%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV299^5 : TPTP v9.2.1. Bugfixed v6.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/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 08:55:44 AM UTC 2026 % Result : Theorem 0.36s 0.59s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV299^5 : TPTP v9.2.1. Bugfixed v6.2.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n021.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 : Tue Jun 2 18:27:50 EDT 2026 % 0.15/0.34 % CPUTime : % 0.28/0.48 %----Proving TH0 % 0.36/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.59 % SZS status Theorem % 0.36/0.59 % SZS output start Proof % 0.36/0.59 ( % 0.36/0.59 (declare-sort $$unsorted 0) % 0.36/0.59 (define tptp.cZERO () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xp" (-> $$unsorted Bool)))) (lambda (@list _let_2) (not (exists (@list _let_1) (_ _let_2 _let_1))))))) % 0.36/0.59 (define tptp.cSUCC () (let ((_let_1 (@var "Xt" $$unsorted))) (let ((_let_2 (@var "Xp" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Xx" $$unsorted))) (let ((_let_4 (@var "Xn" (-> (-> $$unsorted Bool) Bool)))) (lambda (@list _let_4 _let_2) (exists (@list _let_3) (and (_ _let_2 _let_3) (_ _let_4 (lambda (@list _let_1) (and (not (= _let_1 _let_3)) (_ _let_2 _let_1)))))))))))) % 0.36/0.59 (define tptp.cNAT () (let ((_let_1 (@var "Xn" (-> (-> $$unsorted Bool) Bool)))) (let ((_let_2 (@var "Xp" (-> (-> (-> $$unsorted Bool) Bool) Bool)))) (let ((_let_3 (@var "Xx" (-> (-> $$unsorted Bool) Bool)))) (lambda (@list _let_1) (forall (@list _let_2) (=> (and (_ _let_2 tptp.cZERO) (forall (@list _let_3) (=> (_ _let_2 _let_3) (_ _let_2 (_ tptp.cSUCC _let_3))))) (_ _let_2 _let_1)))))))) % 0.36/0.60 (define @t1 () (@var "M" (-> (-> $$unsorted Bool) Bool))) % 0.36/0.60 (define @t2 () (@var "P" (-> (-> (-> $$unsorted Bool) Bool) Bool))) % 0.36/0.60 (define @t3 () (_ @t2 @t1)) % 0.36/0.60 (define @t4 () (=> (_ tptp.cNAT @t1) @t3)) % 0.36/0.60 (define @t5 () (@list @t1)) % 0.36/0.60 (define @t6 () (forall @t5 @t4)) % 0.36/0.60 (define @t7 () (@var "X" (-> (-> $$unsorted Bool) Bool))) % 0.36/0.60 (define @t8 () (_ @t2 @t7)) % 0.36/0.60 (define @t9 () (=> @t8 (_ @t2 (_ tptp.cSUCC @t7)))) % 0.36/0.60 (define @t10 () (@list @t7)) % 0.36/0.60 (define @t11 () (forall @t10 @t9)) % 0.36/0.60 (define @t12 () (and (_ @t2 tptp.cZERO) @t11)) % 0.36/0.60 (define @t13 () (=> @t12 @t6)) % 0.36/0.60 (define @t14 () (@list @t2)) % 0.36/0.60 (define @t15 () (forall @t14 @t13)) % 0.36/0.60 (define @t16 () (not @t15)) % 0.36/0.60 (define @t17 () (@var "Xx" $$unsorted)) % 0.36/0.60 (define @t18 () (@var "Xp" (-> $$unsorted Bool))) % 0.36/0.60 (define @t19 () (_ @t18 @t17)) % 0.36/0.60 (define @t20 () (@list @t17)) % 0.36/0.60 (define @t21 () (exists @t20 @t19)) % 0.36/0.60 (define @t22 () (not @t21)) % 0.36/0.60 (define @t23 () (@list @t18)) % 0.36/0.60 (define @t24 () (lambda @t23 @t22)) % 0.36/0.60 (define @t25 () (@var "Xt" $$unsorted)) % 0.36/0.60 (define @t26 () (_ @t18 @t25)) % 0.36/0.60 (define @t27 () (not (= @t25 @t17))) % 0.36/0.60 (define @t28 () (and @t27 @t26)) % 0.36/0.60 (define @t29 () (@list @t25)) % 0.36/0.60 (define @t30 () (lambda @t29 @t28)) % 0.36/0.60 (define @t31 () (@var "Xn" (-> (-> $$unsorted Bool) Bool))) % 0.36/0.60 (define @t32 () (and @t19 (_ @t31 @t30))) % 0.36/0.60 (define @t33 () (exists @t20 @t32)) % 0.36/0.60 (define @t34 () (@list @t31 @t18)) % 0.36/0.60 (define @t35 () (lambda @t34 @t33)) % 0.36/0.60 (define @t36 () (@var "Xp" (-> (-> (-> $$unsorted Bool) Bool) Bool))) % 0.36/0.60 (define @t37 () (_ @t36 @t31)) % 0.36/0.60 (define @t38 () (@var "Xx" (-> (-> $$unsorted Bool) Bool))) % 0.36/0.60 (define @t39 () (_ @t36 @t38)) % 0.36/0.60 (define @t40 () (=> @t39 (_ @t36 (_ tptp.cSUCC @t38)))) % 0.36/0.60 (define @t41 () (@list @t38)) % 0.36/0.60 (define @t42 () (forall @t41 @t40)) % 0.36/0.60 (define @t43 () (and (_ @t36 tptp.cZERO) @t42)) % 0.36/0.60 (define @t44 () (=> @t43 @t37)) % 0.36/0.60 (define @t45 () (@list @t36)) % 0.36/0.60 (define @t46 () (forall @t45 @t44)) % 0.36/0.60 (define @t47 () (@list @t31)) % 0.36/0.60 (define @t48 () (lambda @t47 @t46)) % 0.36/0.60 (define @t49 () (@var "BOUND_VARIABLE_7628" (-> (-> $$unsorted Bool) Bool))) % 0.36/0.60 (define @t50 () (_ @t2 @t49)) % 0.36/0.60 (define @t51 () (_ @t18 @t25)) % 0.36/0.60 (define @t52 () (not (= @t17 @t25))) % 0.36/0.60 (define @t53 () (and @t52 @t51)) % 0.36/0.60 (define @t54 () (lambda @t29 @t53)) % 0.36/0.60 (define @t55 () (_ @t38 @t54)) % 0.36/0.60 (define @t56 () (not @t55)) % 0.36/0.60 (define @t57 () (_ @t18 @t17)) % 0.36/0.60 (define @t58 () (not @t57)) % 0.36/0.60 (define @t59 () (or @t58 @t56)) % 0.36/0.60 (define @t60 () (forall @t20 @t59)) % 0.36/0.60 (define @t61 () (not @t60)) % 0.36/0.60 (define @t62 () (lambda @t23 @t61)) % 0.36/0.60 (define @t63 () (_ @t36 @t62)) % 0.36/0.60 (define @t64 () (_ @t36 @t38)) % 0.36/0.60 (define @t65 () (forall @t41 (or (not @t64) @t63))) % 0.36/0.60 (define @t66 () (not @t65)) % 0.36/0.60 (define @t67 () (forall @t20 @t58)) % 0.36/0.60 (define @t68 () (lambda @t23 @t67)) % 0.36/0.60 (define @t69 () (_ @t36 @t68)) % 0.36/0.60 (define @t70 () (not @t69)) % 0.36/0.60 (define @t71 () (not (forall @t45 (or @t70 @t66 (_ @t36 @t49))))) % 0.36/0.60 (define @t72 () (_ @t7 @t54)) % 0.36/0.60 (define @t73 () (not @t72)) % 0.36/0.60 (define @t74 () (or @t58 @t73)) % 0.36/0.60 (define @t75 () (forall @t20 @t74)) % 0.36/0.60 (define @t76 () (not @t75)) % 0.36/0.60 (define @t77 () (lambda @t23 @t76)) % 0.36/0.60 (define @t78 () (_ @t2 @t77)) % 0.36/0.60 (define @t79 () (_ @t2 @t7)) % 0.36/0.60 (define @t80 () (forall @t10 (or (not @t79) @t78))) % 0.36/0.60 (define @t81 () (not @t80)) % 0.36/0.60 (define @t82 () (_ @t2 @t68)) % 0.36/0.60 (define @t83 () (not @t82)) % 0.36/0.60 (define @t84 () (or @t83 @t81 @t71 @t50)) % 0.36/0.60 (define @t85 () (or @t71 @t50)) % 0.36/0.60 (define @t86 () (or @t83 @t81 @t85)) % 0.36/0.60 (define @t87 () (@list @t2 @t49)) % 0.36/0.60 (define @t88 () (forall @t87 @t86)) % 0.36/0.60 (define @t89 () (@list @t49)) % 0.36/0.60 (define @t90 () (forall @t89 @t86)) % 0.36/0.60 (define @t91 () (forall @t89 @t85)) % 0.36/0.60 (define @t92 () (or @t83 @t81 @t91)) % 0.36/0.60 (define @t93 () (_ @t2 @t1)) % 0.36/0.60 (define @t94 () (forall @t45 (or @t70 @t66 (_ @t36 @t1)))) % 0.36/0.60 (define @t95 () (not @t94)) % 0.36/0.60 (define @t96 () (forall @t5 (or @t95 @t93))) % 0.36/0.60 (define @t97 () (not @t19)) % 0.36/0.60 (define @t98 () (forall @t20 @t97)) % 0.36/0.60 (define @t99 () (lambda @t23 @t98)) % 0.36/0.60 (define @t100 () (_ @t2 @t68)) % 0.36/0.60 (define @t101 () (not @t100)) % 0.36/0.60 (define @t102 () (or @t101 @t81 @t96)) % 0.36/0.60 (define @t103 () (and @t100 @t80)) % 0.36/0.60 (define @t104 () (or @t95 @t3)) % 0.36/0.60 (define @t105 () (_ @t36 @t31)) % 0.36/0.60 (define @t106 () (_ (lambda @t47 (forall @t45 (or @t70 @t66 @t105))) @t1)) % 0.36/0.60 (define @t107 () (=> @t106 @t3)) % 0.36/0.60 (define @t108 () (forall @t5 @t107)) % 0.36/0.60 (define @t109 () (and @t52 @t26)) % 0.36/0.60 (define @t110 () (lambda @t29 @t109)) % 0.36/0.60 (define @t111 () (lambda @t23 (not (forall @t20 (or @t97 (not (_ @t7 @t110))))))) % 0.36/0.60 (define @t112 () (_ @t2 @t77)) % 0.36/0.60 (define @t113 () (not @t8)) % 0.36/0.60 (define @t114 () (or @t113 @t112)) % 0.36/0.60 (define @t115 () (_ @t31 @t54)) % 0.36/0.60 (define @t116 () (lambda @t34 (not (forall @t20 (or @t58 (not @t115)))))) % 0.36/0.60 (define @t117 () (_ @t116 @t7)) % 0.36/0.60 (define @t118 () (=> @t8 (_ @t2 @t117))) % 0.36/0.60 (define @t119 () (forall @t10 @t118)) % 0.36/0.60 (define @t120 () (and @t100 @t119)) % 0.36/0.60 (define @t121 () (=> @t120 @t108)) % 0.36/0.60 (define @t122 () (forall @t14 @t121)) % 0.36/0.60 (define @t123 () (_ @t36 @t68)) % 0.36/0.60 (define @t124 () (not @t123)) % 0.36/0.60 (define @t125 () (or @t124 @t66 @t37)) % 0.36/0.60 (define @t126 () (and @t123 @t65)) % 0.36/0.60 (define @t127 () (lambda @t23 (not (forall @t20 (or @t97 (not (_ @t38 @t110))))))) % 0.36/0.60 (define @t128 () (_ @t36 @t62)) % 0.36/0.60 (define @t129 () (not @t39)) % 0.36/0.60 (define @t130 () (or @t129 @t128)) % 0.36/0.60 (define @t131 () (_ @t116 @t38)) % 0.36/0.60 (define @t132 () (=> @t39 (_ @t36 @t131))) % 0.36/0.60 (define @t133 () (forall @t41 @t132)) % 0.36/0.60 (define @t134 () (and @t123 @t133)) % 0.36/0.60 (define @t135 () (=> @t134 @t37)) % 0.36/0.60 (define @t136 () (_ @t31 @t110)) % 0.36/0.60 (define @t137 () (not @t136)) % 0.36/0.60 (define @t138 () (or @t97 @t137)) % 0.36/0.60 (define @t139 () (and @t19 @t136)) % 0.36/0.60 (define @t140 () (forall @t20 (not @t139))) % 0.36/0.60 (define @t141 () (not @t140)) % 0.36/0.60 (define @t142 () (not @t98)) % 0.36/0.60 (define @t143 () (forall @t87 @t84)) % 0.36/0.60 (define @t144 () (@quantifiers_skolemize @t143 1)) % 0.36/0.60 (define @t145 () (@quantifiers_skolemize @t143 0)) % 0.36/0.60 (define @t146 () (_ @t145 @t144)) % 0.36/0.60 (define @t147 () (forall @t45 (or @t70 @t66 (_ @t36 @t144)))) % 0.36/0.60 (define @t148 () (not @t147)) % 0.36/0.60 (define @t149 () (forall @t10 (or (not (_ @t145 @t7)) (_ @t145 @t77)))) % 0.36/0.60 (define @t150 () (not @t149)) % 0.36/0.60 (define @t151 () (@purify @t68)) % 0.36/0.60 (define @t152 () (_ @t145 @t151)) % 0.36/0.60 (define @t153 () (not @t152)) % 0.36/0.60 (define @t154 () (or @t153 @t150 @t148 @t146)) % 0.36/0.60 (define @t155 () (not @t154)) % 0.36/0.60 (define @t156 () (not @t143)) % 0.36/0.60 (define @t157 () (_ @t145 @t68)) % 0.36/0.60 (define @t158 () (not @t157)) % 0.36/0.60 (define @t159 () (or @t158 @t150 @t148 @t146)) % 0.36/0.60 (define @t160 () (not @t159)) % 0.36/0.60 (define @t161 () (@list true)) % 0.36/0.60 (define @t162 () (@list @t154)) % 0.36/0.60 (define @t163 () (forall @t41 (or (not (_ @t145 @t38)) (_ @t145 @t62)))) % 0.36/0.60 (define @t164 () (not @t163)) % 0.36/0.60 (define @t165 () (or @t158 @t164 @t146)) % 0.36/0.60 (define @t166 () (or @t153 @t164 @t146)) % 0.36/0.60 (define @t167 () (@quantifiers_skolemize @t163 0)) % 0.36/0.60 (define @t168 () (lambda @t23 (not (forall @t20 (or @t58 (not (_ @t167 @t54))))))) % 0.36/0.60 (define @t169 () (@purify @t168)) % 0.36/0.60 (define @t170 () (not (_ @t145 @t167))) % 0.36/0.60 (define @t171 () (or @t170 (_ @t145 @t169))) % 0.36/0.60 (define @t172 () (not @t171)) % 0.36/0.60 (define @t173 () (_ @t145 @t168)) % 0.36/0.60 (define @t174 () (or @t170 @t173)) % 0.36/0.60 (define @t175 () (not @t174)) % 0.36/0.60 (assume @p1 @t16) % 0.36/0.60 (assume @p2 true) % 0.36/0.60 (step @p3 (= tptp.cZERO @t24) :rule refl :args (@t24)) % 0.36/0.60 (step @p4 (= tptp.cSUCC @t35) :rule refl :args (@t35)) % 0.36/0.60 (step @p5 (= tptp.cNAT @t48) :rule refl :args (@t48)) % 0.36/0.60 (step @p6 :rule aci_norm :args ((= @t86 @t84))) % 0.36/0.60 (step @p7 :rule cong :premises (@p6) :args (@t88)) % 0.36/0.60 (step @p8 :rule quant-merge-prenex :args ((= (forall @t14 @t90) @t88))) % 0.36/0.60 (step @p9 :rule alpha_equiv :args (@t91 (@list @t49) (@list @t1))) % 0.36/0.60 (step @p10 :rule refl :args (@t81)) % 0.36/0.60 (step @p11 :rule refl :args (@t83)) % 0.36/0.60 (step @p12 :rule nary_cong :premises (@p11 @p10 @p9) :args (@t92)) % 0.36/0.60 (step @p13 :rule quant-miniscope-or :args ((= @t90 @t92))) % 0.36/0.60 (step @p14 :rule trans :premises (@p13 @p12)) % 0.36/0.60 (step @p15 :rule symm :premises (@p14)) % 0.36/0.60 (step @p16 :rule cong :premises (@p15) :args ((forall @t14 (or @t83 @t81 @t96)))) % 0.36/0.60 (step @p17 :rule trans :premises (@p16 @p8)) % 0.36/0.60 (step @p18 :rule trans :premises (@p17 @p7)) % 0.36/0.60 (step @p19 :rule refl :args (@t96)) % 0.36/0.60 (step @p20 :rule refl :args ((_ @t2 @t99))) % 0.36/0.60 (step @p21 :rule refl :args (@t57)) % 0.36/0.60 (step @p22 :rule cong :premises (@p21) :args (@t58)) % 0.36/0.60 (step @p23 :rule cong :premises (@p22) :args (@t67)) % 0.36/0.60 (step @p24 :rule cong :premises (@p23) :args (@t68)) % 0.36/0.60 (step @p25 :rule cong :premises (@p24) :args (@t82)) % 0.36/0.60 (step @p26 :rule trans :premises (@p25 @p20)) % 0.36/0.60 (step @p27 :rule refl :args (@t2)) % 0.36/0.60 (step @p28 :rule ho_cong :premises (@p27 @p24)) % 0.36/0.60 (step @p29 :rule cong :premises (@p28 @p26) :args ((= @t100 @t82))) % 0.36/0.60 (step @p30 :rule symm :premises (@p29)) % 0.36/0.60 (step @p31 :rule refl :args ((_ @t2 @t99))) % 0.36/0.60 (step @p32 :rule eq_resolve :premises (@p31 @p30)) % 0.36/0.60 (step @p33 :rule cong :premises (@p32) :args (@t101)) % 0.36/0.60 (step @p34 :rule nary_cong :premises (@p33 @p10 @p19) :args (@t102)) % 0.36/0.60 (step @p35 :rule cong :premises (@p34) :args ((forall @t14 @t102))) % 0.36/0.60 (step @p36 :rule trans :premises (@p35 @p18)) % 0.36/0.60 (step @p37 :rule aci_norm :args ((= (or (or @t101 @t81) @t96) @t102))) % 0.36/0.60 (step @p38 :rule bool-and-de-morgan :args (@t100 @t80 true)) % 0.36/0.60 (step @p39 :rule nary_cong :premises (@p38 @p19) :args ((or (not @t103) @t96))) % 0.36/0.60 (step @p40 :rule trans :premises (@p39 @p37)) % 0.36/0.60 (step @p41 :rule bool-impl-elim :args (@t103 @t96)) % 0.36/0.60 (step @p42 :rule trans :premises (@p41 @p40)) % 0.36/0.60 (step @p43 :rule cong :premises (@p42) :args ((forall @t14 (=> @t103 @t96)))) % 0.36/0.60 (step @p44 :rule trans :premises (@p43 @p36)) % 0.36/0.60 (step @p45 :rule refl :args (@t93)) % 0.36/0.60 (step @p46 :rule refl :args (@t3)) % 0.36/0.60 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t3 @t93))) % 0.36/0.60 (step @p48 :rule symm :premises (@p47)) % 0.36/0.60 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.36/0.60 (step @p50 :rule refl :args (@t95)) % 0.36/0.60 (step @p51 :rule nary_cong :premises (@p50 @p49) :args (@t104)) % 0.36/0.60 (step @p52 :rule cong :premises (@p51) :args ((forall @t5 @t104))) % 0.36/0.60 (step @p53 :rule bool-impl-elim :args (@t94 @t3)) % 0.36/0.60 (step @p54 :rule cong :premises (@p53) :args 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:rule cong :premises (@p324) :args (@t175)) % 0.36/0.60 (step @p326 :rule cong :premises (@p291 @p325) :args ((=> @t164 @t175))) % 0.36/0.60 (assume-push @p348 @t164) % 0.36/0.60 (step @p328 :rule skolemize :premises (@p312)) % 0.36/0.60 (step-pop @p349 :rule scope :premises (@p328)) % 0.36/0.60 (step @p329 :rule process_scope :premises (@p349) :args (@t175)) % 0.36/0.60 (step @p331 :rule eq_resolve :premises (@p329 @p326)) % 0.36/0.60 (step @p332 :rule implies_elim :premises (@p331)) % 0.36/0.60 (step @p333 :rule eq_resolve :premises (@p332 @p315)) % 0.36/0.60 (step @p334 :rule chain_m_resolution :premises (@p333 @p312) :args (@t172 @t161 (@list @t163))) % 0.36/0.60 (step @p335 :rule refl :args (@t149)) % 0.36/0.60 (step @p336 :rule cong :premises (@p335 @p324) :args ((=> @t149 @t174))) % 0.36/0.60 (assume-push @p350 @t149) % 0.36/0.60 (step @p338 :rule instantiate :premises (@p284) :args ((@list @t167))) % 0.36/0.60 (step-pop @p351 :rule scope :premises (@p338)) % 0.36/0.60 (step @p339 :rule process_scope :premises (@p351) :args (@t174)) % 0.36/0.60 (step @p341 :rule eq_resolve :premises (@p339 @p336)) % 0.36/0.60 (step @p342 :rule implies_elim :premises (@p341)) % 0.36/0.60 (step @p343 false :rule chain_m_resolution :premises (@p342 @p334 @p284) :args (false (@list true false) (@list @t171 @t149))) % 0.36/0.60 ) % 0.36/0.60 % SZS output end Proof % 0.36/0.60 % cvc5 exiting %------------------------------------------------------------------------------