%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM913_1 : TPTP v9.2.1. Released v5.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n007.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 08:40:58 AM UTC 2026 % Result : Theorem 0.39s 0.55s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM913_1 : TPTP v9.2.1. Released v5.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n007.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 12:30:56 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.48 %----Proving TF0_ARI % 0.39/0.55 --- Run --finite-model-find --decision=internal at 45... % 0.39/0.55 % SZS status Theorem % 0.39/0.55 % SZS output start Proof % 0.39/0.55 ( % 0.39/0.55 (define @t1 () (@var "Y" Real)) % 0.39/0.55 (define @t2 () (@var "X" Real)) % 0.39/0.55 (define @t3 () (= @t2 @t1)) % 0.39/0.55 (define @t4 () (or (< @t2 @t1) @t3)) % 0.39/0.55 (define @t5 () (= (<= @t2 @t1) @t4)) % 0.39/0.55 (define @t6 () (@list @t2 @t1)) % 0.39/0.55 (define @t7 () (forall @t6 @t5)) % 0.39/0.55 (define @t8 () (not @t7)) % 0.39/0.55 (define @t9 () (+ @t2 (* -1/1 @t1))) % 0.39/0.55 (define @t10 () (>= @t9 0/1)) % 0.39/0.55 (define @t11 () (+ (* -1/1 @t2) @t1)) % 0.39/0.55 (define @t12 () (>= @t11 0/1)) % 0.39/0.55 (define @t13 () (forall @t6 (= @t12 (or (not @t10) @t3)))) % 0.39/0.55 (define @t14 () (@quantifiers_skolemize @t13 1)) % 0.39/0.55 (define @t15 () (* -1/1 @t14)) % 0.39/0.55 (define @t16 () (@quantifiers_skolemize @t13 0)) % 0.39/0.55 (define @t17 () (+ @t16 @t15)) % 0.39/0.55 (define @t18 () (>= @t17 0/1)) % 0.39/0.55 (define @t19 () (= @t16 @t14)) % 0.39/0.55 (define @t20 () (not @t18)) % 0.39/0.55 (define @t21 () (or @t20 @t19)) % 0.39/0.55 (define @t22 () (>= @t2 @t1)) % 0.39/0.55 (define @t23 () (* -1/1 @t16)) % 0.39/0.55 (define @t24 () (+ @t23 @t14)) % 0.39/0.55 (define @t25 () (>= @t24 0/1)) % 0.39/0.55 (define @t26 () (= @t25 @t21)) % 0.39/0.55 (define @t27 () (not @t25)) % 0.39/0.55 (define @t28 () (not @t19)) % 0.39/0.55 (define @t29 () (>= 0/1 @t17)) % 0.39/0.55 (define @t30 () (not @t29)) % 0.39/0.55 (define @t31 () (* -1/1 (- @t16 @t14))) % 0.39/0.55 (define @t32 () (* -1/1 (- @t17 0/1))) % 0.39/0.55 (define @t33 () (= @t32 @t31)) % 0.39/0.55 (define @t34 () (= @t17 0/1)) % 0.39/0.55 (define @t35 () (= @t34 @t19)) % 0.39/0.55 (define @t36 () (* 1/1 (- @t24 0/1))) % 0.39/0.55 (define @t37 () (= (* 1/1 (- 0/1 @t17)) @t36)) % 0.39/0.55 (define @t38 () (= @t29 @t25)) % 0.39/0.55 (define @t39 () (and @t18 @t28 @t25)) % 0.39/0.55 (define @t40 () (>= @t16 @t14)) % 0.39/0.55 (define @t41 () (>= @t14 @t16)) % 0.39/0.55 (define @t42 () (<= @t16 @t14)) % 0.39/0.55 (define @t43 () (not @t40)) % 0.39/0.55 (define @t44 () (not @t42)) % 0.39/0.55 (define @t45 () (not true)) % 0.39/0.55 (define @t46 () (>= 0/1 0/1)) % 0.39/0.55 (define @t47 () (+ @t15 @t14)) % 0.39/0.55 (define @t48 () (+ @t23 @t16)) % 0.39/0.55 (define @t49 () (>= @t48 @t47)) % 0.39/0.55 (define @t50 () (< -1/1 0/1)) % 0.39/0.55 (define @t51 () (* -1/1 0/1)) % 0.39/0.55 (define @t52 () (+ 0/1 @t51)) % 0.39/0.55 (define @t53 () (* 0/1 @t16)) % 0.39/0.55 (define @t54 () (* 0/1 @t14)) % 