%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : DAT029_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 : n021.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 08:14:22 AM UTC 2026 % Result : Theorem 45.68s 45.91s % Output : Proof 45.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : DAT029_1 : TPTP v9.2.1. Released v5.0.0. % 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.33 % Computer : n021.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Mon Jun 1 22:27:19 EDT 2026 % 0.16/0.33 % CPUTime : % 0.30/0.48 %----Proving TF0_ARI % 45.68/45.91 --- Run --finite-model-find --decision=internal at 45... % 45.68/45.91 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 60... % 45.68/45.91 % SZS status Theorem % 45.68/45.91 % SZS output start Proof % 45.68/45.91 ( % 45.68/45.91 (declare-sort tptp.collection 0) % 45.68/45.91 (declare-const tptp.remove (-> Int tptp.collection tptp.collection)) % 45.68/45.91 (declare-const tptp.add (-> Int tptp.collection tptp.collection)) % 45.68/45.91 (declare-const tptp.in (-> Int tptp.collection Bool)) % 45.68/45.91 (declare-const tptp.empty tptp.collection) % 45.68/45.91 (define @t1 () (@var "U" Int)) % 45.68/45.91 (define @t2 () (@var "W" tptp.collection)) % 45.68/45.91 (define @t3 () (@var "V" Int)) % 45.68/45.91 (define @t4 () (@var "Y" tptp.collection)) % 45.68/45.91 (define @t5 () (@var "X" Int)) % 45.68/45.91 (define @t6 () (@var "X1" tptp.collection)) % 45.68/45.91 (define @t7 () (@var "X2" Int)) % 45.68/45.91 (define @t8 () (@var "Z" Int)) % 45.68/45.91 (define @t9 () (@var "X4" tptp.collection)) % 45.68/45.91 (define @t10 () (@var "X5" Int)) % 45.68/45.91 (define @t11 () (@var "X3" Int)) % 45.68/45.91 (define @t12 () (@var "U" tptp.collection)) % 45.68/45.91 (define @t13 () (tptp.in @t8 @t12)) % 45.68/45.91 (define @t14 () (=> @t13 (> @t8 2))) % 45.68/45.91 (define @t15 () (@list @t8)) % 45.68/45.91 (define @t16 () (forall @t15 @t14)) % 45.68/45.91 (define @t17 () (@var "Y" Int)) % 45.68/45.91 (define @t18 () (* 5 @t17)) % 45.68/45.91 (define @t19 () (* 2 @t5)) % 45.68/45.91 (define @t20 () (- @t19 @t18)) % 45.68/45.91 (define @t21 () (@var "V" tptp.collection)) % 45.68/45.91 (define @t22 () (tptp.in @t17 @t21)) % 45.68/45.91 (define @t23 () (and @t22 (> @t20 0))) % 45.68/45.91 (define @t24 () (@list @t17)) % 45.68/45.91 (define @t25 () (exists @t24 @t23)) % 45.68/45.91 (define @t26 () (tptp.in @t5 @t12)) % 45.68/45.91 (define @t27 () (=> @t26 @t25)) % 45.68/45.91 (define @t28 () (@list @t5)) % 45.68/45.91 (define @t29 () (forall @t28 @t27)) % 45.68/45.91 (define @t30 () (@var "W" Int)) % 45.68/45.91 (define @t31 () (tptp.in @t30 @t21)) % 45.68/45.91 (define @t32 () (=> @t31 (> @t30 0))) % 45.68/45.91 (define @t33 () (@list @t30)) % 45.68/45.91 (define @t34 () (forall @t33 @t32)) % 45.68/45.91 (define @t35 () (and @t34 @t29)) % 45.68/45.91 (define @t36 () (=> @t35 @t16)) % 45.68/45.91 (define @t37 () (@list @t12 @t21)) % 45.68/45.91 (define @t38 () (forall @t37 @t36)) % 45.68/45.91 (define @t39 () (not @t38)) % 45.68/45.91 (define @t40 () (@var "BOUND_VARIABLE_7543" Int)) % 45.68/45.91 (define @t41 () (>= @t40 3)) % 45.68/45.91 (define @t42 () (not (tptp.in @t40 @t12))) % 45.68/45.91 (define @t43 () (* -5 @t17)) % 45.68/45.91 (define @t44 () (+ @t19 @t43)) % 45.68/45.91 (define @t45 () (>= @t44 1)) % 45.68/45.91 (define @t46 () (not @t45)) % 45.68/45.91 (define @t47 () (not (forall @t24 (or (not @t22) @t46)))) % 45.68/45.91 (define @t48 () (forall @t28 (or (not @t26) @t47))) % 45.68/45.91 (define @t49 () (not @t48)) % 45.68/45.91 (define @t50 () (>= @t30 1)) % 45.68/45.91 (define @t51 () (forall @t33 (or (not @t31) @t50))) % 45.68/45.91 (define @t52 () (not @t51)) % 45.68/45.91 (define @t53 () (or @t52 @t49 @t42 @t41)) % 45.68/45.91 (define @t54 () (or @t42 @t41)) % 45.68/45.91 (define @t55 () (or @t52 @t49 @t54)) % 45.68/45.91 (define @t56 () (@list @t12 @t21 @t40)) % 45.68/45.91 (define @t57 () (forall @t56 @t55)) % 45.68/45.91 (define @t58 () (@list @t40)) % 45.68/45.91 (define @t59 () (forall @t58 @t55)) % 45.68/45.91 (define @t60 () (forall @t58 @t54)) % 45.68/45.91 (define @t61 () (or @t52 @t49 @t60)) % 45.68/45.91 (define @t62 () (>= @t8 3)) % 45.68/45.91 (define @t63 () (forall @t15 (or (not @t13) @t62))) % 45.68/45.91 (define @t64 () (or @t52 @t49 @t63)) % 45.68/45.91 (define @t65 () (and @t51 @t48)) % 45.68/45.91 (define @t66 () (+ 2 1)) % 45.68/45.91 (define @t67 () (>= @t8 @t66)) % 45.68/45.91 (define @t68 () (and @t22 @t45)) % 45.68/45.91 (define @t69 () (forall @t24 (not @t68))) % 45.68/45.91 (define @t70 () (not @t69)) % 45.68/45.91 (define @t71 () (+ 0 1)) % 45.68/45.91 (define @t72 () (>= @t44 @t71)) % 45.68/45.91 (define @t73 () (* -1 @t18)) % 45.68/45.91 (define @t74 () (+ @t19 @t73)) % 45.68/45.91 (define @t75 () (<= @t20 0)) % 45.68/45.91 (define @t76 () (>= @t30 @t71)) % 45.68/45.91 (define @t77 () (forall @t56 @t53)) % 45.68/45.91 (define @t78 () (@quantifiers_skolemize @t77 2)) % 45.68/45.91 (define @t79 () (>= @t78 3)) % 45.68/45.91 (define @t80 () (@quantifiers_skolemize @t77 0)) % 45.68/45.91 (define @t81 () (tptp.in @t78 @t80)) % 45.68/45.91 (define @t82 () (not @t81)) % 45.68/45.91 (define @t83 () (@quantifiers_skolemize @t77 1)) % 45.68/45.91 (define @t84 () (not (tptp.in @t17 @t83))) % 45.68/45.91 (define @t85 () (forall @t28 (or (not (tptp.in @t5 @t80)) (not (forall @t24 (or @t84 @t46)))))) % 45.68/45.91 (define @t86 () (not @t85)) % 45.68/45.91 (define @t87 () (forall @t33 (or (not (tptp.in @t30 @t83)) @t50))) % 45.68/45.91 (define @t88 () (not @t87)) % 45.68/45.91 (define @t89 () (or @t88 @t86 @t82 @t79)) % 45.68/45.91 (define @t90 () (not @t79)) % 45.68/45.91 (define @t91 () (@list true)) % 45.68/45.91 (define @t92 () (@list @t89)) % 45.68/45.91 (define @t93 () (* -2 @t78)) % 45.68/45.91 (define @t94 () (+ @t18 @t93)) % 45.68/45.91 (define @t95 () (>= @t94 0)) % 45.68/45.91 (define @t96 () (* 2 @t78)) % 45.68/45.91 (define @t97 () (+ @t43 @t96)) % 45.68/45.91 (define @t98 () (+ @t94 1)) % 45.68/45.91 (define @t99 () (+ @t96 @t43)) % 45.68/45.91 (define @t100 () (>= @t99 1)) % 45.68/45.91 (define @t101 () (not @t100)) % 45.68/45.91 (define @t102 () (or @t84 @t101)) % 45.68/45.91 (define @t103 () (forall @t24 @t102)) % 45.68/45.91 (define @t104 () (not @t103)) % 45.68/45.91 (define @t105 () (or @t82 @t104)) % 45.68/45.91 (define @t106 () (forall @t24 (or @t84 @t95))) % 45.68/45.91 (define @t107 () (not @t106)) % 45.68/45.91 (define @t108 () (or @t82 @t107)) % 45.68/45.91 (define @t109 () (@list false false)) % 45.68/45.91 (define @t110 () (@quantifiers_skolemize @t106 0)) % 45.68/45.91 (define @t111 () (+ @t96 (* -5 @t110))) % 45.68/45.91 (define @t112 () (>= @t111 1)) % 45.68/45.91 (define @t113 () (not @t112)) % 45.68/45.91 (define @t114 () (tptp.in @t110 @t83)) % 45.68/45.91 (define @t115 () (not @t114)) % 45.68/45.91 (define @t116 () (or @t115 @t113)) % 45.68/45.91 (define @t117 () (not @t116)) % 45.68/45.91 (define @t118 () (* 5 @t110)) % 45.68/45.91 (define @t119 () (+ @t93 @t118)) % 45.68/45.91 (define @t120 () (+ @t111 1)) % 45.68/45.91 (define @t121 () (+ @t118 @t93)) % 45.68/45.91 (define @t122 () (>= @t121 0)) % 45.68/45.91 (define @t123 () (or @t115 @t122)) % 45.68/45.91 (define @t124 () (not @t123)) % 45.68/45.91 (define @t125 () (@list @t116)) % 45.68/45.91 (define @t126 () (>= @t110 1)) % 45.68/45.91 (define @t127 () (or @t115 @t126)) % 45.68/45.91 (define @t128 () (not @t126)) % 45.68/45.91 (define @t129 () (< @t78 3)) % 45.68/45.91 (define @t130 () (* -1/2 1/1)) % 45.68/45.91 (define @t131 () (* -5/2 1/1)) % 45.68/45.91 (define @t132 () (+ 3/1 @t131 @t130)) % 45.68/45.91 (define @t133 () (to_real @t110)) % 45.68/45.92 (define @t134 () (+ (to_real (* -1 @t78)) (* 5/2 @t133))) % 45.68/45.92 (define @t135 () (* -5/2 @t133)) % 45.68/45.92 (define @t136 () (to_real @t78)) % 45.68/45.92 (define @t137 () (to_real @t111)) % 45.68/45.92 (define @t138 () (* -1/2 @t137)) % 45.68/45.92 (define @t139 () (+ @t136 @t135 @t138)) % 45.68/45.92 (define @t140 () (>= @t139 @t132)) % 45.68/45.92 (define @t141 () (< -1/2 0/1)) % 45.68/45.92 (define @t142 () (to_real 1)) % 45.68/45.92 (define @t143 () (>= @t137 @t142)) % 45.68/45.92 (define @t144 () (< -5/2 0/1)) % 45.68/45.92 (define @t145 () (>= @t133 @t142)) % 45.68/45.92 (define @t146 () (to_real 3)) % 45.68/45.92 (define @t147 () (< @t136 @t146)) % 45.68/45.92 (define @t148 () (and @t112 @t126 @t90)) % 45.68/45.92 (assume @p1 (forall (@list @t1) (not (tptp.in @t1 tptp.empty)))) % 45.68/45.92 (assume @p2 (forall (@list @t3 @t2) (tptp.in @t3 (tptp.add @t3 @t2)))) % 45.68/45.92 (assume @p3 (forall (@list @t5 @t4) (not (tptp.in @t5 (tptp.remove @t5 @t4))))) % 45.68/45.92 (assume @p4 (forall (@list @t8 @t6 @t7) (= (or (tptp.in @t8 @t6) (= @t8 @t7)) (tptp.in @t8 (tptp.add @t7 @t6))))) % 45.68/45.92 (assume @p5 (forall (@list @t11 @t9 @t10) (= (and (tptp.in @t11 @t9) (not (= @t11 @t10))) (tptp.in @t11 (tptp.remove @t10 @t9))))) % 45.68/45.92 (assume @p6 @t39) % 45.68/45.92 (assume @p7 true) % 45.68/45.92 (step @p8 :rule aci_norm :args ((= @t55 @t53))) % 45.68/45.92 (step @p9 :rule cong :premises (@p8) :args (@t57)) % 45.68/45.92 (step @p10 :rule quant-merge-prenex :args ((= (forall @t37 @t59) @t57))) % 45.68/45.92 (step @p11 :rule alpha_equiv :args (@t60 (@list @t40) (@list @t8))) % 45.68/45.92 (step @p12 :rule refl :args (@t49)) % 45.68/45.92 (step @p13 :rule refl :args (@t52)) % 45.68/45.92 (step @p14 :rule nary_cong :premises (@p13 @p12 @p11) :args (@t61)) % 45.68/45.92 (step @p15 :rule quant-miniscope-or :args ((= @t59 @t61))) % 45.68/45.92 (step @p16 :rule trans :premises (@p15 @p14)) % 45.68/45.92 (step @p17 :rule symm :premises (@p16)) % 45.68/45.92 (step @p18 :rule cong :premises (@p17) :args ((forall @t37 @t64))) % 45.68/45.92 (step @p19 :rule trans :premises (@p18 @p10)) % 45.68/45.92 (step @p20 :rule trans :premises (@p19 @p9)) % 45.68/45.92 (step @p21 :rule aci_norm :args ((= (or (or @t52 @t49) @t63) @t64))) % 45.68/45.92 (step @p22 :rule refl :args (@t63)) % 45.68/45.92 (step @p23 :rule bool-and-de-morgan :args (@t51 @t48 true)) % 45.68/45.92 (step @p24 :rule nary_cong :premises (@p23 @p22) :args ((or (not @t65) @t63))) % 45.68/45.92 (step @p25 :rule trans :premises (@p24 @p21)) % 45.68/45.92 (step @p26 :rule bool-impl-elim :args (@t65 @t63)) % 45.68/45.92 (step @p27 :rule trans :premises (@p26 @p25)) % 45.68/45.92 (step @p28 :rule cong :premises (@p27) :args ((forall @t37 (=> @t65 @t63)))) % 45.68/45.92 (step @p29 :rule trans :premises (@p28 @p20)) % 45.68/45.92 (step @p30 :rule bool-impl-elim :args (@t13 @t62)) % 45.68/45.92 (step @p31 :rule cong :premises (@p30) :args ((forall @t15 (=> @t13 @t62)))) % 45.68/45.92 (step @p32 :rule bool-double-not-elim :args (@t62)) % 45.68/45.92 (step @p33 :rule evaluate :args (@t66)) % 45.68/45.92 (step @p34 :rule refl :args (@t8)) % 45.68/45.92 (step @p35 :rule cong :premises (@p34 @p33) :args (@t67)) % 45.68/45.92 (step @p36 :rule cong :premises (@p35) :args ((not @t67))) % 45.68/45.92 (step @p37 :rule arith-leq-norm :args (@t8 2)) % 45.68/45.92 (step @p38 :rule trans :premises (@p37 @p36)) % 45.68/45.92 (step @p39 :rule cong :premises (@p38) :args ((not (<= @t8 2)))) % 45.68/45.92 (step @p40 :rule trans :premises (@p39 @p32)) % 45.68/45.92 (step @p41 :rule arith-elim-leq :args (@t8 2)) % 45.68/45.92 (step @p42 :rule symm :premises (@p41)) % 45.68/45.92 (step @p43 :rule cong :premises (@p42) :args ((not (>= 2 @t8)))) % 45.68/45.92 (step @p44 :rule arith-elim-gt :args (@t8 2)) % 45.68/45.92 (step @p45 :rule trans :premises (@p44 @p43)) % 45.68/45.92 (step @p46 :rule trans :premises (@p45 @p40)) % 45.68/45.92 (step @p47 :rule refl :args (@t13)) % 45.68/45.92 (step @p48 :rule cong :premises (@p47 @p46) :args (@t14)) % 45.68/45.92 (step @p49 :rule cong :premises (@p48) :args (@t16)) % 45.68/45.92 (step @p50 :rule trans :premises (@p49 @p31)) % 45.68/45.92 (step @p51 :rule bool-impl-elim :args (@t26 @t47)) % 45.68/45.92 (step @p52 :rule cong :premises (@p51) :args ((forall @t28 (=> @t26 @t47)))) % 45.68/45.92 (step @p53 :rule bool-and-de-morgan :args (@t22 @t45 true)) % 45.68/45.92 (step @p54 :rule cong :premises (@p53) :args (@t69)) % 45.68/45.92 (step @p55 :rule cong :premises (@p54) :args (@t70)) % 45.68/45.92 (step @p56 :rule exists-elim :args ((= (exists @t24 @t68) @t70))) % 45.68/45.92 (step @p57 :rule trans :premises (@p56 @p55)) % 45.68/45.92 (step @p58 :rule bool-double-not-elim :args (@t45)) % 45.68/45.92 (step @p59 :rule evaluate :args (@t71)) % 45.68/45.92 (step @p60 :rule refl :args (@t44)) % 45.68/45.92 (step @p61 :rule cong :premises (@p60 @p59) :args (@t72)) % 45.68/45.92 (step @p62 :rule cong :premises (@p61) :args ((not @t72))) % 45.68/45.92 (step @p63 :rule arith-leq-norm :args (@t44 0)) % 45.68/45.92 (step @p64 :rule trans :premises (@p63 @p62)) % 45.68/45.92 (step @p65 :rule refl :args (0)) % 45.68/45.92 (step @p66 :rule arith_poly_norm :args ((= @t73 @t43))) % 45.68/45.92 (step @p67 :rule refl :args (@t19)) % 45.68/45.92 (step @p68 :rule nary_cong :premises (@p67 @p66) :args (@t74)) % 45.68/45.92 (step @p69 :rule arith_poly_norm :args ((= @t20 @t74))) % 45.68/45.92 (step @p70 :rule trans :premises (@p69 @p68)) % 45.68/45.92 (step @p71 :rule cong :premises (@p70 @p65) :args (@t75)) % 45.68/45.92 (step @p72 :rule trans :premises (@p71 @p64)) % 45.68/45.92 (step @p73 :rule cong :premises (@p72) :args ((not @t75))) % 45.68/45.92 (step @p74 :rule trans :premises (@p73 @p58)) % 45.68/45.92 (step @p75 :rule arith-elim-leq :args (@t20 0)) % 45.68/45.92 (step @p76 :rule symm :premises (@p75)) % 45.68/45.92 (step @p77 :rule cong :premises (@p76) :args ((not (>= 0 @t20)))) % 45.68/45.92 (step @p78 :rule arith-elim-gt :args (@t20 0)) % 45.68/45.92 (step @p79 :rule trans :premises (@p78 @p77)) % 45.68/45.92 (step @p80 :rule trans :premises (@p79 @p74)) % 45.68/45.92 (step @p81 :rule refl :args (@t22)) % 45.68/45.92 (step @p82 :rule nary_cong :premises (@p81 @p80) :args (@t23)) % 45.68/45.92 (step @p83 :rule cong :premises (@p82) :args (@t25)) % 45.68/45.92 (step @p84 :rule trans :premises (@p83 @p57)) % 45.68/45.92 (step @p85 :rule refl :args (@t26)) % 45.68/45.92 (step @p86 :rule cong :premises (@p85 @p84) :args (@t27)) % 45.68/45.92 (step @p87 :rule cong :premises (@p86) :args (@t29)) % 45.68/45.92 (step @p88 :rule trans :premises (@p87 @p52)) % 45.68/45.92 (step @p89 :rule bool-impl-elim :args (@t31 @t50)) % 45.68/45.92 (step @p90 :rule cong :premises (@p89) :args ((forall @t33 (=> @t31 @t50)))) % 45.68/45.92 (step @p91 :rule bool-double-not-elim :args (@t50)) % 45.68/45.92 (step @p92 :rule refl :args (@t30)) % 45.68/45.92 (step @p93 :rule cong :premises (@p92 @p59) :args (@t76)) % 45.68/45.92 (step @p94 :rule cong :premises (@p93) :args ((not @t76))) % 45.68/45.92 (step @p95 :rule arith-leq-norm :args (@t30 0)) % 45.68/45.92 (step @p96 :rule trans :premises (@p95 @p94)) % 45.68/45.92 (step @p97 :rule cong :premises (@p96) :args ((not (<= @t30 0)))) % 45.68/45.92 (step @p98 :rule trans :premises (@p97 @p91)) % 45.68/45.92 (step @p99 :rule arith-elim-leq :args (@t30 0)) % 45.68/45.92 (step @p100 :rule symm :premises (@p99)) % 45.68/45.92 (step @p101 :rule cong :premises (@p100) :args ((not (>= 0 @t30)))) % 45.68/45.92 (step @p102 :rule arith-elim-gt :args (@t30 0)) % 45.68/45.92 (step @p103 :rule trans :premises (@p102 @p101)) % 45.68/45.92 (step @p104 :rule trans :premises (@p103 @p98)) % 45.68/45.92 (step @p105 :rule refl :args (@t31)) % 45.68/45.92 (step @p106 :rule cong :premises (@p105 @p104) :args (@t32)) % 45.68/45.92 (step @p107 :rule cong :premises (@p106) :args (@t34)) % 45.68/45.92 (step @p108 :rule trans :premises (@p107 @p90)) % 45.68/45.92 (step @p109 :rule nary_cong :premises (@p108 @p88) :args (@t35)) % 45.68/45.92 (step @p110 :rule cong :premises (@p109 @p50) :args (@t36)) % 45.68/45.92 (step @p111 :rule cong :premises (@p110) :args (@t38)) % 45.68/45.92 (step @p112 :rule trans :premises (@p111 @p29)) % 45.68/45.92 (step @p113 :rule cong :premises (@p112) :args (@t39)) % 45.68/45.92 (step @p114 :rule eq_resolve :premises (@p6 @p113)) % 45.68/45.92 (step @p115 :rule skolemize :premises (@p114)) % 45.68/45.92 (step @p116 :rule cnf_or_neg :args (@t89 3)) % 45.68/45.92 (step @p117 :rule chain_m_resolution :premises (@p116 @p115) :args (@t90 @t91 @t92)) % 45.68/45.92 (step @p118 :rule bool-double-not-elim :args (@t85)) % 45.68/45.92 (step @p119 :rule refl :args (@t89)) % 45.68/45.92 (step @p120 :rule nary_cong :premises (@p119 @p118) :args ((or @t89 (not @t86)))) % 45.68/45.92 (step @p121 :rule cnf_or_neg :args (@t89 1)) % 45.68/45.92 (step @p122 :rule eq_resolve :premises (@p121 @p120)) % 45.68/45.92 (step @p123 :rule reordering :premises (@p122) :args ((or @t85 @t89))) % 45.68/45.92 (step @p124 :rule chain_m_resolution :premises (@p123 @p115) :args (@t85 @t91 @t92)) % 45.68/45.92 (step @p125 :rule bool-double-not-elim :args (@t95)) % 45.68/45.92 (step @p126 :rule arith_poly_norm :args ((= (* -1 (- 0 @t98)) (* -1 (- @t97 1))))) % 45.68/45.92 (step @p127 :rule arith_poly_norm_rel :premises (@p126) :args ((= (>= 0 @t98) (>= @t97 1)))) % 45.68/45.92 (step @p128 :rule arith-geq-tighten :args (@t94 0)) % 45.68/45.92 (step @p129 :rule trans :premises (@p128 @p127)) % 45.68/45.92 (step @p130 :rule symm :premises (@p129)) % 45.68/45.92 (step @p131 :rule refl :args (1)) % 45.68/45.92 (step @p132 :rule arith_poly_norm :args ((= @t99 @t97))) % 45.68/45.92 (step @p133 :rule cong :premises (@p132 @p131) :args (@t100)) % 45.68/45.92 (step @p134 :rule trans :premises (@p133 @p130)) % 45.68/45.92 (step @p135 :rule cong :premises (@p134) :args (@t101)) % 45.68/45.92 (step @p136 :rule trans :premises (@p135 @p125)) % 45.68/45.92 (step @p137 :rule refl :args (@t84)) % 45.68/45.92 (step @p138 :rule nary_cong :premises (@p137 @p136) :args (@t102)) % 45.68/45.92 (step @p139 :rule cong :premises (@p138) :args (@t103)) % 45.68/45.92 (step @p140 :rule cong :premises (@p139) :args (@t104)) % 45.68/45.92 (step @p141 :rule refl :args (@t82)) % 45.68/45.92 (step @p142 :rule nary_cong :premises (@p141 @p140) :args (@t105)) % 45.68/45.92 (step @p143 :rule refl :args (@t85)) % 45.68/45.92 (step @p144 :rule cong :premises (@p143 @p142) :args ((=> @t85 @t105))) % 45.68/45.92 (assume-push @p313 @t85) % 45.68/45.92 (step @p146 :rule instantiate :premises (@p124) :args ((@list @t78))) % 45.68/45.92 (step-pop @p314 :rule scope :premises (@p146)) % 45.68/45.92 (step @p147 :rule process_scope :premises (@p314) :args (@t105)) % 45.68/45.92 (step @p149 :rule eq_resolve :premises (@p147 @p144)) % 45.68/45.92 (step @p150 :rule implies_elim :premises (@p149)) % 45.68/45.92 (step @p151 :rule chain_m_resolution :premises (@p150 @p124) :args (@t108 (@list false) (@list @t85))) % 45.68/45.92 (step @p152 :rule bool-double-not-elim :args (@t81)) % 45.68/45.92 (step @p153 :rule nary_cong :premises (@p119 @p152) :args ((or @t89 (not @t82)))) % 45.68/45.92 (step @p154 :rule cnf_or_neg :args (@t89 2)) % 45.68/45.92 (step @p155 :rule eq_resolve :premises (@p154 @p153)) % 45.68/45.92 (step @p156 :rule reordering :premises (@p155) :args ((or @t81 @t89))) % 45.68/45.92 (step @p157 :rule chain_m_resolution :premises (@p156 @p115) :args (@t81 @t91 @t92)) % 45.68/45.92 (step @p158 :rule cnf_or_pos :args (@t108)) % 45.68/45.92 (step @p159 :rule reordering :premises (@p158) :args ((or @t82 @t107 (not @t108)))) % 45.68/45.92 (step @p160 :rule chain_m_resolution :premises (@p159 @p157 @p151) :args (@t107 @t109 (@list @t81 @t108))) % 45.68/45.92 (step @p161 :rule refl :args (@t117)) % 45.68/45.92 (step @p162 :rule bool-double-not-elim :args (@t106)) % 45.68/45.92 (step @p163 :rule nary_cong :premises (@p162 @p161) :args ((or (not @t107) @t117))) % 45.68/45.92 (step @p164 :rule arith_poly_norm :args ((= (* -2 (- 1 @t120)) (* -2 (- @t119 0))))) % 45.68/45.92 (step @p165 :rule arith_poly_norm_rel :premises (@p164) :args ((= (>= 1 @t120) (>= @t119 0)))) % 45.68/45.92 (step @p166 :rule arith-geq-tighten :args (@t111 1)) % 45.68/45.92 (step @p167 :rule trans :premises (@p166 @p165)) % 45.68/45.92 (step @p168 :rule symm :premises (@p167)) % 45.68/45.92 (step @p169 :rule arith_poly_norm :args ((= @t121 @t119))) % 45.68/45.92 (step @p170 :rule cong :premises (@p169 @p65) :args (@t122)) % 45.68/45.92 (step @p171 :rule trans :premises (@p170 @p168)) % 45.68/45.92 (step @p172 :rule refl :args (@t115)) % 45.68/45.92 (step @p173 :rule nary_cong :premises (@p172 @p171) :args (@t123)) % 45.68/45.92 (step @p174 :rule cong :premises (@p173) :args (@t124)) % 45.68/45.92 (step @p175 :rule refl :args (@t107)) % 45.68/45.92 (step @p176 :rule cong :premises (@p175 @p174) :args ((=> @t107 @t124))) % 45.68/45.92 (assume-push @p315 @t107) % 45.68/45.92 (step @p178 :rule skolemize :premises (@p160)) % 45.68/45.92 (step-pop @p316 :rule scope :premises (@p178)) % 45.68/45.92 (step @p179 :rule process_scope :premises (@p316) :args (@t124)) % 45.68/45.92 (step @p181 :rule eq_resolve :premises (@p179 @p176)) % 45.68/45.92 (step @p182 :rule implies_elim :premises (@p181)) % 45.68/45.92 (step @p183 :rule eq_resolve :premises (@p182 @p163)) % 45.68/45.92 (step @p184 :rule chain_m_resolution :premises (@p183 @p160) :args (@t117 @t91 (@list @t106))) % 45.68/45.92 (step @p185 :rule bool-double-not-elim :args (@t112)) % 45.68/45.92 (step @p186 :rule refl :args (@t116)) % 45.68/45.92 (step @p187 :rule nary_cong :premises (@p186 @p185) :args ((or @t116 (not @t113)))) % 45.68/45.92 (step @p188 :rule cnf_or_neg :args (@t116 1)) % 45.68/45.92 (step @p189 :rule eq_resolve :premises (@p188 @p187)) % 45.68/45.92 (step @p190 :rule reordering :premises (@p189) :args ((or @t112 @t116))) % 45.68/45.92 (step @p191 :rule chain_m_resolution :premises (@p190 @p184) :args (@t112 @t91 @t125)) % 45.68/45.92 (step @p192 :rule bool-double-not-elim :args (@t87)) % 45.68/45.92 (step @p193 :rule nary_cong :premises (@p119 @p192) :args ((or @t89 (not @t88)))) % 45.68/45.92 (step @p194 :rule cnf_or_neg :args (@t89 0)) % 45.68/45.92 (step @p195 :rule eq_resolve :premises (@p194 @p193)) % 45.68/45.92 (step @p196 :rule reordering :premises (@p195) :args ((or @t87 @t89))) % 45.68/45.92 (step @p197 :rule chain_m_resolution :premises (@p196 @p115) :args (@t87 @t91 @t92)) % 45.68/45.92 (step @p198 :rule instantiate :premises (@p197) :args ((@list @t110))) % 45.68/45.92 (step @p199 :rule bool-double-not-elim :args (@t114)) % 45.68/45.92 (step @p200 :rule nary_cong :premises (@p186 @p199) :args ((or @t116 (not @t115)))) % 45.68/45.92 (step @p201 :rule cnf_or_neg :args (@t116 0)) % 45.68/45.92 (step @p202 :rule eq_resolve :premises (@p201 @p200)) % 45.68/45.92 (step @p203 :rule reordering :premises (@p202) :args ((or @t114 @t116))) % 45.68/45.92 (step @p204 :rule chain_m_resolution :premises (@p203 @p184) :args (@t114 @t91 @t125)) % 45.68/45.92 (step @p205 :rule cnf_or_pos :args (@t127)) % 45.68/45.92 (step @p206 :rule reordering :premises (@p205) :args ((or @t115 @t126 (not @t127)))) % 45.68/45.92 (step @p207 :rule chain_m_resolution :premises (@p206 @p204 @p198) :args (@t126 @t109 (@list @t114 @t127))) % 45.68/45.92 (step @p208 :rule refl :args (@t128)) % 45.68/45.92 (step @p209 :rule refl :args (@t113)) % 45.68/45.92 (step @p210 :rule bool-double-not-elim :args (@t79)) % 45.68/45.92 (step @p211 :rule nary_cong :premises (@p210 @p209 @p208) :args ((or (not @t90) @t113 @t128))) % 45.68/45.92 (assume-push @p317 @t112) % 45.68/45.92 (assume-push @p318 @t126) % 45.68/45.92 (assume-push @p319 @t90) % 45.68/45.92 (step @p215 :rule arith-elim-lt :args (@t78 3)) % 45.68/45.92 (step @p216 :rule cong :premises (@p215) :args ((not @t129))) % 45.68/45.92 (step @p217 :rule trans :premises (@p216 @p210)) % 45.68/45.92 (step @p218 :rule symm :premises (@p217)) % 45.68/45.92 (assume-push @p320 @t129) % 45.68/45.92 (step @p220 :rule evaluate :args ((not true))) % 45.68/45.92 (step @p221 :rule evaluate :args ((>= 0/1 0/1))) % 45.68/45.92 (step @p222 :rule evaluate :args ((+ 3/1 -5/2 -1/2))) % 45.68/45.92 (step @p223 :rule evaluate :args (@t130)) % 45.68/45.92 (step @p224 :rule evaluate :args (@t131)) % 45.68/45.92 (step @p225 :rule refl :args (3/1)) % 45.68/45.92 (step @p226 :rule nary_cong :premises (@p225 @p224 @p223) :args (@t132)) % 45.68/45.92 (step @p227 :rule trans :premises (@p226 @p222)) % 45.68/45.92 (step @p228 :rule arith_poly_norm :args ((= (+ @t136 @t135 @t134) 0/1))) % 45.68/45.92 (step @p229 :rule arith_poly_norm :args ((= @t138 @t134))) % 45.68/45.92 (step @p230 :rule refl :args (@t135)) % 45.68/45.92 (step @p231 :rule refl :args (@t136)) % 45.68/45.92 (step @p232 :rule nary_cong :premises (@p231 @p230 @p229) :args (@t139)) % 45.68/45.92 (step @p233 :rule trans :premises (@p232 @p228)) % 45.68/45.92 (step @p234 :rule cong :premises (@p233 @p227) :args (@t140)) % 45.68/45.92 (step @p235 :rule trans :premises (@p234 @p221)) % 45.68/45.92 (step @p236 :rule cong :premises (@p235) :args ((not @t140))) % 45.68/45.92 (step @p237 :rule trans :premises (@p236 @p220)) % 45.68/45.92 (step @p238 :rule arith-elim-lt :args (@t139 @t132)) % 45.68/45.92 (step @p239 :rule trans :premises (@p238 @p237)) % 45.68/45.92 (assume-push @p321 @t141) % 45.68/45.92 (assume-push @p322 @t112) % 45.68/45.92 (step @p242 :rule arith_mult_neg :args (-1/2 (>= @t137 1/1))) % 45.68/45.92 (step @p243 :rule evaluate :args (@t142)) % 45.68/45.92 (step @p244 :rule refl :args (@t137)) % 45.68/45.92 (step @p245 :rule cong :premises (@p244 @p243) :args (@t143)) % 45.68/45.92 (step @p246 :rule arith_poly_norm :args ((= (* -1/1 (to_real (- @t111 1))) (* -1/1 (- @t137 @t142))))) % 45.68/45.92 (step @p247 :rule arith_poly_norm_rel :premises (@p246) :args ((= @t112 @t143))) % 45.68/45.92 (step @p248 :rule trans :premises (@p247 @p245)) % 45.68/45.92 (step @p249 :rule eq_resolve :premises (@p317 @p248)) % 45.68/45.92 (step @p250 :rule and_intro :premises (@p321 @p249)) % 45.68/45.92 (step @p251 :rule modus_ponens :premises (@p250 @p242)) % 45.68/45.92 (step-pop @p323 :rule scope :premises (@p251)) % 45.68/45.92 (step-pop @p324 :rule scope :premises (@p323)) % 45.68/45.92 (step @p252 :rule process_scope :premises (@p324) :args ((<= @t138 @t130))) % 45.68/45.92 (step @p255 :rule evaluate :args (@t141)) % 45.68/45.92 (step @p256 :rule true_elim :premises (@p255)) % 45.68/45.92 (step @p257 :rule and_intro :premises (@p256 @p191)) % 45.68/45.92 (step @p258 :rule modus_ponens :premises (@p257 @p252)) % 45.68/45.92 (assume-push @p325 @t144) % 45.68/45.92 (assume-push @p326 @t126) % 45.68/45.92 (step @p261 :rule arith_mult_neg :args (-5/2 (>= @t133 1/1))) % 45.68/45.92 (step @p262 :rule evaluate :args (@t142)) % 45.68/45.92 (step @p263 :rule refl :args (@t133)) % 45.68/45.92 (step @p264 :rule cong :premises (@p263 @p262) :args (@t145)) % 45.68/45.92 (step @p265 :rule arith_poly_norm :args ((= (* -1/1 (to_real (- @t110 1))) (* -1/1 (- @t133 @t142))))) % 45.68/45.92 (step @p266 :rule arith_poly_norm_rel :premises (@p265) :args ((= @t126 @t145))) % 45.68/45.92 (step @p267 :rule trans :premises (@p266 @p264)) % 45.68/45.92 (step @p268 :rule eq_resolve :premises (@p318 @p267)) % 45.68/45.92 (step @p269 :rule and_intro :premises (@p325 @p268)) % 45.68/45.92 (step @p270 :rule modus_ponens :premises (@p269 @p261)) % 45.68/45.92 (step-pop @p327 :rule scope :premises (@p270)) % 45.68/45.92 (step-pop @p328 :rule scope :premises (@p327)) % 45.68/45.92 (step @p271 :rule process_scope :premises (@p328) :args ((<= @t135 @t131))) % 45.68/45.92 (step @p274 :rule evaluate :args (@t144)) % 45.68/45.92 (step @p275 :rule true_elim :premises (@p274)) % 45.68/45.92 (step @p276 :rule and_intro :premises (@p275 @p207)) % 45.68/45.92 (step @p277 :rule modus_ponens :premises (@p276 @p271)) % 45.68/45.92 (step @p278 :rule evaluate :args (@t146)) % 45.68/45.92 (step @p279 :rule refl :args (@t136)) % 45.68/45.92 (step @p280 :rule cong :premises (@p279 @p278) :args (@t147)) % 45.68/45.92 (step @p281 :rule arith_poly_norm :args ((= (* -3/1 (to_real (- @t78 3))) (* -3/1 (- @t136 @t146))))) % 45.68/45.92 (step @p282 :rule arith_poly_norm_rel :premises (@p281) :args ((= @t129 @t147))) % 45.68/45.92 (step @p283 :rule trans :premises (@p282 @p280)) % 45.68/45.92 (step @p284 :rule symm :premises (@p215)) % 45.68/45.92 (step @p285 :rule chain_m_resolution :premises (@p116 @p115) :args (@t90 @t91 @t92)) % 45.68/45.92 (step @p286 :rule eq_resolve :premises (@p285 @p284)) % 45.68/45.92 (step @p287 :rule eq_resolve :premises (@p286 @p283)) % 45.68/45.92 (step @p288 :rule arith_sum_ub :premises (@p287 @p277 @p258)) % 45.68/45.92 (step @p289 false :rule eq_resolve :premises (@p288 @p239)) % 45.68/45.92 (step-pop @p329 :rule scope :premises (@p289)) % 45.68/45.92 (step @p290 :rule process_scope :premises (@p329) :args (false)) % 45.68/45.92 (step @p292 :rule eq_resolve :premises (@p290 @p217)) % 45.68/45.92 (step @p293 :rule eq_resolve :premises (@p292 @p218)) % 45.68/45.92 (step @p284 :rule symm :premises (@p215)) % 45.68/45.92 (step @p294 :rule eq_resolve :premises (@p117 @p284)) % 45.68/45.92 (step @p295 false :rule contra :premises (@p294 @p293)) % 45.68/45.92 (step-pop @p330 :rule scope :premises (@p295)) % 45.68/45.92 (step-pop @p331 :rule scope :premises (@p330)) % 45.68/45.92 (step-pop @p332 :rule scope :premises (@p331)) % 45.68/45.92 (step @p296 :rule process_scope :premises (@p332) :args (false)) % 45.68/45.92 (assume-push @p333 @t90) % 45.68/45.92 (assume-push @p334 @t112) % 45.68/45.92 (assume-push @p335 @t126) % 45.68/45.92 (step @p303 :rule and_intro :premises (@p191 @p207 @p117)) % 45.68/45.92 (step-pop @p336 :rule scope :premises (@p303)) % 45.68/45.92 (step-pop @p337 :rule scope :premises (@p336)) % 45.68/45.92 (step-pop @p338 :rule scope :premises (@p337)) % 45.68/45.92 (step @p304 :rule process_scope :premises (@p338) :args (@t148)) % 45.68/45.92 (step @p308 :rule implies_elim :premises (@p304)) % 45.68/45.92 (step @p309 :rule resolution :premises (@p308 @p296) :args (true @t148)) % 45.68/45.92 (step @p310 :rule not_and :premises (@p309)) % 45.68/45.92 (step @p311 :rule eq_resolve :premises (@p310 @p211)) % 45.68/45.92 (step @p312 false :rule chain_m_resolution :premises (@p311 @p207 @p191 @p117) :args (false (@list false false true) (@list @t126 @t112 @t79))) % 45.68/45.92 ) % 45.68/45.92 % SZS output end Proof % 45.68/45.92 % cvc5 exiting %------------------------------------------------------------------------------