%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ARI582_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 : n027.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 08:07:55 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 % 0.12/0.13 % Problem : ARI582_1 : TPTP v9.2.1. Released v5.1.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n027.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Wed Jun 3 02:29:51 EDT 2026 % 0.18/0.35 % CPUTime : % 0.33/0.50 %----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 "Y" Int)) % 0.38/0.57 (define @t2 () (* @t1 2)) % 0.38/0.57 (define @t3 () (@var "Z" Int)) % 0.38/0.57 (define @t4 () (@var "X" Int)) % 0.38/0.57 (define @t5 () (* @t4 2)) % 0.38/0.57 (define @t6 () (and (< @t5 @t3) (< @t3 @t2))) % 0.38/0.57 (define @t7 () (@list @t3)) % 0.38/0.57 (define @t8 () (exists @t7 @t6)) % 0.38/0.57 (define @t9 () (=> (< @t4 @t1) @t8)) % 0.38/0.57 (define @t10 () (@list @t4 @t1)) % 0.38/0.57 (define @t11 () (forall @t10 @t9)) % 0.38/0.57 (define @t12 () (not @t11)) % 0.38/0.57 (define @t13 () (* -1 @t3)) % 0.38/0.57 (define @t14 () (* 2 @t1)) % 0.38/0.57 (define @t15 () (+ @t14 @t13)) % 0.38/0.57 (define @t16 () (>= @t15 1)) % 0.38/0.57 (define @t17 () (not @t16)) % 0.38/0.57 (define @t18 () (* 2 @t4)) % 0.38/0.57 (define @t19 () (+ @t18 @t13)) % 0.38/0.57 (define @t20 () (>= @t19 0)) % 0.38/0.57 (define @t21 () (not (forall @t7 (or @t20 @t17)))) % 0.38/0.57 (define @t22 () (+ @t4 (* -1 @t1))) % 0.38/0.57 (define @t23 () (>= @t22 0)) % 0.38/0.57 (define @t24 () (not @t23)) % 0.38/0.57 (define @t25 () (not @t20)) % 0.38/0.57 (define @t26 () (and @t25 @t16)) % 0.38/0.57 (define @t27 () (forall @t7 (not @t26))) % 0.38/0.57 (define @t28 () (not @t27)) % 0.38/0.57 (define @t29 () (+ @t15 1)) % 0.38/0.57 (define @t30 () (>= @t3 @t2)) % 0.38/0.57 (define @t31 () (>= @t5 @t3)) % 0.38/0.57 (define @t32 () (>= @t4 @t1)) % 0.38/0.57 (define @t33 () (forall @t10 (or @t23 @t21))) % 0.38/0.57 (define @t34 () (@quantifiers_skolemize @t33 1)) % 0.38/0.57 (define @t35 () (* -2 @t34)) % 0.38/0.57 (define @t36 () (+ @t3 @t35)) % 0.38/0.57 (define @t37 () (>= @t36 0)) % 0.38/0.57 (define @t38 () (@quantifiers_skolemize @t33 0)) % 0.38/0.57 (define @t39 () (* -2 @t38)) % 0.38/0.57 (define @t40 () (+ @t3 @t39)) % 0.38/0.57 (define @t41 () (forall @t7 (or (not (>= @t40 1)) @t37))) % 0.38/0.57 (define @t42 () (not @t41)) % 0.38/0.57 (define @t43 () (+ @t38 (* -1 @t34))) % 0.38/0.57 (define @t44 () (>= @t43 0)) % 0.38/0.57 (define @t45 () (or @t44 @t42)) % 0.38/0.57 (define @t46 () (not @t45)) % 0.38/0.57 (define @t47 () (not @t33)) % 0.38/0.57 (define @t48 () (* 2 @t34)) % 0.38/0.57 (define @t49 () (+ @t13 @t48)) % 0.38/0.57 (define @t50 () (+ @t36 1)) % 0.38/0.57 (define @t51 () (+ @t48 @t13)) % 0.38/0.57 (define @t52 () (>= @t51 1)) % 0.38/0.57 (define @t53 () (not @t52)) % 0.38/0.57 (define @t54 () (* 2 @t38)) % 0.38/0.57 (define @t55 () (+ @t13 @t54)) % 0.38/0.57 (define @t56 () (+ @t40 1)) % 0.38/0.57 (define @t57 () (+ @t54 @t13)) % 0.38/0.57 (define @t58 () (>= @t57 0)) % 0.38/0.57 (define @t59 () (or @t58 @t53)) % 0.38/0.57 (define @t60 () (forall @t7 @t59)) % 0.38/0.57 (define @t61 () (not @t60)) % 0.38/0.57 (define @t62 () (or @t44 @t61)) % 0.38/0.57 (define @t63 () (not @t62)) % 0.38/0.57 (define @t64 () (@list true)) % 0.38/0.57 (define @t65 () (@list @t45)) % 0.38/0.57 (define @t66 () (+ @t35 @t48 -1)) % 0.38/0.57 (define @t67 () (+ -1 @t48)) % 0.38/0.57 (define @t68 () (+ @t67 @t35)) % 0.38/0.57 (define @t69 () (>= @t68 0)) % 0.38/0.57 (define @t70 () (+ -1 @t39 @t48)) % 0.38/0.57 (define @t71 () (+ @t43 1)) % 0.38/0.57 (define @t72 () (+ @t39 @t48 -1)) % 0.38/0.57 (define @t73 () (+ @t67 @t39)) % 0.38/0.57 (define @t74 () (>= @t73 1)) % 0.38/0.57 (define @t75 () (not @t74)) % 0.38/0.57 (define @t76 () (or @t75 @t69)) % 0.38/0.57 (assume @p1 @t12) % 0.38/0.57 (assume @p2 true) % 0.38/0.57 (step @p3 :rule refl :args (@t21)) % 0.38/0.57 (step @p4 :rule bool-double-not-elim :args (@t23)) % 0.38/0.57 (step @p5 :rule nary_cong :premises (@p4 @p3) :args ((or (not @t24) @t21))) % 0.38/0.57 (step @p6 :rule bool-impl-elim :args (@t24 @t21)) % 0.38/0.57 (step @p7 :rule trans :premises (@p6 @p5)) % 0.38/0.57 (step @p8 :rule cong :premises (@p7) :args ((forall @t10 (=> @t24 @t21)))) % 0.38/0.57 (step @p9 :rule refl :args (@t17)) % 0.38/0.57 (step @p10 :rule bool-double-not-elim :args (@t20)) % 0.38/0.57 (step @p11 :rule nary_cong :premises (@p10 @p9) :args ((or (not @t25) @t17))) % 0.38/0.57 (step @p12 :rule bool-and-de-morgan :args (@t25 @t16 true)) % 0.38/0.57 (step @p13 :rule trans :premises (@p12 @p11)) % 0.38/0.57 (step @p14 :rule cong :premises (@p13) :args (@t27)) % 0.38/0.57 (step @p15 :rule cong :premises (@p14) :args (@t28)) % 0.38/0.57 (step @p16 :rule exists-elim :args ((= (exists @t7 @t26) @t28))) % 0.38/0.57 (step @p17 :rule trans :premises (@p16 @p15)) % 0.38/0.57 (step @p18 :rule bool-double-not-elim :args (@t16)) % 0.38/0.57 (step @p19 :rule arith_poly_norm :args ((= (* -2 (- 1 @t29)) (* -2 (- @t3 @t14))))) % 0.38/0.57 (step @p20 :rule arith_poly_norm_rel :premises (@p19) :args ((= (>= 1 @t29) (>= @t3 @t14)))) % 0.38/0.57 (step @p21 :rule arith-geq-tighten :args (@t15 1)) % 0.38/0.57 (step @p22 :rule trans :premises (@p21 @p20)) % 0.38/0.57 (step @p23 :rule symm :premises (@p22)) % 0.38/0.57 (step @p24 :rule arith_poly_norm :args ((= @t2 @t14))) % 0.38/0.57 (step @p25 :rule refl :args (@t3)) % 0.38/0.57 (step @p26 :rule cong :premises (@p25 @p24) :args (@t30)) % 0.38/0.57 (step @p27 :rule trans :premises (@p26 @p23)) % 0.38/0.57 (step @p28 :rule cong :premises (@p27) :args ((not @t30))) % 0.38/0.57 (step @p29 :rule trans :premises (@p28 @p18)) % 0.38/0.57 (step @p30 :rule arith-elim-lt :args (@t3 @t2)) % 0.38/0.57 (step @p31 :rule trans :premises (@p30 @p29)) % 0.38/0.57 (step @p32 :rule arith_poly_norm :args ((= (* 2 (- @t18 @t3)) (* 2 (- @t19 0))))) % 0.38/0.57 (step @p33 :rule arith_poly_norm_rel :premises (@p32) :args ((= (>= @t18 @t3) @t20))) % 0.38/0.57 (step @p34 :rule arith_poly_norm :args ((= @t5 @t18))) % 0.38/0.57 (step @p35 :rule cong :premises (@p34 @p25) :args (@t31)) % 0.38/0.57 (step @p36 :rule trans :premises (@p35 @p33)) % 0.38/0.57 (step @p37 :rule cong :premises (@p36) :args ((not @t31))) % 0.38/0.57 (step @p38 :rule arith-elim-lt :args (@t5 @t3)) % 0.38/0.57 (step @p39 :rule trans :premises (@p38 @p37)) % 0.38/0.57 (step @p40 :rule nary_cong :premises (@p39 @p31) :args (@t6)) % 0.38/0.57 (step @p41 :rule cong :premises (@p40) :args (@t8)) % 0.38/0.57 (step @p42 :rule trans :premises (@p41 @p17)) % 0.38/0.57 (step @p43 :rule arith_poly_norm :args ((= (* 1 (- @t4 @t1)) (* 1 (- @t22 0))))) % 0.38/0.57 (step @p44 :rule arith_poly_norm_rel :premises (@p43) :args ((= @t32 @t23))) % 0.38/0.57 (step @p45 :rule cong :premises (@p44) :args ((not @t32))) % 0.38/0.57 (step @p46 :rule arith-elim-lt :args (@t4 @t1)) % 0.38/0.57 (step @p47 :rule trans :premises (@p46 @p45)) % 0.38/0.57 (step @p48 :rule cong :premises (@p47 @p42) :args (@t9)) % 0.38/0.57 (step @p49 :rule cong :premises (@p48) :args (@t11)) % 0.38/0.57 (step @p50 :rule trans :premises (@p49 @p8)) % 0.38/0.57 (step @p51 :rule cong :premises (@p50) :args (@t12)) % 0.38/0.57 (step @p52 :rule eq_resolve :premises (@p1 @p51)) % 0.38/0.57 (step @p53 :rule refl :args (@t46)) % 0.38/0.57 (step @p54 :rule bool-double-not-elim :args (@t33)) % 0.38/0.57 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or (not @t47) @t46))) % 0.38/0.57 (step @p56 :rule bool-double-not-elim :args (@t37)) % 0.38/0.57 (step @p57 :rule arith_poly_norm :args ((= (* -1 (- 0 @t50)) (* -1 (- @t49 1))))) % 0.38/0.57 (step @p58 :rule arith_poly_norm_rel :premises (@p57) :args ((= (>= 0 @t50) (>= @t49 1)))) % 0.38/0.57 (step @p59 :rule arith-geq-tighten :args (@t36 0)) % 0.38/0.57 (step @p60 :rule trans :premises (@p59 @p58)) % 0.38/0.57 (step @p61 :rule symm :premises (@p60)) % 0.38/0.57 (step @p62 :rule refl :args (1)) % 0.38/0.57 (step @p63 :rule arith_poly_norm :args ((= @t51 @t49))) % 0.38/0.57 (step @p64 :rule cong :premises (@p63 @p62) :args (@t52)) % 0.38/0.57 (step @p65 :rule trans :premises (@p64 @p61)) % 0.38/0.57 (step @p66 :rule cong :premises (@p65) :args (@t53)) % 0.38/0.57 (step @p67 :rule trans :premises (@p66 @p56)) % 0.38/0.57 (step @p68 :rule arith_poly_norm :args ((= (* -1 (- 1 @t56)) (* -1 (- @t55 0))))) % 0.38/0.57 (step @p69 :rule arith_poly_norm_rel :premises (@p68) :args ((= (>= 1 @t56) (>= @t55 0)))) % 0.38/0.57 (step @p70 :rule arith-geq-tighten :args (@t40 1)) % 0.38/0.57 (step @p71 :rule trans :premises (@p70 @p69)) % 0.38/0.57 (step @p72 :rule symm :premises (@p71)) % 0.38/0.57 (step @p73 :rule refl :args (0)) % 0.38/0.57 (step @p74 :rule arith_poly_norm :args ((= @t57 @t55))) % 0.38/0.57 (step @p75 :rule cong :premises (@p74 @p73) :args (@t58)) % 0.38/0.57 (step @p76 :rule trans :premises (@p75 @p72)) % 0.38/0.57 (step @p77 :rule nary_cong :premises (@p76 @p67) :args (@t59)) % 0.38/0.57 (step @p78 :rule cong :premises (@p77) :args (@t60)) % 0.38/0.57 (step @p79 :rule cong :premises (@p78) :args (@t61)) % 0.38/0.57 (step @p80 :rule refl :args (@t44)) % 0.38/0.57 (step @p81 :rule nary_cong :premises (@p80 @p79) :args (@t62)) % 0.38/0.57 (step @p82 :rule cong :premises (@p81) :args (@t63)) % 0.38/0.57 (step @p83 :rule refl :args (@t47)) % 0.38/0.57 (step @p84 :rule cong :premises (@p83 @p82) :args ((=> @t47 @t63))) % 0.38/0.57 (assume-push @p134 @t47) % 0.38/0.57 (step @p86 :rule skolemize :premises (@p52)) % 0.38/0.57 (step-pop @p135 :rule scope :premises (@p86)) % 0.38/0.57 (step @p87 :rule process_scope :premises (@p135) :args (@t63)) % 0.38/0.57 (step @p89 :rule eq_resolve :premises (@p87 @p84)) % 0.38/0.57 (step @p90 :rule implies_elim :premises (@p89)) % 0.38/0.57 (step @p91 :rule eq_resolve :premises (@p90 @p55)) % 0.38/0.57 (step @p92 :rule chain_m_resolution :premises (@p91 @p52) :args (@t46 @t64 (@list @t33))) % 0.38/0.57 (step @p93 :rule cnf_or_neg :args (@t45 0)) % 0.38/0.57 (step @p94 :rule chain_m_resolution :premises (@p93 @p92) :args ((not @t44) @t64 @t65)) % 0.38/0.57 (step @p95 :rule bool-double-not-elim :args (@t41)) % 0.38/0.57 (step @p96 :rule refl :args (@t45)) % 0.38/0.57 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or @t45 (not @t42)))) % 0.38/0.57 (step @p98 :rule cnf_or_neg :args (@t45 1)) % 0.38/0.57 (step @p99 :rule eq_resolve :premises (@p98 @p97)) % 0.38/0.57 (step @p100 :rule reordering :premises (@p99) :args ((or @t41 @t45))) % 0.38/0.57 (step @p101 :rule chain_m_resolution :premises (@p100 @p92) :args (@t41 @t64 @t65)) % 0.38/0.57 (step @p102 :rule aci_norm :args ((= (or @t44 false) @t44))) % 0.38/0.57 (step @p103 :rule evaluate :args ((>= -1 0))) % 0.38/0.57 (step @p104 :rule arith_poly_norm :args ((= @t66 -1))) % 0.38/0.57 (step @p105 :rule arith_poly_norm :args ((= @t68 @t66))) % 0.38/0.57 (step @p106 :rule trans :premises (@p105 @p104)) % 0.38/0.57 (step @p107 :rule cong :premises (@p106 @p73) :args (@t69)) % 0.38/0.57 (step @p108 :rule trans :premises (@p107 @p103)) % 0.38/0.57 (step @p109 :rule bool-double-not-elim :args (@t44)) % 0.38/0.57 (step @p110 :rule arith_poly_norm :args ((= (* -2 (- 0 @t71)) (* -1 (- @t70 1))))) % 0.38/0.57 (step @p111 :rule arith_poly_norm_rel :premises (@p110) :args ((= (>= 0 @t71) (>= @t70 1)))) % 0.38/0.57 (step @p112 :rule arith-geq-tighten :args (@t43 0)) % 0.38/0.57 (step @p113 :rule trans :premises (@p112 @p111)) % 0.38/0.57 (step @p114 :rule symm :premises (@p113)) % 0.38/0.57 (step @p115 :rule arith_poly_norm :args ((= @t72 @t70))) % 0.38/0.57 (step @p116 :rule arith_poly_norm :args ((= @t73 @t72))) % 0.38/0.57 (step @p117 :rule trans :premises (@p116 @p115)) % 0.38/0.57 (step @p118 :rule cong :premises (@p117 @p62) :args (@t74)) % 0.38/0.57 (step @p119 :rule trans :premises (@p118 @p114)) % 0.38/0.57 (step @p120 :rule cong :premises (@p119) :args (@t75)) % 0.38/0.57 (step @p121 :rule trans :premises (@p120 @p109)) % 0.38/0.57 (step @p122 :rule nary_cong :premises (@p121 @p108) :args (@t76)) % 0.38/0.58 (step @p123 :rule trans :premises (@p122 @p102)) % 0.38/0.58 (step @p124 :rule refl :args (@t41)) % 0.38/0.58 (step @p125 :rule cong :premises (@p124 @p123) :args ((=> @t41 @t76))) % 0.38/0.58 (assume-push @p136 @t41) % 0.38/0.58 (step @p127 :rule instantiate :premises (@p101) :args ((@list @t67))) % 0.38/0.58 (step-pop @p137 :rule scope :premises (@p127)) % 0.38/0.58 (step @p128 :rule process_scope :premises (@p137) :args (@t76)) % 0.38/0.58 (step @p130 :rule eq_resolve :premises (@p128 @p125)) % 0.38/0.58 (step @p131 :rule implies_elim :premises (@p130)) % 0.38/0.58 (step @p132 :rule reordering :premises (@p131) :args (@t45)) % 0.38/0.58 (step @p133 false :rule chain_m_resolution :premises (@p132 @p101 @p94) :args (false (@list false true) (@list @t41 @t44))) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------