%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ARI610_1 : TPTP v9.2.1. Released v5.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n017.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 08:07:58 AM UTC 2026 % Result : Theorem 0.44s 0.66s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ARI610_1 : TPTP v9.2.1. Released v5.1.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n017.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Jun 3 02:28:31 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.50 %----Proving TF0_ARI % 0.44/0.66 --- Run --finite-model-find --decision=internal at 45... % 0.44/0.66 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 60... % 0.44/0.66 % SZS status Theorem % 0.44/0.66 % SZS output start Proof % 0.44/0.66 ( % 0.44/0.66 (declare-const tptp.f (-> Int Int)) % 0.44/0.66 (declare-const tptp.a Int) % 0.44/0.66 (declare-const tptp.b Int) % 0.44/0.66 (define @t1 () (- tptp.b)) % 0.44/0.66 (define @t2 () (+ tptp.a @t1)) % 0.44/0.66 (define @t3 () (tptp.f @t2)) % 0.44/0.66 (define @t4 () (tptp.f 0)) % 0.44/0.66 (define @t5 () (<= @t4 @t3)) % 0.44/0.66 (define @t6 () (tptp.f tptp.a)) % 0.44/0.66 (define @t7 () (tptp.f tptp.b)) % 0.44/0.66 (define @t8 () (@var "Y" Int)) % 0.44/0.66 (define @t9 () (tptp.f @t8)) % 0.44/0.66 (define @t10 () (@var "X" Int)) % 0.44/0.66 (define @t11 () (tptp.f @t10)) % 0.44/0.66 (define @t12 () (=> (<= @t10 @t8) (<= @t11 @t9))) % 0.44/0.66 (define @t13 () (@list @t10 @t8)) % 0.44/0.66 (define @t14 () (forall @t13 @t12)) % 0.44/0.66 (define @t15 () (and @t14 (< @t7 @t6))) % 0.44/0.66 (define @t16 () (=> @t15 @t5)) % 0.44/0.66 (define @t17 () (not @t16)) % 0.44/0.66 (define @t18 () (* -1 tptp.b)) % 0.44/0.66 (define @t19 () (+ tptp.a @t18)) % 0.44/0.66 (define @t20 () (tptp.f @t19)) % 0.44/0.66 (define @t21 () (+ @t4 (* -1 @t20))) % 0.44/0.66 (define @t22 () (+ @t20 1)) % 0.44/0.66 (define @t23 () (>= @t21 1)) % 0.44/0.66 (define @t24 () (>= @t4 @t22)) % 0.44/0.66 (define @t25 () (+ @t7 (* -1 @t6))) % 0.44/0.66 (define @t26 () (>= @t25 0)) % 0.44/0.66 (define @t27 () (>= @t7 @t6)) % 0.44/0.66 (define @t28 () (+ @t11 (* -1 @t9))) % 0.44/0.66 (define @t29 () (>= @t28 1)) % 0.44/0.66 (define @t30 () (not @t29)) % 0.44/0.66 (define @t31 () (+ @t10 (* -1 @t8))) % 0.44/0.66 (define @t32 () (>= @t31 1)) % 0.44/0.66 (define @t33 () (not @t32)) % 0.44/0.66 (define @t34 () (+ @t9 1)) % 0.44/0.66 (define @t35 () (>= @t11 @t34)) % 0.44/0.66 (define @t36 () (+ @t8 1)) % 0.44/0.66 (define @t37 () (>= @t10 @t36)) % 0.44/0.66 (define @t38 () (* -1 @t7)) % 0.44/0.66 (define @t39 () (+ @t38 @t6)) % 0.44/0.66 (define @t40 () (+ @t25 1)) % 0.44/0.66 (define @t41 () (+ @t6 @t38)) % 0.44/0.66 (define @t42 () (>= @t41 1)) % 0.44/0.66 (define @t43 () (not @t42)) % 0.44/0.66 (define @t44 () (>= @t19 1)) % 0.44/0.66 (define @t45 () (or @t44 @t43)) % 0.44/0.66 (define @t46 () (forall @t13 (or @t32 @t30))) % 0.44/0.66 (define @t47 () (or @t44 @t26)) % 0.44/0.66 (define @t48 () (@list false)) % 0.44/0.66 (define @t49 () (@list true false)) % 0.44/0.66 (define @t50 () (>= @t19 0)) % 0.44/0.66 (define @t51 () (>= tptp.a tptp.b)) % 0.44/0.66 (define @t52 () (+ tptp.b 1)) % 0.44/0.66 (define @t53 () (>= tptp.a @t52)) % 0.44/0.66 (define @t54 () (<= tptp.a tptp.b)) % 0.44/0.66 (define @t55 () (not @t51)) % 0.44/0.66 (define @t56 () (not @t54)) % 0.44/0.66 (define @t57 () (+ @t18 tptp.b)) % 0.44/0.66 (define @t58 () (* -1 tptp.a)) % 0.44/0.66 (define @t59 () (+ @t58 tptp.a)) % 0.44/0.66 (define @t60 () (>= @t59 @t57)) % 0.44/0.66 (define @t61 () (not @t23)) % 0.44/0.66 (define @t62 () (not @t50)) % 0.44/0.66 (define @t63 () (or @t62 @t61)) % 0.44/0.66 (define @t64 () (not @t63)) % 0.44/0.66 (define @t65 () (+ @t58 tptp.b)) % 0.44/0.66 (define @t66 () (+ @t19 1)) % 0.44/0.66 (define @t67 () (* -1 @t19)) % 0.44/0.66 (define @t68 () (+ 0 @t67)) % 0.44/0.66 (define @t69 () (>= @t68 1)) % 0.44/0.66 (define @t70 () (or @t69 @t61)) % 0.44/0.66 (assume @p1 @t17) % 0.44/0.66 (assume @p2 true) % 0.44/0.66 (step @p3 :rule arith_poly_norm :args ((= (* -1 (- @t4 @t22)) (* -1 (- @t21 1))))) % 0.44/0.66 (step @p4 :rule arith_poly_norm_rel :premises (@p3) :args ((= @t24 @t23))) % 0.44/0.66 (step @p5 :rule cong :premises (@p4) :args ((not @t24))) % 0.44/0.66 (step @p6 :rule arith-leq-norm :args (@t4 @t20)) % 0.44/0.66 (step @p7 :rule trans :premises (@p6 @p5)) % 0.44/0.66 (step @p8 :rule arith_poly_norm :args ((= @t1 @t18))) % 0.44/0.66 (step @p9 :rule refl :args (tptp.a)) % 0.44/0.66 (step @p10 :rule nary_cong :premises (@p9 @p8) :args (@t2)) % 0.44/0.66 (step @p11 :rule cong :premises (@p10) :args (@t3)) % 0.44/0.66 (step @p12 :rule refl :args (@t4)) % 0.44/0.66 (step @p13 :rule cong :premises (@p12 @p11) :args (@t5)) % 0.44/0.66 (step @p14 :rule trans :premises (@p13 @p7)) % 0.44/0.66 (step @p15 :rule arith_poly_norm :args ((= (* 1 (- @t7 @t6)) (* 1 (- @t25 0))))) % 0.44/0.66 (step @p16 :rule arith_poly_norm_rel :premises (@p15) :args ((= @t27 @t26))) % 0.44/0.66 (step @p17 :rule cong :premises (@p16) :args ((not @t27))) % 0.44/0.66 (step @p18 :rule arith-elim-lt :args (@t7 @t6)) % 0.44/0.66 (step @p19 :rule trans :premises (@p18 @p17)) % 0.44/0.66 (step @p20 :rule refl :args (@t30)) % 0.44/0.66 (step @p21 :rule bool-double-not-elim :args (@t32)) % 0.44/0.66 (step @p22 :rule nary_cong :premises (@p21 @p20) :args ((or (not @t33) @t30))) % 0.44/0.66 (step @p23 :rule bool-impl-elim :args (@t33 @t30)) % 0.44/0.66 (step @p24 :rule trans :premises (@p23 @p22)) % 0.44/0.66 (step @p25 :rule cong :premises (@p24) :args ((forall @t13 (=> @t33 @t30)))) % 0.44/0.66 (step @p26 :rule arith_poly_norm :args ((= (* -1 (- @t11 @t34)) (* -1 (- @t28 1))))) % 0.44/0.66 (step @p27 :rule arith_poly_norm_rel :premises (@p26) :args ((= @t35 @t29))) % 0.44/0.66 (step @p28 :rule cong :premises (@p27) :args ((not @t35))) % 0.44/0.66 (step @p29 :rule arith-leq-norm :args (@t11 @t9)) % 0.44/0.66 (step @p30 :rule trans :premises (@p29 @p28)) % 0.44/0.66 (step @p31 :rule arith_poly_norm :args ((= (* -1 (- @t10 @t36)) (* -1 (- @t31 1))))) % 0.44/0.66 (step @p32 :rule arith_poly_norm_rel :premises (@p31) :args ((= @t37 @t32))) % 0.44/0.66 (step @p33 :rule cong :premises (@p32) :args ((not @t37))) % 0.44/0.66 (step @p34 :rule arith-leq-norm :args (@t10 @t8)) % 0.44/0.66 (step @p35 :rule trans :premises (@p34 @p33)) % 0.44/0.66 (step @p36 :rule cong :premises (@p35 @p30) :args (@t12)) % 0.44/0.66 (step @p37 :rule cong :premises (@p36) :args (@t14)) % 0.44/0.66 (step @p38 :rule trans :premises (@p37 @p25)) % 0.44/0.66 (step @p39 :rule nary_cong :premises (@p38 @p19) :args (@t15)) % 0.44/0.66 (step @p40 :rule cong :premises (@p39 @p14) :args (@t16)) % 0.44/0.66 (step @p41 :rule cong :premises (@p40) :args (@t17)) % 0.44/0.66 (step @p42 :rule eq_resolve :premises (@p1 @p41)) % 0.44/0.66 (step @p43 :rule not_implies_elim1 :premises (@p42)) % 0.44/0.66 (step @p44 :rule and_elim :premises (@p43) :args (0)) % 0.44/0.66 (step @p45 :rule bool-double-not-elim :args (@t26)) % 0.44/0.66 (step @p46 :rule arith_poly_norm :args ((= (* -1 (- 0 @t40)) (* -1 (- @t39 1))))) % 0.44/0.66 (step @p47 :rule arith_poly_norm_rel :premises (@p46) :args ((= (>= 0 @t40) (>= @t39 1)))) % 0.44/0.66 (step @p48 :rule arith-geq-tighten :args (@t25 0)) % 0.44/0.66 (step @p49 :rule trans :premises (@p48 @p47)) % 0.44/0.66 (step @p50 :rule symm :premises (@p49)) % 0.44/0.66 (step @p51 :rule refl :args (1)) % 0.44/0.66 (step @p52 :rule arith_poly_norm :args ((= @t41 @t39))) % 0.44/0.66 (step @p53 :rule cong :premises (@p52 @p51) :args (@t42)) % 0.44/0.66 (step @p54 :rule trans :premises (@p53 @p50)) % 0.44/0.66 (step @p55 :rule cong :premises (@p54) :args (@t43)) % 0.44/0.66 (step @p56 :rule trans :premises (@p55 @p45)) % 0.44/0.66 (step @p57 :rule refl :args (@t44)) % 0.44/0.66 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t45)) % 0.44/0.66 (step @p59 :rule refl :args (@t46)) % 0.44/0.66 (step @p60 :rule cong :premises (@p59 @p58) :args ((=> @t46 @t45))) % 0.44/0.66 (assume-push @p158 @t46) % 0.44/0.66 (step @p62 :rule instantiate :premises (@p44) :args ((@list tptp.a tptp.b))) % 0.44/0.66 (step-pop @p159 :rule scope :premises (@p62)) % 0.44/0.66 (step @p63 :rule process_scope :premises (@p159) :args (@t45)) % 0.44/0.66 (step @p65 :rule eq_resolve :premises (@p63 @p60)) % 0.44/0.66 (step @p66 :rule implies_elim :premises (@p65)) % 0.44/0.66 (step @p67 :rule chain_m_resolution :premises (@p66 @p44) :args (@t47 @t48 (@list @t46))) % 0.44/0.66 (step @p68 :rule and_elim :premises (@p43) :args (1)) % 0.44/0.66 (step @p69 :rule cnf_or_pos :args (@t47)) % 0.44/0.66 (step @p70 :rule reordering :premises (@p69) :args ((or @t26 @t44 (not @t47)))) % 0.44/0.66 (step @p71 :rule chain_m_resolution :premises (@p70 @p68 @p67) :args (@t44 @t49 (@list @t26 @t47))) % 0.44/0.66 (step @p72 :rule arith_poly_norm :args ((= (* 1 (- tptp.a tptp.b)) (* 1 (- @t19 