%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU053+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 : n018.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 08:50:31 AM UTC 2026 % Result : Theorem 1.99s 2.30s % Output : Proof 0.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SEU053+1 : TPTP v9.2.1. Released v3.2.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n018.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 16:24:35 EDT 2026 % 0.18/0.36 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 1.99/2.30 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 1.99/2.30 % SZS status Theorem % 1.99/2.30 % SZS output start Proof % 1.99/2.30 ( % 1.99/2.30 (declare-sort $$unsorted 0) % 1.99/2.30 (declare-const tptp.relation_image (-> $$unsorted $$unsorted $$unsorted)) % 1.99/2.30 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 1.99/2.30 (declare-const tptp.disjoint_nonempty (-> $$unsorted $$unsorted Bool)) % 1.99/2.30 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 1.99/2.30 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 1.99/2.30 (declare-const tptp.function (-> $$unsorted Bool)) % 1.99/2.30 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 1.99/2.30 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 1.99/2.30 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 1.99/2.30 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 1.99/2.30 (declare-const tptp.relation (-> $$unsorted Bool)) % 1.99/2.30 (declare-const tptp.empty_set $$unsorted) % 1.99/2.30 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 1.99/2.30 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 1.99/2.30 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 1.99/2.30 (declare-const tptp.empty (-> $$unsorted Bool)) % 1.99/2.30 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 1.99/2.30 (define @t1 () (@var "A" $$unsorted)) % 1.99/2.30 (define @t2 () (@var "B" $$unsorted)) % 1.99/2.30 (define @t3 () (tptp.in @t1 @t2)) % 1.99/2.30 (define @t4 () (@list @t1 @t2)) % 1.99/2.30 (define @t5 () (tptp.function @t1)) % 1.99/2.30 (define @t6 () (tptp.empty @t1)) % 1.99/2.30 (define @t7 () (@list @t1)) % 1.99/2.30 (define @t8 () (tptp.relation @t1)) % 1.99/2.30 (define @t9 () (tptp.one_to_one @t1)) % 1.99/2.30 (define @t10 () (and @t8 @t5 @t9)) % 1.99/2.30 (define @t11 () (and @t8 @t6 @t5)) % 1.99/2.30 (define @t12 () (tptp.set_intersection2 @t1 @t2)) % 1.99/2.30 (define @t13 () (@var "C" $$unsorted)) % 1.99/2.30 (define @t14 () (tptp.singleton @t1)) % 1.99/2.30 (define @t15 () (tptp.disjoint @t1 @t2)) % 1.99/2.30 (define @t16 () (forall @t4 (= @t15 (= @t12 tptp.empty_set)))) % 1.99/2.30 (define @t17 () (= @t2 @t13)) % 1.99/2.30 (define @t18 () (= (tptp.apply @t1 @t2) (tptp.apply @t1 @t13))) % 1.99/2.30 (define @t19 () (tptp.relation_dom @t1)) % 1.99/2.30 (define @t20 () (tptp.in @t13 @t19)) % 1.99/2.30 (define @t21 () (tptp.in @t2 @t19)) % 1.99/2.30 (define @t22 () (and @t21 @t20 @t18)) % 1.99/2.30 (define @t23 () (@list @t2 @t13)) % 1.99/2.30 (define @t24 () (forall @t23 (=> @t22 @t17))) % 1.99/2.30 (define @t25 () (= @t9 @t24)) % 1.99/2.30 (define @t26 () (and @t8 @t5)) % 1.99/2.30 (define @t27 () (=> @t26 @t25)) % 