%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUN024^1 : TPTP v9.2.1. Released v6.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n016.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 08:42:48 AM UTC 2026 % Result : Theorem 0.54s 0.76s % Output : Proof 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : NUN024^1 : TPTP v9.2.1. Released v6.4.0. % 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.19/0.35 % Computer : n016.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Tue Jun 2 12:38:09 EDT 2026 % 0.19/0.35 % CPUTime : % 0.33/0.50 %----Proving TH0 % 0.54/0.76 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.54/0.76 % SZS status Theorem % 0.54/0.76 % SZS output start Proof % 0.54/0.76 ( % 0.54/0.76 (declare-sort $$unsorted 0) % 0.54/0.76 (declare-const tptp.ite (-> Bool $$unsorted $$unsorted $$unsorted)) % 0.54/0.76 (declare-const tptp.s (-> $$unsorted $$unsorted)) % 0.54/0.76 (declare-const tptp.zero $$unsorted) % 0.54/0.76 (define @t1 () (_ tptp.s tptp.zero)) % 0.54/0.76 (define @t2 () (_ tptp.s @t1)) % 0.54/0.76 (define @t3 () (@var "H" (-> $$unsorted $$unsorted))) % 0.54/0.76 (define @t4 () (_ @t3 @t2)) % 0.54/0.76 (define @t5 () (_ @t3 @t1)) % 0.54/0.76 (define @t6 () (_ @t3 tptp.zero)) % 0.54/0.76 (define @t7 () (and (= @t6 @t1) (= @t5 tptp.zero) (= @t4 tptp.zero))) % 0.54/0.76 (define @t8 () (@list @t3)) % 0.54/0.76 (define @t9 () (exists @t8 @t7)) % 0.54/0.76 (define @t10 () (@var "X" $$unsorted)) % 0.54/0.76 (define @t11 () (_ tptp.s @t10)) % 0.54/0.76 (define @t12 () (not (= @t11 @t10))) % 0.54/0.76 (define @t13 () (@list @t10)) % 0.54/0.76 (define @t14 () (forall @t13 @t12)) % 0.54/0.76 (define @t15 () (not (= @t11 tptp.zero))) % 0.54/0.76 (define @t16 () (forall @t13 @t15)) % 0.54/0.76 (define @t17 () (@var "V" $$unsorted)) % 0.54/0.76 (define @t18 () (@var "U" $$unsorted)) % 0.54/0.76 (define @t19 () (@var "X100" Bool)) % 0.54/0.76 (define @t20 () (_ (_ (_ tptp.ite @t19) @t18) @t17)) % 0.54/0.76 (define @t21 () (not @t19)) % 0.54/0.76 (define @t22 () (=> @t21 (= @t20 @t17))) % 0.54/0.76 (define @t23 () (@list @t19 @t18 @t17)) % 0.54/0.76 (define @t24 () (forall @t23 @t22)) % 0.54/0.76 (define @t25 () (=> @t19 (= @t20 @t18))) % 0.54/0.76 (define @t26 () (forall @t23 @t25)) % 0.54/0.76 (define @t27 () (and @t26 @t24 @t16 @t14)) % 0.54/0.76 (define @t28 () (=> @t27 @t9)) % 0.54/0.76 (define @t29 () (not @t28)) % 0.54/0.76 (define @t30 () (tptp.s tptp.zero)) % 0.54/0.76 (define @t31 () (tptp.s @t30)) % 0.54/0.76 (define @t32 () (_ @t3 @t31)) % 0.54/0.76 (define @t33 () (_ tptp.s @t30)) % 0.54/0.76 (define @t34 () (= @t33 @t31)) % 0.54/0.76 (define @t35 () (= @t1 @t30)) % 0.54/0.76 (define @t36 () (= tptp.zero @t4)) % 0.54/0.76 (define @t37 () (not @t36)) % 0.54/0.76 (define @t38 () (_ @t3 @t30)) % 0.54/0.76 (define @t39 () (= tptp.zero @t5)) % 0.54/0.76 (define @t40 () (not @t39)) % 0.54/0.76 (define @t41 () (_ @t3 tptp.zero)) % 0.54/0.76 (define @t42 () (= @t1 @t6)) % 0.54/0.76 (define @t43 () (not @t42)) % 0.54/0.76 (define @t44 () (or @t43 @t40 @t37)) % 0.54/0.76 (define @t45 () (and @t42 @t39 @t36)) % 0.54/0.76 (define @t46 () (forall @t8 (not @t45))) % 0.54/0.76 (define @t47 () (not @t46)) % 0.54/0.76 (define @t48 () (tptp.s @t10)) % 0.54/0.76 (define @t49 () (= @t10 @t11)) % 0.54/0.76 (define @t50 () (not @t49)) % 0.54/0.76 (define @t51 () (= tptp.zero @t11)) % 0.54/0.76 (define @t52 () (not @t51)) % 0.54/0.76 (define @t53 () (= @t17 (tptp.ite false @t18 @t17))) % 0.54/0.76 (define @t54 () (or false @t53)) % 0.54/0.76 (define @t55 () (@list @t18 @t17)) % 0.54/0.76 (define @t56 () (tptp.ite @t19 @t18 @t17)) % 0.54/0.76 (define @t57 () (= @t17 @t56)) % 0.54/0.76 (define @t58 () (@list @t19)) % 0.54/0.76 (define @t59 () (not @t21)) % 0.54/0.76 (define @t60 () (or @t19 @t19 @t57)) % 0.54/0.76 (define @t61 () (or @t19 @t57)) % 0.54/0.76 (define @t62 () (forall @t58 @t61)) % 0.54/0.76 (define @t63 () (forall @t55 @t62)) % 0.54/0.76 (define @t64 () (@list @t18 @t17 @t19)) % 0.54/0.76 (define @t65 () (forall @t64 @t61)) % 0.54/0.76 (define @t66 () (= @t17 @t20)) % 0.54/0.76 (define @t67 () (or @t19 @t66)) % 0.54/0.76 (define @t68 () (= @t18 (tptp.ite true @t18 @t17))) % 0.54/0.76 (define @t69 () (not true)) % 0.54/0.76 (define @t70 () (or @t69 @t68)) % 0.54/0.76 (define @t71 () (= @t18 @t56)) % 0.54/0.76 (define @t72 () (or @t21 @t21 @t71)) % 0.54/0.76 (define @t73 () (or @t21 @t71)) % 0.54/0.76 (define @t74 () (forall @t58 @t73)) % 0.54/0.76 (define @t75 () (forall @t55 @t74)) % 0.54/0.76 (define @t76 () (forall @t64 @t73)) % 0.54/0.76 (define @t77 () (= @t18 @t20)) % 0.54/0.76 (define @t78 () (or @t21 @t77)) % 0.54/0.76 (define @t79 () (@list @t30)) % 0.54/0.76 (define @t80 () (ite @t34 tptp.zero @t33)) % 0.54/0.76 (define @t81 () (= tptp.zero @t31)) % 0.54/0.76 (define @t82 () (ite @t81 @t1 @t80)) % 0.54/0.76 (define @t83 () (@purify @t82)) % 0.54/0.76 (define @t84 () (= @t1 @t31)) % 0.54/0.76 (define @t85 () (ite @t84 tptp.zero @t82)) % 0.54/0.76 (define @t86 () (@purify @t85)) % 0.54/0.76 (define @t87 () (= @t82 @t86)) % 0.54/0.76 (define @t88 () (= tptp.zero @t86)) % 0.54/0.76 (define @t89 () (= @t85 @t82)) % 0.54/0.76 (define @t90 () (= @t85 tptp.zero)) % 0.54/0.76 (define @t91 () (= @t86 @t83)) % 0.54/0.76 (define @t92 () (@list true)) % 0.54/0.76 (define @t93 () (@purify @t80)) % 0.54/0.76 (define @t94 () (= @t80 @t83)) % 0.54/0.76 (define @t95 () (= @t1 @t83)) % 0.54/0.76 (define @t96 () (= @t82 @t80)) % 0.54/0.76 (define @t97 () (= @t82 @t1)) % 0.54/0.76 (define @t98 () (= @t83 @t93)) % 0.54/0.76 (define @t99 () (= tptp.zero @t93)) % 0.54/0.76 (define @t100 () (= @t33 @t93)) % 0.54/0.76 (define @t101 () (= @t80 @t33)) % 0.54/0.76 (define @t102 () (= @t80 tptp.zero)) % 0.54/0.76 (define @t103 () (= tptp.zero @t85)) % 0.54/0.76 (define @t104 () (not @t103)) % 0.54/0.76 (define @t105 () (= tptp.zero @t30)) % 0.54/0.76 (define @t106 () (ite @t105 @t1 (ite (= @t30 @t33) tptp.zero @t33))) % 0.54/0.76 (define @t107 () (ite @t35 tptp.zero @t106)) % 0.54/0.76 (define @t108 () (@purify @t107)) % 0.54/0.76 (define @t109 () (= tptp.zero @t107)) % 0.54/0.76 (define @t110 () (not @t109)) % 0.54/0.76 (define @t111 () (= tptp.zero @t1)) % 0.54/0.76 (define @t112 () (ite @t111 tptp.zero @t1)) % 0.54/0.76 (define @t113 () (@purify @t112)) % 0.54/0.76 (define @t114 () (= @t30 @t112)) % 0.54/0.76 (define @t115 () (not @t114)) % 0.54/0.76 (define @t116 () (or @t115 @t110 @t104)) % 0.54/0.76 (define @t117 () (forall @t8 (or (not (= @t30 @t41)) (not (= tptp.zero @t38)) (not (= tptp.zero @t32))))) % 0.54/0.76 (define @t118 () (@var "BOUND_VARIABLE_43209" $$unsorted)) % 0.54/0.76 (define @t119 () (lambda (@list @t118) (ite (= @t1 @t118) tptp.zero (ite (= tptp.zero @t118) @t1 (ite (= @t33 @t118) tptp.zero @t33))))) % 0.54/0.76 (define @t120 () (_ @t119 @t31)) % 0.54/0.76 (define @t121 () (= tptp.zero @t120)) % 0.54/0.76 (define @t122 () (not @t121)) % 0.54/0.76 (define @t123 () (ite (= @t33 @t30) tptp.zero @t33)) % 0.54/0.76 (define @t124 () (ite @t105 @t1 @t123)) % 0.54/0.76 (define @t125 () (ite @t35 tptp.zero @t124)) % 0.54/0.76 (define @t126 () (_ @t119 @t30)) % 0.54/0.76 (define @t127 () (= tptp.zero @t126)) % 0.54/0.76 (define @t128 () (not @t127)) % 0.54/0.76 (define @t129 () (ite (= @t33 tptp.zero) tptp.zero @t33)) % 0.54/0.76 (define @t130 () (ite (= tptp.zero tptp.zero) @t1 @t129)) % 0.54/0.76 (define @t131 () (ite (= @t1 tptp.zero) tptp.zero @t130)) % 0.54/0.76 (define @t132 () (_ @t119 tptp.zero)) % 0.54/0.76 (define @t133 () (= @t30 @t132)) % 0.54/0.76 (define @t134 () (not @t133)) % 0.54/0.76 (define @t135 () (or @t134 @t128 @t122)) % 0.54/0.76 (define @t136 () (not @t88)) % 0.54/0.76 (define @t137 () (= tptp.zero @t108)) % 0.54/0.76 (define @t138 () (not @t137)) % 0.54/0.76 (define @t139 () (= @t30 @t113)) % 0.54/0.76 (define @t140 () (not @t139)) % 0.54/0.76 (define @t141 () (or @t140 @t138 @t136)) % 0.54/0.76 (define @t142 () (= @t1 @t113)) % 0.54/0.76 (define @t143 () (= tptp.zero @t113)) % 0.54/0.76 (define @t144 () (= @t112 @t1)) % 0.54/0.76 (define @t145 () (= @t112 tptp.zero)) % 0.54/0.76 (define @t146 () (@purify @t106)) % 0.54/0.76 (define @t147 () (= @t106 @t108)) % 0.54/0.76 (define @t148 () (= @t107 @t106)) % 0.54/0.76 (define @t149 () (= @t107 tptp.zero)) % 0.54/0.76 (define @t150 () (and @t91 @t98 @t99)) % 0.54/0.76 (assume @p1 @t29) % 0.54/0.76 (assume @p2 true) % 0.54/0.76 (step @p3 :rule refl :args ((_ @t3 @t2))) % 0.54/0.76 (step @p4 :rule refl :args ((tptp.s @t1))) % 0.54/0.76 (step @p5 :rule refl :args (@t30)) % 0.54/0.76 (step @p6 :rule cong :premises (@p5) :args (@t31)) % 0.54/0.76 (step @p7 :rule trans :premises (@p6 @p4)) % 0.54/0.76 (step @p8 :rule cong :premises (@p7) :args (@t32)) % 0.54/0.76 (step @p9 :rule trans :premises (@p8 @p3)) % 0.54/0.76 (step @p10 :rule refl :args (@t3)) % 0.54/0.76 (step @p11 :rule ho_cong :premises (@p10 @p7)) % 0.54/0.76 (step @p12 :rule cong :premises (@p11 @p9) :args ((= (_ @t3 @t31) @t32))) % 0.54/0.76 (step @p13 :rule symm :premises (@p12)) % 0.54/0.76 (step @p14 :rule refl :args (@t4)) % 0.54/0.76 (step @p15 :rule eq_resolve :premises (@p14 @p13)) % 0.54/0.76 (step @p16 :rule refl :args (tptp.s)) % 0.54/0.76 (step @p17 :rule ho_cong :premises (@p16 @p5)) % 0.54/0.76 (step @p18 :rule cong :premises (@p17 @p7) :args (@t34)) % 0.54/0.76 (step @p19 :rule symm :premises (@p18)) % 0.54/0.76 (step @p20 :rule refl :args (@t2)) % 0.54/0.76 (step @p21 :rule eq_resolve :premises (@p20 @p19)) % 0.54/0.76 (step @p22 :rule refl :args (@t1)) % 0.54/0.76 (step @p23 :rule cong :premises (@p22 @p5) :args (@t35)) % 0.54/0.76 (step @p24 :rule symm :premises (@p23)) % 0.54/0.76 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 0.54/0.76 (step @p26 :rule ho_cong :premises (@p16 @p25)) % 0.54/0.76 (step @p27 :rule trans :premises (@p26 @p21)) % 0.54/0.76 (step @p28 :rule ho_cong :premises (@p10 @p27)) % 0.54/0.76 (step @p29 :rule trans :premises (@p28 @p15)) % 0.54/0.76 (step @p30 :rule refl :args (tptp.zero)) % 0.54/0.76 (step @p31 :rule cong :premises (@p30 @p29) :args (@t36)) % 0.54/0.76 (step @p32 :rule cong :premises (@p31) :args (@t37)) % 0.54/0.76 (step @p33 :rule refl :args ((_ @t3 @t1))) % 0.54/0.76 (step @p34 :rule cong :premises (@p5) :args (@t38)) % 0.54/0.76 (step @p35 :rule trans :premises (@p34 @p33)) % 0.54/0.76 (step @p36 :rule ho_cong :premises (@p10 @p5)) % 0.54/0.76 (step @p37 :rule cong :premises (@p36 @p35) :args ((= (_ @t3 @t30) @t38))) % 0.54/0.76 (step @p38 :rule symm :premises (@p37)) % 0.54/0.76 (step @p39 :rule refl :args (@t5)) % 0.54/0.76 (step @p40 :rule eq_resolve :premises (@p39 @p38)) % 0.54/0.76 (step @p41 :rule ho_cong :premises (@p10 @p25)) % 0.54/0.76 (step @p42 :rule trans :premises (@p41 @p40)) % 0.54/0.76 (step @p43 :rule cong :premises (@p30 @p42) :args (@t39)) % 0.54/0.76 (step @p44 :rule cong :premises (@p43) :args (@t40)) % 0.54/0.76 (step @p45 :rule refl :args (@t41)) % 0.54/0.76 (step @p46 :rule refl :args (@t6)) % 0.54/0.76 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t6 @t41))) % 0.54/0.76 (step @p48 :rule symm :premises (@p47)) % 0.54/0.76 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.54/0.76 (step @p50 :rule cong :premises (@p25 @p49) :args (@t42)) % 0.54/0.76 (step @p51 :rule cong :premises (@p50) :args (@t43)) % 0.54/0.76 (step @p52 :rule nary_cong :premises (@p51 @p44 @p32) :args (@t44)) % 0.54/0.76 (step @p53 :rule cong :premises (@p52) :args ((forall @t8 @t44))) % 0.54/0.76 (step @p54 :rule aci_norm :args ((= (or @t43 (or @t40 @t37)) @t44))) % 0.54/0.76 (step @p55 :rule bool-and-de-morgan :args (@t39 @t36 true)) % 0.54/0.76 (step @p56 :rule refl :args (@t43)) % 0.54/0.76 (step @p57 :rule nary_cong :premises (@p56 @p55) :args ((or @t43 (not (and @t39 @t36))))) % 0.54/0.76 (step @p58 :rule bool-and-de-morgan :args (@t42 @t39 (and @t36))) % 0.54/0.76 (step @p59 :rule trans :premises (@p58 @p57)) % 0.54/0.76 (step @p60 :rule trans :premises (@p59 @p54)) % 0.54/0.76 (step @p61 :rule cong :premises (@p60) :args (@t46)) % 0.54/0.76 (step @p62 :rule trans :premises (@p61 @p53)) % 0.54/0.76 (step @p63 :rule cong :premises (@p62) :args (@t47)) % 0.54/0.76 (step @p64 :rule exists-elim :args ((= (exists @t8 @t45) @t47))) % 0.54/0.76 (step @p65 :rule trans :premises (@p64 @p63)) % 0.54/0.76 (step @p66 :rule eq-symm :args (@t4 tptp.zero)) % 0.54/0.76 (step @p67 :rule eq-symm :args (@t5 tptp.zero)) % 0.54/0.76 (step @p68 :rule eq-symm :args (@t6 @t1)) % 0.54/0.76 (step @p69 :rule nary_cong :premises (@p68 @p67 @p66) :args (@t7)) % 0.54/0.76 (step @p70 :rule cong :premises (@p69) :args (@t9)) % 0.54/0.76 (step @p71 :rule trans :premises (@p70 @p65)) % 0.54/0.76 (step @p72 :rule refl :args (@t48)) % 0.54/0.76 (step @p73 :rule refl :args (@t11)) % 0.54/0.76 (step @p74 :rule cong :premises (@p73 @p72) :args ((= @t11 @t48))) % 0.54/0.76 (step @p75 :rule symm :premises (@p74)) % 0.54/0.76 (step @p76 :rule eq_resolve :premises (@p73 @p75)) % 0.54/0.76 (step @p77 :rule refl :args (@t10)) % 0.54/0.76 (step @p78 :rule cong :premises (@p77 @p76) :args (@t49)) % 0.54/0.76 (step @p79 :rule cong :premises (@p78) :args (@t50)) % 0.54/0.76 (step @p80 :rule cong :premises (@p79) :args ((forall @t13 @t50))) % 0.54/0.76 (step @p81 :rule eq-symm :args (@t11 @t10)) % 0.54/0.76 (step @p82 :rule cong :premises (@p81) :args (@t12)) % 0.54/0.76 (step @p83 :rule cong :premises (@p82) :args (@t14)) % 0.54/0.76 (step @p84 :rule trans :premises (@p83 @p80)) % 0.54/0.76 (step @p85 :rule cong :premises (@p30 @p76) :args (@t51)) % 0.54/0.76 (step @p86 :rule cong :premises (@p85) :args (@t52)) % 0.54/0.76 (step @p87 :rule cong :premises (@p86) :args ((forall @t13 @t52))) % 0.54/0.76 (step @p88 :rule eq-symm :args (@t11 tptp.zero)) % 0.54/0.76 (step @p89 :rule cong :premises (@p88) :args (@t15)) % 0.54/0.76 (step @p90 :rule cong :premises (@p89) :args (@t16)) % 0.54/0.76 (step @p91 :rule trans :premises (@p90 @p87)) % 0.54/0.76 (step @p92 :rule aci_norm :args 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(step @p360 :rule cong :premises (@p270 @p344) :args (@t148)) % 0.54/0.77 (step @p361 :rule cong :premises (@p270 @p204) :args (@t149)) % 0.54/0.77 (step @p362 :rule cong :premises (@p292 @p361 @p360) :args ((ite @t35 @t149 @t148))) % 0.54/0.77 (step @p363 :rule ite_eq :args (@t107)) % 0.54/0.77 (step @p364 :rule eq_resolve :premises (@p363 @p362)) % 0.54/0.77 (step @p365 :rule eq_resolve :premises (@p364 @p359)) % 0.54/0.77 (step @p366 :rule cnf_or_pos :args (@t141)) % 0.54/0.77 (step @p367 :rule reordering :premises (@p366) :args ((or @t136 @t138 @t140 (not @t141)))) % 0.54/0.77 (step @p368 :rule chain_m_resolution :premises (@p367 @p365 @p338 @p319) :args (@t136 (@list false false false) (@list @t137 @t139 @t141))) % 0.54/0.77 (assume-push @p386 @t91) % 0.54/0.77 (assume-push @p387 @t98) % 0.54/0.77 (assume-push @p388 @t99) % 0.54/0.77 (step @p372 :rule symm :premises (@p211)) % 0.54/0.77 (step @p373 :rule symm :premises (@p239)) % 0.54/0.77 (step @p374 :rule trans :premises (@p260 @p373 @p372)) % 0.54/0.77 (step-pop @p389 :rule scope :premises (@p374)) % 0.54/0.77 (step-pop @p390 :rule scope :premises (@p389)) % 0.54/0.77 (step-pop @p391 :rule scope :premises (@p390)) % 0.54/0.77 (step @p375 :rule process_scope :premises (@p391) :args (@t88)) % 0.54/0.77 (step @p379 :rule implies_elim :premises (@p375)) % 0.54/0.77 (step @p380 :rule cnf_and_neg :args (@t150)) % 0.54/0.77 (step @p381 :rule resolution :premises (@p380 @p379) :args (true @t150)) % 0.54/0.77 (step @p382 :rule reordering :premises (@p381) :args ((or @t88 (not @t91) (not @t98) (not @t99)))) % 0.54/0.77 (step @p383 false :rule chain_m_resolution :premises (@p382 @p368 @p260 @p239 @p211) :args (false (@list true false false false) (@list @t88 @t99 @t98 @t91))) % 0.54/0.77 ) % 0.54/0.77 % SZS output end Proof % 0.54/0.77 % cvc5 exiting %------------------------------------------------------------------------------