%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU107+1 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n015.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 08:50:34 AM UTC 2026 % Result : Theorem 18.01s 18.28s % Output : Proof 18.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU107+1 : TPTP v9.2.1. Released v3.2.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.14/0.34 % Computer : n015.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Jun 2 16:29:49 EDT 2026 % 0.14/0.34 % CPUTime : % 0.27/0.49 %----Proving TF0_NAR, FOF, or CNF % 18.01/18.28 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 18.01/18.28 --- Run --no-e-matching --full-saturate-quant at 6... % 18.01/18.28 % SZS status Theorem % 18.01/18.28 % SZS output start Proof % 18.01/18.28 ( % 18.01/18.28 (declare-sort $$unsorted 0) % 18.01/18.28 (declare-const tptp.function (-> $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.cup_closed (-> $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.empty (-> $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.empty_set $$unsorted) % 18.01/18.28 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.relation (-> $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.diff_closed (-> $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.preboolean (-> $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 18.01/18.28 (declare-const tptp.finite (-> $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.prebool_difference (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 18.01/18.28 (declare-const tptp.cap_closed (-> $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.natural (-> $$unsorted Bool)) % 18.01/18.28 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 18.01/18.28 (define @t1 () (@var "A" $$unsorted)) % 18.01/18.28 (define @t2 () (@var "B" $$unsorted)) % 18.01/18.28 (define @t3 () (tptp.in @t1 @t2)) % 18.01/18.28 (define @t4 () (@list @t1 @t2)) % 18.01/18.28 (define @t5 () (tptp.finite @t1)) % 18.01/18.28 (define @t6 () (tptp.empty @t1)) % 18.01/18.28 (define @t7 () (@list @t1)) % 18.01/18.28 (define @t8 () (tptp.diff_closed @t1)) % 18.01/18.28 (define @t9 () (tptp.cup_closed @t1)) % 18.01/18.28 (define @t10 () (and @t9 @t8)) % 18.01/18.28 (define @t11 () (tptp.preboolean @t1)) % 18.01/18.28 (define @t12 () (tptp.finite @t2)) % 18.01/18.28 (define @t13 () (tptp.powerset @t1)) % 18.01/18.28 (define @t14 () (tptp.element @t2 @t13)) % 18.01/18.28 (define @t15 () (@list @t2)) % 18.01/18.28 (define @t16 () (@var "C" $$unsorted)) % 18.01/18.28 (define @t17 () (tptp.prebool_difference @t1 @t2 @t16)) % 18.01/18.28 (define @t18 () (tptp.element @t17 @t1)) % 18.01/18.28 (define @t19 () (tptp.element @t16 @t1)) % 18.01/18.28 (define @t20 () (tptp.element @t2 @t1)) % 18.01/18.28 (define @t21 () (not @t6)) % 18.01/18.28 (define @t22 () (and @t21 @t11 @t20 @t19)) % 18.01/18.28 (define @t23 () (@list @t1 @t2 @t16)) % 18.01/18.28 (define @t24 () (forall @t23 (=> @t22 @t18))) % 18.01/18.28 (define @t25 () (exists @t15 @t20)) % 18.01/18.28 (define @t26 () (forall @t7 @t25)) % 18.01/18.28 (define @t27 () (tptp.set_difference @t1 @t2)) % 18.01/18.28 (define @t28 () (tptp.cap_closed @t1)) % 18.01/18.28 (define @t29 () (and @t21 @t9 @t28 @t8 @t11)) % 18.01/18.28 (define @t30 () (exists @t7 @t29)) % 18.01/18.28 (define @t31 () (tptp.empty @t2)) % 18.01/18.28 (define @t32 () (not @t31)) % 18.01/18.28 (define @t33 () (= @t17 (tptp.set_difference @t2 @t16))) % 18.01/18.28 (define @t34 () (forall @t23 (=> @t22 @t33))) % 18.01/18.28 (define @t35 () (tptp.subset @t1 @t1)) % 18.01/18.28 (define @t36 () (forall @t4 @t35)) % 18.01/18.28 (define @t37 () (tptp.in tptp.empty_set @t1)) % 18.01/18.28 (define @t38 () (and @t21 @t11)) % 18.01/18.28 (define @t39 () (forall @t7 (=> @t38 @t37))) % 18.01/18.28 (define @t40 () (not @t39)) % 18.01/18.28 (define @t41 () (tptp.element @t1 @t2)) % 18.01/18.28 (define @t42 () (or @t31 @t3)) % 