1.99/2.30 (define @t28 () (forall @t7 @t27)) % 1.99/2.30 (define @t29 () (@list @t2)) % 1.99/2.30 (define @t30 () (tptp.relation tptp.empty_set)) % 1.99/2.30 (define @t31 () (tptp.empty tptp.empty_set)) % 1.99/2.30 (define @t32 () (tptp.relation @t2)) % 1.99/2.30 (define @t33 () (tptp.powerset @t1)) % 1.99/2.30 (define @t34 () (tptp.empty @t19)) % 1.99/2.30 (define @t35 () (not @t6)) % 1.99/2.30 (define @t36 () (and @t35 @t8)) % 1.99/2.30 (define @t37 () (tptp.set_intersection2 @t1 @t1)) % 1.99/2.30 (define @t38 () (forall @t4 (= @t37 @t1))) % 1.99/2.30 (define @t39 () (tptp.empty @t2)) % 1.99/2.30 (define @t40 () (not @t39)) % 1.99/2.30 (define @t41 () (and @t35 @t40)) % 1.99/2.30 (define @t42 () (tptp.element @t2 @t33)) % 1.99/2.30 (define @t43 () (tptp.disjoint_nonempty @t1 @t2)) % 1.99/2.30 (define @t44 () (= (tptp.relation_image @t2 @t14) (tptp.singleton (tptp.apply @t2 @t1)))) % 1.99/2.30 (define @t45 () (tptp.in @t1 (tptp.relation_dom @t2))) % 1.99/2.30 (define @t46 () (=> @t45 @t44)) % 1.99/2.30 (define @t47 () (tptp.function @t2)) % 1.99/2.30 (define @t48 () (and @t32 @t47)) % 1.99/2.30 (define @t49 () (forall @t4 (=> @t48 @t46))) % 1.99/2.30 (define @t50 () (tptp.set_intersection2 @t2 @t13)) % 1.99/2.30 (define @t51 () (forall @t23 (= (tptp.relation_image @t1 @t50) (tptp.set_intersection2 (tptp.relation_image @t1 @t2) (tptp.relation_image @t1 @t13))))) % 1.99/2.30 (define @t52 () (=> @t51 @t9)) % 1.99/2.30 (define @t53 () (forall @t7 (=> @t26 @t52))) % 1.99/2.30 (define @t54 () (not @t53)) % 1.99/2.30 (define @t55 () (tptp.relation_image @t1 tptp.empty_set)) % 1.99/2.30 (define @t56 () (=> @t8 (= @t55 tptp.empty_set))) % 1.99/2.30 (define @t57 () (forall @t7 @t56)) % 1.99/2.30 (define @t58 () (tptp.disjoint @t14 (tptp.singleton @t2))) % 1.99/2.30 (define @t59 () (= @t1 @t2)) % 1.99/2.30 (define @t60 () (not @t59)) % 1.99/2.30 (define @t61 () (forall @t4 (=> @t60 @t58))) % 1.99/2.30 (define @t62 () (tptp.element @t1 @t2)) % 1.99/2.30 (define @t63 () (tptp.element @t2 (tptp.powerset @t13))) % 1.99/2.30 (define @t64 () (@list @t1 @t2 @t13)) % 1.99/2.30 (define @t65 () (= tptp.empty_set @t55)) % 1.99/2.30 (define @t66 () (not @t51)) % 1.99/2.30 (define @t67 () (not @t5)) % 1.99/2.30 (define @t68 () (not @t8)) % 1.99/2.30 (define @t69 () (or @t68 @t67 @t66 @t9)) % 1.99/2.30 (define @t70 () (@quantifiers_skolemize (forall @t7 @t69) 0)) % 1.99/2.30 (define @t71 () (@list @t70)) % 1.99/2.30 (define @t72 () (or @t68 @t67)) % 1.99/2.30 (define @t73 () (not @t26)) % 1.99/2.30 (define @t74 () (tptp.relation @t70)) % 1.99/2.30 (define @t75 () (tptp.one_to_one @t70)) % 1.99/2.30 (define @t76 () (forall @t23 (= (tptp.relation_image @t70 @t50) (tptp.set_intersection2 (tptp.relation_image @t70 @t2) (tptp.relation_image @t70 @t13))))) % 1.99/2.30 (define @t77 () (not @t76)) % 1.99/2.30 (define @t78 () (tptp.function @t70)) % 1.99/2.30 (define @t79 () (not @t78)) % 1.99/2.30 (define @t80 () (not @t74)) % 1.99/2.30 (define @t81 () (or @t80 @t79 @t77 @t75)) % 1.99/2.30 (define @t82 () (@list true)) % 1.99/2.30 (define @t83 () (@list @t81)) % 1.99/2.30 (define @t84 () (= tptp.empty_set (tptp.relation_image @t70 tptp.empty_set))) % 1.99/2.30 (define @t85 () (or @t80 @t84)) % 1.99/2.30 (define @t86 () (@list false false)) % 1.99/2.30 (define @t87 () (tptp.relation_dom @t70)) % 1.99/2.30 (define @t88 () (forall @t23 (or (not (tptp.in @t2 @t87)) (not (tptp.in @t13 @t87)) (not (= (tptp.apply @t70 @t2) (tptp.apply @t70 @t13))) @t17))) % 1.99/2.30 (define @t89 () (@quantifiers_skolemize @t88 0)) % 1.99/2.30 (define @t90 () (tptp.singleton @t89)) % 1.99/2.30 (define @t91 () (@quantifiers_skolemize @t88 1)) % 1.99/2.30 (define @t92 () (tptp.singleton @t91)) % 1.99/2.30 (define @t93 () (tptp.set_intersection2 @t92 @t90)) % 1.99/2.30 (define @t94 () (tptp.disjoint @t92 @t90)) % 1.99/2.30 (define @t95 () (= @t94 (= @t93 tptp.empty_set))) % 1.99/2.30 (define @t96 () (@list @t92 @t90)) % 1.99/2.30 (define @t97 () (= tptp.empty_set @t93)) % 1.99/2.30 (define @t98 () (= @t94 @t97)) % 1.99/2.30 (define @t99 () (@list false)) % 1.99/2.30 (define @t100 () (or (= @t91 @t89) @t94)) % 1.99/2.30 (define @t101 () (forall @t4 (or @t59 @t58))) % 1.99/2.30 (define @t102 () (= @t89 @t91)) % 1.99/2.30 (define @t103 () (or @t102 @t94)) % 1.99/2.30 (define @t104 () (not @t18)) % 1.99/2.30 (define @t105 () (not @t20)) % 1.99/2.30 (define @t106 () (not @t21)) % 1.99/2.30 (define @t107 () (or @t106 @t105 @t104 @t17)) % 1.99/2.30 (define @t108 () (= @t9 (forall @t23 @t107))) % 1.99/2.30 (define @t109 () (or @t106 @t105 @t104)) % 1.99/2.30 (define @t110 () (= @t75 @t88)) % 1.99/2.30 (define @t111 () (or @t80 @t79 @t110)) % 1.99/2.30 (define @t112 () (not @t88)) % 1.99/2.30 (define @t113 () (@list true false)) % 1.99/2.30 (define @t114 () (tptp.apply @t70 @t91)) % 1.99/2.30 (define @t115 () (tptp.apply @t70 @t89)) % 1.99/2.30 (define @t116 () (= @t115 @t114)) % 1.99/2.30 (define @t117 () (not @t116)) % 1.99/2.30 (define @t118 () (tptp.in @t91 @t87)) % 1.99/2.30 (define @t119 () (not @t118)) % 1.99/2.30 (define @t120 () (tptp.in @t89 @t87)) % 1.99/2.30 (define @t121 () (not @t120)) % 1.99/2.30 (define @t122 () (or @t121 @t119 @t117 @t102)) % 1.99/2.30 (define @t123 () (@list @t122)) % 1.99/2.30 (define @t124 () (not @t45)) % 1.99/2.30 (define @t125 () (not @t47)) % 1.99/2.30 (define @t126 () (not @t32)) % 1.99/2.30 (define @t127 () (= (tptp.relation_image @t70 @t90) (tptp.singleton @t115))) % 1.99/2.30 (define @t128 () (or @t80 @t79 @t121 @t127)) % 1.99/2.30 (define @t129 () (@list false false false false)) % 1.99/2.30 (define @t130 () (tptp.singleton @t114)) % 1.99/2.30 (define @t131 () (tptp.relation_image @t70 @t92)) % 1.99/2.30 (define @t132 () (= @t131 @t130)) % 1.99/2.30 (define @t133 () (or @t80 @t79 @t119 @t132)) % 1.99/2.30 (define @t134 () (= @t1 @t37)) % 1.99/2.30 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 1.99/2.30 (assume @p2 (forall @t7 (=> @t6 @t5))) % 1.99/2.30 (assume @p3 (forall @t7 (=> @t6 @t8))) % 1.99/2.30 (assume @p4 (forall @t7 (=> @t11 @t10))) % 1.99/2.30 (assume @p5 (forall @t4 (= @t12 (tptp.set_intersection2 @t2 @t1)))) % 1.99/2.30 (assume @p6 (forall @t4 (= (= @t2 @t14) (forall (@list @t13) (= (tptp.in @t13 @t2) (= @t13 @t1)))))) % 1.99/2.30 (assume @p7 @t16) % 1.99/2.30 (assume @p8 @t28) % 1.99/2.30 (assume @p9 (forall @t7 (exists @t29 (tptp.element @t2 @t1)))) % 1.99/2.30 (assume @p10 (and @t31 @t30 (tptp.relation_empty_yielding tptp.empty_set))) % 1.99/2.30 (assume @p11 (forall @t4 (=> (and @t8 @t32) (tptp.relation @t12)))) % 1.99/2.30 (assume @p12 (forall @t7 (not (tptp.empty @t33)))) % 1.99/2.30 (assume @p13 @t31) % 1.99/2.30 (assume @p14 (forall @t7 (not (tptp.empty @t14)))) % 1.99/2.30 (assume @p15 (and @t31 @t30)) % 1.99/2.30 (assume @p16 (forall @t7 (=> @t36 (not @t34)))) % 1.99/2.30 (assume @p17 (forall @t7 (=> @t6 (and @t34 (tptp.relation @t19))))) % 1.99/2.30 (assume @p18 @t38) % 1.99/2.30 (assume @p19 (forall @t4 (=> @t41 (not (tptp.disjoint_nonempty @t1 @t1))))) % 1.99/2.30 (assume @p20 (exists @t7 @t26)) % 1.99/2.30 (assume @p21 (exists @t7 (and @t6 @t8))) % 1.99/2.30 (assume @p22 (forall @t7 (=> @t35 (exists @t29 (and @t42 @t40))))) % 1.99/2.30 (assume @p23 (exists @t7 @t6)) % 1.99/2.30 (assume @p24 (exists @t7 @t11)) % 1.99/2.30 (assume @p25 (exists @t7 @t36)) % 1.99/2.30 (assume @p26 (forall @t7 (exists @t29 (and @t42 @t39)))) % 1.99/2.30 (assume @p27 (exists @t7 @t35)) % 1.99/2.30 (assume @p28 (exists @t7 @t10)) % 1.99/2.30 (assume @p29 (exists @t7 (and @t8 (tptp.relation_empty_yielding @t1)))) % 1.99/2.30 (assume @p30 (forall @t4 (=> @t41 (= @t43 @t15)))) % 1.99/2.30 (assume @p31 (forall @t4 (tptp.subset @t1 @t1))) % 1.99/2.30 (assume @p32 (forall @t4 (=> @t41 (=> @t43 (tptp.disjoint_nonempty @t2 @t1))))) % 1.99/2.30 (assume @p33 (forall @t4 (=> @t15 (tptp.disjoint @t2 @t1)))) % 1.99/2.30 (assume @p34 @t49) % 1.99/2.30 (assume @p35 @t54) % 1.99/2.30 (assume @p36 @t57) % 1.99/2.30 (assume @p37 @t61) % 1.99/2.30 (assume @p38 (forall @t4 (=> @t3 @t62))) % 1.99/2.30 (assume @p39 (forall @t7 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 1.99/2.30 (assume @p40 (forall @t4 (=> @t62 (or @t39 @t3)))) % 1.99/2.30 (assume @p41 (forall @t4 (= (tptp.element @t1 (tptp.powerset @t2)) (tptp.subset @t1 @t2)))) % 1.99/2.30 (assume @p42 (forall @t64 (=> (and @t3 @t63) (tptp.element @t1 @t13)))) % 1.99/2.30 (assume @p43 (forall @t64 (not (and @t3 @t63 (tptp.empty @t13))))) % 1.99/2.30 (assume @p44 (forall @t7 (=> @t6 (= @t1 tptp.empty_set)))) % 1.99/2.30 (assume @p45 (forall @t4 (not (and @t3 @t39)))) % 1.99/2.30 (assume @p46 (forall @t4 (not (and @t6 @t60 @t39)))) % 1.99/2.30 (assume @p47 true) % 1.99/2.30 (step @p48 :rule evaluate :args ((= false true))) % 1.99/2.30 (step @p49 :rule and_elim :premises (@p10) :args (0)) % 1.99/2.30 (step @p50 :rule true_intro :premises (@p49)) % 1.99/2.30 (step @p51 :rule bool-impl-elim :args (@t8 @t65)) % 1.99/2.30 (step @p52 :rule cong :premises (@p51) :args ((forall @t7 (=> @t8 @t65)))) % 1.99/2.30 (step @p53 :rule eq-symm :args (@t55 tptp.empty_set)) % 1.99/2.30 (step @p54 :rule refl :args (@t8)) % 1.99/2.30 (step @p55 :rule cong :premises (@p54 @p53) :args (@t56)) % 1.99/2.30 (step @p56 :rule cong :premises (@p55) :args (@t57)) % 1.99/2.30 (step @p57 :rule trans :premises (@p56 @p52)) % 1.99/2.30 (step @p58 :rule eq_resolve :premises (@p36 @p57)) % 1.99/2.30 (step @p59 :rule instantiate :premises (@p58) :args (@t71)) % 1.99/2.30 (step @p60 :rule aci_norm :args ((= (or @t72 (or @t66 @t9)) @t69))) % 1.99/2.30 (step @p61 :rule bool-impl-elim :args (@t51 @t9)) % 1.99/2.30 (step @p62 :rule bool-and-de-morgan :args (@t8 @t5 true)) % 1.99/2.30 (step @p63 :rule nary_cong :premises (@p62 @p61) :args ((or @t73 @t52))) % 1.99/2.30 (step @p64 :rule trans :premises (@p63 @p60)) % 1.99/2.30 (step @p65 :rule bool-impl-elim :args (@t26 @t52)) % 1.99/2.30 (step @p66 :rule trans :premises (@p65 @p64)) % 1.99/2.30 (step @p67 :rule cong :premises (@p66) :args (@t53)) % 1.99/2.30 (step @p68 :rule cong :premises (@p67) :args (@t54)) % 1.99/2.30 (step @p69 :rule eq_resolve :premises (@p35 @p68)) % 1.99/2.30 (step @p70 :rule skolemize :premises (@p69)) % 1.99/2.30 (step @p71 :rule bool-double-not-elim :args (@t74)) % 1.99/2.30 (step @p72 :rule refl :args (@t81)) % 1.99/2.30 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((or @t81 (not @t80)))) % 1.99/2.30 (step @p74 :rule cnf_or_neg :args (@t81 0)) % 1.99/2.30 (step @p75 :rule eq_resolve :premises (@p74 @p73)) % 1.99/2.30 (step @p76 :rule reordering :premises (@p75) :args ((or @t74 @t81))) % 1.99/2.30 (step @p77 :rule chain_m_resolution :premises (@p76 @p70) :args (@t74 @t82 @t83)) % 1.99/2.30 (step @p78 :rule cnf_or_pos :args (@t85)) % 1.99/2.30 (step @p79 :rule reordering :premises (@p78) :args ((or @t80 @t84 (not @t85)))) % 1.99/2.30 (step @p80 :rule chain_m_resolution :premises (@p79 @p77 @p59) :args (@t84 @t86 (@list @t74 @t85))) % 1.99/2.30 (step @p81 :rule symm :premises (@p80)) % 1.99/2.30 (step @p82 :rule eq-symm :args (@t93 tptp.empty_set)) % 1.99/2.30 (step @p83 :rule refl :args (@t94)) % 1.99/2.30 (step @p84 :rule cong :premises (@p83 @p82) :args (@t95)) % 1.99/2.30 (step @p85 :rule refl :args (@t16)) % 1.99/2.30 (step @p86 :rule cong :premises (@p85 @p84) :args ((=> @t16 @t95))) % 1.99/2.30 (assume-push @p233 @t16) % 1.99/2.30 (step @p88 :rule instantiate :premises (@p7) :args (@t96)) % 1.99/2.30 (step-pop @p234 :rule scope :premises (@p88)) % 1.99/2.30 (step @p89 :rule process_scope :premises (@p234) :args (@t95)) % 1.99/2.30 (step @p91 :rule eq_resolve :premises (@p89 @p86)) % 1.99/2.30 (step @p92 :rule implies_elim :premises (@p91)) % 1.99/2.30 (step @p93 :rule chain_m_resolution :premises (@p92 @p7) :args (@t98 @t99 (@list @t16))) % 1.99/2.30 (step @p94 :rule refl :args (@t58)) % 1.99/2.30 (step @p95 :rule bool-double-not-elim :args (@t59)) % 1.99/2.30 (step @p96 :rule nary_cong :premises (@p95 @p94) :args ((or (not @t60) @t58))) % 1.99/2.30 (step @p97 :rule bool-impl-elim :args (@t60 @t58)) % 1.99/2.30 (step @p98 :rule trans :premises (@p97 @p96)) % 1.99/2.30 (step @p99 :rule cong :premises (@p98) :args (@t61)) % 1.99/2.30 (step @p100 :rule eq_resolve :premises (@p37 @p99)) % 1.99/2.30 (step @p101 :rule eq-symm :args (@t91 @t89)) % 1.99/2.30 (step @p102 :rule nary_cong :premises (@p101 @p83) :args (@t100)) % 1.99/2.30 (step @p103 :rule refl :args (@t101)) % 1.99/2.30 (step @p104 :rule cong :premises (@p103 @p102) :args ((=> @t101 @t100))) % 1.99/2.30 (assume-push @p235 @t101) % 1.99/2.30 (step @p106 :rule instantiate :premises (@p100) :args ((@list @t91 @t89))) % 1.99/2.30 (step-pop @p236 :rule scope :premises (@p106)) % 1.99/2.30 (step @p107 :rule process_scope :premises (@p236) :args (@t100)) % 1.99/2.30 (step @p109 :rule