%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM390+1 : TPTP v9.2.1. Released v3.2.0. % 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 08:39:18 AM UTC 2026 % Result : Theorem 0.40s 0.59s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : NUM390+1 : TPTP v9.2.1. Released v3.2.0. % 0.12/0.13 % 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 : Tue Jun 2 11:17:20 EDT 2026 % 0.16/0.33 % CPUTime : % 0.31/0.48 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.59 % SZS status Theorem % 0.40/0.59 % SZS output start Proof % 0.40/0.59 ( % 0.40/0.59 (declare-sort $$unsorted 0) % 0.40/0.59 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.40/0.59 (declare-const tptp.relation_non_empty (-> $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.function (-> $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.empty_set $$unsorted) % 0.40/0.59 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.40/0.59 (define @t1 () (@var "A" $$unsorted)) % 0.40/0.59 (define @t2 () (@var "B" $$unsorted)) % 0.40/0.59 (define @t3 () (tptp.in @t2 @t1)) % 0.40/0.59 (define @t4 () (tptp.in @t1 @t2)) % 0.40/0.59 (define @t5 () (@list @t1 @t2)) % 0.40/0.59 (define @t6 () (tptp.proper_subset @t1 @t2)) % 0.40/0.59 (define @t7 () (tptp.function @t1)) % 0.40/0.59 (define @t8 () (tptp.empty @t1)) % 0.40/0.59 (define @t9 () (@list @t1)) % 0.40/0.59 (define @t10 () (tptp.epsilon_connected @t1)) % 0.40/0.59 (define @t11 () (tptp.epsilon_transitive @t1)) % 0.40/0.59 (define @t12 () (and @t11 @t10)) % 0.40/0.59 (define @t13 () (tptp.ordinal @t1)) % 0.40/0.59 (define @t14 () (forall @t9 (=> @t13 @t12))) % 0.40/0.59 (define @t15 () (tptp.relation @t1)) % 0.40/0.59 (define @t16 () (and @t15 @t7 (tptp.one_to_one @t1))) % 0.40/0.59 (define @t17 () (and @t15 @t8 @t7)) % 0.40/0.59 (define @t18 () (tptp.subset @t2 @t1)) % 0.40/0.59 (define @t19 () (@list @t2)) % 0.40/0.59 (define @t20 () (forall @t19 (=> @t3 @t18))) % 0.40/0.59 (define @t21 () (= @t11 @t20)) % 0.40/0.59 (define @t22 () (forall @t9 @t21)) % 0.40/0.59 (define @t23 () (not (= @t1 @t2))) % 0.40/0.59 (define @t24 () (tptp.subset @t1 @t2)) % 0.40/0.59 (define @t25 () (tptp.relation tptp.empty_set)) % 0.40/0.59 (define @t26 () (tptp.empty tptp.empty_set)) % 0.40/0.59 (define @t27 () (not @t8)) % 0.40/0.59 (define @t28 () (tptp.relation_empty_yielding @t1)) % 0.40/0.59 (define @t29 () (tptp.element @t1 @t2)) % 0.40/0.59 (define @t30 () (@var "C" $$unsorted)) % 0.40/0.59 (define @t31 () (tptp.subset @t1 @t30)) % 0.40/0.59 (define @t32 () (tptp.subset @t2 @t30)) % 0.40/0.59 (define @t33 () (and @t24 @t32)) % 0.40/0.59 (define @t34 () (@list @t1 @t2 @t30)) % 0.40/0.59 (define @t35 () (forall @t34 (=> @t33 @t31))) % 0.40/0.59 (define @t36 () (=> @t6 @t4)) % 0.40/0.59 (define @t37 () (tptp.ordinal @t2)) % 0.40/0.59 (define @t38 () (forall @t19 (=> @t37 @t36))) % 0.40/0.59 (define @t39 () (=> @t11 @t38)) % 0.40/0.59 (define @t40 () (forall @t9 @t39)) % 0.40/0.59 (define @t41 () (tptp.in @t1 @t30)) % 0.40/0.59 (define @t42 () (tptp.in @t2 @t30)) % 0.40/0.59 (define @t43 () (and @t24 @t42)) % 0.40/0.59 (define @t44 () (=> @t43 @t41)) % 0.40/0.59 (define @t45 () (tptp.ordinal @t30)) % 0.40/0.59 (define @t46 () (@list @t30)) % 0.40/0.59 (define @t47 () (forall @t46 (=> @t45 @t44))) % 0.40/0.59 (define @t48 () (=> @t37 @t47)) % 0.40/0.59 (define @t49 () (forall @t19 @t48)) % 0.40/0.59 (define @t50 () (=> @t11 @t49)) % 0.40/0.59 (define @t51 () (forall @t9 @t50)) % 0.40/0.59 (define @t52 () (not @t51)) % 0.40/0.59 (define @t53 () (tptp.empty @t2)) % 0.40/0.59 (define @t54 () (tptp.element @t2 (tptp.powerset @t30))) % 0.40/0.59 (define @t55 () (forall @t5 (not (and @t4 @t18)))) % 0.40/0.59 (define @t56 () (@var "BOUND_VARIABLE_7748" $$unsorted)) % 0.40/0.59 (define @t57 () (tptp.in @t1 @t56)) % 0.40/0.59 (define @t58 () (@var "BOUND_VARIABLE_7746" $$unsorted)) % 0.40/0.59 (define @t59 () (not (tptp.in @t58 @t56))) % 0.40/0.59 (define @t60 () (not (tptp.ordinal @t56))) % 0.40/0.59 (define @t61 () (not (tptp.subset @t1 @t58))) % 0.40/0.59 (define @t62 () (not (tptp.ordinal @t58))) % 0.40/0.59 (define @t63 () (not @t11)) % 0.40/0.59 (define @t64 () (or @t63 @t62 @t61 @t60 @t59 @t57)) % 0.40/0.59 (define @t65 () (@list @t1 @t58 @t56)) % 0.40/0.59 (define @t66 () (forall @t65 @t64)) % 0.40/0.59 (define @t67 () (@quantifiers_skolemize @t66 1)) % 0.40/0.59 (define @t68 () (@quantifiers_skolemize @t66 0)) % 0.40/0.59 (define @t69 () (@list @t68 @t67)) % 0.40/0.59 (define @t70 () (@var "BOUND_VARIABLE_7701" $$unsorted)) % 0.40/0.59 (define @t71 () (tptp.in @t1 @t70)) % 0.40/0.59 (define @t72 () (not (tptp.proper_subset @t1 @t70))) % 0.40/0.59 (define @t73 () (not (tptp.ordinal @t70))) % 0.40/0.59 (define @t74 () (or @t73 @t72 @t71)) % 0.40/0.59 (define @t75 () (or @t63 @t74)) % 0.40/0.59 (define @t76 () (forall (@list @t1 @t70) @t75)) % 0.40/0.59 (define @t77 () (@list @t70)) % 0.40/0.59 (define @t78 () (forall @t77 @t75)) % 0.40/0.59 (define @t79 () (forall @t77 @t74)) % 0.40/0.59 (define @t80 () (or @t63 @t79)) % 0.40/0.59 (define @t81 () (not @t6)) % 0.40/0.59 (define @t82 () (not @t37)) % 0.40/0.59 (define @t83 () (or @t82 @t81 @t4)) % 0.40/0.59 (define @t84 () (forall @t19 @t83)) % 0.40/0.59 (define @t85 () (or @t62 @t61 @t60 @t59 @t57)) % 0.40/0.59 (define @t86 () (or @t63 @t85)) % 0.40/0.59 (define @t87 () (forall @t65 @t86)) % 0.40/0.59 (define @t88 () (@list @t58 @t56)) % 0.40/0.59 (define @t89 () (forall @t88 @t86)) % 0.40/0.59 (define @t90 () (forall @t88 @t85)) % 0.40/0.59 (define @t91 () (@var "BOUND_VARIABLE_7729" $$unsorted)) % 0.40/0.59 (define @t92 () (or @t63 @t90)) % 0.40/0.59 (define @t93 () (tptp.in @t1 @t91)) % 0.40/0.59 (define @t94 () (not (tptp.in @t2 @t91))) % 0.40/0.59 (define @t95 () (not (tptp.ordinal @t91))) % 0.40/0.59 (define @t96 () (not @t24)) % 0.40/0.59 (define @t97 () (or @t82 @t96 @t95 @t94 @t93)) % 0.40/0.59 (define @t98 () (@list @t2 @t91)) % 0.40/0.59 (define @t99 () (forall @t98 @t97)) % 0.40/0.59 (define @t100 () (or @t95 @t94 @t93)) % 0.40/0.59 (define @t101 () (or @t82 @t96 @t100)) % 0.40/0.59 (define @t102 () (forall @t98 @t101)) % 0.40/0.59 (define @t103 () (@list @t91)) % 0.40/0.59 (define @t104 () (forall @t103 @t101)) % 0.40/0.59 (define @t105 () (forall @t103 @t100)) % 0.40/0.59 (define @t106 () (or @t82 @t96 @t105)) % 0.40/0.59 (define @t107 () (not @t42)) % 0.40/0.59 (define @t108 () (not @t45)) % 0.40/0.59 (define @t109 () (or @t108 @t107 @t41)) % 0.40/0.59 (define @t110 () (forall @t46 @t109)) % 0.40/0.59 (define @t111 () (or @t82 @t96 @t110)) % 0.40/0.59 (define @t112 () (or @t96 @t110)) % 0.40/0.59 (define @t113 () (or @t96 @t109)) % 0.40/0.59 (define @t114 () (or @t108 @t96 @t107 @t41)) % 0.40/0.59 (define @t115 () (or @t96 @t107 @t41)) % 0.40/0.59 (define @t116 () (@quantifiers_skolemize @t66 2)) % 0.40/0.59 (define @t117 () (tptp.in @t68 @t116)) % 0.40/0.59 (define @t118 () (tptp.in @t67 @t116)) % 0.40/0.59 (define @t119 () (not @t118)) % 0.40/0.59 (define @t120 () (tptp.ordinal @t116)) % 0.40/0.59 (define @t121 () (not @t120)) % 0.40/0.59 (define @t122 () (tptp.subset @t68 @t67)) % 0.40/0.59 (define @t123 () (not @t122)) % 0.40/0.59 (define @t124 () (tptp.ordinal @t67)) % 0.40/0.59 (define @t125 () (not @t124)) % 0.40/0.59 (define @t126 () (tptp.epsilon_transitive @t68)) % 0.40/0.59 (define @t127 () (not @t126)) % 0.40/0.59 (define @t128 () (or @t127 @t125 @t123 @t121 @t119 @t117)) % 0.40/0.59 (define @t129 () (not @t117)) % 0.40/0.59 (define @t130 () (@list true)) % 0.40/0.59 (define @t131 () (@list @t128)) % 0.40/0.59 (define @t132 () (= @t68 @t67)) % 0.40/0.59 (define @t133 () (not @t132)) % 0.40/0.59 (define @t134 () (and @t118 @t132 @t129)) % 0.40/0.59 (define @t135 () (@list false true)) % 0.40/0.59 (define @t136 () (and @t122 @t133)) % 0.40/0.59 (define @t137 () (tptp.proper_subset @t68 @t67)) % 0.40/0.59 (define @t138 () (= @t137 @t136)) % 0.40/0.59 (define @t139 () (@list false false)) % 0.40/0.59 (define @t140 () (tptp.in @t68 @t67)) % 0.40/0.59 (define @t141 () (not @t137)) % 0.40/0.59 (define @t142 () (or @t127 @t125 @t141 @t140)) % 0.40/0.59 (define @t143 () (tptp.subset @t67 @t68)) % 0.40/0.59 (define @t144 () (not @t143)) % 0.40/0.59 (define @t145 () (not @t140)) % 0.40/0.59 (define @t146 () (or @t145 @t144)) % 0.40/0.59 (define @t147 () (@list @t116)) % 0.40/0.59 (define @t148 () (tptp.epsilon_transitive @t116)) % 0.40/0.59 (define @t149 () (and @t148 (tptp.epsilon_connected @t116))) % 0.40/0.59 (define @t150 () (or @t121 @t149)) % 0.40/0.59 (define @t151 () (forall @t19 (or (not (tptp.in @t2 @t116)) (tptp.subset @t2 @t116)))) % 0.40/0.59 (define @t152 () (= @t148 @t151)) % 0.40/0.59 (define @t153 () (tptp.subset @t67 @t116)) % 0.40/0.59 (define @t154 () (or @t119 @t153)) % 0.40/0.59 (define @t155 () (not @t32)) % 0.40/0.59 (define @t156 () (tptp.subset @t68 @t116)) % 0.40/0.59 (define @t157 () (not @t153)) % 0.40/0.59 (define @t158 () (or @t123 @t157 @t156)) % 0.40/0.59 (define @t159 () (@list @t68 @t116)) % 0.40/0.59 (define @t160 () (tptp.proper_subset @t68 @t116)) % 0.40/0.59 (define @t161 () (not @t160)) % 0.40/0.59 (define @t162 () (or @t127 @t121 @t161 @t117)) % 0.40/0.59 (define @t163 () (= @t68 @t116)) % 0.40/0.59 (define @t164 () (not @t163)) % 0.40/0.59 (define @t165 () (and @t156 @t164)) % 0.40/0.59 (define @t166 () (= @t160 @t165)) % 0.40/0.59 (define @t167 () (not @t165)) % 0.40/0.59 (define @t168 () (@list true false)) % 0.40/0.59 (define @t169 () (not @t156)) % 0.40/0.59 (define @t170 () (and @t144 @t163 @t153)) % 0.40/0.59 (assume @p1 (forall @t5 (=> @t4 (not @t3)))) % 0.40/0.59 (assume @p2 (forall @t5 (=> @t6 (not (tptp.proper_subset @t2 @t1))))) % 0.40/0.59 (assume @p3 (forall @t9 (=> @t8 @t7))) % 0.40/0.59 (assume @p4 @t14) % 0.40/0.59 (assume @p5 (forall @t9 (=> @t8 @t15))) % 0.40/0.59 (assume @p6 (forall @t9 (=> @t17 @t16))) % 0.40/0.59 (assume @p7 (forall @t9 (=> @t12 @t13))) % 0.40/0.59 (assume @p8 @t22) % 0.40/0.59 (assume @p9 (forall @t5 (= @t6 (and @t24 @t23)))) % 0.40/0.59 (assume @p10 (forall @t9 (exists @t19 (tptp.element @t2 @t1)))) % 0.40/0.59 (assume @p11 (and @t26 @t25 (tptp.relation_empty_yielding tptp.empty_set))) % 0.40/0.59 (assume @p12 @t26) % 0.40/0.59 (assume @p13 (and @t26 @t25)) % 0.40/0.59 (assume @p14 (forall @t5 (not (tptp.proper_subset @t1 @t1)))) % 0.40/0.59 (assume @p15 (exists @t9 (and @t15 @t7))) % 0.40/0.59 (assume @p16 (exists @t9 (and @t11 @t10 @t13))) % 0.40/0.59 (assume @p17 (exists @t9 (and @t8 @t15))) % 0.40/0.59 (assume @p18 (exists @t9 @t8)) % 0.40/0.59 (assume @p19 (exists @t9 @t17)) % 0.40/0.59 (assume @p20 (exists @t9 (and @t27 @t15))) % 0.40/0.59 (assume @p21 (exists @t9 @t27)) % 0.40/0.59 (assume @p22 (exists @t9 @t16)) % 0.40/0.59 (assume @p23 (exists @t9 (and @t15 @t28))) % 0.40/0.59 (assume @p24 (exists @t9 (and @t15 @t28 @t7))) % 0.40/0.59 (assume @p25 (exists @t9 (and @t15 (tptp.relation_non_empty @t1) @t7))) % 0.40/0.59 (assume @p26 (forall @t5 (tptp.subset @t1 @t1))) % 0.40/0.59 (assume @p27 (forall @t5 (=> @t4 @t29))) % 0.40/0.59 (assume @p28 @t35) % 0.40/0.59 (assume @p29 @t40) % 0.40/0.59 (assume @p30 @t52) % 0.40/0.59 (assume @p31 (forall @t5 (=> @t29 (or @t53 @t4)))) % 0.40/0.59 (assume @p32 (forall @t5 (= (tptp.element @t1 (tptp.powerset @t2)) @t24))) % 0.40/0.59 (assume @p33 (forall @t34 (=> (and @t4 @t54) (tptp.element @t1 @t30)))) % 0.40/0.59 (assume @p34 (forall @t34 (not (and @t4 @t54 (tptp.empty @t30))))) % 0.40/0.59 (assume @p35 (forall @t9 (=> @t8 (= @t1 tptp.empty_set)))) % 0.40/0.59 (assume @p36 (forall @t5 (not (and @t4 @t53)))) % 0.40/0.59 (assume @p37 @t55) % 0.40/0.59 (assume @p38 (forall @t5 (not (and @t8 @t23 @t53)))) % 0.40/0.59 (assume @p39 true) % 0.40/0.59 (step @p40 :rule bool-and-de-morgan :args (@t4 @t18 true)) % 0.40/0.59 (step @p41 :rule cong :premises (@p40) :args (@t55)) % 0.40/0.59 (step @p42 :rule eq_resolve :premises (@p37 @p41)) % 0.40/0.59 (step @p43 :rule instantiate :premises (@p42) :args (@t69)) % 0.40/0.59 (step @p44 :rule aci_norm :args ((= @t75 (or @t63 @t73 @t72 @t71)))) % 0.40/0.59 (step @p45 :rule cong :premises (@p44) :args (@t76)) % 0.40/0.59 (step @p46 :rule quant-merge-prenex :args ((= (forall @t9 @t78) @t76))) % 0.40/0.59 (step @p47 :rule alpha_equiv :args (@t79 (@list @t70) (@list @t2))) % 0.40/0.59 (step @p48 :rule refl :args (@t63)) % 0.40/0.59 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t80)) % 0.40/0.59 (step @p50 :rule quant-miniscope-or :args ((= @t78 @t80))) % 0.40/0.59 (step @p51 :rule trans :premises (@p50 @p49)) % 0.40/0.59 (step @p52 :rule symm :premises (@p51)) % 0.40/0.59 (step @p53 :rule cong :premises (@p52) :args ((forall @t9 (or @t63 @t84)))) % 0.40/0.59 (step @p54 :rule trans :premises (@p53 @p46)) % 0.40/0.59 (step @p55 :rule trans :premises (@p54 @p45)) % 0.40/0.59 (step @p56 :rule bool-impl-elim :args (@t11 @t84)) % 0.40/0.59 (step @p57 :rule cong :premises (@p56) :args ((forall @t9 (=> @t11 @t84)))) % 0.40/0.59 (step @p58 :rule trans :premises (@p57 @p55)) % 0.40/0.59 (step @p59 :rule aci_norm :args ((= (or @t82 (or @t81 @t4)) @t83))) % 0.40/0.59 (step @p60 :rule bool-impl-elim :args (@t6 @t4)) % 0.40/0.59 (step @p61 :rule refl :args (@t82)) % 0.40/0.59 (step @p62 :rule nary_cong :premises (@p61 @p60) :args ((or @t82 @t36))) % 0.40/0.59 (step @p63 :rule trans :premises (@p62 @p59)) % 0.40/0.59 (step @p64 :rule bool-impl-elim :args (@t37 @t36)) % 0.40/0.59 (step @p65 :rule trans :premises (@p64 @p63)) % 0.40/0.59 (step @p66 :rule cong :premises (@p65) :args (@t38)) % 0.40/0.59 (step @p67 :rule refl :args (@t11)) % 0.40/0.59 (step @p68 :rule cong :premises (@p67 @p66) :args (@t39)) % 0.40/0.59 (step @p69 :rule cong :premises (@p68) :args (@t40)) % 0.40/0.59 (step @p70 :rule trans :premises (@p69 @p58)) % 0.40/0.59 (step @p71 :rule eq_resolve :premises (@p29 @p70)) % 0.40/0.59 (step @p72 :rule instantiate :premises (@p71) :args (@t69)) % 0.40/0.59 (step @p73 :rule instantiate :premises (@p9) :args (@t69)) % 0.40/0.59 (step @p74 :rule aci_norm :args ((= @t86 @t64))) % 0.40/0.59 (step @p75 :rule cong :premises (@p74) :args (@t87)) % 0.40/0.59 (step @p76 :rule quant-merge-prenex :args ((= (forall @t9 @t89) @t87))) % 0.40/0.59 (step @p77 :rule alpha_equiv :args (@t90 (@list @t58 @t56) (@list @t2 @t91))) % 0.40/0.59 (step @p78 :rule nary_cong :premises (@p48 @p77) :args (@t92)) % 0.40/0.59 (step @p79 :rule quant-miniscope-or :args ((= @t89 @t92))) % 0.40/0.59 (step @p80 :rule trans :premises (@p79 @p78)) % 0.40/0.59 (step @p81 :rule symm :premises (@p80)) % 0.40/0.59 (step @p82 :rule cong :premises (@p81) :args ((forall @t9 (or @t63 @t99)))) % 0.40/0.59 (step @p83 :rule trans :premises (@p82 @p76)) % 0.40/0.59 (step @p84 :rule trans :premises (@p83 @p75)) % 0.40/0.59 (step @p85 :rule bool-impl-elim :args (@t11 @t99)) % 0.40/0.59 (step @p86 :rule cong :premises (@p85) :args ((forall @t9 (=> @t11 @t99)))) % 0.40/0.59 (step @p87 :rule trans :premises (@p86 @p84)) % 0.40/0.59 (step @p88 :rule aci_norm :args ((= @t101 @t97))) % 0.40/0.59 (step @p89 :rule cong :premises (@p88) :args (@t102)) % 0.40/0.59 (step @p90 :rule quant-merge-prenex :args ((= (forall @t19 @t104) @t102))) % 0.40/0.59 (step @p91 :rule alpha_equiv :args (@t105 (@list @t91) (@list @t30))) % 0.40/0.59 (step @p92 :rule refl :args (@t96)) % 0.40/0.59 (step @p93 :rule nary_cong :premises (@p61 @p92 @p91) :args (@t106)) % 0.40/0.59 (step @p94 :rule quant-miniscope-or :args ((= @t104 @t106))) % 0.40/0.59 (step @p95 :rule trans :premises (@p94 @p93)) % 0.40/0.59 (step @p96 :rule symm :premises (@p95)) % 0.40/0.59 (step @p97 :rule cong :premises (@p96) :args ((forall @t19 @t111))) % 0.40/0.59 (step @p98 :rule trans :premises (@p97 @p90)) % 0.40/0.59 (step @p99 :rule trans :premises (@p98 @p89)) % 0.40/0.59 (step @p100 :rule aci_norm :args ((= (or @t82 @t112) @t111))) % 0.40/0.59 (step @p101 :rule bool-impl-elim :args (@t37 @t112)) % 0.40/0.59 (step @p102 :rule trans :premises (@p101 @p100)) % 0.40/0.59 (step @p103 :rule cong :premises (@p102) :args ((forall @t19 (=> @t37 @t112)))) % 0.40/0.59 (step @p104 :rule trans :premises (@p103 @p99)) % 0.40/0.59 (step @p105 :rule quant-miniscope-or :args ((= (forall @t46 @t113) @t112))) % 0.40/0.59 (step @p106 :rule aci_norm :args ((= @t114 @t113))) % 0.40/0.59 (step @p107 :rule cong :premises (@p106) :args ((forall @t46 @t114))) % 0.40/0.59 (step @p108 :rule trans :premises (@p107 @p105)) % 0.40/0.59 (step @p109 :rule aci_norm :args ((= (or @t108 @t115) @t114))) % 0.40/0.59 (step @p110 :rule aci_norm :args ((= (or (or @t96 @t107) @t41) @t115))) % 0.40/0.59 (step @p111 :rule refl :args (@t41)) % 0.40/0.59 (step @p112 :rule bool-and-de-morgan :args (@t24 @t42 true)) % 0.40/0.59 (step @p113 :rule nary_cong :premises (@p112 @p111) :args ((or (not @t43) @t41))) % 0.40/0.59 (step @p114 :rule trans :premises (@p113 @p110)) % 0.40/0.59 (step @p115 :rule bool-impl-elim :args (@t43 @t41)) % 0.40/0.59 (step @p116 :rule trans :premises (@p115 @p114)) % 0.40/0.59 (step @p117 :rule refl :args (@t108)) % 0.40/0.59 (step @p118 :rule nary_cong :premises (@p117 @p116) :args ((or @t108 @t44))) % 0.40/0.59 (step @p119 :rule trans :premises (@p118 @p109)) % 0.40/0.59 (step @p120 :rule bool-impl-elim :args (@t45 @t44)) % 0.40/0.59 (step @p121 :rule trans :premises (@p120 @p119)) % 0.40/0.59 (step @p122 :rule cong :premises (@p121) :args (@t47)) % 0.40/0.59 (step @p123 :rule trans :premises (@p122 @p108)) % 0.40/0.59 (step @p124 :rule refl :args (@t37)) % 0.40/0.59 (step @p125 :rule cong :premises (@p124 @p123) :args (@t48)) % 0.40/0.59 (step @p126 :rule cong :premises (@p125) :args (@t49)) % 0.40/0.59 (step @p127 :rule trans :premises (@p126 @p104)) % 0.40/0.59 (step @p128 :rule cong :premises (@p67 @p127) :args (@t50)) % 0.40/0.59 (step @p129 :rule cong :premises (@p128) :args (@t51)) % 0.40/0.59 (step @p130 :rule trans :premises (@p129 @p87)) % 0.40/0.59 (step @p131 :rule cong :premises (@p130) :args (@t52)) % 0.40/0.59 (step @p132 :rule eq_resolve :premises (@p30 @p131)) % 0.40/0.59 (step @p133 :rule skolemize :premises (@p132)) % 0.40/0.59 (step @p134 :rule cnf_or_neg :args (@t128 5)) % 0.40/0.59 (step @p135 :rule chain_m_resolution :premises (@p134 @p133) :args (@t129 @t130 @t131)) % 0.40/0.59 (step @p136 :rule bool-double-not-elim :args (@t118)) % 0.40/0.59 (step @p137 :rule refl :args (@t128)) % 0.40/0.59 (step @p138 :rule nary_cong :premises (@p137 @p136) :args ((or @t128 (not @t119)))) % 0.40/0.59 (step @p139 :rule cnf_or_neg :args (@t128 4)) % 0.40/0.59 (step @p140 :rule eq_resolve :premises (@p139 @p138)) % 0.40/0.59 (step @p141 :rule reordering :premises (@p140) :args ((or @t118 @t128))) % 0.40/0.59 (step @p142 :rule chain_m_resolution :premises (@p141 @p133) :args (@t118 @t130 @t131)) % 0.40/0.59 (step @p143 :rule refl :args (@t133)) % 0.40/0.59 (step @p144 :rule bool-double-not-elim :args (@t117)) % 0.40/0.59 (step @p145 :rule refl :args (@t119)) % 0.40/0.59 (step @p146 :rule nary_cong :premises (@p145 @p144 @p143) :args ((or @t119 (not @t129) @t133))) % 0.40/0.59 (assume-push @p301 @t118) % 0.40/0.59 (assume-push @p302 @t132) % 0.40/0.59 (assume-push @p303 @t129) % 