p15 :rule refl :args (@t23)) % 0.33/0.57 (step @p16 :rule bool-double-not-elim :args (@t14)) % 0.33/0.57 (step @p17 :rule nary_cong :premises (@p16 @p15) :args ((or (not @t24) @t23))) % 0.33/0.57 (step @p18 :rule arith_poly_norm :args ((= (* -1 (- 0 @t28)) (* -1 (- @t27 1))))) % 0.33/0.57 (step @p19 :rule arith_poly_norm_rel :premises (@p18) :args ((= (>= 0 @t28) (>= @t27 1)))) % 0.33/0.57 (step @p20 :rule arith-geq-tighten :args (@t21 0)) % 0.33/0.57 (step @p21 :rule trans :premises (@p20 @p19)) % 0.33/0.57 (step @p22 :rule symm :premises (@p21)) % 0.33/0.57 (step @p23 :rule refl :args (1)) % 0.33/0.57 (step @p24 :rule arith_poly_norm :args ((= (+ @t25 @t26) @t27))) % 0.33/0.57 (step @p25 :rule arith_reduction :args (@t19)) % 0.33/0.57 (step @p26 :rule and_elim :premises (@p25) :args (0)) % 0.33/0.57 (step @p27 :rule refl :args (-1)) % 0.33/0.57 (step @p28 :rule nary_cong :premises (@p27 @p26) :args (@t29)) % 0.33/0.57 (step @p29 :rule arith_reduction :args (@t16)) % 0.33/0.57 (step @p30 :rule and_elim :premises (@p29) :args (0)) % 0.33/0.57 (step @p31 :rule refl :args (2)) % 0.33/0.57 (step @p32 :rule nary_cong :premises (@p31 @p30) :args (@t30)) % 0.33/0.57 (step @p33 :rule nary_cong :premises (@p32 @p28) :args (@t31)) % 0.33/0.57 (step @p34 :rule trans :premises (@p33 @p24)) % 0.33/0.57 (step @p35 :rule cong :premises (@p34 @p23) :args (@t32)) % 0.33/0.57 (step @p36 :rule trans :premises (@p35 @p22)) % 0.33/0.57 (step @p37 :rule refl :args (@t24)) % 0.33/0.57 (step @p38 :rule cong :premises (@p37 @p36) :args ((=> @t24 @t32))) % 0.33/0.57 (step @p39 :rule bool-double-not-elim :args (@t32)) % 0.33/0.57 (step @p40 :rule cong :premises (@p37 @p39) :args ((=> @t24 @t33))) % 0.33/0.57 (step @p41 :rule trans :premises (@p40 @p38)) % 0.33/0.57 (assume-push @p180 @t24) % 0.33/0.57 (step @p43 :rule skolemize :premises (@p14)) % 0.33/0.57 (step-pop @p181 :rule scope :premises (@p43)) % 0.33/0.57 (step @p44 :rule process_scope :premises (@p181) :args (@t33)) % 0.33/0.57 (step @p46 :rule eq_resolve :premises (@p44 @p41)) % 0.33/0.57 (step @p47 :rule implies_elim :premises (@p46)) % 0.33/0.57 (step @p48 :rule eq_resolve :premises (@p47 @p17)) % 0.33/0.57 (step @p49 :rule chain_m_resolution :premises (@p48 @p14) :args (@t23 (@list true) (@list @t14))) % 0.33/0.57 (step @p50 :rule arith_poly_norm :args ((= (* -1/2 (- @t38 1/1)) (* -1/1 (- @t36 1/2))))) % 0.33/0.57 (step @p51 :rule arith_poly_norm_rel :premises (@p50) :args ((= (>= @t38 1/1) @t39))) % 0.33/0.57 (step @p52 :rule refl :args (1/1)) % 0.33/0.57 (step @p53 :rule arith_poly_norm :args ((= @t40 @t37))) % 0.33/0.57 (step @p54 :rule refl :args (@t18)) % 0.33/0.57 (step @p55 :rule nary_cong :premises (@p54 @p53) :args (@t41)) % 0.33/0.57 (step @p56 :rule arith_poly_norm :args ((= @t42 @t41))) % 0.33/0.57 (step @p57 :rule trans :premises (@p56 @p55)) % 0.33/0.57 (step @p58 :rule cong :premises (@p57 @p52) :args (@t43)) % 0.33/0.57 (step @p59 :rule trans :premises (@p58 @p51)) % 0.33/0.57 (step @p60 :rule cong :premises (@p59) :args ((not @t43))) % 0.33/0.57 (step @p61 :rule arith-elim-lt :args (@t42 1/1)) % 0.33/0.57 (step @p62 :rule trans :premises (@p61 @p60)) % 0.33/0.57 (step @p63 :rule arith_poly_norm :args ((= (* 1/1 (- @t38 0/1)) (* 2/1 (- @t36 0/1))))) % 0.33/0.57 (step @p64 :rule arith_poly_norm_rel :premises (@p63) :args ((= (>= @t38 0/1) (>= @t36 0/1)))) % 0.33/0.57 (step @p65 :rule arith-elim-leq :args (0/1 @t38)) % 0.33/0.57 (step @p66 :rule trans :premises (@p65 @p64)) % 0.33/0.57 (step @p67 :rule refl :args (0/1)) % 0.33/0.57 (step @p68 :rule cong :premises (@p67 @p57) :args (@t44)) % 0.33/0.57 (step @p69 :rule trans :premises (@p68 @p66)) % 0.33/0.57 (step @p70 :rule nary_cong :premises (@p69 @p62) :args ((and @t44 (< @t42 1/1)))) % 0.33/0.57 (step @p71 :rule and_elim :premises (@p25) :args (1)) % 0.33/0.57 (step @p72 :rule eq_resolve :premises (@p71 @p70)) % 0.33/0.57 (step @p73 :rule and_elim :premises (@p72) :args (1)) % 0.33/0.57 (step @p74 :rule arith_poly_norm :args ((= @t47 @t45))) % 0.33/0.57 (step @p75 :rule refl :args (@t15)) % 0.33/0.57 (step @p76 :rule nary_cong :premises (@p75 @p74) :args (@t48)) % 0.33/0.57 (step @p77 :rule arith_poly_norm :args ((= @t49 @t48))) % 0.33/0.57 (step @p78 :rule trans :premises (@p77 @p76)) % 0.33/0.57 (step @p79 :rule cong :premises (@p78 @p52) :args (@t50)) % 0.33/0.57 (step @p80 :rule cong :premises (@p79) :args ((not @t50))) % 0.33/0.57 (step @p81 :rule arith-elim-lt :args (@t49 1/1)) % 0.33/0.57 (step @p82 :rule trans :premises (@p81 @p80)) % 0.33/0.57 (step @p83 :rule arith-elim-leq :args (0/1 @t51)) % 0.33/0.57 (step @p84 :rule cong :premises (@p67 @p78) :args (@t52)) % 0.33/0.57 (step @p85 :rule trans :premises (@p84 @p83)) % 0.33/0.57 (step @p86 :rule nary_cong :premises (@p85 @p82) :args ((and @t52 (< @t49 1/1)))) % 0.33/0.57 (step @p87 :rule and_elim :premises (@p29) :args (1)) % 0.33/0.57 (step @p88 :rule eq_resolve :premises (@p87 @p86)) % 0.33/0.57 (step @p89 :rule and_elim :premises (@p88) :args (0)) % 0.33/0.57 (step @p90 :rule refl :args (@t54)) % 0.33/0.57 (step @p91 :rule bool-double-not-elim :args (@t39)) % 0.33/0.57 (step @p92 :rule bool-double-not-elim :args (@t22)) % 0.33/0.57 (step @p93 :rule nary_cong :premises (@p92 @p91 @p90) :args ((or (not @t23) (not @t55) @t54))) % 0.33/0.57 (assume-push @p182 @t55) % 0.33/0.57 (assume-push @p183 @t23) % 0.33/0.57 (assume-push @p184 @t53) % 0.33/0.57 (step @p97 :rule arith-elim-lt :args (@t51 0/1)) % 0.33/0.57 (step @p98 :rule symm :premises (@p97)) % 0.33/0.57 (assume-push @p185 @t53) % 0.33/0.57 (step @p100 :rule evaluate :args ((not true))) % 0.33/0.57 (step @p101 :rule evaluate :args ((>= 0/1 0/1))) % 0.33/0.57 (step @p102 :rule evaluate :args ((+ 0/1 -1/2 1/2))) % 0.33/0.57 (step @p103 :rule refl :args (1/2)) % 0.33/0.57 (step @p104 :rule evaluate :args (@t56)) % 0.33/0.57 (step @p105 :rule evaluate :args (@t57)) % 0.33/0.57 (step @p106 :rule nary_cong :premises (@p105 @p104 @p103) :args (@t58)) % 0.33/0.57 (step @p107 :rule trans :premises (@p106 @p102)) % 0.33/0.57 (step @p108 :rule arith_poly_norm :args ((= (+ @t46 @t35 @t45 @t59 0/1) 0/1))) % 0.33/0.57 (step @p109 :rule arith_poly_norm :args ((= @t60 0/1))) % 0.33/0.57 (step @p110 :rule refl :args (@t59)) % 0.33/0.57 (step @p111 :rule refl :args (@t45)) % 0.33/0.57 (step @p112 :rule refl :args (@t35)) % 0.33/0.58 (step @p113 :rule refl :args (@t46)) % 0.33/0.58 (step @p114 :rule nary_cong :premises (@p113 @p112 @p111 @p110 @p109) :args (@t61)) % 0.33/0.58 (step @p115 :rule trans :premises (@p114 @p108)) % 0.33/0.58 (step @p116 :rule arith_poly_norm :args ((= @t64 @t61))) % 0.33/0.58 (step @p117 :rule trans :premises (@p116 @p115)) % 0.33/0.58 (step @p118 :rule cong :premises (@p117 @p107) :args (@t65)) % 0.33/0.58 (step @p119 :rule trans :premises (@p118 @p101)) % 0.33/0.58 (step @p120 :rule cong :premises (@p119) :args ((not @t65))) % 0.33/0.58 (step @p121 :rule trans :premises (@p120 @p100)) % 0.33/0.58 (step @p122 :rule arith-elim-lt :args (@t64 @t58)) % 0.33/0.58 (step @p123 :rule trans :premises (@p122 @p121)) % 0.33/0.58 (step @p124 :rule arith-elim-lt :args (@t36 1/2)) % 0.33/0.58 (step @p125 :rule symm :premises (@p124)) % 0.33/0.58 (step @p126 :rule eq_resolve :premises (@p73 @p125)) % 0.33/0.58 (assume-push @p186 @t66) % 0.33/0.58 (assume-push @p187 @t67) % 0.33/0.58 (step @p129 :rule arith_mult_pos :args (1/2 (<= @t62 -1/1))) % 0.33/0.58 (step @p130 :rule evaluate :args (@t68)) % 0.33/0.58 (step @p131 :rule refl :args (@t62)) % 0.33/0.58 (step @p132 :rule cong :premises (@p131 @p130) :args (@t69)) % 0.33/0.58 (step @p133 :rule arith_poly_norm :args ((= (* 1/1 (to_real (- @t21 -1))) (* 1/1 (- @t62 @t68))))) % 0.33/0.58 (step @p134 :rule arith_poly_norm_rel :premises (@p133) :args ((= @t67 @t69))) % 0.33/0.58 (step @p135 :rule trans :premises (@p134 @p132)) % 0.33/0.58 (step @p136 :rule eq_resolve :premises (@p187 @p135)) % 0.33/0.58 (step @p137 :rule and_intro :premises (@p186 @p136)) % 0.33/0.58 (step @p138 :rule modus_ponens :premises (@p137 @p129)) % 0.33/0.58 (step-pop @p188 :rule scope :premises (@p138)) % 0.33/0.58 (step-pop @p189 :rule scope :premises (@p188)) % 0.33/0.58 (step @p139 :rule process_scope :premises (@p189) :args ((<= @t63 @t56))) % 0.33/0.58 (step @p142 :rule arith-elim-lt :args (@t21 0)) % 0.33/0.58 (step @p143 :rule symm :premises (@p142)) % 0.33/0.58 (step @p144 :rule eq_resolve :premises (@p49 @p143)) % 0.33/0.58 (step @p145 :rule int_tight_ub :premises (@p144)) % 0.33/0.58 (step @p146 :rule evaluate :args (@t66)) % 0.33/0.58 (step @p147 :rule true_elim :premises (@p146)) % 0.33/0.58 (step @p148 :rule and_intro :premises (@p147 @p145)) % 0.33/0.58 (step @p149 :rule modus_ponens :premises (@p148 @p139)) % 0.33/0.58 (step @p150 :rule arith_mult_neg :args (-1/1 @t53)) % 0.33/0.58 (step @p151 :rule and_elim :premises (@p88) :args (0)) % 0.33/0.58 (step @p152 :rule evaluate :args ((< -1/1 0/1))) % 0.33/0.58 (step @p153 :rule true_elim :premises (@p152)) % 0.33/0.58 (step @p154 :rule and_intro :premises (@p153 @p151)) % 0.33/0.58 (step @p155 :rule modus_ponens :premises (@p154 @p150)) % 0.33/0.58 (step @p156 :rule arith_sum_ub :premises (@p155 @p149 @p126)) % 0.33/0.58 (step @p157 false :rule eq_resolve :premises (@p156 @p123)) % 0.33/0.58 (step-pop @p190 :rule scope :premises (@p157)) % 0.33/0.58 (step @p158 :rule process_scope :premises (@p190) :args (false)) % 0.33/0.58 (step @p160 :rule eq_resolve :premises (@p158 @p98)) % 0.33/0.58 (step @p161 :rule eq_resolve :premises (@p160 @p97)) % 0.33/0.58 (step @p162 false :rule contra :premises (@p89 @p161)) % 0.33/0.58 (step-pop @p191 :rule scope :premises (@p162)) % 0.33/0.58 (step-pop @p192 :rule scope :premises (@p191)) % 0.33/0.58 (step-pop @p193 :rule scope :premises (@p192)) % 0.33/0.58 (step @p163 :rule process_scope :premises (@p193) :args (false)) % 0.33/0.58 (assume-push @p194 @t23) % 0.33/0.58 (assume-push @p195 @t55) % 0.33/0.58 (assume-push @p196 @t53) % 0.33/0.58 (step @p170 :rule and_intro :premises (@p73 @p49 @p89)) % 0.33/0.58 (step-pop @p197 :rule scope :premises (@p170)) % 0.33/0.58 (step-pop @p198 :rule scope :premises (@p197)) % 0.33/0.58 (step-pop @p199 :rule scope :premises (@p198)) % 0.33/0.58 (step @p171 :rule process_scope :premises (@p199) :args (@t70)) % 0.33/0.58 (step @p175 :rule implies_elim :premises (@p171)) % 0.33/0.58 (step @p176 :rule resolution :premises (@p175 @p163) :args (true @t70)) % 0.33/0.58 (step @p177 :rule not_and :premises (@p176)) % 0.33/0.58 (step @p178 :rule eq_resolve :premises (@p177 @p93)) % 0.33/0.58 (step @p179 false :rule chain_m_resolution :premises (@p178 @p89 @p73 @p49) :args (false (@list false true true) (@list @t53 @t39 @t22))) % 0.33/0.58 ) % 0.33/0.58 % SZS output end Proof % 0.33/0.58 % cvc5 exiting %------------------------------------------------------------------------------