eq_resolve :premises (@p107 @p104)) % 1.99/2.30 (step @p110 :rule implies_elim :premises (@p109)) % 1.99/2.30 (step @p111 :rule chain_m_resolution :premises (@p110 @p100) :args (@t103 @t99 (@list @t101))) % 1.99/2.30 (step @p112 :rule aci_norm :args ((= (or @t72 @t108) (or @t68 @t67 @t108)))) % 1.99/2.30 (step @p113 :rule refl :args (@t108)) % 1.99/2.30 (step @p114 :rule nary_cong :premises (@p62 @p113) :args ((or @t73 @t108))) % 1.99/2.30 (step @p115 :rule trans :premises (@p114 @p112)) % 1.99/2.30 (step @p116 :rule bool-impl-elim :args (@t26 @t108)) % 1.99/2.30 (step @p117 :rule trans :premises (@p116 @p115)) % 1.99/2.30 (step @p118 :rule cong :premises (@p117) :args ((forall @t7 (=> @t26 @t108)))) % 1.99/2.30 (step @p119 :rule aci_norm :args ((= (or @t109 @t17) @t107))) % 1.99/2.30 (step @p120 :rule refl :args (@t17)) % 1.99/2.30 (step @p121 :rule aci_norm :args ((= (or @t106 (or @t105 @t104)) @t109))) % 1.99/2.30 (step @p122 :rule bool-and-de-morgan :args (@t20 @t18 true)) % 1.99/2.30 (step @p123 :rule refl :args (@t106)) % 1.99/2.30 (step @p124 :rule nary_cong :premises (@p123 @p122) :args ((or @t106 (not (and @t20 @t18))))) % 1.99/2.30 (step @p125 :rule bool-and-de-morgan :args (@t21 @t20 (and @t18))) % 1.99/2.30 (step @p126 :rule trans :premises (@p125 @p124)) % 1.99/2.30 (step @p127 :rule trans :premises (@p126 @p121)) % 1.99/2.30 (step @p128 :rule nary_cong :premises (@p127 @p120) :args ((or (not @t22) @t17))) % 1.99/2.30 (step @p129 :rule trans :premises (@p128 @p119)) % 1.99/2.30 (step @p130 :rule bool-impl-elim :args (@t22 @t17)) % 1.99/2.30 (step @p131 :rule trans :premises (@p130 @p129)) % 1.99/2.30 (step @p132 :rule cong :premises (@p131) :args (@t24)) % 1.99/2.30 (step @p133 :rule refl :args (@t9)) % 1.99/2.30 (step @p134 :rule cong :premises (@p133 @p132) :args (@t25)) % 1.99/2.30 (step @p135 :rule refl :args (@t26)) % 1.99/2.30 (step @p136 :rule cong :premises (@p135 @p134) :args (@t27)) % 1.99/2.30 (step @p137 :rule cong :premises (@p136) :args (@t28)) % 1.99/2.30 (step @p138 :rule trans :premises (@p137 @p118)) % 1.99/2.30 (step @p139 :rule eq_resolve :premises (@p8 @p138)) % 1.99/2.30 (step @p140 :rule instantiate :premises (@p139) :args (@t71)) % 1.99/2.30 (step @p141 :rule bool-double-not-elim :args (@t78)) % 1.99/2.30 (step @p142 :rule nary_cong :premises (@p72 @p141) :args ((or @t81 (not @t79)))) % 1.99/2.30 (step @p143 :rule cnf_or_neg :args (@t81 1)) % 1.99/2.30 (step @p144 :rule eq_resolve :premises (@p143 @p142)) % 1.99/2.30 (step @p145 :rule reordering :premises (@p144) :args ((or @t78 @t81))) % 1.99/2.30 (step @p146 :rule chain_m_resolution :premises (@p145 @p70) :args (@t78 @t82 @t83)) % 1.99/2.30 (step @p147 :rule cnf_or_pos :args (@t111)) % 1.99/2.30 (step @p148 :rule reordering :premises (@p147) :args ((or @t80 @t79 @t110 (not @t111)))) % 1.99/2.30 (step @p149 :rule chain_m_resolution :premises (@p148 @p77 @p146 @p140) :args (@t110 (@list false false false) (@list @t74 @t78 @t111))) % 1.99/2.30 (step @p150 :rule cnf_or_neg :args (@t81 3)) % 1.99/2.30 (step @p151 :rule chain_m_resolution :premises (@p150 @p70) :args ((not @t75) @t82 @t83)) % 1.99/2.30 (step @p152 :rule cnf_equiv_pos2 :args (@t110)) % 