0.40/0.59 (step @p150 :rule evaluate :args ((= false true))) % 0.40/0.59 (step @p151 :rule true_intro :premises (@p142)) % 0.40/0.59 (step @p152 :rule refl :args (@t116)) % 0.40/0.59 (step @p153 :rule cong :premises (@p302 @p152) :args (@t117)) % 0.40/0.59 (step @p154 :rule false_intro :premises (@p135)) % 0.40/0.59 (step @p155 :rule symm :premises (@p154)) % 0.40/0.59 (step @p156 :rule trans :premises (@p155 @p153 @p151)) % 0.40/0.59 (step @p157 false :rule eq_resolve :premises (@p156 @p150)) % 0.40/0.59 (step-pop @p304 :rule scope :premises (@p157)) % 0.40/0.59 (step-pop @p305 :rule scope :premises (@p304)) % 0.40/0.59 (step-pop @p306 :rule scope :premises (@p305)) % 0.40/0.59 (step @p158 :rule process_scope :premises (@p306) :args (false)) % 0.40/0.59 (assume-push @p307 @t118) % 0.40/0.59 (assume-push @p308 @t129) % 0.40/0.59 (assume-push @p309 @t132) % 0.40/0.59 (step @p165 :rule and_intro :premises (@p142 @p309 @p135)) % 0.40/0.59 (step-pop @p310 :rule scope :premises (@p165)) % 0.40/0.59 (step-pop @p311 :rule scope :premises (@p310)) % 0.40/0.59 (step-pop @p312 :rule scope :premises (@p311)) % 0.40/0.59 (step @p166 :rule process_scope :premises (@p312) :args (@t134)) % 0.40/0.59 (step @p170 :rule implies_elim :premises (@p166)) % 0.40/0.59 (step @p171 :rule resolution :premises (@p170 @p158) :args (true @t134)) % 0.40/0.59 (step @p172 :rule not_and :premises (@p171)) % 0.40/0.59 (step @p173 :rule eq_resolve :premises (@p172 @p146)) % 0.40/0.59 (step @p174 :rule chain_m_resolution :premises (@p173 @p142 @p135) :args (@t133 @t135 (@list @t118 @t117))) % 0.40/0.59 (step @p175 :rule bool-double-not-elim :args (@t122)) % 0.40/0.59 (step @p176 :rule nary_cong :premises (@p137 @p175) :args ((or @t128 (not @t123)))) % 0.40/0.59 (step @p177 :rule cnf_or_neg :args (@t128 2)) % 0.40/0.59 (step @p178 :rule eq_resolve :premises (@p177 @p176)) % 0.40/0.59 (step @p179 :rule reordering :premises (@p178) :args ((or @t122 @t128))) % 0.40/0.59 (step @p180 :rule chain_m_resolution :premises (@p179 @p133) :args (@t122 @t130 @t131)) % 0.40/0.59 (step @p181 :rule bool-double-not-elim :args (@t132)) % 0.40/0.59 (step @p182 :rule refl :args (@t123)) % 0.40/0.59 (step @p183 :rule refl :args (@t136)) % 0.40/0.59 (step @p184 :rule nary_cong :premises (@p183 @p182 @p181) :args ((or @t136 @t123 (not @t133)))) % 0.40/0.59 (step @p185 :rule cnf_and_neg :args (@t136)) % 0.40/0.59 (step @p186 :rule eq_resolve :premises (@p185 @p184)) % 0.40/0.59 (step @p187 :rule reordering :premises (@p186) :args ((or @t123 @t132 @t136))) % 0.40/0.59 (step @p188 :rule chain_m_resolution :premises (@p187 @p180 @p174) :args (@t136 @t135 (@list @t122 @t132))) % 0.40/0.59 (step @p189 :rule cnf_equiv_pos2 :args (@t138)) % 0.40/0.59 (step @p190 :rule reordering :premises (@p189) :args ((or @t137 (not @t136) (not @t138)))) % 0.40/0.59 (step @p191 :rule chain_m_resolution :premises (@p190 @p188 @p73) :args (@t137 @t139 (@list @t136 @t138))) % 0.40/0.59 (step @p192 :rule bool-double-not-elim :args (@t124)) % 0.40/0.59 (step @p193 :rule nary_cong :premises (@p137 @p192) :args ((or @t128 (not @t125)))) % 0.40/0.59 (step @p194 :rule cnf_or_neg :args (@t128 1)) % 0.40/0.59 (step @p195 :rule eq_resolve :premises (@p194 @p193)) % 0.40/0.59 (step @p196 :rule reordering :premises (@p195) :args ((or @t124 @t128))) % 0.40/0.59 (step @p197 :rule chain_m_resolution :premises (@p196 @p133) :args (@t124 @t130 @t131)) % 0.40/0.59 (step @p198 :rule bool-double-not-elim :args (@t126)) % 0.40/0.59 (step @p199 :rule nary_cong :premises (@p137 @p198) :args ((or @t128 (not @t127)))) % 0.40/0.59 (step @p200 :rule cnf_or_neg :args (@t128 0)) % 0.40/0.59 (step @p201 :rule eq_resolve :premises (@p200 @p199)) % 0.40/0.59 (step @p202 :rule reordering :premises (@p201) :args ((or @t126 @t128))) % 0.40/0.59 (step @p203 :rule