%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ARI179_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 : n028.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 08:07:14 AM UTC 2026 % Result : Theorem 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : ARI179_1 : TPTP v9.2.1. Released v5.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n028.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Wed Jun 3 02:26:20 EDT 2026 % 0.16/0.35 % CPUTime : % 0.32/0.50 %----Proving TF0_ARI % 0.38/0.57 --- Run --finite-model-find --decision=internal at 45... % 0.38/0.57 % SZS status Theorem % 0.38/0.57 % SZS output start Proof % 0.38/0.57 ( % 0.38/0.57 (define @t1 () (@var "V" Int)) % 0.38/0.57 (define @t2 () (= @t1 2)) % 0.38/0.57 (define @t3 () (@var "U" Int)) % 0.38/0.57 (define @t4 () (+ @t3 (* 2 @t1))) % 0.38/0.57 (define @t5 () (and (< @t3 5) (< @t1 3) (> @t4 7))) % 0.38/0.57 (define @t6 () (=> @t5 @t2)) % 0.38/0.57 (define @t7 () (@list @t3 @t1 (@var "W" Int))) % 0.38/0.57 (define @t8 () (forall @t7 @t6)) % 0.38/0.57 (define @t9 () (not @t8)) % 0.38/0.57 (define @t10 () (>= @t4 8)) % 0.38/0.57 (define @t11 () (not @t10)) % 0.38/0.57 (define @t12 () (>= @t1 3)) % 0.38/0.57 (define @t13 () (>= @t3 5)) % 0.38/0.57 (define @t14 () (or @t13 @t12 @t11 @t2)) % 0.38/0.57 (define @t15 () (forall (@list @t3 @t1) @t14)) % 0.38/0.57 (define @t16 () (not @t12)) % 0.38/0.57 (define @t17 () (not @t16)) % 0.38/0.57 (define @t18 () (not @t13)) % 0.38/0.57 (define @t19 () (not @t18)) % 0.38/0.57 (define @t20 () (or @t19 @t17 @t11)) % 0.38/0.57 (define @t21 () (and @t18 @t16 @t10)) % 0.38/0.57 (define @t22 () (+ 7 1)) % 0.38/0.57 (define @t23 () (>= @t4 @t22)) % 0.38/0.57 (define @t24 () (@quantifiers_skolemize @t15 1)) % 0.38/0.57 (define @t25 () (= @t24 2)) % 0.38/0.57 (define @t26 () (@quantifiers_skolemize @t15 0)) % 0.38/0.57 (define @t27 () (+ @t26 (* 2 @t24))) % 0.38/0.57 (define @t28 () (>= @t27 8)) % 0.38/0.57 (define @t29 () (not @t28)) % 0.38/0.57 (define @t30 () (>= @t24 3)) % 0.38/0.57 (define @t31 () (>= @t26 5)) % 0.38/0.57 (define @t32 () (or @t31 @t30 @t29 @t25)) % 0.38/0.57 (define @t33 () (not @t31)) % 0.38/0.57 (define @t34 () (@list true)) % 0.38/0.57 (define @t35 () (@list @t32)) % 0.38/0.57 (define @t36 () (not @t30)) % 0.38/0.57 (define @t37 () (not @t25)) % 0.38/0.57 (define @t38 () (+ 1 1)) % 0.38/0.57 (define @t39 () (>= @t24 @t38)) % 0.38/0.57 (define @t40 () (<= @t24 1)) % 0.38/0.57 (define @t41 () (* 1/2 5/1)) % 0.38/0.57 (define @t42 () (* -1/2 8/1)) % 0.38/0.57 (define @t43 () (+ 1/1 @t42 @t41)) % 0.38/0.57 (define @t44 () (to_real @t26)) % 0.38/0.57 (define @t45 () (* 1/2 @t44)) % 