%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ARI670_1 : TPTP v9.2.1. Released v6.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n012.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 08:08:06 AM UTC 2026 % Result : Theorem 0.18s 0.39s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : ARI670_1 : TPTP v9.2.1. Released v6.3.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.08/0.25 % Computer : n012.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 : Wed Jun 3 02:31:48 EDT 2026 % 0.08/0.25 % CPUTime : % 0.18/0.33 %----Proving TF0_ARI % 0.18/0.39 --- Run --finite-model-find --decision=internal at 45... % 0.18/0.39 % SZS status Theorem % 0.18/0.39 % SZS output start Proof % 0.18/0.39 ( % 0.18/0.39 (declare-const tptp.a Int) % 0.18/0.39 (define @t1 () (* tptp.a tptp.a)) % 0.18/0.39 (define @t2 () (<= tptp.a @t1)) % 0.18/0.39 (define @t3 () (not @t2)) % 0.18/0.39 (define @t4 () (* tptp.a tptp.a)) % 0.18/0.39 (define @t5 () (>= @t4 1)) % 0.18/0.39 (define @t6 () (= tptp.a 0)) % 0.18/0.39 (define @t7 () (not @t6)) % 0.18/0.39 (define @t8 () (not @t7)) % 0.18/0.39 (define @t9 () (+ 0 1)) % 0.18/0.39 (define @t10 () (>= @t4 @t9)) % 0.18/0.39 (define @t11 () (* -1 @t4)) % 0.18/0.39 (define @t12 () (+ tptp.a @t11)) % 0.18/0.39 (define @t13 () (>= @t12 1)) % 0.18/0.39 (define @t14 () (* -1 (- @t12 1))) % 0.18/0.39 (define @t15 () (+ @t4 1)) % 0.18/0.39 (define @t16 () (>= tptp.a @t15)) % 0.18/0.39 (define @t17 () (>= tptp.a 0)) % 0.18/0.39 (define @t18 () (not @t5)) % 0.18/0.39 (define @t19 () (not @t13)) % 0.18/0.39 (define @t20 () (not @t17)) % 0.18/0.39 (define @t21 () (< tptp.a 0)) % 0.18/0.39 (define @t22 () (not true)) % 0.18/0.39 (define @t23 () (* -1 1)) % 0.18/0.39 (define @t24 () (+ 0 @t23 @t23)) % 0.18/0.39 (define @t25 () (* -1 tptp.a)) % 0.18/0.39 (define @t26 () (+ @t25 @t4)) % 0.18/0.39 (define @t27 () (* -1 @t12)) % 0.18/0.39 (define @t28 () (= @t27 @t26)) % 0.18/0.39 (define @t29 () (+ tptp.a @t11 @t27)) % 0.18/0.39 (define @t30 () (>= @t29 @t24)) % 0.18/0.39 (define @t31 () (< -1 0)) % 0.18/0.39 (define @t32 () (>= tptp.a 2)) % 0.18/0.39 (define @t33 () (not @t32)) % 0.18/0.39 (define @t34 () (+ 2 @t23 @t23)) % 0.18/0.39 (define @t35 () (+ tptp.a @t27 @t11)) % 0.18/0.39 (define @t36 () (>= @t35 @t34)) % 0.18/0.39 (define @t37 () (>= @t4 -1)) % 0.18/0.39 (define @t38 () (not @t37)) % 0.18/0.39 (define @t39 () (+ -2 1)) % 0.18/0.39 (define @t40 () (>= @t4 @t39)) % 0.18/0.39 (define @t41 () (<= @t4 -2)) % 0.18/0.39 (define @t42 () (+ -2 @t23)) % 0.18/0.39 (define @t43 () (+ @t4 @t11)) % 0.18/0.39 (define @t44 () (and @t38 @t5)) % 0.18/0.39 (define @t45 () (>= @t12 0)) % 0.18/0.39 (define @t46 () (not @t45)) % 0.18/0.39 (define @t47 () (+ -1 1)) % 0.18/0.39 (define @t48 () (>= @t12 @t47)) % 0.18/0.39 (define @t49 () (<= @t12 -1)) % 0.18/0.39 (define @t50 () (+ -1 @t23)) % 0.18/0.39 (define @t51 () (* 0 tptp.a)) % 