0))))) % 0.44/0.66 (step @p73 :rule arith_poly_norm_rel :premises (@p72) :args ((= @t51 @t50))) % 0.44/0.66 (step @p74 :rule arith_poly_norm :args ((= (* -1 (- tptp.a @t52)) (* -1 (- @t19 1))))) % 0.44/0.66 (step @p75 :rule arith_poly_norm_rel :premises (@p74) :args ((= @t53 @t44))) % 0.44/0.66 (step @p76 :rule cong :premises (@p75) :args ((not @t53))) % 0.44/0.66 (step @p77 :rule arith-leq-norm :args (tptp.a tptp.b)) % 0.44/0.66 (step @p78 :rule trans :premises (@p77 @p76)) % 0.44/0.66 (step @p79 :rule nary_cong :premises (@p78 @p73) :args ((or @t54 @t51))) % 0.44/0.66 (step @p80 :rule symm :premises (@p79)) % 0.44/0.66 (step @p81 :rule bool-double-not-elim :args (@t51)) % 0.44/0.66 (step @p82 :rule trans :premises (@p81 @p73)) % 0.44/0.66 (step @p83 :rule bool-double-not-elim :args (@t54)) % 0.44/0.66 (step @p84 :rule trans :premises (@p83 @p78)) % 0.44/0.66 (step @p85 :rule nary_cong :premises (@p84 @p82) :args ((or (not @t56) (not @t55)))) % 0.44/0.66 (step @p86 :rule trans :premises (@p85 @p80)) % 0.44/0.66 (assume-push @p160 @t56) % 0.44/0.66 (assume-push @p161 @t55) % 0.44/0.66 (step @p89 :rule evaluate :args ((not true))) % 0.44/0.66 (step @p90 :rule evaluate :args ((>= 0 0))) % 0.44/0.66 (step @p91 :rule arith_poly_norm :args ((= @t57 0))) % 0.44/0.66 (step @p92 :rule arith_poly_norm :args ((= @t59 0))) % 0.44/0.66 (step @p93 :rule cong :premises (@p92 @p91) :args (@t60)) % 0.44/0.66 (step @p94 :rule trans :premises (@p93 @p90)) % 0.44/0.66 (step @p95 :rule cong :premises (@p94) :args ((not @t60))) % 0.44/0.66 (step @p96 :rule trans :premises (@p95 @p89)) % 0.44/0.66 (step @p97 :rule arith-elim-lt :args (@t59 @t57)) % 0.44/0.66 (step @p98 :rule trans :premises (@p97 @p96)) % 0.44/0.66 (step @p99 :rule cong :premises (@p73) :args (@t55)) % 0.44/0.66 (step @p100 :rule arith-elim-lt :args (tptp.a tptp.b)) % 0.44/0.66 (step @p101 :rule trans :premises (@p100 @p99)) % 0.44/0.66 (step @p102 :rule symm :premises (@p101)) % 0.44/0.66 (step @p103 :rule trans :premises (@p99 @p102)) % 0.44/0.66 (step @p104 :rule eq_resolve :premises (@p161 @p103)) % 0.44/0.66 (step @p105 :rule arith_mult_neg :args (-1 (> tptp.a tptp.b))) % 0.44/0.66 (step @p106 :rule bool-double-not-elim :args (@t44)) % 0.44/0.66 (step @p107 :rule cong :premises (@p78) :args (@t56)) % 0.44/0.66 (step @p108 :rule trans :premises (@p107 @p106)) % 0.44/0.66 (step @p109 :rule arith-elim-leq :args (tptp.a tptp.b)) % 0.44/0.66 (step @p110 :rule symm :premises (@p109)) % 0.44/0.66 (step @p111 :rule cong :premises (@p110) :args ((not (>= tptp.b tptp.a)))) % 0.44/0.66 (step @p112 :rule arith-elim-gt :args (tptp.a tptp.b)) % 0.44/0.66 (step @p113 :rule trans :premises (@p112 @p111)) % 0.44/0.66 (step @p114 :rule trans :premises (@p113 @p108)) % 0.44/0.66 (step @p115 :rule symm :premises (@p114)) % 0.44/0.66 (step @p116 :rule trans :premises (@p108 @p115)) % 0.44/0.66 (step @p117 :rule eq_resolve :premises (@p160 @p116)) % 0.44/0.66 (step @p118 :rule