%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : DAT099_1 : TPTP v9.2.1. Released v6.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n014.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 08:14:31 AM UTC 2026 % Result : Theorem 0.39s 0.64s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : DAT099_1 : TPTP v9.2.1. Released v6.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n014.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Mon Jun 1 22:28:43 EDT 2026 % 0.15/0.34 % CPUTime : % 0.27/0.50 %----Proving TF0_ARI % 0.39/0.64 --- Run --finite-model-find --decision=internal at 45... % 0.39/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 60... % 0.39/0.64 % SZS status Theorem % 0.39/0.64 % SZS output start Proof % 0.39/0.64 ( % 0.39/0.64 (declare-sort tptp.list 0) % 0.39/0.64 (declare-const tptp.inRange (-> Int tptp.list Bool)) % 0.39/0.64 (declare-const tptp.nil tptp.list) % 0.39/0.64 (declare-const tptp.tail (-> tptp.list tptp.list)) % 0.39/0.64 (declare-const tptp.head (-> tptp.list Int)) % 0.39/0.64 (declare-const tptp.cons (-> Int tptp.list tptp.list)) % 0.39/0.64 (define @t1 () (@var "K" Int)) % 0.39/0.64 (define @t2 () (@var "L" tptp.list)) % 0.39/0.64 (define @t3 () (tptp.cons @t1 @t2)) % 0.39/0.64 (define @t4 () (@list @t1 @t2)) % 0.39/0.64 (define @t5 () (= @t2 tptp.nil)) % 0.39/0.64 (define @t6 () (@var "T" tptp.list)) % 0.39/0.64 (define @t7 () (@var "N" Int)) % 0.39/0.64 (define @t8 () (tptp.inRange @t7 @t6)) % 0.39/0.64 (define @t9 () (tptp.cons @t1 @t6)) % 0.39/0.64 (define @t10 () (= @t2 @t9)) % 0.39/0.64 (define @t11 () (and @t10 (<= 0 @t1) (< @t1 @t7) @t8)) % 0.39/0.64 (define @t12 () (@list @t1 @t6)) % 0.39/0.64 (define @t13 () (exists @t12 @t11)) % 0.39/0.64 (define @t14 () (or @t5 @t13)) % 0.39/0.64 (define @t15 () (tptp.inRange @t7 @t2)) % 0.39/0.64 (define @t16 () (= @t15 @t14)) % 0.39/0.64 (define @t17 () (@list @t7 @t2)) % 0.39/0.64 (define @t18 () (forall @t17 @t16)) % 0.39/0.64 (define @t19 () (tptp.cons 2 tptp.nil)) % 0.39/0.64 (define @t20 () (tptp.cons 3 @t19)) % 0.39/0.64 (define @t21 () (tptp.cons 1 @t20)) % 0.39/0.64 (define @t22 () (tptp.inRange @t7 @t21)) % 0.39/0.64 (define @t23 () (>= @t7 4)) % 0.39/0.64 (define @t24 () (@list @t7)) % 0.39/0.64 (define @t25 () (forall @t24 (=> @t23 @t22))) % 0.39/0.64 (define @t26 () (not @t25)) % 0.39/0.64 (define @t27 () (not @t8)) % 0.39/0.64 (define @t28 () (+ @t1 (* -1 @t7))) % 0.39/0.64 (define @t29 () (>= @t28 0)) % 0.39/0.64 (define @t30 () (>= @t1 0)) % 0.39/0.64 (define @t31 () (not @t30)) % 0.39/0.64 (define @t32 () (not @t10)) % 0.39/0.64 (define @t33 () (not @t29)) % 0.39/0.64 (define @t34 () (not @t33)) % 