0.38/0.57 (define @t46 () (+ (* -1/2 @t44) (to_real (* -1 @t24)))) % 0.38/0.57 (define @t47 () (to_real @t24)) % 0.38/0.57 (define @t48 () (to_real @t27)) % 0.38/0.57 (define @t49 () (* -1/2 @t48)) % 0.38/0.57 (define @t50 () (+ @t47 @t49 @t45)) % 0.38/0.57 (define @t51 () (>= @t50 @t43)) % 0.38/0.57 (define @t52 () (> 1/2 0/1)) % 0.38/0.57 (define @t53 () (< @t26 5)) % 0.38/0.57 (define @t54 () (to_real 5)) % 0.38/0.57 (define @t55 () (< @t44 @t54)) % 0.38/0.57 (define @t56 () (< -1/2 0/1)) % 0.38/0.57 (define @t57 () (to_real 8)) % 0.38/0.57 (define @t58 () (>= @t48 @t57)) % 0.38/0.57 (define @t59 () (to_real 1)) % 0.38/0.57 (define @t60 () (<= @t47 @t59)) % 0.38/0.57 (define @t61 () (and @t33 @t28 @t36 @t37)) % 0.38/0.57 (assume @p1 @t9) % 0.38/0.57 (assume @p2 true) % 0.38/0.57 (step @p3 :rule quant-unused-vars :args ((= (forall @t7 @t14) @t15))) % 0.38/0.57 (step @p4 :rule aci_norm :args ((= (or (or @t13 @t12 @t11) @t2) @t14))) % 0.38/0.57 (step @p5 :rule refl :args (@t2)) % 0.38/0.57 (step @p6 :rule refl :args (@t11)) % 0.38/0.57 (step @p7 :rule bool-double-not-elim :args (@t12)) % 0.38/0.57 (step @p8 :rule bool-double-not-elim :args (@t13)) % 0.38/0.57 (step @p9 :rule nary_cong :premises (@p8 @p7 @p6) :args (@t20)) % 0.38/0.57 (step @p10 :rule aci_norm :args ((= (or @t19 (or @t17 @t11)) @t20))) % 0.38/0.57 (step @p11 :rule trans :premises (@p10 @p9)) % 0.38/0.57 (step @p12 :rule bool-and-de-morgan :args (@t16 @t10 true)) % 0.38/0.57 (step @p13 :rule refl :args (@t19)) % 0.38/0.57 (step @p14 :rule nary_cong :premises (@p13 @p12) :args ((or @t19 (not (and @t16 @t10))))) % 0.38/0.57 (step @p15 :rule bool-and-de-morgan :args (@t18 @t16 (and @t10))) % 0.38/0.57 (step @p16 :rule trans :premises (@p15 @p14)) % 0.38/0.57 (step @p17 :rule trans :premises (@p16 @p11)) % 0.38/0.57 (step @p18 :rule nary_cong :premises (@p17 @p5) :args ((or (not @t21) @t2))) % 0.38/0.57 (step @p19 :rule trans :premises (@p18 @p4)) % 0.38/0.57 (step @p20 :rule bool-impl-elim :args (@t21 @t2)) % 0.38/0.57 (step @p21 :rule trans :premises (@p20 @p19)) % 0.38/0.57 (step @p22 :rule cong :premises (@p21) :args ((forall @t7 (=> @t21 @t2)))) % 0.38/0.57 (step @p23 :rule trans :premises (@p22 @p3)) % 0.38/0.57 (step @p24 :rule refl :args (@t2)) % 0.38/0.57 (step @p25 :rule bool-double-not-elim :args (@t10)) % 0.38/0.57 (step @p26 :rule evaluate :args (@t22)) % 0.38/0.57 (step @p27 :rule refl :args (@t4)) % 0.38/0.57 (step @p28 :rule cong :premises (@p27 @p26) :args (@t23)) % 0.38/0.57 (step @p29 :rule cong :premises (@p28) :args ((not @t23))) % 0.38/0.57 (step @p30 :rule arith-leq-norm :args (@t4 7)) % 0.38/0.57 (step @p31 :rule trans :premises (@p30 @p29)) % 0.38/0.57 (step @p32 :rule cong :premises (@p31) :args ((not (<= @t4 7)))) % 0.38/0.57 (step @p33 :rule trans :premises (@p32 @p25)) % 0.38/0.57 (step @p34 :rule arith-elim-leq :args (@t4 7)) % 0.38/0.57 (step @p35 :rule symm :premises (@p34)) % 0.38/0.57 (step @p36 :rule cong :premises (@p35) :args ((not (>= 7 @t4)))) % 0.38/0.57 (step @p37 :rule arith-elim-gt :args (@t4 7)) % 0.38/0.57 (step @p38 :rule trans :premises (@p37 @p36)) % 0.38/0.57 (step @p39 :rule trans :premises (@p38 @p33)) % 0.38/0.57 (step @p40 :rule arith-elim-lt :args (@t1 3)) % 0.38/0.57 (step @p41 :rule arith-elim-lt :args (@t3 5)) % 0.38/0.57 (step @p42 :rule nary_cong :premises (@p41 @p40 @p39) :args (@t5)) % 0.38/0.57 (step @p43 :rule cong :premises (@p42 @p24) :args (@t6)) % 0.38/0.57 (step @p44 :rule cong :premises (@p43) :args (@t8)) % 0.38/0.57 (step @p45 :rule trans :premises (@p44 @p23)) % 0.38/0.57 (step @p46 :rule cong :premises (@p45) :args (@t9)) % 0.38/0.57 (step @p47 :rule eq_resolve :premises (@p1 @p46)) % 0.38/0.57 (step @p48 :rule skolemize :premises (@p47)) % 0.38/0.57 (step @p49 :rule cnf_or_neg :args (@t32 0)) % 0.38/0.57 (step @p50 :rule chain_m_resolution :premises (@p49 @p48) :args (@t33 @t34 @t35)) % 0.38/0.57 (step @p51 :rule cnf_or_neg :args (@t32 1)) % 0.38/0.57 (step @p52 :rule chain_m_resolution :premises (@p51 @p48) :args (@t36 @t34 @t35)) % 0.38/0.57 (step @p53 :rule bool-double-not-elim :args (@t28)) % 0.38/0.57 (step @p54 :rule refl :args (@t32)) % 0.38/0.57 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or @t32 (not @t29)))) % 0.38/0.57 (step @p56 :rule cnf_or_neg :args (@t32 2)) % 0.38/0.57 (step @p57 :rule eq_resolve :premises (@p56 @p55)) % 0.38/0.57 (step @p58 :rule reordering :premises (@p57) :args ((or @t28 @t32))) % 0.38/0.57 (step @p59 :rule chain_m_resolution :premises (@p58 @p48) :args (@t28 @t34 @t35)) % 0.38/0.57 (step @p60 :rule cnf_or_neg :args (@t32 3)) % 0.38/0.57 (step @p61 :rule chain_m_resolution :premises (@p60 @p48) :args (@t37 @t34 @t35)) % 0.38/0.57 (step @p62 :rule bool-double-not-elim :args (@t25)) % 0.38/0.57 (step @p63 :rule bool-double-not-elim :args (@t30)) % 0.38/0.57 (step @p64 :rule bool-double-not-elim :args (@t31)) % 0.38/0.57 (step @p65 :rule refl :args (@t29)) % 0.38/0.57 (step @p66 :rule nary_cong :premises (@p65 @p64 @p63 @p62) :args ((or @t29 (not @t33) (not @t36) (not @t37)))) % 0.38/0.57 (assume-push @p192 @t33) % 0.38/0.57 (assume-push @p193 @t28) % 0.38/0.57 (assume-push @p194 @t36) % 0.38/0.57 (assume-push @p195 @t37) % 0.38/0.57 (step @p71 :rule arith-elim-leq :args (@t24 1)) % 0.38/0.57 (step @p72 :rule symm :premises (@p71)) % 0.38/0.57 (step @p73 :rule cong :premises (@p72) :args ((not (>= 1 @t24)))) % 0.38/0.57 (step @p74 :rule arith-elim-gt :args (@t24 1)) % 0.38/0.57 (step @p75 :rule trans :premises (@p74 @p73)) % 0.38/0.57 (step @p76 :rule bool-double-not-elim :args ((>= @t24 2))) % 0.38/0.57 (step @p77 :rule evaluate :args (@t38)) % 0.38/0.57 (step @p78 :rule refl :args (@t24)) % 0.38/0.57 (step @p79 :rule cong :premises (@p78 @p77) :args (@t39)) % 0.38/0.57 (step @p80 :rule cong :premises (@p79) :args ((not @t39))) % 0.38/0.57 (step @p81 :rule arith-leq-norm :args (@t24 1)) % 0.38/0.57 (step @p82 :rule trans :premises (@p81 @p80)) % 0.38/0.57 (step @p83 :rule cong :premises (@p82) :args ((not @t40))) % 0.38/0.57 (step @p84 :rule trans :premises (@p83 @p76)) % 0.38/0.57 (step @p85 :rule trans :premises (@p75 @p84)) % 0.38/0.57 (step @p86 :rule symm :premises (@p85)) % 0.38/0.57 (step @p87 :rule trans :premises (@p84 @p86)) % 0.38/0.57 (assume-push @p196 @t40) % 0.38/0.57 (step @p89 :rule evaluate :args ((not true))) % 0.38/0.57 (step @p90 :rule evaluate :args ((>= 0/1 -1/2))) % 0.38/0.57 (step @p91 :rule evaluate :args ((+ 1/1 -4/1 5/2))) % 0.38/0.57 (step @p92 :rule evaluate :args (@t41)) % 0.38/0.57 (step @p93 :rule evaluate :args (@t42)) % 0.38/0.57 (step @p94 :rule refl :args (1/1)) % 0.38/0.57 (step @p95 :rule nary_cong :premises (@p94 @p93 @p92) :args (@t43)) % 0.38/0.57 (step @p96 :rule trans :premises (@p95 @p91)) % 0.38/0.57 (step @p97 :rule arith_poly_norm :args ((= (+ @t47 @t46 @t45) 0/1))) % 0.38/0.57 (step @p98 :rule refl :args (@t45)) % 0.38/0.57 (step @p99 :rule arith_poly_norm :args ((= @t49 @t46))) % 0.38/0.57 (step @p100 :rule refl :args (@t47)) % 0.38/0.57 (step @p101 :rule nary_cong :premises (@p100 @p99 @p98) :args (@t50)) % 0.38/0.57 (step @p102 :rule trans :premises (@p101 @p97)) % 0.38/0.57 (step @p103 :rule cong :premises (@p102 @p96) :args (@t51)) % 0.38/0.57 (step @p104 :rule trans :premises (@p103 @p90)) % 0.38/0.57 (step @p105 :rule cong :premises (@p104) :args ((not @t51))) % 0.38/0.57 (step @p106 :rule trans :premises (@p105 @p89)) % 0.38/0.57 (step @p107 :rule arith-elim-lt :args (@t50 @t43)) % 0.38/0.57 (step @p108 :rule trans :premises (@p107 @p106)) % 0.38/0.57 (assume-push @p197 @t52) % 0.38/0.57 (assume-push @p198 @t53) % 0.38/0.57 (step @p111 :rule arith_mult_pos :args (1/2 (< @t44 5/1))) % 0.38/0.57 (step @p112 :rule evaluate :args (@t54)) % 0.38/0.57 (step @p113 :rule refl :args (@t44)) % 0.38/0.57 (step @p114 :rule cong :premises (@p113 @p112) :args (@t55)) % 0.38/0.57 (step @p115 :rule arith_poly_norm :args ((= (* -5/1 (to_real (- @t26 5))) (* -5/1 (- @t44 @t54))))) % 0.38/0.57 (step @p116 :rule