chain_m_resolution :premises (@p202 @p133) :args (@t126 @t130 @t131)) % 0.40/0.59 (step @p204 :rule cnf_or_pos :args (@t142)) % 0.40/0.59 (step @p205 :rule reordering :premises (@p204) :args ((or @t127 @t125 @t141 @t140 (not @t142)))) % 0.40/0.59 (step @p206 :rule chain_m_resolution :premises (@p205 @p203 @p197 @p191 @p72) :args (@t140 (@list false false false false) (@list @t126 @t124 @t137 @t142))) % 0.40/0.59 (step @p207 :rule cnf_or_pos :args (@t146)) % 0.40/0.59 (step @p208 :rule reordering :premises (@p207) :args ((or @t145 @t144 (not @t146)))) % 0.40/0.59 (step @p209 :rule chain_m_resolution :premises (@p208 @p206 @p43) :args (@t144 @t139 (@list @t140 @t146))) % 0.40/0.59 (step @p210 :rule bool-impl-elim :args (@t3 @t18)) % 0.40/0.59 (step @p211 :rule cong :premises (@p210) :args (@t20)) % 0.40/0.59 (step @p212 :rule cong :premises (@p67 @p211) :args (@t21)) % 0.40/0.59 (step @p213 :rule cong :premises (@p212) :args (@t22)) % 0.40/0.59 (step @p214 :rule eq_resolve :premises (@p8 @p213)) % 0.40/0.59 (step @p215 :rule instantiate :premises (@p214) :args (@t147)) % 0.40/0.59 (step @p216 :rule bool-impl-elim :args (@t13 @t12)) % 0.40/0.59 (step @p217 :rule cong :premises (@p216) :args (@t14)) % 0.40/0.59 (step @p218 :rule eq_resolve :premises (@p4 @p217)) % 0.40/0.59 (step @p219 :rule instantiate :premises (@p218) :args (@t147)) % 0.40/0.59 (step @p220 :rule bool-double-not-elim :args (@t120)) % 0.40/0.59 (step @p221 :rule nary_cong :premises (@p137 @p220) :args ((or @t128 (not @t121)))) % 0.40/0.59 (step @p222 :rule cnf_or_neg :args (@t128 3)) % 0.40/0.59 (step @p223 :rule eq_resolve :premises (@p222 @p221)) % 0.40/0.59 (step @p224 :rule reordering :premises (@p223) :args ((or @t120 @t128))) % 0.40/0.59 (step @p225 :rule chain_m_resolution :premises (@p224 @p133) :args (@t120 @t130 @t131)) % 0.40/0.59 (step @p226 :rule cnf_or_pos :args (@t150)) % 0.40/0.59 (step @p227 :rule reordering :premises (@p226) :args ((or @t121 @t149 (not @t150)))) % 0.40/0.59 (step @p228 :rule chain_m_resolution :premises (@p227 @p225 @p219) :args (@t149 @t139 (@list @t120 @t150))) % 0.40/0.59 (step @p229 :rule cnf_and_pos :args (@t149 0)) % 0.40/0.59 (step @p230 :rule reordering :premises (@p229) :args ((or @t148 (not @t149)))) % 0.40/0.59 (step @p231 :rule chain_m_resolution :premises (@p230 @p228) :args (@t148 (@list false) (@list @t149))) % 0.40/0.59 (step @p232 :rule cnf_equiv_pos1 :args (@t152)) % 0.40/0.59 (step @p233 :rule reordering :premises (@p232) :args ((or (not @t148) @t151 (not @t152)))) % 0.40/0.59 (step @p234 :rule chain_m_resolution :premises (@p233 @p231 @p215) :args (@t151 @t139 (@list @t148 @t152))) % 0.40/0.59 (step @p235 :rule instantiate :premises (@p234) :args ((@list @t67))) % 0.40/0.59 (step @p236 :rule cnf_or_pos :args (@t154)) % 0.40/0.59 (step @p237 :rule reordering :premises (@p236) :args ((or @t119 @t153 (not @t154)))) % 0.40/0.59 (step @p238 :rule chain_m_resolution :premises (@p237 @p142 @p235) :args (@t153 @t139 (@list @t118 @t154))) % 0.40/0.59 (step @p239 :rule aci_norm :args ((= (or (or @t96 @t155) @t31) (or @t96 @t155 @t31)))) % 0.40/0.59 (step @p240 :rule refl :args (@t31)) % 0.40/0.59 (step @p241 :rule bool-and-de-morgan :args (@t24 @t32 true)) % 0.40/0.59 (step @p242 :rule nary_cong :premises (@p241 @p240) :args ((or (not @t33) @t31))) % 0.40/0.59 (step @p243 :rule trans :premises (@p242 @p239)) % 0.40/0.59 (step @p244 :rule bool-impl-elim :args (@t33 @t31)) % 0.40/0.59 (step @p245 :rule trans :premises (@p244 @p243)) % 0.40/0.59 (step @p246 :rule cong :premises (@p245) :args (@t35)) % 0.40/0.59 (step @p247 :rule eq_resolve :premises (@p28 @p246)) % 0.40/0.59 (step @p248 :rule instantiate :premises (@p247) :args ((@list @t68 @t67 @t116))) % 0.40/0.59 (step @p249 :rule cnf_or_pos :args (@t158)) % 0.40/0.59 (step @p250 :rule reordering :premises (@p249) :args ((or @t123 @t156 @t157 (not @t158)))) % 0.40/0.59 (step @p251 :rule chain_m_resolution :premises (@p250 @p180 @p238 @p248) :args (@t156 (@list false false false) (@list @t122 @t153 @t158))) % 0.40/0.59 (step @p252 :rule instantiate :premises (@p9) :args (@t159)) % 0.40/0.59 (step @p253 :rule instantiate :premises (@p71) :args (@t159)) % 0.40/0.59 (step @p254 :rule cnf_or_pos :args (@t162)) % 0.40/0.59 (step @p255 :rule reordering :premises (@p254) :args ((or @t127 @t121 @t117 @t161 (not @t162)))) % 0.40/0.59 (step @p256 :rule chain_m_resolution :premises (@p255 @p203 @p225 @p135 @p253) :args (@t161 (@list false false true false) (@list @t126 @t120 @t117 @t162))) % 0.40/0.59 (step @p257 :rule cnf_equiv_pos2 :args (@t166)) % 0.40/0.59 (step @p258 :rule reordering :premises (@p257) :args ((or @t160 @t167 (not @t166)))) % 0.40/0.59 (step @p259 :rule chain_m_resolution :premises (@p258 @p256 @p252) :args (@t167 @t168 (@list @t160 @t166))) % 0.40/0.59 (step @p260 :rule bool-double-not-elim :args (@t163)) % 0.40/0.59 (step @p261 :rule refl :args (@t169)) % 0.40/0.59 (step @p262 :rule refl :args (@t165)) % 0.40/0.59 (step @p263 :rule nary_cong :premises (@p262 @p261 @p260) :args ((or @t165 @t169 (not @t164)))) % 0.40/0.59 (step @p264 :rule cnf_and_neg :args (@t165)) % 0.40/0.59 (step @p265 :rule eq_resolve :premises (@p264 @p263)) % 0.40/0.59 (step @p266 :rule reordering :premises (@p265) :args ((or @t163 @t165 @t169))) % 0.40/0.59 (step @p267 :rule chain_m_resolution :premises (@p266 @p259 @p251) :args (@t163 @t168 (@list @t165 @t156))) % 0.40/0.59 (step @p268 :rule refl :args (@t157)) % 0.40/0.59 (step @p269 :rule bool-double-not-elim :args (@t143)) % 0.40/0.59 (step @p270 :rule refl :args (@t164)) % 0.40/0.59 (step @p271 :rule nary_cong :premises (@p270 @p269 @p268) :args ((or @t164 (not @t144) @t157))) % 0.40/0.59 (assume-push @p313 @t144) % 0.40/0.59 (assume-push @p314 @t163) % 0.40/0.59 (assume-push @p315 @t153) % 0.40/0.59 (step @p275 :rule evaluate :args ((= true false))) % 0.40/0.59 (step @p276 :rule false_intro :premises (@p313)) % 0.40/0.59 (step @p277 :rule symm :premises (@p267)) % 0.40/0.59 (step @p278 :rule refl :args (@t67)) % 0.40/0.59 (step @p279 :rule cong :premises (@p278 @p277) :args (@t153)) % 0.40/0.59 (step @p280 :rule true_intro :premises (@p238)) % 0.40/0.59 (step @p281 :rule symm :premises (@p280)) % 0.40/0.59 (step @p282 :rule trans :premises (@p281 @p279 @p276)) % 0.40/0.59 (step @p283 false :rule eq_resolve :premises (@p282 @p275)) % 0.40/0.59 (step-pop @p316 :rule scope :premises (@p283)) % 0.40/0.59 (step-pop @p317 :rule scope :premises (@p316)) % 0.40/0.59 (step-pop @p318 :rule scope :premises (@p317)) % 0.40/0.59 (step @p284 :rule process_scope :premises (@p318) :args (false)) % 0.40/0.59 (assume-push @p319 @t163) % 0.40/0.59 (assume-push @p320 @t144) % 0.40/0.59 (assume-push @p321 @t153) % 0.40/0.59 (step @p291 :rule and_intro :premises (@p320 @p267 @p238)) % 0.40/0.59 (step-pop @p322 :rule scope :premises (@p291)) % 0.40/0.59 (step-pop @p323 :rule scope :premises (@p322)) % 0.40/0.59 (step-pop @p324 :rule scope :premises (@p323)) % 0.40/0.59 (step @p292 :rule process_scope :premises (@p324) :args (@t170)) % 0.40/0.59 (step @p296 :rule implies_elim :premises (@p292)) % 0.40/0.59 (step @p297 :rule resolution :premises (@p296 @p284) :args (true @t170)) % 0.40/0.59 (step @p298 :rule not_and :premises (@p297)) % 0.40/0.59 (step @p299 :rule eq_resolve :premises (@p298 @p271)) % 0.40/0.59 (step @p300 false :rule chain_m_resolution :premises (@p299 @p267 @p238 @p209) :args (false (@list false false true) (@list @t163 @t153 @t143))) % 0.40/0.59 ) % 0.40/0.59 % SZS output end Proof % 0.40/0.59 % cvc5 exiting %------------------------------------------------------------------------------