%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ARI716_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 : n024.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 08:08:11 AM UTC 2026 % Result : Theorem 0.15s 0.37s % Output : Proof 0.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.07 % Problem : ARI716_1 : TPTP v9.2.1. Released v6.3.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.08/0.25 % Computer : n024.cluster.edu % 0.08/0.25 % Model : x86_64 x86_64 % 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.25 % Memory : 8042.1875MB % 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.25 % CPULimit : 300 % 0.08/0.25 % WCLimit : 300 % 0.08/0.25 % DateTime : Tue Jun 2 21:32:15 EDT 2026 % 0.08/0.26 % CPUTime : % 0.15/0.33 %----Proving TF0_ARI % 0.15/0.37 --- Run --finite-model-find --decision=internal at 45... % 0.15/0.37 % SZS status Theorem % 0.15/0.37 % SZS output start Proof % 0.15/0.37 ( % 0.15/0.37 (define @t1 () (@var "X" Real)) % 0.15/0.37 (define @t2 () (to_int @t1)) % 0.15/0.37 (define @t3 () (/ 1 2)) % 0.15/0.37 (define @t4 () (+ @t1 @t3)) % 0.15/0.37 (define @t5 () (to_int @t4)) % 0.15/0.37 (define @t6 () (>= @t5 @t2)) % 0.15/0.37 (define @t7 () (@list @t1)) % 0.15/0.37 (define @t8 () (forall @t7 @t6)) % 0.15/0.37 (define @t9 () (not @t8)) % 0.15/0.37 (define @t10 () (+ 1/2 @t1)) % 0.15/0.37 (define @t11 () (to_int @t10)) % 0.15/0.37 (define @t12 () (+ @t2 (* -1 @t11))) % 0.15/0.37 (define @t13 () (+ @t12 1)) % 0.15/0.37 (define @t14 () (forall @t7 (not (>= @t12 1)))) % 0.15/0.37 (define @t15 () (@quantifiers_skolemize @t14 0)) % 0.15/0.37 (define @t16 () (to_int @t15)) % 0.15/0.37 (define @t17 () (@purify @t16)) % 0.15/0.37 (define @t18 () (* -1 @t17)) % 0.15/0.37 (define @t19 () (+ 1/2 @t15)) % 0.15/0.37 (define @t20 () (to_int @t19)) % 0.15/0.37 (define @t21 () (@purify @t20)) % 0.15/0.37 (define @t22 () (+ @t21 @t18)) % 0.15/0.37 (define @t23 () (>= @t22 0)) % 0.15/0.37 (define @t24 () (not @t23)) % 0.15/0.37 (define @t25 () (not @t14)) % 0.15/0.37 (define @t26 () (* -1 @t21)) % 0.15/0.37 (define @t27 () (+ @t26 @t17)) % 0.15/0.37 (define @t28 () (+ @t22 1)) % 0.15/0.37 (define @t29 () (* -1 @t20)) % 0.15/0.37 (define @t30 () (+ @t16 @t29)) % 0.15/0.37 (define @t31 () (>= @t30 1)) % 0.15/0.37 (define @t32 () (not (not @t31))) % 0.15/0.37 (define @t33 () (to_real @t26)) % 0.15/0.37 (define @t34 () (+ @t15 @t33)) % 0.15/0.37 (define @t35 () (+ 1/2 @t15 @t33)) % 0.15/0.37 (define @t36 () (>= @t34 1/2)) % 0.15/0.37 (define @t37 () (to_real @t21)) % 0.15/0.37 (define @t38 () (* -1/1 @t37)) % 0.15/0.37 (define @t39 () (+ @t38 @t15 1/2)) % 0.15/0.37 (define @t40 () (+ @t19 @t38)) % 0.15/0.37 (define @t41 () (- @t19 @t37)) % 0.15/0.37 (define @t42 () (>= @t41 1/1)) % 0.15/0.37 (define @t43 () (<= 0/1 @t41)) % 0.15/0.37 (define @t44 () (to_real @t18)) % 0.15/0.37 (define @t45 () (to_real @t17)) % 0.15/0.37 (define @t46 () (* -1/1 @t45)) % 0.15/0.37 (define @t47 () (+ @t15 @t46)) % 0.15/0.37 (define @t48 () (- @t15 @t45)) % 0.15/0.37 (define @t49 () (>= @t48 1/1)) % 0.15/0.37 (define @t50 () (+ @t15 @t44)) % 0.15/0.37 (define @t51 () (<= 0/1 @t48)) % 0.15/0.37 (define @t52 () (>= @t50 0/1)) % 0.15/0.37 (define @t53 () (not @t52)) % 0.15/0.37 (define @t54 () (not @t36)) % 0.15/0.37 (define @t55 () (* -1/1 0/1)) % 0.15/0.37 (define @t56 () (+ @t55 -1/1 1/2)) % 0.15/0.37 (define @t57 () (* 0/1 @t15)) % 0.15/0.37 (define @t58 () (* 0 @t17)) % 0.15/0.37 (define @t59 () (to_real @t58)) % 0.15/0.37 (define @t60 () (+ @t59 @t33 @t37 @t57)) % 0.15/0.37 (define @t61 () (to_real @t22)) % 0.15/0.37 (define @t62 () (+ (* -1/1 @t50) @t61 @t34)) % 0.15/0.37 (define @t63 () (>= @t62 @t56)) % 0.15/0.37 (define @t64 () (to_real -1)) % 0.15/0.37 (define @t65 () (<= @t61 @t64)) % 0.15/0.37 (define @t66 () (and @t54 @t24 @t52)) % 0.15/0.37 (assume @p1 @t9) % 0.15/0.37 (assume @p2 true) % 0.15/0.37 (step @p3 :rule arith_poly_norm :args ((= (* -1 (- 1 @t13)) (* -1 (- @t11 @t2))))) % 0.15/0.37 (step @p4 :rule arith_poly_norm_rel :premises (@p3) :args ((= (>= 1 @t13) (>= @t11 @t2)))) % 0.15/0.37 (step @p5 :rule arith-geq-tighten :args (@t12 1)) % 0.15/0.37 (step @p6 :rule trans :premises (@p5 @p4)) % 0.15/0.37 (step @p7 :rule symm :premises (@p6)) % 0.15/0.37 (step @p8 :rule refl :args (@t2)) % 0.15/0.37 (step @p9 :rule arith_poly_norm :args ((= (+ @t1 1/2) @t10))) % 0.15/0.37 (step @p10 :rule evaluate :args (@t3)) % 0.15/0.37 (step @p11 :rule refl :args (@t1)) % 0.15/0.37 (step @p12 :rule nary_cong :premises (@p11 @p10) :args (@t4)) % 0.15/0.37 (step @p13 :rule trans :premises (@p12 @p9)) % 0.15/0.37 (step @p14 :rule cong :premises (@p13) :args (@t5)) % 0.15/0.37 (step @p15 :rule cong :premises (@p14 @p8) :args (@t6)) % 0.15/0.37 (step @p16 :rule trans :premises (@p15 @p7)) % 0.15/0.37 (step @p17 :rule cong :premises (@p16) :args (@t8)) % 0.15/0.37 (step @p18 :rule cong :premises (@p17) :args (@t9)) % 0.15/0.37 (step @p19 :rule eq_resolve :premises (@p1 @p18)) % 0.15/0.37 (step @p20 :rule refl :args (@t24)) % 0.15/0.37 (step @p21 :rule bool-double-not-elim :args (@t14)) % 0.15/0.37 (step @p22 :rule nary_cong :premises (@p21 @p20) :args ((or (not @t25) @t24))) % 0.15/0.37 (step @p23 :rule arith_poly_norm :args ((= (* -1 (- 0 @t28)) (* -1 (- @t27 1))))) % 0.15/0.37 (step @p24 :rule arith_poly_norm_rel :premises (@p23) :args ((= (>= 0 @t28) (>= @t27 1)))) % 0.15/0.37 (step @p25 :rule arith-geq-tighten :args (@t22 0)) % 0.15/0.37 (step @p26 :rule trans :premises (@p25 @p24)) % 0.15/0.37 (step @p27 :rule symm :premises (@p26)) % 0.15/0.37 (step @p28 :rule refl :args (1)) % 0.15/0.37 (step @p29 :rule arith_poly_norm :args ((= (+ @t17 @t26) @t27))) % 0.15/0.37 (step @p30 :rule arith_reduction :args (@t20)) % 0.15/0.37 (step @p31 :rule and_elim :premises (@p30) :args (0)) % 0.15/0.37 (step @p32 :rule refl :args (-1)) % 0.15/0.37 (step @p33 :rule nary_cong :premises (@p32 @p31) :args (@t29)) % 0.15/0.37 (step @p34 :rule arith_reduction :args (@t16)) % 0.15/0.37 (step @p35 :rule and_elim :premises (@p34) :args (0)) % 0.15/0.37 (step @p36 :rule nary_cong :premises (@p35 @p33) :args (@t30)) % 0.15/0.37 (step @p37 :rule trans :premises (@p36 @p29)) % 0.15/0.37 (step @p38 :rule cong :premises (@p37 @p28) :args (@t31)) % 0.15/0.37 (step @p39 :rule trans :premises (@p38 @p27)) % 0.15/0.37 (step @p40 :rule refl :args (@t25)) % 0.15/0.37 (step @p41 :rule cong :premises (@p40 @p39) :args ((=> @t25 @t31))) % 0.15/0.37 (step @p42 :rule bool-double-not-elim :args (@t31)) % 0.15/0.37 (step @p43 :rule cong :premises (@p40 @p42) :args ((=> @t25 @t32))) % 0.15/0.37 (step @p44 :rule trans :premises (@p43 @p41)) % 0.15/0.37 (assume-push @p176 @t25) % 0.15/0.37 (step @p46 :rule skolemize :premises (@p19)) % 0.15/0.37 (step-pop @p177 :rule scope :premises (@p46)) % 0.15/0.37 (step @p47 :rule process_scope :premises (@p177) :args (@t32)) % 0.15/0.37 (step @p49 :rule eq_resolve :premises (@p47 @p44)) % 0.15/0.37 (step @p50 :rule implies_elim :premises (@p49)) % 0.15/0.37 (step @p51 :rule eq_resolve :premises (@p50 @p22)) % 0.15/0.37 (step @p52 :rule chain_m_resolution :premises (@p51 @p19) :args (@t24 (@list true) (@list @t14))) % 0.15/0.37 (step @p53 :rule arith_poly_norm :args ((= (* -1/2 (- @t35 1/1)) (* -1/2 (- @t34 1/2))))) % 0.15/0.37 (step @p54 :rule arith_poly_norm_rel :premises (@p53) :args ((= (>= @t35 1/1) @t36))) % 0.15/0.37 (step @p55 :rule refl :args (1/1)) % 0.15/0.37 (step @p56 :rule arith_poly_norm :args ((= (+ @t33 @t15 1/2) @t35))) % 0.15/0.37 (step @p57 :rule refl :args (1/2)) % 0.15/0.37 (step @p58 :rule refl :args (@t15)) % 0.15/0.37 (step @p59 :rule arith_poly_norm :args ((= @t38 @t33))) % 0.15/0.37 (step @p60 :rule nary_cong :premises (@p59 @p58 @p57) :args (@t39)) % 0.15/0.37 (step @p61 :rule trans :premises (@p60 @p56)) % 0.15/0.37 (step @p62 :rule arith_poly_norm :args ((= @t40 @t39))) % 0.15/0.37 (step @p63 :rule trans :premises (@p62 @p61)) % 0.15/0.37 (step @p64 :rule arith_poly_norm :args ((= @t41 @t40))) % 0.15/0.37 (step @p65 :rule trans :premises (@p64 @p63)) % 0.15/0.37 (step @p66 :rule cong :premises (@p65 @p55) :args (@t42)) % 0.15/0.37 (step @p67 :rule trans :premises (@p66 @p54)) % 0.15/0.37 (step @p68 :rule cong :premises (@p67) :args ((not @t42))) % 0.15/0.37 (step @p69 :rule arith-elim-lt :args (@t41 1/1)) % 0.15/0.37 (step @p70 :rule trans :premises (@p69 @p68)) % 0.15/0.37 (step @p71 :rule arith_poly_norm :args ((= (* 1/2 (- @t35 0/1)) (* 1/2 (- @t34 -1/2))))) % 0.15/0.37 (step @p72 :rule arith_poly_norm_rel :premises (@p71) :args ((= (>= @t35 0/1) (>= @t34 -1/2)))) % 0.15/0.37 (step @p73 :rule arith-elim-leq :args (0/1 @t35)) % 0.15/0.37 (step @p74 :rule trans :premises (@p73 @p72)) % 0.15/0.37 (step @p75 :rule refl :args (0/1)) % 0.15/0.37 (step @p76 :rule cong :premises (@p75 @p65) :args (@t43)) % 0.15/0.37 (step @p77 :rule trans :premises (@p76 @p74)) % 0.15/0.37 (step @p78 :rule nary_cong :premises (@p77 @p70) :args ((and @t43 (< @t41 1/1)))) % 0.15/0.37 (step @p79 :rule and_elim :premises (@p30) :args (1)) % 0.15/0.37 (step @p80 :rule eq_resolve :premises (@p79 @p78)) % 0.15/0.37 (step @p81 :rule and_elim :premises (@p80) :args (1)) % 0.15/0.37 (step @p82 :rule arith_poly_norm :args ((= @t46 @t44))) % 0.15/0.37 (step @p83 :rule nary_cong :premises (@p58 @p82) :args (@t47)) % 0.15/0.37 (step @p84 :rule arith_poly_norm :args ((= @t48 @t47))) % 0.15/0.37 (step @p85 :rule trans :premises (@p84 @p83)) % 0.15/0.37 (step @p86 :rule cong :premises (@p85 @p55) :args (@t49)) % 0.15/0.37 (step @p87 :rule cong :premises (@p86) :args ((not @t49))) % 0.15/0.37 (step @p88 :rule arith-elim-lt :args (@t48 1/1)) % 0.15/0.37 (step @p89 :rule trans :premises (@p88 @p87)) % 0.15/0.37 (step @p90 :rule arith-elim-leq :args (0/1 @t50)) % 0.15/0.37 (step @p91 :rule cong :premises (@p75 @p85) :args (@t51)) % 0.15/0.37 (step @p92 :rule trans :premises (@p91 @p90)) % 0.15/0.37 (step @p93 :rule nary_cong :premises (@p92 @p89) :args ((and @t51 (< @t48 1/1)))) % 0.15/0.37 (step @p94 :rule and_elim :premises (@p34) :args (1)) % 0.15/0.37 (step @p95 :rule eq_resolve :premises (@p94 @p93)) % 0.15/0.37 (step @p96 :rule and_elim :premises (@p95) :args (0)) % 0.15/0.37 (step @p97 :rule refl :args (@t53)) % 0.15/0.37 (step @p98 :rule bool-double-not-elim :args (@t36)) % 0.15/0.37 (step @p99 :rule bool-double-not-elim :args (@t23)) % 0.15/0.37 (step @p100 :rule nary_cong :premises (@p99 @p98 @p97) :args ((or (not @t24) (not @t54) @t53))) % 0.15/0.37 (assume-push @p178 @t54) % 0.15/0.37 (assume-push @p179 @t24) % 0.15/0.37 (assume-push @p180 @t52) % 0.15/0.37 (step @p104 :rule arith-elim-lt :args (@t50 0/1)) % 0.15/0.37 (step @p105 :rule symm :premises (@p104)) % 0.15/0.37 (assume-push @p181 @t52) % 0.15/0.37 (step @p107 :rule evaluate :args ((not true))) % 0.15/0.37 (step @p108 :rule evaluate :args ((>= 0/1 -1/2))) % 0.15/0.37 (step @p109 :rule evaluate :args ((+ 0/1 -1/1 1/2))) % 0.15/0.37 (step @p110 :rule refl :args (-1/1)) % 0.15/0.37 (step @p111 :rule evaluate :args (@t55)) % 0.15/0.37 (step @p112 :rule nary_cong :premises (@p111 @p110 @p57) :args (@t56)) % 0.15/0.37 (step @p113 :rule trans :premises (@p112 @p109)) % 0.15/0.37 (step @p114 :rule arith_poly_norm :args ((= (+ 0/1 @t33 @t37 0/1) 0/1))) % 0.15/0.37 (step @p115 :rule arith_poly_norm :args ((= @t57 0/1))) % 0.15/0.37 (step @p116 :rule refl :args (@t37)) % 0.15/0.37 (step @p117 :rule refl :args (@t33)) % 0.15/0.37 (step @p118 :rule evaluate :args ((to_real 0))) % 0.15/0.37 (step @p119 :rule arith_poly_norm :args ((= @t58 0))) % 0.15/0.37 (step @p120 :rule cong :premises (@p119) :args (@t59)) % 0.15/0.37 (step @p121 :rule trans :premises (@p120 @p118)) % 0.15/0.37 (step @p122 :rule nary_cong :premises (@p121 @p117 @p116 @p115) :args (@t60)) % 0.15/0.37 (step @p123 :rule trans :premises (@p122 @p114)) % 0.15/0.37 (step @p124 :rule arith_poly_norm :args ((= @t62 @t60))) % 0.15/0.37 (step @p125 :rule trans :premises (@p124 @p123)) % 0.15/0.37 (step @p126 :rule cong :premises (@p125 @p113) :args (@t63)) % 0.15/0.37 (step @p127 :rule trans :premises (@p126 @p108)) % 0.15/0.37 (step @p128 :rule cong :premises (@p127) :args ((not @t63))) % 0.15/0.37 (step @p129 :rule trans :premises (@p128 @p107)) % 0.15/0.37 (step @p130 :rule arith-elim-lt :args (@t62 @t56)) % 0.15/0.37 (step @p131 :rule trans :premises (@p130 @p129)) % 0.15/0.37 (step @p132 :rule arith-elim-lt :args (@t34 1/2)) % 0.15/0.37 (step @p133 :rule symm :premises (@p132)) % 0.15/0.37 (step @p134 :rule eq_resolve :premises (@p81 @p133)) % 0.15/0.37 (step @p135 :rule evaluate :args (@t64)) % 0.15/0.37 (step @p136 :rule refl :args (@t61)) % 0.15/0.37 (step @p137 :rule cong :premises (@p136 @p135) :args (@t65)) % 0.15/0.37 (step @p138 :rule arith_poly_norm :args ((= (* 1/1 (to_real (- @t22 -1))) (* 1/1 (- @t61 @t64))))) % 0.15/0.37 (step @p139 :rule arith_poly_norm_rel :premises (@p138) :args ((= (<= @t22 -1) @t65))) % 0.15/0.37 (step @p140 :rule trans :premises (@p139 @p137)) % 0.15/0.37 (step @p141 :rule arith-elim-lt :args (@t22 0)) % 0.15/0.37 (step @p142 :rule symm :premises (@p141)) % 0.15/0.37 (step @p143 :rule eq_resolve :premises (@p52 @p142)) % 0.15/0.37 (step @p144 :rule int_tight_ub :premises (@p143)) % 0.15/0.37 (step @p145 :rule eq_resolve :premises (@p144 @p140)) % 0.15/0.37 (step @p146 :rule arith_mult_neg :args (-1/1 @t52)) % 0.15/0.37 (step @p147 :rule and_elim :premises (@p95) :args (0)) % 0.15/0.37 (step @p148 :rule evaluate :args ((< -1/1 0/1))) % 0.15/0.37 (step @p149 :rule true_elim :premises (@p148)) % 0.15/0.37 (step @p150 :rule and_intro :premises (@p149 @p147)) % 0.15/0.37 (step @p151 :rule modus_ponens :premises (@p150 @p146)) % 0.15/0.37 (step @p152 :rule arith_sum_ub :premises (@p151 @p145 @p134)) % 0.15/0.37 (step @p153 false :rule eq_resolve :premises (@p152 @p131)) % 0.15/0.37 (step-pop @p182 :rule scope :premises (@p153)) % 0.15/0.37 (step @p154 :rule process_scope :premises (@p182) :args (false)) % 0.15/0.37 (step @p156 :rule eq_resolve :premises (@p154 @p105)) % 0.15/0.37 (step @p157 :rule eq_resolve :premises (@p156 @p104)) % 0.15/0.37 (step @p158 false :rule contra :premises (@p96 @p157)) % 0.15/0.37 (step-pop @p183 :rule scope :premises (@p158)) % 0.15/0.37 (step-pop @p184 :rule scope :premises (@p183)) % 0.15/0.37 (step-pop @p185 :rule scope :premises (@p184)) % 0.15/0.37 (step @p159 :rule process_scope :premises (@p185) :args (false)) % 0.15/0.37 (assume-push @p186 @t24) % 0.15/0.37 (assume-push @p187 @t54) % 0.15/0.37 (assume-push @p188 @t52) % 0.15/0.37 (step @p166 :rule and_intro :premises (@p81 @p52 @p96)) % 0.15/0.37 (step-pop @p189 :rule scope :premises (@p166)) % 0.15/0.37 (step-pop @p190 :rule scope :premises (@p189)) % 0.15/0.37 (step-pop @p191 :rule scope :premises (@p190)) % 0.15/0.37 (step @p167 :rule process_scope :premises (@p191) :args (@t66)) % 0.15/0.37 (step @p171 :rule implies_elim :premises (@p167)) % 0.15/0.37 (step @p172 :rule resolution :premises (@p171 @p159) :args (true @t66)) % 0.15/0.37 (step @p173 :rule not_and :premises (@p172)) % 0.15/0.37 (step @p174 :rule eq_resolve :premises (@p173 @p100)) % 0.15/0.37 (step @p175 false :rule chain_m_resolution :premises (@p174 @p96 @p81 @p52) :args (false (@list false true true) (@list @t52 @t36 @t23))) % 0.15/0.37 ) % 0.15/0.37 % SZS output end Proof % 0.15/0.37 % cvc5 exiting %------------------------------------------------------------------------------