0.39/0.55 (define @t55 () (+ @t54 @t53)) % 0.39/0.55 (define @t56 () (+ @t17 (* -1/1 @t17))) % 0.39/0.55 (define @t57 () (>= @t56 @t52)) % 0.39/0.55 (assume @p1 @t8) % 0.39/0.55 (assume @p2 true) % 0.39/0.55 (step @p3 :rule bool-double-not-elim :args (@t18)) % 0.39/0.55 (step @p4 :rule refl :args (@t21)) % 0.39/0.55 (step @p5 :rule nary_cong :premises (@p4 @p3) :args ((or @t21 (not @t20)))) % 0.39/0.55 (step @p6 :rule cnf_or_neg :args (@t21 0)) % 0.39/0.55 (step @p7 :rule eq_resolve :premises (@p6 @p5)) % 0.39/0.55 (step @p8 :rule reordering :premises (@p7) :args ((or @t18 @t21))) % 0.39/0.55 (step @p9 :rule cnf_or_neg :args (@t21 1)) % 0.39/0.55 (step @p10 :rule refl :args (@t3)) % 0.39/0.55 (step @p11 :rule arith_poly_norm :args ((= (* 1/1 (- @t2 @t1)) (* 1/1 (- @t9 0/1))))) % 0.39/0.55 (step @p12 :rule arith_poly_norm_rel :premises (@p11) :args ((= @t22 @t10))) % 0.39/0.55 (step @p13 :rule cong :premises (@p12) :args ((not @t22))) % 0.39/0.55 (step @p14 :rule arith-elim-lt :args (@t2 @t1)) % 0.39/0.55 (step @p15 :rule trans :premises (@p14 @p13)) % 0.39/0.55 (step @p16 :rule nary_cong :premises (@p15 @p10) :args (@t4)) % 0.39/0.55 (step @p17 :rule arith_poly_norm :args ((= (* -1/1 (- @t1 @t2)) (* -1/1 (- @t11 0/1))))) % 0.39/0.55 (step @p18 :rule arith_poly_norm_rel :premises (@p17) :args ((= (>= @t1 @t2) @t12))) % 0.39/0.55 (step @p19 :rule arith-elim-leq :args (@t2 @t1)) % 0.39/0.55 (step @p20 :rule trans :premises (@p19 @p18)) % 0.39/0.55 (step @p21 :rule cong :premises (@p20 @p16) :args (@t5)) % 0.39/0.55 (step @p22 :rule cong :premises (@p21) :args (@t7)) % 0.39/0.55 (step @p23 :rule cong :premises (@p22) :args (@t8)) % 0.39/0.55 (step @p24 :rule eq_resolve :premises (@p1 @p23)) % 0.39/0.55 (step @p25 :rule skolemize :premises (@p24)) % 0.39/0.55 (step @p26 :rule cnf_equiv_neg1 :args (@t26)) % 0.39/0.55 (step @p27 :rule reordering :premises (@p26) :args ((or @t25 @t21 @t26))) % 0.39/0.55 (step @p28 :rule bool-double-not-elim :args (@t19)) % 0.39/0.55 (step @p29 :rule refl :args (@t20)) % 0.39/0.55 (step @p30 :rule refl :args (@t27)) % 0.39/0.55 (step @p31 :rule nary_cong :premises (@p30 @p29 @p28) :args ((or @t27 @t20 (not @t28)))) % 0.39/0.55 (assume-push @p175 @t18) % 0.39/0.55 (assume-push @p176 @t28) % 0.39/0.55 (assume-push @p177 @t25) % 0.39/0.55 (step @p35 :rule arith-elim-leq :args (@t17 0/1)) % 0.39/0.55 (step @p36 :rule symm :premises (@p35)) % 0.39/0.55 (step @p37 :rule cong :premises (@p36) :args (@t30)) % 0.39/0.55 (step @p38 :rule arith-elim-gt :args (@t17 0/1)) % 0.39/0.55 (step @p39 :rule trans :premises (@p38 @p37)) % 0.39/0.55 (step @p40 :rule arith_poly_norm :args (@t33)) % 0.39/0.55 (step @p41 :rule arith_poly_norm_rel :premises (@p40) :args (@t35)) % 0.39/0.55 (step @p42 :rule cong :premises (@p41) :args ((not @t34))) % 0.39/0.55 (step @p43 :rule symm :premises (@p42)) % 0.39/0.55 (step @p44 :rule eq_resolve :premises (@p176 @p43)) % 0.39/0.55 (step @p45 :rule arith_trichotomy :premises (@p175 @p44)) % 0.39/0.55 (step @p46 :rule eq_resolve :premises (@p45 @p39)) % 0.39/0.55 (step @p47 :rule arith_poly_norm :args (@t37)) % 0.39/0.55 (step @p48 :rule arith_poly_norm_rel :premises (@p47) :args (@t38)) % 0.39/0.55 (step @p49 :rule trans :premises (@p35 @p48)) % 0.39/0.55 (step @p50 :rule symm :premises (@p49)) % 0.39/0.55 (step @p51 :rule eq_resolve :premises (@p177 @p50)) % 0.39/0.55 (step @p52 false :rule contra :premises (@p51 @p46)) % 0.39/0.55 (step-pop @p178 :rule scope :premises (@p52)) % 0.39/0.55 (step-pop @p179 :rule scope :premises (@p178)) % 0.39/0.55 (step-pop @p180 :rule scope :premises (@p179)) % 0.39/0.55 (step @p53 :rule process_scope :premises (@p180) :args (false)) % 0.39/0.55 (assume-push @p181 @t25) % 0.39/0.55 (assume-push @p182 @t18) % 0.39/0.55 (assume-push @p183 @t28) % 0.39/0.55 (step @p60 :rule and_intro :premises (@p182 @p183 @p181)) % 0.39/0.55 (step-pop @p184 :rule scope :premises (@p60)) % 0.39/0.55 (step-pop @p185 :rule scope :premises (@p184)) % 0.39/0.55 (step-pop @p186 :rule scope :premises (@p185)) % 0.39/0.55 (step @p61 :rule process_scope :premises (@p186) :args (@t39)) % 0.39/0.55 (step @p65 :rule implies_elim :premises (@p61)) % 0.39/0.55 (step @p66 :rule resolution :premises (@p65 @p53) :args (true @t39)) % 0.39/0.55 (step @p67 :rule not_and :premises (@p66)) % 0.39/0.55 (step @p68 :rule eq_resolve :premises (@p67 @p31)) % 0.39/0.55 (step @p69 :rule reordering :premises (@p68) :args ((or @t20 @t19 @t27))) % 0.39/0.55 (step @p70 :rule chain_m_resolution :premises (@p69 @p27 @p25 @p9 @p8) :args (@t21 (@list false true true false) (@list @t25 @t26 @t19 @t18))) % 0.39/0.55 (step @p71 :rule cnf_equiv_neg2 :args (@t26)) % 0.39/0.55 (step @p72 :rule chain_m_resolution :premises (@p71 @p25 @p70) :args (@t27 (@list true false) (@list @t26 @t21))) % 0.39/0.55 (step @p73 :rule arith_poly_norm :args ((= @t31 @t32))) % 0.39/0.55 (step @p74 :rule arith_poly_norm_rel :premises (@p73) :args ((= @t40 @t18))) % 0.39/0.55 (step @p75 :rule arith_poly_norm :args ((= (* 1/1 (- @t14 @t16)) @t36))) % 0.39/0.55 (step @p76 :rule arith_poly_norm_rel :premises (@p75) :args ((= @t41 @t25))) % 0.39/0.55 (step @p77 :rule arith-elim-leq :args (@t16 @t14)) % 0.39/0.55 (step @p78 :rule trans :premises (@p77 @p76)) % 0.39/0.55 (step @p79 :rule nary_cong :premises (@p78 @p74) :args ((or @t42 @t40))) % 0.39/0.55 (step @p80 :rule symm :premises (@p79)) % 0.39/0.55 (step @p81 :rule bool-double-not-elim :args (@t40)) % 0.39/0.55 (step @p82 :rule trans :premises (@p81 @p74)) % 0.39/0.55 (step @p83 :rule bool-double-not-elim :args (@t42)) % 0.39/0.55 (step @p84 :rule trans :premises (@p83 @p78)) % 0.39/0.55 (step @p85 :rule nary_cong :premises (@p84 @p82) :args ((or (not @t44) (not @t43)))) % 0.39/0.55 (step @p86 :rule trans :premises (@p85 @p80)) % 0.39/0.55 (assume-push @p187 @t44) % 0.39/0.55 (assume-push @p188 @t43) % 0.39/0.55 (step @p89 :rule evaluate :args (@t45)) % 0.39/0.55 (step @p90 :rule evaluate :args (@t46)) % 0.39/0.55 (step @p91 :rule arith_poly_norm :args ((= @t47 0/1))) % 0.39/0.55 (step @p92 :rule arith_poly_norm :args ((= @t48 0/1))) % 0.39/0.55 (step @p93 :rule cong :premises (@p92 @p91) :args (@t49)) % 0.39/0.55 (step @p94 :rule trans :premises (@p93 @p90)) % 0.39/0.55 (step @p95 :rule cong :premises (@p94) :args ((not @t49))) % 0.39/0.55 (step @p96 :rule trans :premises (@p95 @p89)) % 0.39/0.55 (step @p97 :rule arith-elim-lt :args (@t48 @t47)) % 0.39/0.55 (step @p98 :rule trans :premises (@p97 @p96)) % 0.39/0.55 (step @p99 :rule cong :premises (@p74) :args (@t43)) % 0.39/0.55 (step @p100 :rule arith-elim-lt :args (@t16 @t14)) % 0.39/0.55 (step @p101 :rule trans :premises (@p100 @p99)) % 0.39/0.55 (step @p102 :rule symm :premises (@p101)) % 0.39/0.55 (step @p103 :rule trans :premises (@p99 @p102)) % 0.39/0.55 (step @p104 :rule eq_resolve :premises (@p188 @p103)) % 0.39/0.55 (step @p105 :rule arith_mult_neg :args (-1/1 (> @t16 @t14))) % 0.39/0.55 (step @p106 :rule cong :premises (@p78) :args (@t44)) % 0.39/0.55 (step @p107 :rule symm :premises (@p77)) % 0.39/0.55 (step @p108 :rule cong :premises (@p107) :args ((not @t41))) % 0.39/0.55 (step @p109 :rule arith-elim-gt :args (@t16 @t14)) % 0.39/0.55 (step @p110 :rule trans :premises (@p109 @p108)) % 0.39/0.55 (step @p111 :rule trans :premises (@p110 @p106)) % 0.39/0.55 (step @p112 :rule symm :premises (@p111)) % 0.39/0.55 (step @p113 :rule trans :premises (@p106 @p112)) % 0.39/0.55 (step @p114 :rule eq_resolve :premises (@p187 @p113)) % 0.39/0.55 (step @p115 :rule evaluate :args (@t50)) % 0.39/0.55 (step @p116 :rule true_elim :premises (@p115)) % 0.39/0.55 (step @p117 :rule and_intro :premises (@p116 @p114)) % 0.39/0.55 (step @p118 :rule modus_ponens :premises (@p117 @p105)) % 0.39/0.55 (step @p119 :rule arith_sum_ub :premises (@p118 @p104)) % 0.39/0.56 (step @p120 false :rule eq_resolve :premises (@p119 @p98)) % 0.39/0.56 (step-pop @p189 :rule scope :premises (@p120)) % 0.39/0.56 (step-pop @p190 :rule scope :premises (@p189)) % 0.39/0.56 (step @p121 :rule process_scope :premises (@p190) :args (false)) % 0.39/0.56 (step @p124 :rule not_and :premises (@p121)) % 0.39/0.56 (step @p125 :rule eq_resolve :premises (@p124 @p86)) % 0.39/0.56 (step @p126 :rule eq_resolve :premises (@p125 @p79)) % 0.39/0.56 (step @p127 :rule chain_m_resolution :premises (@p126 @p72) :args (@t18 (@list true) (@list @t25))) % 0.39/0.56 (step @p128 :rule cnf_or_pos :args (@t21)) % 0.39/0.56 (step @p129 :rule reordering :premises (@p128) :args ((or @t20 @t19 (not @t21)))) % 0.39/0.56 (step @p130 :rule chain_m_resolution :premises (@p129 @p127 @p70) :args (@t19 (@list false false) (@list @t18 @t21))) % 0.39/0.56 (step @p131 :rule bool-double-not-elim :args (@t25)) % 0.39/0.56 (step @p132 :rule refl :args (@t28)) % 0.39/0.56 (step @p133 :rule nary_cong :premises (@p132 @p131) :args ((or @t28 (not @t27)))) % 0.39/0.56 (assume-push @p191 @t19) % 0.39/0.56 (assume-push @p192 @t27) % 0.39/0.56 (assume-push @p193 @t34) % 0.39/0.56 (step @p89 :rule evaluate :args (@t45)) % 0.39/0.56 (step @p90 :rule evaluate :args (@t46)) % 0.39/0.56 (step @p137 :rule evaluate :args ((+ 0/1 0/1))) % 0.39/0.56 (step @p138 :rule evaluate :args (@t51)) % 0.39/0.56 (step @p139 :rule refl :args (0/1)) % 0.39/0.56 (step @p140 :rule nary_cong :premises (@p139 @p138) :args (@t52)) % 0.39/0.56 (step @p141 :rule trans :premises (@p140 @p137)) % 0.39/0.56 (step @p142 :rule