0.18/0.39 (define @t52 () (* 0 @t4)) % 0.18/0.39 (define @t53 () (+ @t52 @t51)) % 0.18/0.39 (define @t54 () (+ @t12 @t27)) % 0.18/0.39 (define @t55 () (and @t46 @t13)) % 0.18/0.39 (define @t56 () (@list false)) % 0.18/0.39 (define @t57 () (+ tptp.a @t4)) % 0.18/0.39 (define @t58 () (>= @t57 1)) % 0.18/0.39 (define @t59 () (ite @t17 @t46 @t58)) % 0.18/0.39 (define @t60 () (>= tptp.a -1)) % 0.18/0.39 (define @t61 () (not @t60)) % 0.18/0.39 (define @t62 () (ite @t17 @t32 @t61)) % 0.18/0.39 (define @t63 () (not @t62)) % 0.18/0.39 (define @t64 () (and @t62 @t7)) % 0.18/0.39 (define @t65 () (- 1)) % 0.18/0.39 (define @t66 () (- @t4)) % 0.18/0.39 (define @t67 () (<= @t66 @t65)) % 0.18/0.39 (define @t68 () (<= @t66 1)) % 0.18/0.39 (define @t69 () (>= 1 0)) % 0.18/0.39 (define @t70 () (ite @t69 (> @t66 1) (> @t66 @t65))) % 0.18/0.39 (define @t71 () (>= @t4 2)) % 0.18/0.39 (define @t72 () (>= @t4 0)) % 0.18/0.39 (define @t73 () (>= @t4 @t47)) % 0.18/0.39 (define @t74 () (<= @t4 @t65)) % 0.18/0.39 (define @t75 () (+ 1 1)) % 0.18/0.39 (define @t76 () (>= @t4 @t75)) % 0.18/0.39 (define @t77 () (ite @t69 (> @t4 1) (> @t4 @t65))) % 0.18/0.39 (define @t78 () (ite @t72 @t77 @t70)) % 0.18/0.39 (define @t79 () (>= tptp.a 1)) % 0.18/0.39 (define @t80 () (- tptp.a)) % 0.18/0.39 (define @t81 () (<= @t80 @t65)) % 0.18/0.39 (define @t82 () (<= @t80 1)) % 0.18/0.39 (define @t83 () (ite @t69 (> @t80 1) (> @t80 @t65))) % 0.18/0.39 (define @t84 () (>= tptp.a @t47)) % 0.18/0.39 (define @t85 () (<= tptp.a @t65)) % 0.18/0.39 (define @t86 () (>= tptp.a @t75)) % 0.18/0.39 (define @t87 () (ite @t69 (> tptp.a 1) (> tptp.a @t65))) % 0.18/0.39 (define @t88 () (ite @t17 @t87 @t83)) % 0.18/0.39 (define @t89 () (and @t88 @t7)) % 0.18/0.39 (define @t90 () (abs @t4)) % 0.18/0.39 (define @t91 () (>= @t90 @t75)) % 0.18/0.39 (define @t92 () (abs 1)) % 0.18/0.39 (define @t93 () (<= @t90 @t92)) % 0.18/0.39 (define @t94 () (* 1 1)) % 0.18/0.39 (define @t95 () (abs @t94)) % 0.18/0.39 (define @t96 () (<= @t90 @t95)) % 0.18/0.39 (define @t97 () (ite @t72 @t71 @t38)) % 0.18/0.39 (define @t98 () (+ @t25 1)) % 0.18/0.39 (define @t99 () (>= @t11 @t98)) % 0.18/0.39 (define @t100 () (<= @t66 @t80)) % 0.18/0.39 (define @t101 () (>= @t57 0)) % 0.18/0.39 (define @t102 () (<= @t66 tptp.a)) % 0.18/0.39 (define @t103 () (ite @t17 (> @t66 tptp.a) (> @t66 @t80))) % 0.18/0.39 (define @t104 () (>= @t4 @t98)) % 0.18/0.39 (define @t105 () (<= @t4 @t80)) % 0.18/0.39 (define @t106 () (>= tptp.a @t4)) % 0.18/0.39 (define @t107 () (ite @t17 (> @t4 tptp.a) (> @t4 @t80))) % 0.18/0.39 (define @t108 () (ite @t72 @t107 @t103)) % 0.18/0.39 (define @t109 () (abs tptp.a)) % 0.18/0.39 (define @t110 () (+ @t109 (* -1 @t90))) % 0.18/0.39 (define @t111 () (>= @t109 @t90)) % 0.18/0.39 (define @t112 () (* 1 tptp.a)) % 0.18/0.39 (define @t113 () (abs @t112)) % 0.18/0.39 (define @t114 () (<= @t90 @t113)) % 0.18/0.39 (define @t115 () (ite @t72 @t59 (ite @t17 (not @t101) @t13))) % 0.18/0.39 (define @t116 () (not @t72)) % 0.18/0.39 (define @t117 () (<= 0 -1)) % 0.18/0.39 (define @t118 () (* -1 0)) % 0.18/0.39 (define @t119 () (+ @t118 @t23 0)) % 0.18/0.39 (define @t120 () (+ @t11 @t27 tptp.a)) % 0.18/0.39 (define @t121 () (* 0 0)) % 0.18/0.39 (define @t122 () (= @t4 0)) % 0.18/0.39 (define @t123 () (not @t122)) % 0.18/0.39 (define @t124 () (+ @t118 -1)) % 0.18/0.39 (define @t125 () (+ @t11 @t4)) % 0.18/0.39 (define @t126 () (and @t122 @t116)) % 0.18/0.39 (assume @p1 @t3) % 0.18/0.39 (assume @p2 true) % 0.18/0.39 (step @p3 :rule refl :args (@t5)) % 0.18/0.39 (step @p4 :rule bool-double-not-elim :args (@t6)) % 0.18/0.39 (step @p5 :rule nary_cong :premises (@p4 @p3) :args ((or @t8 @t5))) % 0.18/0.39 (step @p6 :rule bool-double-not-elim :args (@t5)) % 0.18/0.39 (step @p7 :rule evaluate :args (@t9)) % 0.18/0.39 (step @p8 :rule refl :args (@t4)) % 0.18/0.39 (step @p9 :rule cong :premises (@p8 @p7) :args (@t10)) % 0.18/0.39 (step @p10 :rule cong :premises (@p9) :args ((not @t10))) % 0.18/0.39 (step @p11 :rule arith-leq-norm :args (@t4 0)) % 0.18/0.39 (step @p12 :rule trans :premises (@p11 @p10)) % 0.18/0.39 (step @p13 :rule cong :premises (@p12) :args ((not (<= @t4 0)))) % 0.18/0.39 (step @p14 :rule trans :premises (@p13 @p6)) % 0.18/0.39 (step @p15 :rule arith-elim-leq :args (@t4 0)) % 0.18/0.39 (step @p16 :rule symm :premises (@p15)) % 0.18/0.39 (step @p17 :rule cong :premises (@p16) :args ((not (>= 0 @t4)))) % 0.18/0.39 (step @p18 :rule arith-elim-gt :args (@t4 0)) % 0.18/0.39 (step @p19 :rule trans :premises (@p18 @p17)) % 0.18/0.39 (step @p20 :rule trans :premises (@p19 @p14)) % 0.18/0.39 (step @p21 :rule refl :args (@t7)) % 0.18/0.39 (step @p22 :rule cong :premises (@p21 @p20) :args ((=> @t7 (> @t4 0)))) % 0.18/0.39 (step @p23 :rule arith_mult_sign :args (@t7 @t4)) % 0.18/0.39 (step @p24 :rule eq_resolve :premises (@p23 @p22)) % 0.18/0.39 (step @p25 :rule implies_elim :premises (@p24)) % 0.18/0.39 (step @p26 :rule eq_resolve :premises (@p25 @p5)) % 0.18/0.39 (step @p27 :rule bool-double-not-elim :args (@t13)) % 0.18/0.39 (step @p28 :rule arith_poly_norm :args ((= (* -1 (- tptp.a @t15)) @t14))) % 0.18/0.39 (step @p29 :rule arith_poly_norm_rel :premises (@p28) :args ((= @t16 @t13))) % 0.18/0.39 (step @p30 :rule cong :premises (@p29) :args ((not @t16))) % 0.18/0.39 (step @p31 :rule arith-leq-norm :args (tptp.a @t4)) % 0.18/0.39 (step @p32 :rule trans :premises (@p31 @p30)) % 0.18/0.39 (step @p33 :rule arith_poly_norm :args ((= @t1 @t4))) % 0.18/0.39 (step @p34 :rule refl :args (tptp.a)) % 0.18/0.39 (step @p35 :rule cong :premises (@p34 @p33) :args (@t2)) % 0.18/0.39 (step @p36 :rule trans :premises (@p35 @p32)) % 0.18/0.39 (step @p37 :rule cong :premises (@p36) :args (@t3)) % 0.18/0.39 (step @p38 :rule trans :premises (@p37 @p27)) % 0.18/0.39 (step @p39 :rule eq_resolve :premises (@p1 @p38)) % 0.18/0.39 (step @p40 :rule bool-double-not-elim :args (@t17)) % 0.18/0.39 (step @p41 :rule refl :args (@t18)) % 0.18/0.39 (step @p42 :rule refl :args (@t19)) % 0.18/0.39 (step @p43 :rule nary_cong :premises (@p42 @p41 @p40) :args ((or @t19 @t18 (not @t20)))) % 0.18/0.39 (assume-push @p609 @t13) % 0.18/0.39 (assume-push @p610 @t5) % 0.18/0.39 (assume-push @p611 @t20) % 0.18/0.39 (step @p47 :rule arith-elim-lt :args (tptp.a 0)) % 0.18/0.39 (step @p48 :rule cong :premises (@p47) :args ((not @t21))) % 0.18/0.39 (step @p49 :rule trans :premises (@p48 @p40)) % 0.18/0.39 (step @p50 :rule symm :premises (@p49)) % 0.18/0.39 (assume-push @p612 @t21) % 0.18/0.39 (step @p52 :rule evaluate :args (@t22)) % 0.18/0.39 (step @p53 :rule evaluate :args ((>= 0 -2))) % 0.18/0.39 (step @p54 :rule evaluate :args ((+ 0 -1 -1))) % 0.18/0.39 (step @p55 :rule evaluate :args (@t23)) % 0.18/0.39 (step @p56 :rule refl :args (0)) % 0.18/0.39 (step @p57 :rule nary_cong :premises (@p56 @p55 @p55) :args (@t24)) % 0.18/0.39 (step @p58 :rule trans :premises (@p57 @p54)) % 0.18/0.39 (step @p59 :rule arith_poly_norm :args ((= (+ tptp.a @t11 @t26) 0))) % 0.18/0.39 (step @p60 :rule arith_poly_norm :args (@t28)) % 0.18/0.39 (step @p61 :rule refl :args (@t11)) % 0.18/0.39 (step @p62 :rule nary_cong :premises (@p34 @p61 @p60) :args (@t29)) % 0.18/0.39 (step @p63 :rule trans :premises (@p62 @p59)) % 0.18/0.39 (step @p64 :rule cong :premises (@p63 @p58) :args (@t30)) % 0.18/0.39 (step @p65 :rule trans :premises (@p64 @p53)) % 0.18/0.39 (step @p66 :rule cong :premises (@p65) :args ((not @t30))) % 0.18/0.39 (step @p67 :rule trans :premises (@p66 @p52)) % 0.18/0.39 (step @p68 :rule arith-elim-lt :args (@t29 @t24)) % 0.18/0.39 (step @p69 :rule trans :premises (@p68 @p67)) % 0.18/0.39 (step @p70 :rule arith_mult_neg :args (-1 @t13)) % 0.18/0.39 (step @p71 :rule evaluate :args (@t31)) % 0.18/0.39 (step @p72 :rule true_elim :premises (@p71)) % 0.18/0.39 (step @p73 :rule and_intro :premises (@p72 @p39)) % 0.18/0.39 (step @p74 :rule modus_ponens :premises (@p73 @p70)) % 0.18/0.39 (step @p75 :rule arith_mult_neg :args (-1 @t5)) % 0.18/0.39 (step @p76 :rule and_intro :premises (@p72 @p610)) % 0.18/0.39 (step @p77 :rule modus_ponens :premises (@p76 @p75)) % 0.18/0.39 (step @p78 :rule arith_sum_ub :premises (@p612 @p77 @p74)) % 0.18/0.39 (step @p79 false :rule eq_resolve :premises (@p78 @p69)) % 0.18/0.39 (step-pop @p613 :rule scope :premises (@p79)) % 0.18/0.39 (step @p80 :rule process_scope :premises (@p613) :args (false)) % 0.18/0.39 (step @p82 :rule eq_resolve :premises (@p80 @p49)) % 0.18/0.39 (step @p83 :rule eq_resolve :premises (@p82 @p50)) % 0.18/0.39 (step @p84 :rule symm :premises (@p47)) % 0.18/0.39 (step @p85 :rule eq_resolve :premises (@p611 @p84)) % 0.18/0.39 (step @p86 false :rule contra :premises (@p85 @p83)) % 0.18/0.39 (step-pop @p614 :rule scope :premises (@p86)) % 0.18/0.39 (step-pop @p615 :rule scope :premises (@p614)) % 0.18/0.39 (step-pop @p616 :rule scope :premises (@p615)) % 0.18/0.39 (step @p87 :rule process_scope :premises (@p616) :args (false)) % 0.18/0.39 (step @p91 :rule not_and :premises (@p87)) % 0.18/0.39 (step @p92 :rule eq_resolve :premises (@p91 @p43)) % 0.18/0.39 (step @p93 :rule bool-double-not-elim :args (@t32)) % 0.18/0.39 (step @p94 :rule nary_cong :premises (@p42 @p41 @p93) :args ((or @t19 @t18 (not @t33)))) % 0.18/0.39 (assume-push @p617 @t13) % 0.18/0.39 (assume-push @p618 @t5) % 0.18/0.39 (assume-push @p619 @t33) % 0.18/0.39 (step @p52 :rule evaluate :args (@t22)) % 0.18/0.39 (step @p98 :rule evaluate :args ((>= 0 0))) % 0.18/0.39 (step @p99 :rule evaluate :args ((+ 2 -1 -1))) % 0.18/0.39 (step @p55 :rule evaluate :args (@t23)) % 0.18/0.39 (step @p100 :rule refl :args (2)) % 0.18/0.39 (step @p101 :rule nary_cong :premises (@p100 @p55 @p55) :args (@t34)) % 0.18/0.39 (step @p102 :rule trans :premises (@p101 @p99)) % 0.18/0.39 (step @p103 :rule arith_poly_norm :args ((= (+ tptp.a @t26 @t11) 0))) % 0.18/0.39 (step @p61 :rule refl :args (@t11)) % 0.18/0.39 (step @p60 :rule arith_poly_norm :args (@t28)) % 0.18/0.39 (step @p104 :rule nary_cong :premises (@p34 @p60 @p61) :args (@t35)) % 0.18/0.39 (step @p105 :rule trans :premises (@p104 @p103)) % 0.18/0.39 (step @p106 :rule cong :premises (@p105 @p102) :args (@t36)) % 0.18/0.39 (step @p107 :rule trans :premises (@p106 @p98)) % 0.18/0.39 (step @p108 :rule cong :premises (@p107) :args ((not @t36))) % 0.18/0.39 (step @p109 :rule trans :premises (@p108 @p52)) % 0.18/0.39 (step @p110 :rule arith-elim-lt :args (@t35 @t34)) % 0.18/0.39 (step @p111 :rule trans :premises (@p110 @p109)) % 0.18/0.39 (step @p75 :rule arith_mult_neg :args (-1 @t5)) % 0.18/0.39 (step @p71 :rule evaluate :args (@t31)) % 0.18/0.39 (step @p72 :rule true_elim :premises (@p71)) % 0.18/0.39 (step @p112 :rule and_intro :premises (@p72 @p618)) % 0.18/0.39 (step @p113 :rule modus_ponens :premises (@p112 @p75)) % 0.18/0.39 (step @p70 :rule arith_mult_neg :args (-1 @t13)) % 0.18/0.39 (step @p73 :rule and_intro :premises (@p72 @p39)) % 0.18/0.39 (step @p74 :rule modus_ponens :premises (@p73 @p70)) % 0.18/0.39 (step @p114 :rule arith-elim-lt :args (tptp.a 2)) % 0.18/0.39 (step @p115 :rule symm :premises (@p114)) % 0.18/0.39 (step @p116 :rule eq_resolve :premises (@p619 @p115)) % 0.18/0.39 (step @p117 :rule 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0.18/0.40 (step @p606 :rule not_and :premises (@p605)) % 0.18/0.40 (step @p607 :rule eq_resolve :premises (@p606 @p573)) % 0.18/0.40 (step @p608 false :rule chain_m_resolution :premises (@p607 @p571 @p558) :args (false (@list false true) (@list @t122 @t72))) % 0.18/0.40 ) % 0.18/0.40 % SZS output end Proof % 0.18/0.40 % cvc5 exiting %------------------------------------------------------------------------------