1.99/2.30 (step @p153 :rule reordering :premises (@p152) :args ((or @t75 @t112 (not @t110)))) % 1.99/2.30 (step @p154 :rule chain_m_resolution :premises (@p153 @p151 @p149) :args (@t112 @t113 (@list @t75 @t110))) % 1.99/2.30 (step @p155 :rule skolemize :premises (@p154)) % 1.99/2.30 (step @p156 :rule cnf_or_neg :args (@t122 3)) % 1.99/2.30 (step @p157 :rule chain_m_resolution :premises (@p156 @p155) :args ((not @t102) @t82 @t123)) % 1.99/2.30 (step @p158 :rule cnf_or_pos :args (@t103)) % 1.99/2.30 (step @p159 :rule reordering :premises (@p158) :args ((or @t102 @t94 (not @t103)))) % 1.99/2.30 (step @p160 :rule chain_m_resolution :premises (@p159 @p157 @p111) :args (@t94 @t113 (@list @t102 @t103))) % 1.99/2.30 (step @p161 :rule cnf_equiv_pos1 :args (@t98)) % 1.99/2.30 (step @p162 :rule reordering :premises (@p161) :args ((or (not @t94) @t97 (not @t98)))) % 1.99/2.30 (step @p163 :rule chain_m_resolution :premises (@p162 @p160 @p93) :args (@t97 @t86 (@list @t94 @t98))) % 1.99/2.30 (step @p164 :rule symm :premises (@p163)) % 1.99/2.30 (step @p165 :rule refl :args (@t70)) % 1.99/2.30 (step @p166 :rule cong :premises (@p165 @p164) :args ((tptp.relation_image @t70 @t93))) % 1.99/2.30 (step @p167 :rule bool-double-not-elim :args (@t76)) % 1.99/2.30 (step @p168 :rule nary_cong :premises (@p72 @p167) :args ((or @t81 (not @t77)))) % 1.99/2.30 (step @p169 :rule cnf_or_neg :args (@t81 2)) % 1.99/2.30 (step @p170 :rule eq_resolve :premises (@p169 @p168)) % 1.99/2.30 (step @p171 :rule reordering :premises (@p170) :args ((or @t76 @t81))) % 0.33/2.31 (step @p172 :rule chain_m_resolution :premises (@p171 @p70) :args (@t76 @t82 @t83)) % 0.33/2.31 (step @p173 :rule instantiate :premises (@p172) :args (@t96)) % 0.33/2.31 (step @p174 :rule symm :premises (@p173)) % 0.33/2.31 (step @p175 :rule aci_norm :args ((= (or (or @t126 @t125) (or @t124 @t44)) (or @t126 @t125 @t124 @t44)))) % 0.33/2.31 (step @p176 :rule bool-impl-elim :args (@t45 @t44)) % 0.33/2.31 (step @p177 :rule bool-and-de-morgan :args (@t32 @t47 true)) % 0.33/2.31 (step @p178 :rule nary_cong :premises (@p177 @p176) :args ((or (not @t48) @t46))) % 0.33/2.31 (step @p179 :rule trans :premises (@p178 @p175)) % 0.33/2.31 (step @p180 :rule bool-impl-elim :args (@t48 @t46)) % 0.33/2.31 (step @p181 :rule trans :premises (@p180 @p179)) % 0.33/2.31 (step @p182 :rule cong :premises (@p181) :args (@t49)) % 0.33/2.31 (step @p183 :rule eq_resolve :premises (@p34 @p182)) % 0.33/2.31 (step @p184 :rule instantiate :premises (@p183) :args ((@list @t89 @t70))) % 0.33/2.31 (step @p185 :rule bool-double-not-elim :args (@t120)) % 0.33/2.31 (step @p186 :rule refl :args (@t122)) % 0.33/2.31 (step @p187 :rule nary_cong :premises (@p186 @p185) :args ((or @t122 (not @t121)))) % 0.33/2.31 (step @p188 :rule cnf_or_neg :args (@t122 0)) % 0.33/2.31 (step @p189 :rule eq_resolve :premises (@p188 @p187)) % 0.33/2.31 (step @p190 :rule reordering :premises (@p189) :args ((or @t120 @t122))) % 0.33/2.31 (step @p191 :rule chain_m_resolution :premises (@p190 @p155) :args (@t120 @t82 @t123)) % 0.33/2.31 (step @p192 :rule cnf_or_pos :args (@t128)) % 0.33/2.31 (step @p193 :rule reordering :premises (@p192) :args ((or @t80 @t79 @t121 @t127 (not @t128)))) % 0.33/2.31 (step @p194 :rule chain_m_resolution :premises (@p193 @p77 @p146 @p191 @p184) :args (@t127 @t129 (@list @t74 @t78 @t120 @t128))) % 0.33/2.31 (step @p195 :rule symm :premises (@p194)) % 0.33/2.31 (step @p196 :rule bool-double-not-elim :args (@t116)) % 0.33/2.31 (step @p197 :rule nary_cong :premises (@p186 @p196) :args ((or @t122 (not @t117)))) % 0.33/2.31 (step @p198 :rule cnf_or_neg :args (@t122 2)) % 0.33/2.31 (step @p199 :rule eq_resolve :premises (@p198 @p197)) % 0.33/2.31 (step @p200 :rule reordering :premises (@p199) :args ((or @t116 @t122))) % 0.33/2.31 (step @p201 :rule chain_m_resolution :premises (@p200 @p155) :args (@t116 @t82 @t123)) % 0.33/2.31 (step @p202 :rule symm :premises (@p201)) % 0.33/2.31 (step @p203 :rule cong :premises (@p202) :args (@t130)) % 0.33/2.31 (step @p204 :rule instantiate :premises (@p183) :args ((@list @t91 @t70))) % 0.33/2.31 (step @p205 :rule bool-double-not-elim :args (@t118)) % 0.33/2.31 (step @p206 :rule nary_cong :premises (@p186 @p205) :args ((or @t122 (not @t119)))) % 0.33/2.31 (step @p207 :rule cnf_or_neg :args (@t122 1)) % 0.33/2.31 (step @p208 :rule eq_resolve :premises (@p207 @p206)) % 0.33/2.31 (step @p209 :rule reordering :premises (@p208) :args ((or @t118 @t122))) % 0.33/2.31 (step @p210 :rule chain_m_resolution :premises (@p209 @p155) :args (@t118 @t82 @t123)) % 0.33/2.31 (step @p211 :rule cnf_or_pos :args (@t133)) % 0.33/2.31 (step @p212 :rule reordering :premises (@p211) :args ((or @t80 @t79 @t119 @t132 (not @t133)))) % 0.33/2.31 (step @p213 :rule chain_m_resolution :premises (@p212 @p77 @p146 @p210 @p204) :args (@t132 @t129 (@list @t74 @t78 @t118 @t133))) % 0.33/2.31 (step @p214 :rule trans :premises (@p213 @p203 @p195)) % 0.33/2.31 (step @p215 :rule refl :args (@t131)) % 0.33/2.31 (step @p216 :rule cong :premises (@p215 @p214) :args ((tptp.set_intersection2 @t131 @t131))) % 0.33/2.31 (step @p217 :rule instantiate :premises (@p172) :args ((@list @t92 @t92))) % 0.33/2.31 (step @p218 :rule quant-unused-vars :args ((= (forall @t4 @t134) (forall @t7 @t134)))) % 0.33/2.31 (step @p219 :rule eq-symm :args (@t37 @t1)) % 0.33/2.31 (step @p220 :rule cong :premises (@p219) :args (@t38)) % 0.33/2.31 (step @p221 :rule trans :premises (@p220 @p218)) % 0.33/2.31 (step @p222 :rule eq_resolve :premises (@p18 @p221)) % 0.33/2.31 (step @p223 :rule instantiate :premises (@p222) :args ((@list @t92))) % 0.33/2.31 (step @p224 :rule cong :premises (@p165 @p223) :args (@t131)) % 0.33/2.31 (step @p225 :rule symm :premises (@p213)) % 0.33/2.31 (step @p226 :rule trans :premises (@p225 @p224 @p217 @p216 @p174 @p166 @p81)) % 0.33/2.31 (step @p227 :rule cong :premises (@p226) :args ((tptp.empty @t130))) % 0.33/2.31 (step @p228 :rule instantiate :premises (@p14) :args ((@list @t114))) % 0.33/2.31 (step @p229 :rule false_intro :premises (@p228)) % 0.33/2.31 (step @p230 :rule symm :premises (@p229)) % 0.33/2.31 (step @p231 :rule trans :premises (@p230 @p227 @p50)) % 0.33/2.31 (step @p232 false :rule eq_resolve :premises (@p231 @p48)) % 0.33/2.31 ) % 0.33/2.31 % SZS output end Proof % 0.33/2.31 % cvc5 exiting %------------------------------------------------------------------------------