arith_poly_norm :args ((= @t53 0/1))) % 0.39/0.56 (step @p143 :rule arith_poly_norm :args ((= @t54 0/1))) % 0.39/0.56 (step @p144 :rule nary_cong :premises (@p143 @p142) :args (@t55)) % 0.39/0.56 (step @p145 :rule trans :premises (@p144 @p137)) % 0.39/0.56 (step @p146 :rule arith_poly_norm :args ((= @t56 @t55))) % 0.39/0.56 (step @p147 :rule trans :premises (@p146 @p145)) % 0.39/0.56 (step @p148 :rule cong :premises (@p147 @p141) :args (@t57)) % 0.39/0.56 (step @p149 :rule trans :premises (@p148 @p90)) % 0.39/0.56 (step @p150 :rule cong :premises (@p149) :args ((not @t57))) % 0.39/0.56 (step @p151 :rule trans :premises (@p150 @p89)) % 0.39/0.56 (step @p152 :rule arith-elim-lt :args (@t56 @t52)) % 0.39/0.56 (step @p153 :rule trans :premises (@p152 @p151)) % 0.39/0.56 (step @p154 :rule arith_mult_neg :args (-1/1 (> @t17 0/1))) % 0.39/0.56 (step @p47 :rule arith_poly_norm :args (@t37)) % 0.39/0.56 (step @p48 :rule arith_poly_norm_rel :premises (@p47) :args (@t38)) % 0.39/0.56 (step @p35 :rule arith-elim-leq :args (@t17 0/1)) % 0.39/0.56 (step @p49 :rule trans :premises (@p35 @p48)) % 0.39/0.56 (step @p155 :rule cong :premises (@p49) :args ((not (<= @t17 0/1)))) % 0.39/0.56 (step @p36 :rule symm :premises (@p35)) % 0.39/0.56 (step @p37 :rule cong :premises (@p36) :args (@t30)) % 0.39/0.56 (step @p38 :rule arith-elim-gt :args (@t17 0/1)) % 0.39/0.56 (step @p39 :rule trans :premises (@p38 @p37)) % 0.39/0.56 (step @p156 :rule trans :premises (@p39 @p155)) % 0.39/0.56 (step @p157 :rule symm :premises (@p156)) % 0.39/0.56 (step @p158 :rule eq_resolve :premises (@p192 @p157)) % 0.39/0.56 (step @p115 :rule evaluate :args (@t50)) % 0.39/0.56 (step @p116 :rule true_elim :premises (@p115)) % 0.39/0.56 (step @p159 :rule and_intro :premises (@p116 @p158)) % 0.39/0.56 (step @p160 :rule modus_ponens :premises (@p159 @p154)) % 0.39/0.56 (step @p161 :rule arith_sum_ub :premises (@p193 @p160)) % 0.39/0.56 (step @p162 false :rule eq_resolve :premises (@p161 @p153)) % 0.39/0.56 (step-pop @p194 :rule scope :premises (@p162)) % 0.39/0.56 (step @p163 :rule process_scope :premises (@p194) :args (false)) % 0.39/0.56 (step @p40 :rule arith_poly_norm :args (@t33)) % 0.39/0.56 (step @p41 :rule arith_poly_norm_rel :premises (@p40) :args (@t35)) % 0.39/0.56 (step @p165 :rule symm :premises (@p41)) % 0.39/0.56 (step @p166 :rule eq_resolve :premises (@p191 @p165)) % 0.39/0.56 (step @p167 false :rule contra :premises (@p166 @p163)) % 0.39/0.56 (step-pop @p195 :rule scope :premises (@p167)) % 0.39/0.56 (step-pop @p196 :rule scope :premises (@p195)) % 0.39/0.56 (step @p168 :rule process_scope :premises (@p196) :args (false)) % 0.39/0.56 (step @p171 :rule not_and :premises (@p168)) % 0.39/0.56 (step @p172 :rule eq_resolve :premises (@p171 @p133)) % 0.39/0.56 (step @p173 :rule reordering :premises (@p172) :args ((or @t25 @t28))) % 0.39/0.56 (step @p174 false :rule chain_m_resolution :premises (@p173 @p130 @p72) :args (false (@list false true) (@list @t19 @t25))) % 0.39/0.56 ) % 0.39/0.56 % SZS output end Proof % 0.39/0.56 % cvc5 exiting %------------------------------------------------------------------------------