0.39/0.64 (define @t35 () (or @t32 @t31 @t34 @t27)) % 0.39/0.64 (define @t36 () (and @t10 @t30 @t33 @t8)) % 0.39/0.64 (define @t37 () (forall @t12 (not @t36))) % 0.39/0.64 (define @t38 () (not @t37)) % 0.39/0.64 (define @t39 () (>= @t1 @t7)) % 0.39/0.64 (define @t40 () (@quantifiers_skolemize (forall @t24 (or (not @t23) @t22)) 0)) % 0.39/0.64 (define @t41 () (not (tptp.inRange @t40 @t6))) % 0.39/0.64 (define @t42 () (* -1 @t40)) % 0.39/0.64 (define @t43 () (>= (+ @t1 @t42) 0)) % 0.39/0.64 (define @t44 () (not (= @t19 @t9))) % 0.39/0.64 (define @t45 () (or @t44 @t31 @t43 @t41)) % 0.39/0.64 (define @t46 () (forall @t12 @t45)) % 0.39/0.64 (define @t47 () (not @t46)) % 0.39/0.64 (define @t48 () (= tptp.nil @t19)) % 0.39/0.64 (define @t49 () (or @t48 @t47)) % 0.39/0.64 (define @t50 () (tptp.inRange @t40 @t19)) % 0.39/0.64 (define @t51 () (= @t50 @t49)) % 0.39/0.64 (define @t52 () (forall @t17 (= @t15 (or (= tptp.nil @t2) (not (forall @t12 (or @t32 @t31 @t29 @t27))))))) % 0.39/0.64 (define @t53 () (forall @t12 (or (not (= @t9 @t19)) @t31 @t43 @t41))) % 0.39/0.64 (define @t54 () (not @t53)) % 0.39/0.64 (define @t55 () (or @t48 @t54)) % 0.39/0.64 (define @t56 () (= @t50 @t55)) % 0.39/0.64 (define @t57 () (@list false)) % 0.39/0.64 (define @t58 () (@list @t52)) % 0.39/0.64 (define @t59 () (not (= @t20 @t9))) % 0.39/0.64 (define @t60 () (or @t59 @t31 @t43 @t41)) % 0.39/0.64 (define @t61 () (forall @t12 @t60)) % 0.39/0.64 (define @t62 () (not @t61)) % 0.39/0.64 (define @t63 () (= tptp.nil @t20)) % 0.39/0.64 (define @t64 () (or @t63 @t62)) % 0.39/0.64 (define @t65 () (tptp.inRange @t40 @t20)) % 0.39/0.64 (define @t66 () (= @t65 @t64)) % 0.39/0.64 (define @t67 () (forall @t12 (or (not (= @t9 @t20)) @t31 @t43 @t41))) % 0.39/0.64 (define @t68 () (not @t67)) % 0.39/0.64 (define @t69 () (or @t63 @t68)) % 0.39/0.64 (define @t70 () (= @t65 @t69)) % 0.39/0.64 (define @t71 () (not (= @t21 @t9))) % 0.39/0.64 (define @t72 () (or @t71 @t31 @t43 @t41)) % 0.39/0.64 (define @t73 () (forall @t12 @t72)) % 0.39/0.64 (define @t74 () (not @t73)) % 0.39/0.64 (define @t75 () (= tptp.nil @t21)) % 0.39/0.64 (define @t76 () (or @t75 @t74)) % 0.39/0.64 (define @t77 () (tptp.inRange @t40 @t21)) % 0.39/0.64 (define @t78 () (= @t77 @t76)) % 0.39/0.64 (define @t79 () (forall @t12 (or (not (= @t9 @t21)) @t31 @t43 @t41))) % 0.39/0.64 (define @t80 () (not @t79)) % 0.39/0.64 (define @t81 () (or @t75 @t80)) % 0.39/0.64 (define @t82 () (= @t77 @t81)) % 0.39/0.64 (define @t83 () (>= @t40 4)) % 0.39/0.64 (define @t84 () (not @t83)) % 0.39/0.64 (define @t85 () (or @t84 @t77)) % 0.39/0.64 (define @t86 () (@list true)) % 0.39/0.64 (define @t87 () (@list @t85)) % 