18.01/18.28 (define @t43 () (forall @t4 (=> @t41 @t42))) % 18.01/18.28 (define @t44 () (tptp.subset @t1 @t2)) % 18.01/18.28 (define @t45 () (forall @t4 (= (= @t27 tptp.empty_set) @t44))) % 18.01/18.28 (define @t46 () (tptp.set_difference @t1 tptp.empty_set)) % 18.01/18.28 (define @t47 () (forall @t7 (= @t46 @t1))) % 18.01/18.28 (define @t48 () (tptp.element @t2 (tptp.powerset @t16))) % 18.01/18.28 (define @t49 () (not @t41)) % 18.01/18.28 (define @t50 () (not @t11)) % 18.01/18.28 (define @t51 () (or @t6 @t50 @t37)) % 18.01/18.28 (define @t52 () (@quantifiers_skolemize (forall @t7 @t51) 0)) % 18.01/18.28 (define @t53 () (tptp.prebool_difference @t52 tptp.empty_set tptp.empty_set)) % 18.01/18.28 (define @t54 () (not @t19)) % 18.01/18.28 (define @t55 () (not @t20)) % 18.01/18.28 (define @t56 () (or @t6 @t50 @t55 @t54)) % 18.01/18.28 (define @t57 () (not @t21)) % 18.01/18.28 (define @t58 () (or @t57 @t50 @t55 @t54)) % 18.01/18.28 (define @t59 () (not @t22)) % 18.01/18.28 (define @t60 () (forall @t15 (not (tptp.element @t2 @t52)))) % 18.01/18.28 (define @t61 () (@quantifiers_skolemize @t60 0)) % 18.01/18.28 (define @t62 () (@list @t52 @t61 @t61)) % 18.01/18.28 (define @t63 () (tptp.element @t61 @t52)) % 18.01/18.28 (define @t64 () (not @t60)) % 18.01/18.28 (define @t65 () (not @t63)) % 18.01/18.28 (define @t66 () (not @t65)) % 18.01/18.28 (define @t67 () (@list true)) % 18.01/18.28 (define @t68 () (tptp.preboolean @t52)) % 18.01/18.28 (define @t69 () (tptp.in tptp.empty_set @t52)) % 18.01/18.28 (define @t70 () (not @t68)) % 18.01/18.28 (define @t71 () (tptp.empty @t52)) % 18.01/18.28 (define @t72 () (or @t71 @t70 @t69)) % 18.01/18.28 (define @t73 () (@list @t72)) % 18.01/18.28 (define @t74 () (tptp.prebool_difference @t52 @t61 @t61)) % 18.01/18.28 (define @t75 () (tptp.element @t74 @t52)) % 18.01/18.28 (define @t76 () (or @t71 @t70 @t65 @t65 @t75)) % 18.01/18.28 (define @t77 () (@list true false false false)) % 18.01/18.28 (define @t78 () (or @t6 @t50 @t55 @t54 @t33)) % 18.01/18.28 (define @t79 () (tptp.set_difference @t61 @t61)) % 18.01/18.28 (define @t80 () (= @t74 @t79)) % 18.01/18.28 (define @t81 () (or @t71 @t70 @t65 @t65 @t80)) % 18.01/18.28 (define @t82 () (tptp.subset @t61 @t61)) % 18.01/18.28 (define @t83 () (= @t79 tptp.empty_set)) % 18.01/18.28 (define @t84 () (= @t83 @t82)) % 18.01/18.28 (define @t85 () (= tptp.empty_set @t79)) % 18.01/18.28 (define @t86 () (= @t82 @t85)) % 18.01/18.28 (define @t87 () (@list false)) % 18.01/18.28 (define @t88 () (@list @t45)) % 18.01/18.28 (define @t89 () (@list false false)) % 18.01/18.28 (define @t90 () (tptp.element tptp.empty_set @t52)) % 18.01/18.28 (define @t91 () (tptp.element @t53 @t52)) % 18.01/18.28 (define @t92 () (not @t90)) % 18.01/18.28 (define @t93 () (or @t71 @t70 @t92 @t92 @t91)) % 18.01/18.28 (define @t94 () (tptp.in @t53 @t52)) % 18.01/18.28 (define @t95 () (not @t91)) % 18.01/18.28 (define @t96 () (or @t95 @t71 @t94)) % 18.01/18.28 (define @t97 () (not @t8)) % 18.01/18.28 (define @t98 () (not @t28)) % 18.01/18.28 (define @t99 () (not @t9)) % 18.01/18.28 (define @t100 () (@quantifiers_skolemize (forall @t7 (or @t6 @t99 @t98 @t97 @t50)) 0)) % 18.01/18.28 (define @t101 () (tptp.prebool_difference @t100 tptp.empty_set tptp.empty_set)) % 18.01/18.28 (define @t102 () (tptp.set_difference tptp.empty_set tptp.empty_set)) % 18.01/18.28 (define @t103 () (tptp.element tptp.empty_set @t100)) % 18.01/18.28 (define @t104 () (not @t103)) % 18.01/18.28 (define @t105 () (tptp.preboolean @t100)) % 18.01/18.28 (define @t106 () (not @t105)) % 18.01/18.28 (define @t107 () (tptp.empty @t100)) % 18.01/18.28 (define @t108 () (or @t107 @t106 @t104 @t104 (= @t101 @t102))) % 18.01/18.28 (define @t109 () (forall @t23 @t78)) % 18.01/18.28 (define @t110 () (= @t102 @t101)) % 18.01/18.28 (define @t111 () (or @t107 @t106 @t104 @t104 @t110)) % 18.01/18.28 (define @t112 () (@list @t109)) % 18.01/18.28 (define @t113 () (forall @t15 (not (tptp.element @t2 @t100)))) % 18.01/18.28 (define @t114 () (@quantifiers_skolemize @t113 0)) % 18.01/18.28 (define @t115 () (@list @t100 @t114 @t114)) % 18.01/18.28 (define @t116 () (tptp.element @t114 @t100)) % 18.01/18.28 (define @t117 () (not @t113)) % 18.01/18.28 (define @t118 () (not @t116)) % 18.01/18.28 (define @t119 () (not @t118)) % 18.01/18.29 (define @t120 () (or @t57 @t99 @t98 @t97 @t50)) % 18.01/18.29 (define @t121 () (forall @t7 (not @t29))) % 18.01/18.29 (define @t122 () (not @t121)) % 18.01/18.29 (define @t123 () (or @t107 (not (tptp.cup_closed @t100)) (not (tptp.cap_closed @t100)) (not (tptp.diff_closed @t100)) @t106)) % 18.01/18.29 (define @t124 () (@list @t123)) % 18.01/18.29 (define @t125 () (tptp.prebool_difference @t100 @t114 @t114)) % 18.01/18.29 (define @t126 () (tptp.element @t125 @t100)) % 18.01/18.29 (define @t127 () (or @t107 @t106 @t118 @t118 @t126)) % 18.01/18.29 (define @t128 () (tptp.set_difference @t114 @t114)) % 18.01/18.29 (define @t129 () (= @t125 @t128)) % 18.01/18.29 (define @t130 () (or @t107 @t106 @t118 @t118 @t129)) % 18.01/18.29 (define @t131 () (tptp.subset @t114 @t114)) % 18.01/18.29 (define @t132 () (= @t128 tptp.empty_set)) % 18.01/18.29 (define @t133 () (= @t132 @t131)) % 18.01/18.29 (define @t134 () (= tptp.empty_set @t128)) % 18.01/18.29 (define @t135 () (= @t131 @t134)) % 18.01/18.29 (define @t136 () (tptp.prebool_difference @t52 @t101 @t101)) % 18.01/18.29 (define @t137 () (tptp.set_difference @t101 @t101)) % 18.01/18.29 (define @t138 () (tptp.element @t101 @t52)) % 18.01/18.29 (define @t139 () (not @t138)) % 18.01/18.29 (define @t140 () (or @t71 @t70 @t139 @t139 (= @t136 @t137))) % 18.01/18.29 (define @t141 () (= @t137 @t136)) % 18.01/18.29 (define @t142 () (or @t71 @t70 @t139 @t139 @t141)) % 18.01/18.29 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 18.01/18.29 (assume @p2 (forall @t7 (=> @t6 @t5))) % 18.01/18.29 (assume @p3 (forall @t7 (=> @t11 @t10))) % 18.01/18.29 (assume @p4 (forall @t7 (=> @t5 (forall @t15 (=> @t14 @t12))))) % 18.01/18.29 (assume @p5 (forall @t7 (=> @t10 @t11))) % 18.01/18.29 (assume @p6 @t24) % 18.01/18.29 (assume @p7 @t26) % 18.01/18.29 (assume @p8 (forall @t4 (=> @t5 (tptp.finite @t27)))) % 18.01/18.29 (assume @p9 (forall @t7 (not (tptp.empty @t13)))) % 18.01/18.29 (assume @p10 (tptp.empty tptp.empty_set)) % 18.01/18.29 (assume @p11 (exists @t7 (and @t21 @t5))) % 18.01/18.29 (assume @p12 @t30) % 18.01/18.29 (assume @p13 (forall @t7 (=> @t21 (exists @t15 (and @t14 @t32))))) % 18.01/18.29 (assume @p14 (exists @t7 @t6)) % 18.01/18.29 (assume @p15 (forall @t7 (exists @t15 (and @t14 @t31 (tptp.relation @t2) (tptp.function @t2) (tptp.one_to_one @t2) (tptp.epsilon_transitive @t2) (tptp.epsilon_connected @t2) (tptp.ordinal @t2) (tptp.natural @t2) @t12)))) % 18.01/18.29 (assume @p16 (forall @t7 (exists @t15 (and @t14 @t31)))) % 18.01/18.29 (assume @p17 (exists @t7 @t21)) % 18.01/18.29 (assume @p18 (forall @t7 (=> @t21 (exists @t15 (and @t14 @t32 @t12))))) % 18.01/18.29 (assume @p19 @t34) % 18.01/18.29 (assume @p20 @t36) % 18.01/18.29 (assume @p21 @t40) % 18.01/18.29 (assume @p22 (forall @t4 (=> @t3 @t41))) % 18.01/18.29 (assume @p23 @t43) % 18.01/18.29 (assume @p24 @t45) % 18.01/18.29 (assume @p25 @t47) % 18.01/18.29 (assume @p26 (forall @t4 (= (tptp.element @t1 (tptp.powerset @t2)) @t44))) % 18.01/18.29 (assume @p27 (forall @t7 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 18.01/18.29 (assume @p28 (forall @t23 (=> (and @t3 @t48) (tptp.element @t1 @t16)))) % 18.01/18.29 (assume @p29 (forall @t23 (not (and @t3 @t48 (tptp.empty @t16))))) % 18.01/18.29 (assume @p30 (forall @t7 (=> @t6 (= @t1 tptp.empty_set)))) % 18.01/18.29 (assume @p31 (forall @t4 (not (and @t3 @t31)))) % 18.01/18.29 (assume @p32 (forall @t4 (not (and @t6 (not (= @t1 @t2)) @t31)))) % 18.01/18.29 (assume @p33 true) % 18.01/18.29 (step @p34 :rule evaluate :args ((= false true))) % 18.01/18.29 (step @p35 :rule aci_norm :args ((= (or @t49 @t42) (or @t49 @t31 @t3)))) % 18.01/18.29 (step @p36 :rule bool-impl-elim :args (@t41 @t42)) % 18.01/18.29 (step @p37 :rule trans :premises (@p36 @p35)) % 18.01/18.29 (step @p38 :rule cong :premises (@p37) :args (@t43)) % 18.01/18.29 (step @p39 :rule eq_resolve :premises (@p23 @p38)) % 18.01/18.29 (step @p40 :rule instantiate :premises (@p39) :args ((@list @t53 @t52))) % 18.01/18.29 (step @p41 :rule aci_norm :args ((= (or @t56 @t18) (or @t6 @t50 @t55 @t54 @t18)))) % 18.01/18.29 (step @p42 :rule refl :args (@t18)) % 18.01/18.29 (step @p43 :rule refl :args (@t54)) % 18.01/18.29 (step @p44 :rule refl :args (@t55)) % 18.01/18.29 (step @p45 :rule refl :args (@t50)) % 18.01/18.29 (step @p46 :rule bool-double-not-elim :args (@t6)) % 18.01/18.29 (step @p47 :rule nary_cong :premises (@p46 @p45 @p44 @p43) :args (@t58)) % 18.01/18.29 (step @p48 :rule aci_norm :args ((= (or @t57 (or @t50 (or @t55 @t54))) @t58))) % 18.01/18.29 (step @p49 :rule trans :premises (@p48 @p47)) % 18.01/18.29 (step @p50 :rule bool-and-de-morgan :args (@t20 @t19 true)) % 18.01/18.29 (step @p51 :rule nary_cong :premises (@p45 @p50) :args ((or @t50 (not (and @t20 @t19))))) % 18.01/18.29 (step @p52 :rule bool-and-de-morgan :args (@t11 @t20 (and @t19))) % 18.01/18.29 (step @p53 :rule trans :premises (@p52 @p51)) % 18.01/18.29 (step @p54 :rule refl :args (@t57)) % 18.01/18.29 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or @t57 (not (and @t11 @t20 @t19))))) % 18.01/18.29 (step @p56 :rule bool-and-de-morgan :args (@t21 @t11 (and @t20 @t19))) % 18.01/18.29 (step @p57 :rule trans :premises (@p56 @p55)) % 18.01/18.29 (step @p58 :rule trans :premises (@p57 @p49)) % 18.01/18.29 (step @p59 :rule nary_cong :premises (@p58 @p42) :args ((or @t59 @t18))) % 18.01/18.29 (step @p60 :rule trans :premises (@p59 @p41)) % 18.01/18.29 (step @p61 :rule bool-impl-elim :args (@t22 @t18)) % 18.01/18.29 (step @p62 :rule trans :premises (@p61 @p60)) % 18.01/18.29 (step @p63 :rule cong :premises (@p62) :args (@t24)) % 18.01/18.29 (step @p64 :rule eq_resolve :premises (@p6 @p63)) % 18.01/18.29 (step @p65 :rule instantiate :premises (@p64) :args ((@list @t52 tptp.empty_set tptp.empty_set))) % 18.01/18.29 (step @p66 :rule instantiate :premises (@p64) :args (@t62)) % 18.01/18.29 (step @p67 :rule exists-elim :args ((= @t25 (not (forall @t15 @t55))))) % 18.01/18.29 (step @p68 :rule cong :premises (@p67) :args (@t26)) % 18.01/18.29 (step @p69 :rule eq_resolve :premises (@p7 @p68)) % 18.01/18.29 (step @p70 :rule instantiate :premises (@p69) :args ((@list @t52))) % 18.01/18.29 (step @p71 :rule refl :args (@t63)) % 18.01/18.29 (step @p72 :rule bool-double-not-elim :args (@t60)) % 18.01/18.29 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((or (not @t64) @t63))) % 18.01/18.29 (step @p74 :rule bool-double-not-elim :args (@t63)) % 18.01/18.29 (step @p75 :rule refl :args (@t64)) % 18.01/18.29 (step @p76 :rule cong :premises (@p75 @p74) :args ((=> @t64 @t66))) % 18.01/18.29 (assume-push @p298 @t64) % 18.01/18.29 (step @p78 :rule skolemize :premises (@p70)) % 18.01/18.29 (step-pop @p299 :rule scope :premises (@p78)) % 18.01/18.29 (step @p79 :rule process_scope :premises (@p299) :args (@t66)) % 18.01/18.29 (step @p81 :rule eq_resolve :premises (@p79 @p76)) % 18.01/18.29 (step @p82 :rule implies_elim :premises (@p81)) % 18.01/18.29 (step @p83 :rule eq_resolve :premises (@p82 @p73)) % 18.01/18.29 (step @p84 :rule chain_m_resolution :premises (@p83 @p70) :args (@t63 @t67 (@list @t60))) % 18.01/18.29 (step @p85 :rule aci_norm :args ((= (or (or @t6 @t50) @t37) @t51))) % 18.01/18.29 (step @p86 :rule refl :args (@t37)) % 18.01/18.29 (step @p87 :rule nary_cong :premises (@p46 @p45) :args ((or @t57 @t50))) % 18.01/18.29 (step @p88 :rule bool-and-de-morgan :args (@t21 @t11 true)) % 18.01/18.29 (step @p89 :rule trans :premises (@p88 @p87)) % 18.01/18.29 (step @p90 :rule nary_cong :premises (@p89 @p86) :args ((or (not @t38) @t37))) % 18.01/18.29 (step @p91 :rule trans :premises (@p90 @p85)) % 18.01/18.29 (step @p92 :rule bool-impl-elim :args (@t38 @t37)) % 18.01/18.29 (step @p93 :rule trans :premises (@p92 @p91)) % 18.01/18.29 (step @p94 :rule cong :premises (@p93) :args (@t39)) % 18.01/18.29 (step @p95 :rule cong :premises (@p94) :args (@t40)) % 18.01/18.29 (step @p96 :rule eq_resolve :premises (@p21 @p95)) % 18.01/18.29 (step @p97 :rule skolemize :premises (@p96)) % 18.01/18.29 (step @p98 :rule bool-double-not-elim :args (@t68)) % 18.01/18.29 (step @p99 :rule refl :args (@t72)) % 18.01/18.29 (step @p100 :rule nary_cong :premises (@p99 @p98) :args ((or @t72 (not @t70)))) % 18.01/18.29 (step @p101 :rule cnf_or_neg :args (@t72 1)) % 18.01/18.29 (step @p102 :rule eq_resolve :premises (@p101 @p100)) % 18.01/18.29 (step @p103 :rule reordering :premises (@p102) :args ((or @t68 @t72))) % 18.01/18.29 (step @p104 :rule chain_m_resolution :premises (@p103 @p97) :args (@t68 @t67 @t73)) % 18.01/18.29 (step @p105 :rule cnf_or_neg :args (@t72 0)) % 18.01/18.29 (step @p106 :rule chain_m_resolution :premises (@p105 @p97) :args ((not @t71) @t67 @t73)) % 18.01/18.29 (step @p107 :rule cnf_or_pos :args (@t76)) % 18.01/18.29 (step @p108 :rule factoring :premises (@p107)) % 18.01/18.29 (step @p109 :rule reordering :premises (@p108) :args ((or @t71 @t70 @t65 @t75 (not @t76)))) % 18.01/18.29 (step @p110 :rule chain_m_resolution :premises (@p109 @p106 @p104 @p84 @p66) :args (@t75 @t77 (@list @t71 @t68 @t63 @t76))) % 18.01/18.29 (step @p111 :rule true_intro :premises (@p110)) % 18.01/18.29 (step @p112 :rule refl :args (@t52)) % 18.01/18.29 (step @p113 :rule aci_norm :args ((= (or @t56 @t33) @t78))) % 18.01/18.29 (step @p114 :rule refl :args (@t33)) % 18.01/18.29 (step @p115 :rule nary_cong :premises (@p58 @p114) :args ((or @t59 @t33))) % 18.01/18.29 (step @p116 :rule trans :premises (@p115 @p113)) % 18.01/18.29 (step @p117 :rule bool-impl-elim :args (@t22 @t33)) % 18.01/18.29 (step @p118 :rule trans :premises (@p117 @p116)) % 18.01/18.29 (step @p119 :rule cong :premises (@p118) :args (@t34)) % 18.01/18.29 (step @p120 :rule eq_resolve :premises (@p19 @p119)) % 18.01/18.29 (step @p121 :rule instantiate :premises (@p120) :args (@t62)) % 18.01/18.29 (step @p122 :rule cnf_or_pos :args (@t81)) % 18.01/18.29 (step @p123 :rule factoring :premises (@p122)) % 18.01/18.29 (step @p124 :rule reordering :premises (@p123) :args ((or @t71 @t70 @t65 @t80 (not @t81)))) % 18.01/18.29 (step @p125 :rule chain_m_resolution :premises (@p124 @p106 @p104 @p84 @p121) :args (@t80 @t77 (@list @t71 @t68 @t63 @t81))) % 18.01/18.29 (step @p126 :rule symm :premises (@p125)) % 18.01/18.29 (step @p127 :rule eq-symm :args (@t79 tptp.empty_set)) % 18.01/18.29 (step @p128 :rule refl :args (@t82)) % 18.01/18.29 (step @p129 :rule cong :premises (@p128 @p127) :args ((= @t82 @t83))) % 18.01/18.29 (step @p130 :rule eq-symm :args (@t83 @t82)) % 18.01/18.29 (step @p131 :rule trans :premises (@p130 @p129)) % 18.01/18.29 (step @p132 :rule refl :args (@t45)) % 18.01/18.29 (step @p133 :rule cong :premises (@p132 @p131) :args ((=> @t45 @t84))) % 18.01/18.29 (assume-push @p300 @t45) % 18.01/18.29 (step @p135 :rule instantiate :premises (@p24) :args ((@list @t61 @t61))) % 18.01/18.29 (step-pop @p301 :rule scope :premises (@p135)) % 18.01/18.29 (step @p136 :rule process_scope :premises (@p301) :args (@t84)) % 18.01/18.29 (step @p138 :rule eq_resolve :premises (@p136 @p133)) % 18.01/18.29 (step @p139 :rule implies_elim :premises (@p138)) % 18.01/18.29 (step @p140 :rule chain_m_resolution :premises (@p139 @p24) :args (@t86 @t87 @t88)) % 18.01/18.29 (step @p141 :rule quant-unused-vars :args ((= @t36 (forall @t7 @t35)))) % 18.01/18.29 (step @p142 :rule eq_resolve :premises (@p20 @p141)) % 18.01/18.29 (step @p143 :rule instantiate :premises (@p142) :args ((@list @t61))) % 18.01/18.29 (step @p144 :rule cnf_equiv_pos1 :args (@t86)) % 18.01/18.29 (step @p145 :rule reordering :premises (@p144) :args ((or (not @t82) @t85 (not @t86)))) % 18.01/18.29 (step @p146 :rule chain_m_resolution :premises (@p145 @p143 @p140) :args (@t85 @t89 (@list @t82 @t86))) % 18.01/18.29 (step @p147 :rule trans :premises (@p146 @p126)) % 18.01/18.29 (step @p148 :rule cong :premises (@p147 @p112) :args (@t90)) % 18.01/18.29 (step @p149 :rule trans :premises (@p148 @p111)) % 18.01/18.29 (step @p150 :rule true_elim :premises (@p149)) % 18.01/18.29 (step @p151 :rule cnf_or_pos :args (@t93)) % 18.01/18.29 (step @p152 :rule factoring :premises (@p151)) % 18.01/18.29 (step @p153 :rule reordering :premises (@p152) :args ((or @t71 @t70 @t92 @t91 (not @t93)))) % 18.01/18.29 (step @p154 :rule chain_m_resolution :premises (@p153 @p106 @p104 @p150 @p65) :args (@t91 @t77 (@list @t71 @t68 @t90 @t93))) % 18.01/18.29 (step @p155 :rule cnf_or_pos :args (@t96)) % 18.01/18.29 (step @p156 :rule reordering :premises (@p155) :args ((or @t71 @t95 @t94 (not @t96)))) % 18.01/18.29 (step @p157 :rule chain_m_resolution :premises (@p156 @p106 @p154 @p40) :args (@t94 (@list true false false) (@list @t71 @t91 @t96))) % 18.01/18.29 (step @p158 :rule true_intro :premises (@p157)) % 18.01/18.29 (step @p159 :rule eq-symm :args (@t46 @t1)) % 18.01/18.29 (step @p160 :rule cong :premises (@p159) :args (@t47)) % 18.01/18.29 (step @p161 :rule eq_resolve :premises (@p25 @p160)) % 18.01/18.29 (step @p162 :rule instantiate :premises (@p161) :args ((@list tptp.empty_set))) % 18.01/18.29 (step @p163 :rule symm :premises (@p162)) % 18.01/18.29 (step @p164 :rule eq-symm :args (@t101 @t102)) % 18.01/18.29 (step @p165 :rule refl :args (@t104)) % 18.01/18.29 (step @p166 :rule refl :args (@t106)) % 18.01/18.29 (step @p167 :rule refl :args (@t107)) % 18.01/18.29 (step @p168 :rule nary_cong :premises (@p167 @p166 @p165 @p165 @p164) :args (@t108)) % 18.01/18.29 (step @p169 :rule refl :args (@t109)) % 18.01/18.29 (step @p170 :rule cong :premises (@p169 @p168) :args ((=> @t109 @t108))) % 18.01/18.29 (assume-push @p302 @t109) % 18.01/18.29 (step @p172 :rule instantiate :premises (@p120) :args ((@list @t100 tptp.empty_set tptp.empty_set))) % 18.01/18.29 (step-pop @p303 :rule scope :premises (@p172)) % 18.01/18.29 (step @p173 :rule process_scope :premises (@p303) :args (@t108)) % 18.01/18.29 (step @p175 :rule eq_resolve :premises (@p173 @p170)) % 18.01/18.29 (step @p176 :rule implies_elim :premises (@p175)) % 18.01/18.29 (step @p177 :rule chain_m_resolution :premises (@p176 @p120) :args (@t111 @t87 @t112)) % 18.01/18.29 (step @p178 :rule instantiate :premises (@p64) :args (@t115)) % 18.01/18.29 (step @p179 :rule instantiate :premises (@p69) :args ((@list @t100))) % 18.01/18.29 (step @p180 :rule refl :args (@t116)) % 18.01/18.29 (step @p181 :rule bool-double-not-elim :args (@t113)) % 18.01/18.29 (step @p182 :rule nary_cong :premises (@p181 @p180) :args ((or (not @t117) @t116))) % 18.01/18.29 (step @p183 :rule bool-double-not-elim :args (@t116)) % 18.01/18.29 (step @p184 :rule refl :args (@t117)) % 18.01/18.29 (step @p185 :rule cong :premises (@p184 @p183) :args ((=> @t117 @t119))) % 18.01/18.29 (assume-push @p304 @t117) % 18.01/18.29 (step @p187 :rule skolemize :premises (@p179)) % 18.01/18.29 (step-pop @p305 :rule scope :premises (@p187)) % 18.01/18.29 (step @p188 :rule process_scope :premises (@p305) :args (@t119)) % 18.01/18.29 (step @p190 :rule eq_resolve :premises (@p188 @p185)) % 18.01/18.29 (step @p191 :rule implies_elim :premises (@p190)) % 18.01/18.29 (step @p192 :rule eq_resolve :premises (@p191 @p182)) % 18.01/18.29 (step @p193 :rule chain_m_resolution :premises (@p192 @p179) :args (@t116 @t67 (@list @t113))) % 18.01/18.29 (step @p194 :rule refl :args (@t97)) % 18.01/18.29 (step @p195 :rule refl :args (@t98)) % 18.01/18.29 (step @p196 :rule refl :args (@t99)) % 18.01/18.29 (step @p197 :rule nary_cong :premises (@p46 @p196 @p195 @p194 @p45) :args (@t120)) % 18.01/18.29 (step @p198 :rule aci_norm :args ((= (or @t57 (or @t99 (or @t98 (or @t97 @t50)))) @t120))) % 18.01/18.29 (step @p199 :rule trans :premises (@p198 @p197)) % 18.01/18.29 (step @p200 :rule bool-and-de-morgan :args (@t8 @t11 true)) % 18.01/18.29 (step @p201 :rule nary_cong :premises (@p195 @p200) :args ((or @t98 (not (and @t8 @t11))))) % 18.01/18.29 (step @p202 :rule bool-and-de-morgan :args (@t28 @t8 (and @t11))) % 18.01/18.29 (step @p203 :rule trans :premises (@p202 @p201)) % 18.01/18.29 (step @p204 :rule nary_cong :premises (@p196 @p203) :args ((or @t99 (not (and @t28 @t8 @t11))))) % 18.01/18.29 (step @p205 :rule bool-and-de-morgan :args (@t9 @t28 (and @t8 @t11))) % 18.01/18.29 (step @p206 :rule trans :premises (@p205 @p204)) % 18.01/18.29 (step @p207 :rule nary_cong :premises (@p54 @p206) :args ((or @t57 (not (and @t9 @t28 @t8 @t11))))) % 18.01/18.29 (step @p208 :rule bool-and-de-morgan :args (@t21 @t9 (and @t28 @t8 @t11))) % 18.01/18.29 (step @p209 :rule trans :premises (@p208 @p207)) % 18.01/18.29 (step @p210 :rule trans :premises (@p209 @p199)) % 18.01/18.29 (step @p211 :rule cong :premises (@p210) :args (@t121)) % 18.01/18.29 (step @p212 :rule cong :premises (@p211) :args (@t122)) % 18.01/18.29 (step @p213 :rule exists-elim :args ((= @t30 @t122))) % 18.01/18.29 (step @p214 :rule trans :premises (@p213 @p212)) % 18.01/18.29 (step @p215 :rule eq_resolve :premises (@p12 @p214)) % 18.01/18.29 (step @p216 :rule skolemize :premises (@p215)) % 18.01/18.29 (step @p217 :rule bool-double-not-elim :args (@t105)) % 18.01/18.29 (step @p218 :rule refl :args (@t123)) % 18.01/18.29 (step @p219 :rule nary_cong :premises (@p218 @p217) :args ((or @t123 (not @t106)))) % 18.01/18.29 (step @p220 :rule cnf_or_neg :args (@t123 4)) % 18.01/18.29 (step @p221 :rule eq_resolve :premises (@p220 @p219)) % 18.01/18.29 (step @p222 :rule reordering :premises (@p221) :args ((or @t105 @t123))) % 18.01/18.29 (step @p223 :rule chain_m_resolution :premises (@p222 @p216) :args (@t105 @t67 @t124)) % 18.01/18.29 (step @p224 :rule cnf_or_neg :args (@t123 0)) % 18.01/18.29 (step @p225 :rule chain_m_resolution :premises (@p224 @p216) :args ((not @t107) @t67 @t124)) % 18.01/18.29 (step @p226 :rule cnf_or_pos :args (@t127)) % 18.01/18.29 (step @p227 :rule factoring :premises (@p226)) % 18.01/18.29 (step @p228 :rule reordering :premises (@p227) :args ((or @t107 @t106 @t118 @t126 (not @t127)))) % 18.01/18.29 (step @p229 :rule chain_m_resolution :premises (@p228 @p225 @p223 @p193 @p178) :args (@t126 @t77 (@list @t107 @t105 @t116 @t127))) % 18.01/18.29 (step @p230 :rule true_intro :premises (@p229)) % 18.01/18.29 (step @p231 :rule refl :args (@t100)) % 18.01/18.29 (step @p232 :rule instantiate :premises (@p120) :args (@t115)) % 18.01/18.29 (step @p233 :rule cnf_or_pos :args (@t130)) % 18.01/18.29 (step @p234 :rule factoring :premises (@p233)) % 18.01/18.29 (step @p235 :rule reordering :premises (@p234) :args ((or @t107 @t106 @t118 @t129 (not @t130)))) % 18.01/18.29 (step @p236 :rule chain_m_resolution :premises (@p235 @p225 @p223 @p193 @p232) :args (@t129 @t77 (@list @t107 @t105 @t116 @t130))) % 18.01/18.29 (step @p237 :rule symm :premises (@p236)) % 18.01/18.29 (step @p238 :rule eq-symm :args (@t128 tptp.empty_set)) % 18.01/18.29 (step @p239 :rule refl :args (@t131)) % 18.01/18.29 (step @p240 :rule cong :premises (@p239 @p238) :args ((= @t131 @t132))) % 18.01/18.29 (step @p241 :rule eq-symm :args (@t132 @t131)) % 18.01/18.29 (step @p242 :rule trans :premises (@p241 @p240)) % 18.01/18.29 (step @p243 :rule cong :premises (@p132 @p242) :args ((=> @t45 @t133))) % 18.01/18.29 (assume-push @p306 @t45) % 18.01/18.29 (step @p245 :rule instantiate :premises (@p24) :args ((@list @t114 @t114))) % 18.01/18.29 (step-pop @p307 :rule scope :premises (@p245)) % 18.01/18.29 (step @p246 :rule process_scope :premises (@p307) :args (@t133)) % 18.01/18.29 (step @p248 :rule eq_resolve :premises (@p246 @p243)) % 18.01/18.29 (step @p249 :rule implies_elim :premises (@p248)) % 18.01/18.29 (step @p250 :rule chain_m_resolution :premises (@p249 @p24) :args (@t135 @t87 @t88)) % 18.01/18.29 (step @p251 :rule instantiate :premises (@p142) :args ((@list @t114))) % 18.01/18.29 (step @p252 :rule cnf_equiv_pos1 :args (@t135)) % 18.01/18.29 (step @p253 :rule reordering :premises (@p252) :args ((or (not @t131) @t134 (not @t135)))) % 18.01/18.29 (step @p254 :rule chain_m_resolution :premises (@p253 @p251 @p250) :args (@t134 @t89 (@list @t131 @t135))) % 18.01/18.29 (step @p255 :rule trans :premises (@p254 @p237)) % 18.01/18.29 (step @p256 :rule cong :premises (@p255 @p231) :args (@t103)) % 18.01/18.29 (step @p257 :rule trans :premises (@p256 @p230)) % 18.01/18.29 (step @p258 :rule true_elim :premises (@p257)) % 18.01/18.29 (step @p259 :rule cnf_or_pos :args (@t111)) % 18.01/18.29 (step @p260 :rule factoring :premises (@p259)) % 18.01/18.29 (step @p261 :rule reordering :premises (@p260) :args ((or @t107 @t106 @t104 @t110 (not @t111)))) % 18.01/18.29 (step @p262 :rule chain_m_resolution :premises (@p261 @p225 @p223 @p258 @p177) :args (@t110 @t77 (@list @t107 @t105 @t103 @t111))) % 18.01/18.29 (step @p263 :rule symm :premises (@p262)) % 18.01/18.29 (step @p264 :rule trans :premises (@p263 @p163)) % 18.01/18.29 (step @p265 :rule cong :premises (@p112 @p264 @p264) :args (@t136)) % 18.01/18.29 (step @p266 :rule eq-symm :args (@t136 @t137)) % 18.01/18.29 (step @p267 :rule refl :args (@t139)) % 18.01/18.29 (step @p268 :rule refl :args (@t70)) % 18.01/18.29 (step @p269 :rule refl :args (@t71)) % 18.01/18.29 (step @p270 :rule nary_cong :premises (@p269 @p268 @p267 @p267 @p266) :args (@t140)) % 18.01/18.29 (step @p271 :rule cong :premises (@p169 @p270) :args ((=> @t109 @t140))) % 18.01/18.29 (assume-push @p308 @t109) % 18.01/18.29 (step @p273 :rule instantiate :premises (@p120) :args ((@list @t52 @t101 @t101))) % 18.01/18.29 (step-pop @p309 :rule scope :premises (@p273)) % 18.01/18.29 (step @p274 :rule process_scope :premises (@p309) :args (@t140)) % 18.01/18.29 (step @p276 :rule eq_resolve :premises (@p274 @p271)) % 18.01/18.29 (step @p277 :rule implies_elim :premises (@p276)) % 18.01/18.29 (step @p278 :rule chain_m_resolution :premises (@p277 @p120) :args (@t142 @t87 @t112)) % 18.01/18.29 (step @p279 :rule cong :premises (@p264 @p112) :args (@t138)) % 18.01/18.29 (step @p280 :rule trans :premises (@p279 @p148 @p111)) % 18.01/18.29 (step @p281 :rule true_elim :premises (@p280)) % 18.01/18.29 (step @p282 :rule cnf_or_pos :args (@t142)) % 18.01/18.29 (step @p283 :rule factoring :premises (@p282)) % 18.01/18.29 (step @p284 :rule reordering :premises (@p283) :args ((or @t71 @t70 @t139 @t141 (not @t142)))) % 18.01/18.29 (step @p285 :rule chain_m_resolution :premises (@p284 @p106 @p104 @p281 @p278) :args (@t141 @t77 (@list @t71 @t68 @t138 @t142))) % 18.01/18.29 (step @p286 :rule symm :premises (@p264)) % 18.01/18.29 (step @p287 :rule refl :args (@t101)) % 18.01/18.29 (step @p288 :rule cong :premises (@p287 @p286) :args ((tptp.set_difference @t101 tptp.empty_set))) % 18.01/18.29 (step @p289 :rule instantiate :premises (@p161) :args ((@list @t101))) % 18.01/18.29 (step @p290 :rule trans :premises (@p162 @p262 @p289 @p288 @p285 @p265)) % 18.01/18.29 (step @p291 :rule cong :premises (@p290 @p112) :args (@t69)) % 18.01/18.29 (step @p292 :rule cnf_or_neg :args (@t72 2)) % 18.01/18.29 (step @p293 :rule chain_m_resolution :premises (@p292 @p97) :args ((not @t69) @t67 @t73)) % 18.01/18.29 (step @p294 :rule false_intro :premises (@p293)) % 18.01/18.29 (step @p295 :rule symm :premises (@p294)) % 18.01/18.29 (step @p296 :rule trans :premises (@p295 @p291 @p158)) % 18.01/18.29 (step @p297 false :rule eq_resolve :premises (@p296 @p34)) % 18.01/18.29 ) % 18.01/18.29 % SZS output end Proof % 18.01/18.29 % cvc5 exiting %------------------------------------------------------------------------------