%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU628^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n022.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 08:52:29 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 % 0.12/0.13 % Problem : SEU628^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n022.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 17:43:38 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.50 %----Proving TH0 % 0.40/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.59 % SZS status Theorem % 0.40/0.59 % SZS output start Proof % 0.40/0.59 ( % 0.40/0.59 (declare-sort $$unsorted 0) % 0.40/0.59 (declare-const tptp.ubforcartprodlem1 Bool) % 0.40/0.59 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.59 (declare-const tptp.emptyset $$unsorted) % 0.40/0.59 (declare-const tptp.binunion (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.59 (declare-const tptp.powersetI1 Bool) % 0.40/0.59 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.40/0.59 (define @t1 () (@var "A" $$unsorted)) % 0.40/0.59 (define @t2 () (_ tptp.powerset @t1)) % 0.40/0.59 (define @t3 () (@var "B" $$unsorted)) % 0.40/0.59 (define @t4 () (_ tptp.in @t3)) % 0.40/0.59 (define @t5 () (_ @t4 @t2)) % 0.40/0.59 (define @t6 () (_ (_ tptp.subset @t3) @t1)) % 0.40/0.59 (define @t7 () (@list @t1 @t3)) % 0.40/0.59 (define @t8 () (forall @t7 (=> @t6 @t5))) % 0.40/0.59 (define @t9 () (= tptp.powersetI1 @t8)) % 0.40/0.59 (define @t10 () (_ (_ tptp.binunion @t1) @t3)) % 0.40/0.59 (define @t11 () (_ tptp.powerset @t10)) % 0.40/0.59 (define @t12 () (@var "Xy" $$unsorted)) % 0.40/0.59 (define @t13 () (_ (_ tptp.setadjoin @t12) tptp.emptyset)) % 0.40/0.59 (define @t14 () (@var "Xx" $$unsorted)) % 0.40/0.59 (define @t15 () (_ tptp.setadjoin @t14)) % 0.40/0.59 (define @t16 () (_ @t15 @t13)) % 0.40/0.59 (define @t17 () (_ (_ tptp.setadjoin @t16) tptp.emptyset)) % 0.40/0.59 (define @t18 () (_ @t15 tptp.emptyset)) % 0.40/0.59 (define @t19 () (_ (_ tptp.setadjoin @t18) @t17)) % 0.40/0.59 (define @t20 () (_ (_ tptp.subset @t19) @t11)) % 0.40/0.59 (define @t21 () (_ (_ tptp.in @t12) @t3)) % 0.40/0.59 (define @t22 () (@list @t12)) % 0.40/0.59 (define @t23 () (forall @t22 (=> @t21 @t20))) % 0.40/0.59 (define @t24 () (_ (_ tptp.in @t14) @t1)) % 0.40/0.59 (define @t25 () (=> @t24 @t23)) % 0.40/0.59 (define @t26 () (@list @t1 @t3 @t14)) % 0.40/0.59 (define @t27 () (forall @t26 @t25)) % 0.40/0.59 (define @t28 () (= tptp.ubforcartprodlem1 @t27)) % 0.40/0.59 (define @t29 () (_ tptp.powerset @t11)) % 0.40/0.59 (define @t30 () (_ (_ tptp.in @t19) @t29)) % 0.40/0.59 (define @t31 () (forall @t22 (=> @t21 @t30))) % 0.40/0.59 (define @t32 () (=> @t24 @t31)) % 0.40/0.59 (define @t33 () (forall @t26 @t32)) % 0.40/0.59 (define @t34 () (=> tptp.ubforcartprodlem1 @t33)) % 0.40/0.59 (define @t35 () (=> tptp.powersetI1 @t34)) % 0.40/0.59 (define @t36 () (not @t35)) % 0.40/0.59 (define @t37 () (tptp.binunion @t1 @t3)) % 0.40/0.59 (define @t38 () (tptp.powerset @t37)) % 0.40/0.59 (define @t39 () (tptp.powerset @t38)) % 0.40/0.59 (define @t40 () (@var "BOUND_VARIABLE_7542" $$unsorted)) % 0.40/0.59 (define @t41 () (tptp.setadjoin @t14 tptp.emptyset)) % 0.40/0.59 (define @t42 () (tptp.in (tptp.setadjoin @t41 (tptp.setadjoin (tptp.setadjoin @t14 (tptp.setadjoin @t40 tptp.emptyset)) tptp.emptyset)) @t39)) % 0.40/0.59 (define @t43 () (not (tptp.in @t40 @t3))) % 0.40/0.59 (define @t44 () (tptp.in @t14 @t1)) % 0.40/0.59 (define @t45 () (not @t44)) % 0.40/0.59 (define @t46 () (or @t45 @t43 @t42)) % 0.40/0.59 (define @t47 () (@list @t1 @t3 @t14 @t40)) % 0.40/0.59 (define @t48 () (forall @t47 @t46)) % 0.40/0.59 (define @t49 () (@var "BOUND_VARIABLE_7510" $$unsorted)) % 0.40/0.59 (define @t50 () (tptp.subset (tptp.setadjoin @t41 (tptp.setadjoin (tptp.setadjoin @t14 (tptp.setadjoin @t49 tptp.emptyset)) tptp.emptyset)) @t38)) % 0.40/0.59 (define @t51 () (not (tptp.in @t49 @t3))) % 0.40/0.59 (define @t52 () (or @t45 @t51 @t50)) % 0.40/0.59 (define @t53 () (or @t51 @t50)) % 0.40/0.59 (define @t54 () (or @t45 @t53)) % 0.40/0.59 (define @t55 () (@list @t1 @t3 @t14 @t49)) % 0.40/0.59 (define @t56 () (forall @t55 @t54)) % 0.40/0.59 (define @t57 () (@list @t49)) % 0.40/0.59 (define @t58 () (forall @t57 @t54)) % 0.40/0.59 (define @t59 () (forall @t57 @t53)) % 0.40/0.59 (define @t60 () (@list @t12)) % 0.40/0.59 (define @t61 () (or @t45 @t59)) % 0.40/0.59 (define @t62 () (tptp.setadjoin @t12 tptp.emptyset)) % 0.40/0.59 (define @t63 () (tptp.setadjoin @t14 @t62)) % 0.40/0.59 (define @t64 () (tptp.setadjoin @t63 tptp.emptyset)) % 0.40/0.59 (define @t65 () (tptp.setadjoin @t41 @t64)) % 0.40/0.59 (define @t66 () (tptp.subset @t65 @t38)) % 0.40/0.59 (define @t67 () (tptp.in @t12 @t3)) % 0.40/0.59 (define @t68 () (not @t67)) % 0.40/0.59 (define @t69 () (forall @t22 (or @t68 @t66))) % 0.40/0.59 (define @t70 () (not @t24)) % 0.40/0.59 (define @t71 () (or @t70 @t69)) % 0.40/0.59 (define @t72 () (not @t21)) % 0.40/0.59 (define @t73 () (or @t72 @t20)) % 0.40/0.59 (define @t74 () (=> tptp.ubforcartprodlem1 @t48)) % 0.40/0.59 (define @t75 () (tptp.powerset @t1)) % 0.40/0.59 (define @t76 () (tptp.in @t3 @t75)) % 0.40/0.59 (define @t77 () (tptp.subset @t3 @t1)) % 0.40/0.59 (define @t78 () (not @t6)) % 0.40/0.59 (define @t79 () (or @t78 @t5)) % 0.40/0.59 (define @t80 () (=> tptp.powersetI1 @t74)) % 0.40/0.59 (define @t81 () (or @t43 @t42)) % 0.40/0.59 (define @t82 () (or @t45 @t81)) % 0.40/0.59 (define @t83 () (forall @t47 @t82)) % 0.40/0.59 (define @t84 () (@list @t40)) % 0.40/0.59 (define @t85 () (forall @t84 @t82)) % 0.40/0.59 (define @t86 () (forall @t84 @t81)) % 0.40/0.59 (define @t87 () (or @t45 @t86)) % 0.40/0.59 (define @t88 () (tptp.in @t65 @t39)) % 0.40/0.59 (define @t89 () (forall @t22 (or @t68 @t88))) % 0.40/0.59 (define @t90 () (or @t70 @t89)) % 0.40/0.59 (define @t91 () (or @t72 @t30)) % 0.40/0.59 (define @t92 () (@quantifiers_skolemize @t48 3)) % 0.40/0.59 (define @t93 () (@quantifiers_skolemize @t48 2)) % 0.40/0.59 (define @t94 () (tptp.setadjoin (tptp.setadjoin @t93 tptp.emptyset) (tptp.setadjoin (tptp.setadjoin @t93 (tptp.setadjoin @t92 tptp.emptyset)) tptp.emptyset))) % 0.40/0.59 (define @t95 () (@quantifiers_skolemize @t48 1)) % 0.40/0.59 (define @t96 () (@quantifiers_skolemize @t48 0)) % 0.40/0.59 (define @t97 () (tptp.powerset (tptp.binunion @t96 @t95))) % 0.40/0.59 (define @t98 () (tptp.in @t94 (tptp.powerset @t97))) % 0.40/0.59 (define @t99 () (tptp.in @t92 @t95)) % 0.40/0.59 (define @t100 () (not @t99)) % 0.40/0.59 (define @t101 () (tptp.in @t93 @t96)) % 0.40/0.59 (define @t102 () (not @t101)) % 0.40/0.59 (define @t103 () (or @t102 @t100 @t98)) % 0.40/0.59 (define @t104 () (@list true)) % 0.40/0.59 (define @t105 () (@list @t103)) % 0.40/0.59 (define @t106 () (tptp.subset @t94 @t97)) % 0.40/0.59 (define @t107 () (not @t106)) % 0.40/0.59 (define @t108 () (or @t107 @t98)) % 0.40/0.59 (define @t109 () (@list true false)) % 0.40/0.59 (define @t110 () (or @t102 @t100 @t106)) % 0.40/0.59 (define @t111 () (not @t110)) % 0.40/0.59 (define @t112 () (forall @t55 @t52)) % 0.40/0.59 (assume @p1 @t9) % 0.40/0.59 (assume @p2 @t28) % 0.40/0.59 (assume @p3 @t36) % 0.40/0.59 (assume @p4 true) % 0.40/0.59 (step @p5 :rule refl :args (@t48)) % 0.40/0.59 (step @p6 :rule aci_norm :args ((= @t54 @t52))) % 0.40/0.59 (step @p7 :rule cong :premises (@p6) :args (@t56)) % 0.40/0.59 (step @p8 :rule quant-merge-prenex :args ((= (forall @t26 @t58) @t56))) % 0.40/0.59 (step @p9 :rule alpha_equiv :args (@t59 (@list @t49) @t60)) % 0.40/0.59 (step @p10 :rule refl :args (@t45)) % 0.40/0.59 (step @p11 :rule nary_cong :premises (@p10 @p9) :args (@t61)) % 0.40/0.59 (step @p12 :rule quant-miniscope-or :args ((= @t58 @t61))) % 0.40/0.59 (step @p13 :rule trans :premises (@p12 @p11)) % 0.40/0.59 (step @p14 :rule symm :premises (@p13)) % 0.40/0.59 (step @p15 :rule cong :premises (@p14) :args ((forall @t26 (or @t45 @t69)))) % 0.40/0.59 (step @p16 :rule trans :premises (@p15 @p8)) % 0.40/0.59 (step @p17 :rule trans :premises (@p16 @p7)) % 0.40/0.59 (step @p18 :rule refl :args (@t69)) % 0.40/0.59 (step @p19 :rule refl :args (@t44)) % 0.40/0.59 (step @p20 :rule refl :args (@t24)) % 0.40/0.59 (step @p21 :rule cong :premises (@p20 @p19) :args ((= @t24 @t44))) % 0.40/0.59 (step @p22 :rule symm :premises (@p21)) % 0.40/0.59 (step @p23 :rule eq_resolve :premises (@p20 @p22)) % 0.40/0.59 (step @p24 :rule cong :premises (@p23) :args (@t70)) % 0.40/0.59 (step @p25 :rule nary_cong :premises (@p24 @p18) :args (@t71)) % 0.40/0.59 (step @p26 :rule cong :premises (@p25) :args ((forall @t26 @t71))) % 0.40/0.59 (step @p27 :rule trans :premises (@p26 @p17)) % 0.40/0.59 (step @p28 :rule bool-impl-elim :args (@t24 @t69)) % 0.40/0.59 (step @p29 :rule cong :premises (@p28) :args ((forall @t26 (=> @t24 @t69)))) % 0.40/0.59 (step @p30 :rule trans :premises (@p29 @p27)) % 0.40/0.59 (step @p31 :rule refl :args ((tptp.subset @t19 @t11))) % 0.40/0.59 (step @p32 :rule refl :args ((tptp.powerset @t10))) % 0.40/0.59 (step @p33 :rule refl :args (@t37)) % 0.40/0.59 (step @p34 :rule cong :premises (@p33) :args (@t38)) % 0.40/0.59 (step @p35 :rule trans :premises (@p34 @p32)) % 0.40/0.59 (step @p36 :rule refl :args ((tptp.setadjoin @t18 @t17))) % 0.40/0.59 (step @p37 :rule refl :args ((tptp.setadjoin @t16 tptp.emptyset))) % 0.40/0.59 (step @p38 :rule refl :args (tptp.emptyset)) % 0.40/0.59 (step @p39 :rule refl :args ((tptp.setadjoin @t14 @t13))) % 0.40/0.59 (step @p40 :rule refl :args (@t62)) % 0.40/0.59 (step @p41 :rule refl :args (@t14)) % 0.40/0.59 (step @p42 :rule cong :premises (@p41 @p40) :args (@t63)) % 0.40/0.59 (step @p43 :rule trans :premises (@p42 @p39)) % 0.40/0.59 (step @p44 :rule cong :premises (@p43 @p38) :args (@t64)) % 0.40/0.59 (step @p45 :rule trans :premises (@p44 @p37)) % 0.40/0.59 (step @p46 :rule refl :args (@t41)) % 0.40/0.59 (step @p47 :rule cong :premises (@p46 @p45) :args (@t65)) % 0.40/0.59 (step @p48 :rule trans :premises (@p47 @p36)) % 0.40/0.59 (step @p49 :rule cong :premises (@p48 @p35) :args (@t66)) % 0.40/0.59 (step @p50 :rule trans :premises (@p49 @p31)) % 0.40/0.59 (step @p51 :rule refl :args (tptp.subset)) % 0.40/0.59 (step @p52 :rule ho_cong :premises (@p51 @p48)) % 0.40/0.59 (step @p53 :rule ho_cong :premises (@p52 @p35)) % 0.40/0.59 (step @p54 :rule cong :premises (@p53 @p50) :args ((= (_ (_ tptp.subset @t65) @t38) @t66))) % 0.40/0.59 (step @p55 :rule symm :premises (@p54)) % 0.40/0.59 (step @p56 :rule refl :args (@t20)) % 0.40/0.59 (step @p57 :rule eq_resolve :premises (@p56 @p55)) % 0.40/0.59 (step @p58 :rule refl :args (tptp.powerset)) % 0.40/0.59 (step @p59 :rule ho_cong :premises (@p58 @p33)) % 0.40/0.59 (step @p60 :rule cong :premises (@p59 @p35) :args ((= (_ tptp.powerset @t37) @t38))) % 0.40/0.59 (step @p61 :rule symm :premises (@p60)) % 0.40/0.59 (step @p62 :rule refl :args (@t11)) % 0.40/0.59 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 0.40/0.59 (step @p64 :rule refl :args (@t10)) % 0.40/0.59 (step @p65 :rule cong :premises (@p64 @p33) :args ((= @t10 @t37))) % 0.40/0.59 (step @p66 :rule symm :premises (@p65)) % 0.40/0.59 (step @p67 :rule eq_resolve :premises (@p64 @p66)) % 0.40/0.59 (step @p68 :rule ho_cong :premises (@p58 @p67)) % 0.40/0.59 (step @p69 :rule trans :premises (@p68 @p63)) % 0.40/0.59 (step @p70 :rule refl :args (tptp.setadjoin)) % 0.40/0.59 (step @p71 :rule ho_cong :premises (@p70 @p46)) % 0.40/0.59 (step @p72 :rule ho_cong :premises (@p71 @p45)) % 0.40/0.59 (step @p73 :rule cong :premises (@p72 @p48) :args ((= (_ (_ tptp.setadjoin @t41) @t64) @t65))) % 0.40/0.59 (step @p74 :rule symm :premises (@p73)) % 0.40/0.59 (step @p75 :rule refl :args (@t19)) % 0.40/0.59 (step @p76 :rule eq_resolve :premises (@p75 @p74)) % 0.40/0.59 (step @p77 :rule ho_cong :premises (@p70 @p43)) % 0.40/0.59 (step @p78 :rule ho_cong :premises (@p77 @p38)) % 0.40/0.59 (step @p79 :rule cong :premises (@p78 @p45) :args ((= (_ (_ tptp.setadjoin @t63) tptp.emptyset) @t64))) % 0.40/0.59 (step @p80 :rule symm :premises (@p79)) % 0.40/0.59 (step @p81 :rule refl :args (@t17)) % 0.40/0.59 (step @p82 :rule eq_resolve :premises (@p81 @p80)) % 0.40/0.59 (step @p83 :rule refl :args (@t15)) % 0.40/0.59 (step @p84 :rule ho_cong :premises (@p83 @p40)) % 0.40/0.59 (step @p85 :rule cong :premises (@p84 @p43) :args ((= (_ @t15 @t62) @t63))) % 0.40/0.59 (step @p86 :rule symm :premises (@p85)) % 0.40/0.59 (step @p87 :rule refl :args (@t16)) % 0.40/0.59 (step @p88 :rule eq_resolve :premises (@p87 @p86)) % 0.40/0.59 (step @p89 :rule refl :args (@t13)) % 0.40/0.59 (step @p90 :rule cong :premises (@p89 @p40) :args ((= @t13 @t62))) % 0.40/0.59 (step @p91 :rule symm :premises (@p90)) % 0.40/0.59 (step @p92 :rule eq_resolve :premises (@p89 @p91)) % 0.40/0.59 (step @p93 :rule ho_cong :premises (@p83 @p92)) % 0.40/0.59 (step @p94 :rule trans :premises (@p93 @p88)) % 0.40/0.59 (step @p95 :rule ho_cong :premises (@p70 @p94)) % 0.40/0.59 (step @p96 :rule ho_cong :premises (@p95 @p38)) % 0.40/0.59 (step @p97 :rule trans :premises (@p96 @p82)) % 0.40/0.59 (step @p98 :rule refl :args (@t18)) % 0.40/0.59 (step @p99 :rule cong :premises (@p98 @p46) :args ((= @t18 @t41))) % 0.40/0.59 (step @p100 :rule symm :premises (@p99)) % 0.40/0.59 (step @p101 :rule eq_resolve :premises (@p98 @p100)) % 0.40/0.59 (step @p102 :rule ho_cong :premises (@p70 @p101)) % 0.40/0.59 (step @p103 :rule ho_cong :premises (@p102 @p97)) % 0.40/0.59 (step @p104 :rule trans :premises (@p103 @p76)) % 0.40/0.59 (step @p105 :rule ho_cong :premises (@p51 @p104)) % 0.40/0.59 (step @p106 :rule ho_cong :premises (@p105 @p69)) % 0.40/0.59 (step @p107 :rule trans :premises (@p106 @p57)) % 0.40/0.59 (step @p108 :rule refl :args (@t67)) % 0.40/0.59 (step @p109 :rule refl :args (@t21)) % 0.40/0.59 (step @p110 :rule cong :premises (@p109 @p108) :args ((= @t21 @t67))) % 0.40/0.59 (step @p111 :rule symm :premises (@p110)) % 0.40/0.59 (step @p112 :rule eq_resolve :premises (@p109 @p111)) % 0.40/0.59 (step @p113 :rule cong :premises (@p112) :args (@t72)) % 0.40/0.59 (step @p114 :rule nary_cong :premises (@p113 @p107) :args (@t73)) % 0.40/0.59 (step @p115 :rule cong :premises (@p114) :args ((forall @t22 @t73))) % 0.40/0.59 (step @p116 :rule bool-impl-elim :args (@t21 @t20)) % 0.40/0.59 (step @p117 :rule cong :premises (@p116) :args (@t23)) % 0.40/0.59 (step @p118 :rule trans :premises (@p117 @p115)) % 0.40/0.59 (step @p119 :rule refl :args (@t24)) % 0.40/0.59 (step @p120 :rule cong :premises (@p119 @p118) :args (@t25)) % 0.40/0.59 (step @p121 :rule cong :premises (@p120) :args (@t27)) % 0.40/0.59 (step @p122 :rule trans :premises (@p121 @p30)) % 