0.39/0.64 (define @t88 () (not @t81)) % 0.39/0.64 (define @t89 () (@list true false)) % 0.39/0.64 (define @t90 () (not @t65)) % 0.39/0.64 (define @t91 () (>= @t40 2)) % 0.39/0.64 (define @t92 () (not @t91)) % 0.39/0.64 (define @t93 () (or @t92 @t90)) % 0.39/0.64 (define @t94 () (+ 1 @t42)) % 0.39/0.64 (define @t95 () (+ @t40 1)) % 0.39/0.64 (define @t96 () (>= @t94 0)) % 0.39/0.64 (define @t97 () (>= 1 0)) % 0.39/0.64 (define @t98 () (not @t97)) % 0.39/0.64 (define @t99 () (not (= @t21 @t21))) % 0.39/0.64 (define @t100 () (or @t99 @t98 @t96 @t90)) % 0.39/0.64 (define @t101 () (+ 1 1)) % 0.39/0.64 (define @t102 () (>= @t40 @t101)) % 0.39/0.64 (define @t103 () (<= @t40 1)) % 0.39/0.64 (define @t104 () (* -1 4)) % 0.39/0.64 (define @t105 () (+ 1 @t104)) % 0.39/0.64 (define @t106 () (+ @t40 @t42)) % 0.39/0.64 (define @t107 () (= @t106 0)) % 0.39/0.64 (define @t108 () (< -1 0)) % 0.39/0.64 (define @t109 () (and @t92 @t83)) % 0.39/0.64 (define @t110 () (@list @t83)) % 0.39/0.64 (define @t111 () (@list false false)) % 0.39/0.64 (define @t112 () (not @t69)) % 0.39/0.64 (define @t113 () (not @t50)) % 0.39/0.64 (define @t114 () (or @t84 @t113)) % 0.39/0.64 (define @t115 () (+ 3 @t42)) % 0.39/0.64 (define @t116 () (>= @t115 0)) % 0.39/0.64 (define @t117 () (>= 3 0)) % 0.39/0.64 (define @t118 () (not @t117)) % 0.39/0.64 (define @t119 () (not (= @t20 @t20))) % 0.39/0.64 (define @t120 () (or @t119 @t118 @t116 @t113)) % 0.39/0.64 (define @t121 () (not @t55)) % 0.39/0.64 (define @t122 () (>= @t40 3)) % 0.39/0.64 (define @t123 () (not @t122)) % 0.39/0.64 (define @t124 () (+ 2 1)) % 0.39/0.64 (define @t125 () (>= @t40 @t124)) % 0.39/0.64 (define @t126 () (<= @t40 2)) % 0.39/0.64 (define @t127 () (+ 2 @t104)) % 0.39/0.64 (define @t128 () (and @t123 @t83)) % 0.39/0.64 (define @t129 () (tptp.inRange @t40 tptp.nil)) % 0.39/0.64 (define @t130 () (not (forall @t12 (or (not (= tptp.nil @t9)) @t31 @t43 @t41)))) % 0.39/0.64 (define @t131 () (or (= tptp.nil tptp.nil) @t130)) % 0.39/0.64 (define @t132 () (= @t129 @t131)) % 0.39/0.64 (define @t133 () (not @t129)) % 0.39/0.64 (define @t134 () (or @t123 @t133)) % 0.39/0.64 (define @t135 () (not @t134)) % 0.39/0.64 (define @t136 () (+ 2 @t42)) % 0.39/0.64 (define @t137 () (>= @t136 0)) % 0.39/0.64 (define @t138 () (>= 2 0)) % 0.39/0.64 (define @t139 () (not @t138)) % 0.39/0.64 (define @t140 () (not (= @t19 @t19))) % 0.39/0.64 (define @t141 () (or @t140 @t139 @t137 @t133)) % 0.39/0.64 (assume @p1 (forall @t4 (= (tptp.head @t3) @t1))) % 0.39/0.64 (assume @p2 (forall @t4 (= (tptp.tail @t3) @t2))) % 0.39/0.64 (assume @p3 (forall (@list @t2) (or @t5 (= @t2 (tptp.cons (tptp.head @t2) (tptp.tail @t2)))))) % 0.39/0.64 (assume @p4 (forall @t4 (not (= @t3 tptp.nil)))) % 0.39/0.64 (assume @p5 @t18) % 0.39/0.64 (assume @p6 @t26) % 0.39/0.64 (assume @p7 true) % 0.39/0.64 (step @p8 :rule refl :args (@t27)) % 0.39/0.64 (step @p9 :rule bool-double-not-elim :args (@t29)) % 0.39/0.64 (step @p10 :rule refl :args (@t31)) % 0.39/0.64 (step @p11 :rule refl :args (@t32)) % 0.39/0.64 (step @p12 :rule nary_cong :premises (@p11 @p10 @p9 @p8) :args (@t35)) % 0.39/0.64 (step @p13 :rule aci_norm :args ((= (or @t32 (or @t31 (or @t34 @t27))) @t35))) % 0.39/0.64 (step @p14 :rule trans :premises (@p13 @p12)) % 0.39/0.64 (step @p15 :rule bool-and-de-morgan :args (@t33 @t8 true)) % 0.39/0.64 (step @p16 :rule nary_cong :premises (@p10 @p15) :args ((or @t31 (not (and @t33 @t8))))) % 0.39/0.64 (step @p17 :rule bool-and-de-morgan :args (@t30 @t33 (and @t8))) % 0.39/0.64 (step @p18 :rule trans :premises (@p17 @p16)) % 0.39/0.64 (step @p19 :rule nary_cong :premises (@p11 @p18) :args ((or @t32 (not (and @t30 @t33 @t8))))) % 0.39/0.64 (step @p20 :rule bool-and-de-morgan :args (@t10 @t30 (and @t33 @t8))) % 0.39/0.64 (step @p21 :rule trans :premises (@p20 @p19)) % 0.39/0.64 (step @p22 :rule trans :premises (@p21 @p14)) % 0.39/0.64 (step @p23 :rule cong :premises (@p22) :args (@t37)) % 0.39/0.64 (step @p24 :rule cong :premises (@p23) :args (@t38)) % 0.39/0.64 (step @p25 :rule exists-elim :args ((= (exists @t12 @t36) @t38))) % 0.39/0.64 (step @p26 :rule trans :premises (@p25 @p24)) % 0.39/0.64 (step @p27 :rule refl :args (@t8)) % 0.39/0.64 (step @p28 :rule arith_poly_norm :args ((= (* 1 (- @t1 @t7)) (* 1 (- @t28 0))))) % 0.39/0.64 (step @p29 :rule arith_poly_norm_rel :premises (@p28) :args ((= @t39 @t29))) % 0.39/0.64 (step @p30 :rule cong :premises (@p29) :args ((not @t39))) % 0.39/0.64 (step @p31 :rule arith-elim-lt :args (@t1 @t7)) % 0.39/0.64 (step @p32 :rule trans :premises (@p31 @p30)) % 0.39/0.64 (step @p33 :rule arith-elim-leq :args (0 @t1)) % 0.39/0.64 (step @p34 :rule refl :args (@t10)) % 0.39/0.64 (step @p35 :rule nary_cong :premises (@p34 @p33 @p32 @p27) :args (@t11)) % 0.39/0.64 (step @p36 :rule cong :premises (@p35) :args (@t13)) % 0.39/0.64 (step @p37 :rule trans :premises (@p36 @p26)) % 0.39/0.64 (step @p38 :rule eq-symm :args (@t2 tptp.nil)) % 0.39/0.64 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t14)) % 0.39/0.64 (step @p40 :rule refl :args (@t15)) % 0.39/0.64 (step @p41 :rule cong :premises (@p40 @p39) :args (@t16)) % 0.39/0.64 (step @p42 :rule cong :premises (@p41) :args (@t18)) % 0.39/0.64 (step @p43 :rule eq_resolve :premises (@p5 @p42)) % 0.39/0.64 (step @p44 :rule refl :args (@t41)) % 0.39/0.64 (step @p45 :rule refl :args (@t43)) % 0.39/0.64 (step @p46 :rule refl :args (@t31)) % 0.39/0.64 (step @p47 :rule eq-symm :args (@t19 @t9)) % 0.39/0.64 (step @p48 :rule cong :premises (@p47) :args (@t44)) % 0.39/0.64 (step @p49 :rule nary_cong :premises (@p48 @p46 @p45 @p44) :args (@t45)) % 0.39/0.64 (step @p50 :rule cong :premises (@p49) :args (@t46)) % 0.39/0.64 (step @p51 :rule cong :premises (@p50) :args (@t47)) % 0.39/0.64 (step @p52 :rule refl :args (@t48)) % 0.39/0.64 (step @p53 :rule nary_cong :premises (@p52 @p51) :args (@t49)) % 0.39/0.64 (step @p54 :rule refl :args (@t50)) % 0.39/0.64 (step @p55 :rule cong :premises (@p54 @p53) :args (@t51)) % 0.39/0.64 (step @p56 :rule refl :args (@t52)) % 0.39/0.64 (step @p57 :rule cong :premises (@p56 @p55) :args ((=> @t52 @t51))) % 0.39/0.64 (assume-push @p361 @t52) % 0.39/0.64 (step @p59 :rule instantiate :premises (@p43) :args ((@list @t40 @t19))) % 0.39/0.64 (step-pop @p362 :rule scope :premises (@p59)) % 0.39/0.64 (step @p60 :rule process_scope :premises (@p362) :args (@t51)) % 0.39/0.64 (step @p62 :rule eq_resolve :premises (@p60 @p57)) % 0.39/0.64 (step @p63 :rule implies_elim :premises (@p62)) % 0.39/0.64 (step @p64 :rule chain_m_resolution :premises (@p63 @p43) :args (@t56 @t57 @t58)) % 0.39/0.64 (step @p65 :rule eq-symm :args (@t20 @t9)) % 0.39/0.64 (step @p66 :rule cong :premises (@p65) :args (@t59)) % 0.39/0.64 (step @p67 :rule nary_cong :premises (@p66 @p46 @p45 @p44) :args (@t60)) % 0.39/0.64 (step @p68 :rule cong :premises (@p67) :args (@t61)) % 0.39/0.64 (step @p69 :rule cong :premises (@p68) :args (@t62)) % 0.39/0.64 (step @p70 :rule refl :args (@t63)) % 0.39/0.64 (step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t64)) % 0.39/0.64 (step @p72 :rule refl :args (@t65)) % 0.39/0.64 (step @p73 :rule cong :premises (@p72 @p71) :args (@t66)) % 0.39/0.64 (step @p74 :rule cong :premises (@p56 @p73) :args ((=> @t52 @t66))) % 0.39/0.64 (assume-push @p363 @t52) % 0.39/0.64 (step @p76 :rule instantiate :premises (@p43) :args ((@list @t40 @t20))) % 0.39/0.64 (step-pop @p364 :rule scope :premises (@p76)) % 0.39/0.64 (step @p77 :rule process_scope :premises (@p364) :args (@t66)) % 0.39/0.64 (step @p79 :rule eq_resolve :premises (@p77 @p74)) % 0.39/0.64 (step @p80 :rule implies_elim :premises (@p79)) % 0.39/0.64 (step @p81 :rule chain_m_resolution :premises (@p80 @p43) :args (@t70 @t57 @t58)) % 0.39/0.64 (step @p82 :rule eq-symm :args (@t21 @t9)) % 0.39/0.64 (step @p83 :rule cong :premises (@p82) :args (@t71)) % 0.39/0.64 (step @p84 :rule nary_cong :premises (@p83 @p46 @p45 @p44) :args (@t72)) % 0.39/0.64 (step @p85 :rule cong :premises (@p84) :args (@t73)) % 0.39/0.64 (step @p86 :rule cong :premises (@p85) :args (@t74)) % 0.39/0.64 (step @p87 :rule refl :args (@t75)) % 0.39/0.64 (step @p88 :rule nary_cong :premises (@p87 @p86) :args (@t76)) % 0.39/0.64 (step @p89 :rule refl :args (@t77)) % 0.39/0.64 (step @p90 :rule cong :premises (@p89 @p88) :args (@t78)) % 0.39/0.64 (step @p91 :rule cong :premises (@p56 @p90) :args ((=> @t52 @t78))) % 0.39/0.64 (assume-push @p365 @t52) % 0.39/0.64 (step @p93 :rule instantiate :premises (@p43) :args ((@list @t40 @t21))) % 0.39/0.64 (step-pop @p366 :rule scope :premises (@p93)) % 0.39/0.64 (step @p94 :rule process_scope :premises (@p366) :args (@t78)) % 0.39/0.64 (step @p96 :rule eq_resolve :premises (@p94 @p91)) % 0.39/0.64 (step @p97 :rule implies_elim :premises (@p96)) % 0.39/0.64 (step @p98 :rule chain_m_resolution :premises (@p97 @p43) :args (@t82 @t57 @t58)) % 0.39/0.64 (step @p99 :rule bool-impl-elim :args (@t23 @t22)) % 0.39/0.64 (step @p100 :rule cong :premises (@p99) :args (@t25)) % 0.39/0.64 (step @p101 :rule cong :premises (@p100) :args (@t26)) % 0.39/0.64 (step @p102 :rule eq_resolve :premises (@p6 @p101)) % 0.39/0.64 (step @p103 :rule skolemize :premises (@p102)) % 0.39/0.64 (step @p104 :rule cnf_or_neg :args (@t85 1)) % 0.39/0.64 (step @p105 :rule chain_m_resolution :premises (@p104 @p103) :args ((not @t77) @t86 @t87)) % 0.39/0.64 (step @p106 :rule cnf_equiv_pos2 :args (@t82)) % 0.39/0.64 (step @p107 :rule reordering :premises (@p106) :args ((or @t77 @t88 (not @t82)))) % 0.39/0.64 (step @p108 :rule chain_m_resolution :premises (@p107 @p105 @p98) :args (@t88 @t89 (@list @t77 @t82))) % 0.39/0.64 (step @p109 :rule bool-double-not-elim :args (@t79)) % 0.39/0.64 (step @p110 :rule refl :args (@t81)) % 0.39/0.64 (step @p111 :rule nary_cong :premises (@p110 @p109) :args ((or @t81 (not @t80)))) % 0.39/0.64 (step @p112 :rule cnf_or_neg :args (@t81 1)) % 0.39/0.64 (step @p113 :rule eq_resolve :premises (@p112 @p111)) % 0.39/0.64 (step @p114 :rule reordering :premises (@p113) :args ((or @t79 @t81))) % 0.39/0.64 (step @p115 :rule chain_m_resolution :premises (@p114 @p108) :args (@t79 @t86 (@list @t81))) % 0.39/0.64 (step @p116 :rule aci_norm :args ((= (or false false @t92 @t90) @t93))) % 0.39/0.64 (step @p117 :rule refl :args (@t90)) % 0.39/0.64 (step @p118 :rule arith_poly_norm :args ((= (* 1 (- 2 @t95)) (* 1 (- @t94 0))))) % 0.39/0.64 (step @p119 :rule arith_poly_norm_rel :premises (@p118) :args ((= (>= 2 @t95) @t96))) % 0.39/0.64 (step @p120 :rule arith-geq-tighten :args (@t40 2)) % 0.39/0.64 (step @p121 :rule trans :premises (@p120 @p119)) % 0.39/0.64 (step @p122 :rule symm :premises 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