arith_poly_norm_rel :premises (@p115) :args ((= @t53 @t55))) % 0.38/0.57 (step @p117 :rule trans :premises (@p116 @p114)) % 0.38/0.57 (step @p118 :rule eq_resolve :premises (@p198 @p117)) % 0.38/0.57 (step @p119 :rule and_intro :premises (@p197 @p118)) % 0.38/0.57 (step @p120 :rule modus_ponens :premises (@p119 @p111)) % 0.38/0.57 (step-pop @p199 :rule scope :premises (@p120)) % 0.38/0.57 (step-pop @p200 :rule scope :premises (@p199)) % 0.38/0.57 (step @p121 :rule process_scope :premises (@p200) :args ((< @t45 @t41))) % 0.38/0.57 (step @p124 :rule arith-elim-lt :args (@t26 5)) % 0.38/0.57 (step @p125 :rule symm :premises (@p124)) % 0.38/0.57 (step @p126 :rule eq_resolve :premises (@p50 @p125)) % 0.38/0.57 (step @p127 :rule evaluate :args (@t52)) % 0.38/0.57 (step @p128 :rule true_elim :premises (@p127)) % 0.38/0.57 (step @p129 :rule and_intro :premises (@p128 @p126)) % 0.38/0.57 (step @p130 :rule modus_ponens :premises (@p129 @p121)) % 0.38/0.57 (assume-push @p201 @t56) % 0.38/0.57 (assume-push @p202 @t28) % 0.38/0.57 (step @p133 :rule arith_mult_neg :args (-1/2 (>= @t48 8/1))) % 0.38/0.57 (step @p134 :rule evaluate :args (@t57)) % 0.38/0.57 (step @p135 :rule refl :args (@t48)) % 0.38/0.57 (step @p136 :rule cong :premises (@p135 @p134) :args (@t58)) % 0.38/0.57 (step @p137 :rule arith_poly_norm :args ((= (* -8/1 (to_real (- @t27 8))) (* -8/1 (- @t48 @t57))))) % 0.38/0.57 (step @p138 :rule arith_poly_norm_rel :premises (@p137) :args ((= @t28 @t58))) % 0.38/0.57 (step @p139 :rule trans :premises (@p138 @p136)) % 0.38/0.57 (step @p140 :rule eq_resolve :premises (@p193 @p139)) % 0.38/0.57 (step @p141 :rule and_intro :premises (@p201 @p140)) % 0.38/0.57 (step @p142 :rule modus_ponens :premises (@p141 @p133)) % 0.38/0.57 (step-pop @p203 :rule scope :premises (@p142)) % 0.38/0.57 (step-pop @p204 :rule scope :premises (@p203)) % 0.38/0.57 (step @p143 :rule process_scope :premises (@p204) :args ((<= @t49 @t42))) % 0.38/0.57 (step @p146 :rule evaluate :args (@t56)) % 0.38/0.57 (step @p147 :rule true_elim :premises (@p146)) % 0.38/0.57 (step @p148 :rule and_intro :premises (@p147 @p59)) % 0.38/0.57 (step @p149 :rule modus_ponens :premises (@p148 @p143)) % 0.38/0.57 (step @p150 :rule evaluate :args (@t59)) % 0.38/0.57 (step @p151 :rule refl :args (@t47)) % 0.38/0.57 (step @p152 :rule cong :premises (@p151 @p150) :args (@t60)) % 0.38/0.57 (step @p153 :rule arith_poly_norm :args ((= (* -1/1 (to_real (- @t24 1))) (* -1/1 (- @t47 @t59))))) % 0.38/0.57 (step @p154 :rule arith_poly_norm_rel :premises (@p153) :args ((= @t40 @t60))) % 0.38/0.57 (step @p155 :rule trans :premises (@p154 @p152)) % 0.38/0.57 (step @p156 :rule arith-elim-lt :args (@t24 3)) % 0.38/0.57 (step @p157 :rule symm :premises (@p156)) % 0.38/0.57 (step @p158 :rule eq_resolve :premises (@p52 @p157)) % 0.38/0.57 (step @p159 :rule int_tight_ub :premises (@p158)) % 0.38/0.57 (step @p160 :rule arith_trichotomy :premises (@p159 @p61)) % 0.38/0.57 (step @p161 :rule int_tight_ub :premises (@p160)) % 0.38/0.57 (step @p162 :rule eq_resolve :premises (@p161 @p155)) % 0.38/0.57 (step @p163 :rule arith_sum_ub :premises (@p162 @p149 @p130)) % 0.38/0.57 (step @p164 false :rule eq_resolve :premises (@p163 @p108)) % 0.38/0.57 (step-pop @p205 :rule scope :premises (@p164)) % 0.38/0.57 (step @p165 :rule process_scope :premises (@p205) :args (false)) % 0.38/0.57 (step @p167 :rule eq_resolve :premises (@p165 @p87)) % 0.38/0.57 (step @p168 :rule eq_resolve :premises (@p167 @p75)) % 0.38/0.57 (step @p156 :rule arith-elim-lt :args (@t24 3)) % 0.38/0.57 (step @p157 :rule symm :premises (@p156)) % 0.38/0.57 (step @p158 :rule eq_resolve :premises (@p52 @p157)) % 0.38/0.57 (step @p159 :rule int_tight_ub :premises (@p158)) % 0.38/0.57 (step @p160 :rule arith_trichotomy :premises (@p159 @p61)) % 0.38/0.57 (step @p169 :rule int_tight_ub :premises (@p160)) % 0.38/0.57 (step @p170 false :rule contra :premises (@p169 @p168)) % 0.38/0.57 (step-pop @p206 :rule scope :premises (@p170)) % 0.38/0.57 (step-pop @p207 :rule scope :premises (@p206)) % 0.38/0.57 (step-pop @p208 :rule scope :premises (@p207)) % 0.38/0.58 (step-pop @p209 :rule scope :premises (@p208)) % 0.38/0.58 (step @p171 :rule process_scope :premises (@p209) :args (false)) % 0.38/0.58 (assume-push @p210 @t28) % 0.38/0.58 (assume-push @p211 @t33) % 0.38/0.58 (assume-push @p212 @t36) % 0.38/0.58 (assume-push @p213 @t37) % 0.38/0.58 (step @p180 :rule and_intro :premises (@p50 @p59 @p52 @p61)) % 0.38/0.58 (step-pop @p214 :rule scope :premises (@p180)) % 0.38/0.58 (step-pop @p215 :rule scope :premises (@p214)) % 0.38/0.58 (step-pop @p216 :rule scope :premises (@p215)) % 0.38/0.58 (step-pop @p217 :rule scope :premises (@p216)) % 0.38/0.58 (step @p181 :rule process_scope :premises (@p217) :args (@t61)) % 0.38/0.58 (step @p186 :rule implies_elim :premises (@p181)) % 0.38/0.58 (step @p187 :rule resolution :premises (@p186 @p171) :args (true @t61)) % 0.38/0.58 (step @p188 :rule not_and :premises (@p187)) % 0.38/0.58 (step @p189 :rule eq_resolve :premises (@p188 @p66)) % 0.38/0.58 (step @p190 :rule reordering :premises (@p189) :args (@t32)) % 0.38/0.58 (step @p191 false :rule chain_m_resolution :premises (@p190 @p61 @p59 @p52 @p50) :args (false (@list true false true true) (@list @t25 @t28 @t30 @t31))) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------