evaluate :args ((< -1 0))) % 0.44/0.66 (step @p119 :rule true_elim :premises (@p118)) % 0.44/0.66 (step @p120 :rule and_intro :premises (@p119 @p117)) % 0.44/0.66 (step @p121 :rule modus_ponens :premises (@p120 @p105)) % 0.44/0.66 (step @p122 :rule arith_sum_ub :premises (@p121 @p104)) % 0.44/0.66 (step @p123 false :rule eq_resolve :premises (@p122 @p98)) % 0.44/0.66 (step-pop @p162 :rule scope :premises (@p123)) % 0.44/0.66 (step-pop @p163 :rule scope :premises (@p162)) % 0.44/0.66 (step @p124 :rule process_scope :premises (@p163) :args (false)) % 0.44/0.66 (step @p127 :rule not_and :premises (@p124)) % 0.44/0.66 (step @p128 :rule eq_resolve :premises (@p127 @p86)) % 0.44/0.66 (step @p129 :rule eq_resolve :premises (@p128 @p79)) % 0.44/0.66 (step @p130 :rule chain_m_resolution :premises (@p129 @p71) :args (@t50 @t48 (@list @t44))) % 0.44/0.66 (step @p131 :rule not_implies_elim2 :premises (@p42)) % 0.44/0.66 (step @p132 :rule not_not_elim :premises (@p131)) % 0.44/0.66 (step @p133 :rule cnf_or_pos :args (@t63)) % 0.44/0.66 (step @p134 :rule reordering :premises (@p133) :args ((or @t61 @t62 @t64))) % 0.44/0.66 (step @p135 :rule chain_m_resolution :premises (@p134 @p132 @p130) :args (@t64 (@list false false) (@list @t23 @t50))) % 0.44/0.66 (step @p136 :rule refl :args (@t61)) % 0.44/0.66 (step @p137 :rule arith_poly_norm :args ((= (* -1 (- 0 @t66)) (* -1 (- @t65 1))))) % 0.44/0.66 (step @p138 :rule arith_poly_norm_rel :premises (@p137) :args ((= (>= 0 @t66) (>= @t65 1)))) % 0.44/0.66 (step @p139 :rule arith-geq-tighten :args (@t19 0)) % 0.44/0.66 (step @p140 :rule trans :premises (@p139 @p138)) % 0.44/0.66 (step @p141 :rule symm :premises (@p140)) % 0.44/0.66 (step @p142 :rule arith_poly_norm :args ((= (+ 0 @t65) @t65))) % 0.44/0.66 (step @p143 :rule arith_poly_norm :args ((= @t67 @t65))) % 0.44/0.66 (step @p144 :rule refl :args (0)) % 0.44/0.66 (step @p145 :rule nary_cong :premises (@p144 @p143) :args (@t68)) % 0.44/0.66 (step @p146 :rule trans :premises (@p145 @p142)) % 0.44/0.66 (step @p147 :rule cong :premises (@p146 @p51) :args (@t69)) % 0.44/0.66 (step @p148 :rule trans :premises (@p147 @p141)) % 0.44/0.66 (step @p149 :rule nary_cong :premises (@p148 @p136) :args (@t70)) % 0.44/0.66 (step @p150 :rule cong :premises (@p59 @p149) :args ((=> @t46 @t70))) % 0.44/0.66 (assume-push @p164 @t46) % 0.44/0.66 (step @p152 :rule instantiate :premises (@p44) :args ((@list 0 @t19))) % 0.44/0.66 (step-pop @p165 :rule scope :premises (@p152)) % 0.44/0.66 (step @p153 :rule process_scope :premises (@p165) :args (@t70)) % 0.44/0.66 (step @p155 :rule eq_resolve :premises (@p153 @p150)) % 0.44/0.66 (step @p156 :rule implies_elim :premises (@p155)) % 0.44/0.66 (step @p157 false :rule chain_m_resolution :premises (@p156 @p135 @p44) :args (false @t49 (@list @t63 @t46))) % 0.44/0.66 ) % 0.44/0.66 % SZS output end Proof % 0.44/0.66 % cvc5 exiting %------------------------------------------------------------------------------