0.40/0.59 (step @p123 :rule refl :args (tptp.ubforcartprodlem1)) % 0.40/0.59 (step @p124 :rule cong :premises (@p123 @p122) :args (@t28)) % 0.40/0.59 (step @p125 :rule eq_resolve :premises (@p2 @p124)) % 0.40/0.59 (step @p126 :rule cong :premises (@p125 @p5) :args (@t74)) % 0.40/0.59 (step @p127 :rule refl :args ((tptp.in @t3 @t2))) % 0.40/0.59 (step @p128 :rule refl :args (@t75)) % 0.40/0.59 (step @p129 :rule refl :args (@t3)) % 0.40/0.59 (step @p130 :rule cong :premises (@p129 @p128) :args (@t76)) % 0.40/0.59 (step @p131 :rule trans :premises (@p130 @p127)) % 0.40/0.59 (step @p132 :rule refl :args (@t4)) % 0.40/0.59 (step @p133 :rule ho_cong :premises (@p132 @p128)) % 0.40/0.59 (step @p134 :rule cong :premises (@p133 @p131) :args ((= (_ @t4 @t75) @t76))) % 0.40/0.59 (step @p135 :rule symm :premises (@p134)) % 0.40/0.59 (step @p136 :rule refl :args (@t5)) % 0.40/0.59 (step @p137 :rule eq_resolve :premises (@p136 @p135)) % 0.40/0.59 (step @p138 :rule refl :args (@t2)) % 0.40/0.59 (step @p139 :rule cong :premises (@p138 @p128) :args ((= @t2 @t75))) % 0.40/0.59 (step @p140 :rule symm :premises (@p139)) % 0.40/0.59 (step @p141 :rule eq_resolve :premises (@p138 @p140)) % 0.40/0.59 (step @p142 :rule ho_cong :premises (@p132 @p141)) % 0.40/0.59 (step @p143 :rule trans :premises (@p142 @p137)) % 0.40/0.59 (step @p144 :rule refl :args (@t77)) % 0.40/0.59 (step @p145 :rule refl :args (@t6)) % 0.40/0.59 (step @p146 :rule cong :premises (@p145 @p144) :args ((= @t6 @t77))) % 0.40/0.59 (step @p147 :rule symm :premises (@p146)) % 0.40/0.59 (step @p148 :rule eq_resolve :premises (@p145 @p147)) % 0.40/0.59 (step @p149 :rule cong :premises (@p148) :args (@t78)) % 0.40/0.59 (step @p150 :rule nary_cong :premises (@p149 @p143) :args (@t79)) % 0.40/0.59 (step @p151 :rule cong :premises (@p150) :args ((forall @t7 @t79))) % 0.40/0.59 (step @p152 :rule bool-impl-elim :args (@t6 @t5)) % 0.40/0.59 (step @p153 :rule cong :premises (@p152) :args (@t8)) % 0.40/0.59 (step @p154 :rule trans :premises (@p153 @p151)) % 0.40/0.59 (step @p155 :rule refl :args (tptp.powersetI1)) % 0.40/0.59 (step @p156 :rule cong :premises (@p155 @p154) :args (@t9)) % 0.40/0.59 (step @p157 :rule eq_resolve :premises (@p1 @p156)) % 0.40/0.59 (step @p158 :rule cong :premises (@p157 @p126) :args (@t80)) % 0.40/0.59 (step @p159 :rule cong :premises (@p158) :args ((not @t80))) % 0.40/0.59 (step @p160 :rule aci_norm :args ((= @t82 @t46))) % 0.40/0.59 (step @p161 :rule cong :premises (@p160) :args (@t83)) % 0.40/0.59 (step @p162 :rule quant-merge-prenex :args ((= (forall @t26 @t85) @t83))) % 0.40/0.59 (step @p163 :rule alpha_equiv :args (@t86 (@list @t40) @t60)) % 0.40/0.59 (step @p164 :rule nary_cong :premises (@p10 @p163) :args (@t87)) % 0.40/0.59 (step @p165 :rule quant-miniscope-or :args ((= @t85 @t87))) % 0.40/0.59 (step @p166 :rule trans :premises (@p165 @p164)) % 0.40/0.59 (step @p167 :rule symm :premises (@p166)) % 0.40/0.59 (step @p168 :rule cong :premises (@p167) :args ((forall @t26 (or @t45 @t89)))) % 0.40/0.59 (step @p169 :rule trans :premises (@p168 @p162)) % 0.40/0.59 (step @p170 :rule trans :premises (@p169 @p161)) % 0.40/0.59 (step @p171 :rule refl :args (@t89)) % 0.40/0.59 (step @p172 :rule nary_cong :premises (@p24 @p171) :args (@t90)) % 0.40/0.59 (step @p173 :rule cong :premises (@p172) :args ((forall @t26 @t90))) % 0.40/0.59 (step @p174 :rule trans :premises (@p173 @p170)) % 0.40/0.59 (step @p175 :rule bool-impl-elim :args (@t24 @t89)) % 0.40/0.59 (step @p176 :rule cong :premises (@p175) :args ((forall @t26 (=> @t24 @t89)))) % 0.40/0.59 (step @p177 :rule trans :premises (@p176 @p174)) % 0.40/0.59 (step @p178 :rule refl :args ((tptp.in @t19 @t29))) % 0.40/0.59 (step @p179 :rule refl :args ((tptp.powerset @t11))) % 0.40/0.59 (step @p180 :rule cong :premises (@p35) :args (@t39)) % 0.40/0.59 (step @p181 :rule trans :premises (@p180 @p179)) % 0.40/0.59 (step @p182 :rule cong :premises (@p48 @p181) :args (@t88)) % 0.40/0.59 (step @p183 :rule trans :premises (@p182 @p178)) % 0.40/0.59 (step @p184 :rule refl :args (tptp.in)) % 0.40/0.59 (step @p185 :rule ho_cong :premises (@p184 @p48)) % 0.40/0.59 (step @p186 :rule ho_cong :premises (@p185 @p181)) % 0.40/0.59 (step @p187 :rule cong :premises (@p186 @p183) :args ((= (_ (_ tptp.in @t65) @t39) @t88))) % 0.40/0.59 (step @p188 :rule symm :premises (@p187)) % 0.40/0.59 (step @p189 :rule refl :args (@t30)) % 0.40/0.59 (step @p190 :rule eq_resolve :premises (@p189 @p188)) % 0.40/0.59 (step @p191 :rule ho_cong :premises (@p58 @p35)) % 0.40/0.59 (step @p192 :rule cong :premises (@p191 @p181) :args ((= (_ tptp.powerset @t38) @t39))) % 0.40/0.59 (step @p193 :rule symm :premises (@p192)) % 0.40/0.59 (step @p194 :rule refl :args (@t29)) % 0.40/0.59 (step @p195 :rule eq_resolve :premises (@p194 @p193)) % 0.40/0.59 (step @p196 :rule ho_cong :premises (@p58 @p69)) % 0.40/0.59 (step @p197 :rule trans :premises (@p196 @p195)) % 0.40/0.59 (step @p198 :rule ho_cong :premises (@p184 @p104)) % 0.40/0.59 (step @p199 :rule ho_cong :premises (@p198 @p197)) % 0.40/0.59 (step @p200 :rule trans :premises (@p199 @p190)) % 0.40/0.59 (step @p201 :rule nary_cong :premises (@p113 @p200) :args (@t91)) % 0.40/0.59 (step @p202 :rule cong :premises (@p201) :args ((forall @t22 @t91))) % 0.40/0.59 (step @p203 :rule bool-impl-elim :args (@t21 @t30)) % 0.40/0.59 (step @p204 :rule cong :premises (@p203) :args (@t31)) % 0.40/0.59 (step @p205 :rule trans :premises (@p204 @p202)) % 0.40/0.59 (step @p206 :rule cong :premises (@p119 @p205) :args (@t32)) % 0.40/0.59 (step @p207 :rule cong :premises (@p206) :args (@t33)) % 0.40/0.59 (step @p208 :rule trans :premises (@p207 @p177)) % 0.40/0.59 (step @p209 :rule cong :premises (@p123 @p208) :args (@t34)) % 0.40/0.59 (step @p210 :rule cong :premises (@p155 @p209) :args (@t35)) % 0.40/0.59 (step @p211 :rule cong :premises (@p210) :args (@t36)) % 0.40/0.59 (step @p212 :rule trans :premises (@p211 @p159)) % 0.40/0.59 (step @p213 :rule eq_resolve :premises (@p3 @p212)) % 0.40/0.59 (step @p214 :rule not_implies_elim2 :premises (@p213)) % 0.40/0.59 (step @p215 :rule not_implies_elim1 :premises (@p214)) % 0.40/0.59 (step @p216 :rule not_implies_elim1 :premises (@p213)) % 0.40/0.59 (step @p217 :rule instantiate :premises (@p216) :args ((@list @t97 @t94))) % 0.40/0.59 (step @p218 :rule not_implies_elim2 :premises (@p214)) % 0.40/0.59 (step @p219 :rule skolemize :premises (@p218)) % 0.40/0.59 (step @p220 :rule cnf_or_neg :args (@t103 2)) % 0.40/0.59 (step @p221 :rule chain_m_resolution :premises (@p220 @p219) :args ((not @t98) @t104 @t105)) % 0.40/0.59 (step @p222 :rule cnf_or_pos :args (@t108)) % 0.40/0.59 (step @p223 :rule reordering :premises (@p222) :args ((or @t98 @t107 (not @t108)))) % 0.40/0.59 (step @p224 :rule chain_m_resolution :premises (@p223 @p221 @p217) :args (@t107 @t109 (@list @t98 @t108))) % 0.40/0.59 (step @p225 :rule bool-double-not-elim :args (@t99)) % 0.40/0.59 (step @p226 :rule refl :args (@t103)) % 0.40/0.59 (step @p227 :rule nary_cong :premises (@p226 @p225) :args ((or @t103 (not @t100)))) % 0.40/0.59 (step @p228 :rule cnf_or_neg :args (@t103 1)) % 0.40/0.59 (step @p229 :rule eq_resolve :premises (@p228 @p227)) % 0.40/0.59 (step @p230 :rule reordering :premises (@p229) :args ((or @t99 @t103))) % 0.40/0.59 (step @p231 :rule chain_m_resolution :premises (@p230 @p219) :args (@t99 @t104 @t105)) % 0.40/0.59 (step @p232 :rule bool-double-not-elim :args (@t101)) % 0.40/0.59 (step @p233 :rule nary_cong :premises (@p226 @p232) :args ((or @t103 (not @t102)))) % 0.40/0.59 (step @p234 :rule cnf_or_neg :args (@t103 0)) % 0.40/0.59 (step @p235 :rule eq_resolve :premises (@p234 @p233)) % 0.40/0.59 (step @p236 :rule reordering :premises (@p235) :args ((or @t101 @t103))) % 0.40/0.59 (step @p237 :rule chain_m_resolution :premises (@p236 @p219) :args (@t101 @t104 @t105)) % 0.40/0.59 (step @p238 :rule cnf_or_pos :args (@t110)) % 0.40/0.59 (step @p239 :rule reordering :premises (@p238) :args ((or @t102 @t100 @t106 @t111))) % 0.40/0.59 (step @p240 :rule chain_m_resolution :premises (@p239 @p237 @p231 @p224) :args (@t111 (@list false false true) (@list @t101 @t99 @t106))) % 0.40/0.59 (assume-push @p247 @t112) % 0.40/0.59 (step @p242 :rule instantiate :premises (@p215) :args ((@list @t96 @t95 @t93 @t92))) % 0.40/0.59 (step-pop @p248 :rule scope :premises (@p242)) % 0.40/0.59 (step @p243 :rule process_scope :premises (@p248) :args (@t110)) % 0.40/0.59 (step @p245 :rule implies_elim :premises (@p243)) % 0.40/0.59 (step @p246 false :rule chain_m_resolution :premises (@p245 @p240 @p215) :args (false @t109 (@list @t110 @t112))) % 0.40/0.59 ) % 0.40/0.59 % SZS output end Proof % 0.40/0.59 % cvc5 exiting %------------------------------------------------------------------------------