%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU499^1 : 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 : n004.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 08:51:57 AM UTC 2026 % Result : Theorem 0.40s 0.58s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU499^1 : 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 % 0.18/0.36 % Computer : n004.cluster.edu % 0.18/0.36 % Model : x86_64 x86_64 % 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.36 % Memory : 8042.1875MB % 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.36 % CPULimit : 300 % 0.18/0.36 % WCLimit : 300 % 0.18/0.36 % DateTime : Tue Jun 2 17:39:07 EDT 2026 % 0.18/0.36 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.40/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.58 % SZS status Theorem % 0.40/0.58 % SZS output start Proof % 0.40/0.58 ( % 0.40/0.58 (declare-sort $$unsorted 0) % 0.40/0.58 (declare-const tptp.dsetconstrI Bool) % 0.40/0.58 (declare-const tptp.descrp Bool) % 0.40/0.58 (declare-const tptp.descr (-> (-> $$unsorted Bool) $$unsorted)) % 0.40/0.58 (declare-const tptp.wellorderingAx Bool) % 0.40/0.58 (declare-const tptp.replAx Bool) % 0.40/0.58 (declare-const tptp.omegaIndAx Bool) % 0.40/0.58 (declare-const tptp.dsetconstrEL Bool) % 0.40/0.58 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.40/0.58 (declare-const tptp.setextAx Bool) % 0.40/0.58 (declare-const tptp.emptyset $$unsorted) % 0.40/0.58 (declare-const tptp.foundationAx Bool) % 0.40/0.58 (declare-const tptp.emptysetAx Bool) % 0.40/0.58 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.dsetconstrER Bool) % 0.40/0.58 (declare-const tptp.setadjoinAx Bool) % 0.40/0.58 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.40/0.58 (declare-const tptp.powersetAx Bool) % 0.40/0.58 (declare-const tptp.omegaSAx Bool) % 0.40/0.58 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.omega0Ax Bool) % 0.40/0.58 (declare-const tptp.setunionAx Bool) % 0.40/0.58 (declare-const tptp.omega $$unsorted) % 0.40/0.58 (define tptp.exu () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "Xphi" (-> $$unsorted Bool)))) (lambda (@list _let_3) (exists (@list _let_2) (and (_ _let_3 _let_2) (forall (@list _let_1) (=> (_ _let_3 _let_1) (= _let_2 _let_1)))))))))) % 0.40/0.58 (define @t1 () (@var "B" $$unsorted)) % 0.40/0.58 (define @t2 () (@var "A" $$unsorted)) % 0.40/0.58 (define @t3 () (@var "Xx" $$unsorted)) % 0.40/0.58 (define @t4 () (_ tptp.in @t3)) % 0.40/0.58 (define @t5 () (_ @t4 @t1)) % 0.40/0.58 (define @t6 () (_ @t4 @t2)) % 0.40/0.58 (define @t7 () (@list @t3)) % 0.40/0.58 (define @t8 () (@list @t2 @t1)) % 0.40/0.58 (define @t9 () (@var "Xy" $$unsorted)) % 0.40/0.58 (define @t10 () (_ tptp.in @t9)) % 0.40/0.58 (define @t11 () (_ @t10 @t2)) % 0.40/0.58 (define @t12 () (_ tptp.setadjoin @t3)) % 0.40/0.58 (define @t13 () (_ tptp.in @t1)) % 0.40/0.58 (define @t14 () (_ @t13 @t2)) % 0.40/0.58 (define @t15 () (@list @t1)) % 0.40/0.58 (define @t16 () (_ tptp.in tptp.emptyset)) % 0.40/0.58 (define @t17 () (_ tptp.in (_ @t12 @t3))) % 0.40/0.58 (define @t18 () (_ @t4 tptp.omega)) % 0.40/0.58 (define @t19 () (@list @t2)) % 0.40/0.58 (define @t20 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.40/0.58 (define @t21 () (@list @t9)) % 0.40/0.58 (define @t22 () (@var "E" $$unsorted)) % 0.40/0.58 (define @t23 () (@var "D" $$unsorted)) % 0.40/0.58 (define @t24 () (_ @t10 @t23)) % 0.40/0.58 (define @t25 () (@var "C" $$unsorted)) % 0.40/0.58 (define @t26 () (_ @t10 @t25)) % 0.40/0.58 (define @t27 () (_ @t4 @t25)) % 0.40/0.58 (define @t28 () (_ (_ tptp.in @t23) @t1)) % 0.40/0.58 (define @t29 () (forall @t7 (=> @t27 @t6))) % 0.40/0.58 (define @t30 () (@list @t25)) % 0.40/0.58 (define @t31 () (_ @t4 @t23)) % 0.40/0.58 (define @t32 () (_ (_ tptp.in @t25) @t1)) % 0.40/0.58 (define @t33 () (= @t3 @t9)) % 0.40/0.58 (define @t34 () (@var "Xphi" (-> $$unsorted Bool))) % 0.40/0.58 (define @t35 () (_ @t34 @t3)) % 0.40/0.58 (define @t36 () (lambda @t7 @t35)) % 0.40/0.58 (define @t37 () (_ tptp.exu @t36)) % 0.40/0.58 (define @t38 () (@list @t34)) % 0.40/0.58 (define @t39 () (_ @t34 @t9)) % 0.40/0.58 (define @t40 () (_ @t4 (_ (_ tptp.dsetconstr @t2) (lambda @t21 @t39)))) % 0.40/0.58 (define @t41 () (@list @t2 @t34 @t3)) % 0.40/0.58 (define @t42 () (forall @t21 (=> @t39 @t33))) % 0.40/0.58 (define @t43 () (and @t35 @t42)) % 0.40/0.58 (define @t44 () (exists @t7 @t43)) % 0.40/0.58 (define @t45 () (=> @t37 @t44)) % 0.40/0.58 (define @t46 () (forall @t38 @t45)) % 0.40/0.58 (define @t47 () (=> tptp.dsetconstrER @t46)) % 0.40/0.58 (define @t48 () (=> tptp.dsetconstrEL @t47)) % 0.40/0.58 (define @t49 () (=> tptp.dsetconstrI @t48)) % 0.40/0.58 (define @t50 () (=> tptp.descrp @t49)) % 0.40/0.58 (define @t51 () (=> tptp.wellorderingAx @t50)) % 0.40/0.58 (define @t52 () (=> tptp.foundationAx @t51)) % 0.40/0.58 (define @t53 () (=> tptp.replAx @t52)) % 0.40/0.58 (define @t54 () (=> tptp.omegaIndAx @t53)) % 0.40/0.58 (define @t55 () (=> tptp.omegaSAx @t54)) % 0.40/0.58 (define @t56 () (=> tptp.omega0Ax @t55)) % 0.40/0.58 (define @t57 () (=> tptp.setunionAx @t56)) % 0.40/0.58 (define @t58 () (=> tptp.powersetAx @t57)) % 0.40/0.58 (define @t59 () (=> tptp.setadjoinAx @t58)) % 0.40/0.58 (define @t60 () (=> tptp.emptysetAx @t59)) % 0.40/0.58 (define @t61 () (=> tptp.setextAx @t60)) % 0.40/0.58 (define @t62 () (not @t61)) % 0.40/0.58 (define @t63 () (lambda @t38 @t44)) % 0.40/0.58 (define @t64 () (_ @t34 @t9)) % 0.40/0.58 (define @t65 () (forall @t21 (or (not @t64) @t33))) % 0.40/0.58 (define @t66 () (not @t65)) % 0.40/0.58 (define @t67 () (_ @t34 @t3)) % 0.40/0.58 (define @t68 () (forall @t7 (or (not @t67) @t66))) % 0.40/0.58 (define @t69 () (not @t68)) % 0.40/0.58 (define @t70 () (not @t35)) % 0.40/0.58 (define @t71 () (or @t70 @t66)) % 0.40/0.58 (define @t72 () (and @t35 @t65)) % 0.40/0.58 (define @t73 () (forall @t7 (not @t72))) % 0.40/0.58 (define @t74 () (not @t73)) % 0.40/0.58 (define @t75 () (not @t39)) % 0.40/0.58 (define @t76 () (or @t75 @t33)) % 0.40/0.58 (define @t77 () (_ @t36 @t9)) % 0.40/0.58 (define @t78 () (not @t77)) % 0.40/0.58 (define @t79 () (or @t78 @t33)) % 0.40/0.58 (define @t80 () (forall @t21 @t79)) % 0.40/0.58 (define @t81 () (not @t80)) % 0.40/0.58 (define @t82 () (_ @t36 @t3)) % 0.40/0.58 (define @t83 () (not @t82)) % 0.40/0.58 (define @t84 () (or @t83 @t81)) % 0.40/0.58 (define @t85 () (forall @t7 @t84)) % 0.40/0.58 (define @t86 () (not @t85)) % 0.40/0.58 (define @t87 () (_ (lambda @t38 @t69) @t36)) % 0.40/0.58 (define @t88 () (=> @t87 @t44)) % 0.40/0.58 (define @t89 () (forall @t38 @t88)) % 0.40/0.58 (define @t90 () (=> tptp.dsetconstrER @t89)) % 0.40/0.58 (define @t91 () (=> tptp.dsetconstrEL @t90)) % 0.40/0.58 (define @t92 () (=> tptp.dsetconstrI @t91)) % 0.40/0.58 (define @t93 () (=> tptp.descrp @t92)) % 0.40/0.58 (define @t94 () (=> tptp.wellorderingAx @t93)) % 0.40/0.58 (define @t95 () (=> tptp.foundationAx @t94)) % 0.40/0.58 (define @t96 () (=> tptp.replAx @t95)) % 0.40/0.58 (define @t97 () (=> tptp.omegaIndAx @t96)) % 0.40/0.58 (define @t98 () (=> tptp.omegaSAx @t97)) % 0.40/0.58 (define @t99 () (=> tptp.omega0Ax @t98)) % 0.40/0.58 (define @t100 () (=> tptp.setunionAx @t99)) % 0.40/0.58 (define @t101 () (=> tptp.powersetAx @t100)) % 0.40/0.58 (define @t102 () (=> tptp.setadjoinAx @t101)) % 0.40/0.58 (define @t103 () (=> tptp.emptysetAx @t102)) % 0.40/0.58 (define @t104 () (=> tptp.setextAx @t103)) % 0.40/0.58 (assume @p1 (= tptp.setextAx (forall @t8 (=> (forall @t7 (= @t6 @t5)) (= @t2 @t1))))) % 0.40/0.58 (assume @p2 (= tptp.emptysetAx (forall @t7 (not (_ @t4 tptp.emptyset))))) % 0.40/0.58 (assume @p3 (= tptp.setadjoinAx (forall (@list @t3 @t2 @t9) (= (_ @t10 (_ @t12 @t2)) (or (= @t9 @t3) @t11))))) % 0.40/0.58 (assume @p4 (= tptp.powersetAx (forall @t8 (= (_ @t13 (_ tptp.powerset @t2)) (forall @t7 (=> @t5 @t6)))))) % 0.40/0.58 (assume @p5 (= tptp.setunionAx (forall (@list @t2 @t3) (= (_ @t4 (_ tptp.setunion @t2)) (exists @t15 (and @t5 @t14)))))) % 0.40/0.58 (assume @p6 (= tptp.omega0Ax (_ @t16 tptp.omega))) % 0.40/0.58 (assume @p7 (= tptp.omegaSAx (forall @t7 (=> @t18 (_ @t17 tptp.omega))))) % 0.40/0.58 (assume @p8 (= tptp.omegaIndAx (forall @t19 (=> (and (_ @t16 @t2) (forall @t7 (=> (and @t18 @t6) (_ @t17 @t2)))) (forall @t7 (=> @t18 @t6)))))) % 0.40/0.58 (assume @p9 (= tptp.replAx (forall (@list @t20 @t2) (=> (forall @t7 (=> @t6 (_ tptp.exu (lambda @t21 (_ (_ @t20 @t3) @t9))))) (exists @t15 (forall @t7 (= @t5 (exists @t21 (and @t11 (_ (_ @t20 @t9) @t3)))))))))) % 0.40/0.58 (assume @p10 (= tptp.foundationAx (forall @t19 (=> (exists @t7 @t6) (exists @t15 (and @t14 (not (exists @t7 (and @t5 @t6))))))))) % 0.40/0.58 (assume @p11 (= tptp.wellorderingAx (forall @t19 (exists @t15 (and (forall @t30 (=> @t32 @t29)) (forall (@list @t3 @t9) (=> (and @t6 @t11) (=> (forall @t30 (=> @t32 (= @t27 @t26))) @t33))) (forall (@list @t25 @t23) (=> (and @t32 @t28) (or (forall @t7 (=> @t27 @t31)) (forall @t7 (=> @t31 @t27))))) (forall @t30 (=> (and @t29 (exists @t7 @t27)) (exists (@list @t23 @t3) (and @t28 @t27 (not (exists @t21 (and @t24 @t26))) (forall (@list @t22) (=> (_ (_ tptp.in @t22) @t1) (or (forall @t21 (=> (_ @t10 @t22) @t24)) (_ @t4 @t22))))))))))))) % 0.40/0.58 (assume @p12 (= tptp.descrp (forall @t38 (=> @t37 (_ @t34 (_ tptp.descr @t36)))))) % 0.40/0.58 (assume @p13 (= tptp.dsetconstrI (forall @t41 (=> @t6 (=> @t35 @t40))))) % 0.40/0.58 (assume @p14 (= tptp.dsetconstrEL (forall @t41 (=> @t40 @t6)))) % 0.40/0.58 (assume @p15 (= tptp.dsetconstrER (forall @t41 (=> @t40 @t35)))) % 0.40/0.58 (assume @p16 @t62) % 0.40/0.58 (assume @p17 true) % 0.40/0.58 (step @p18 (= tptp.exu @t63) :rule refl :args (@t63)) % 0.40/0.58 (step @p19 :rule evaluate :args ((not true))) % 0.40/0.58 (step @p20 :rule bool-impl-true1 :args (tptp.setextAx)) % 0.40/0.58 (step @p21 :rule bool-impl-true1 :args (tptp.emptysetAx)) % 0.40/0.58 (step @p22 :rule bool-impl-true1 :args (tptp.setadjoinAx)) % 0.40/0.58 (step @p23 :rule bool-impl-true1 :args (tptp.powersetAx)) % 0.40/0.58 (step @p24 :rule bool-impl-true1 :args (tptp.setunionAx)) % 0.40/0.58 (step @p25 :rule bool-impl-true1 :args (tptp.omega0Ax)) % 0.40/0.58 (step @p26 :rule bool-impl-true1 :args (tptp.omegaSAx)) % 0.40/0.58 (step @p27 :rule bool-impl-true1 :args (tptp.omegaIndAx)) % 0.40/0.58 (step @p28 :rule bool-impl-true1 :args (tptp.replAx)) % 0.40/0.58 (step @p29 :rule bool-impl-true1 :args (tptp.foundationAx)) % 0.40/0.58 (step @p30 :rule bool-impl-true1 :args (tptp.wellorderingAx)) % 0.40/0.58 (step @p31 :rule bool-impl-true1 :args (tptp.descrp)) % 0.40/0.58 (step @p32 :rule bool-impl-true1 :args (tptp.dsetconstrI)) % 0.40/0.58 (step @p33 :rule bool-impl-true1 :args (tptp.dsetconstrEL)) % 0.40/0.58 (step @p34 :rule bool-impl-true1 :args (tptp.dsetconstrER)) % 0.40/0.58 (step @p35 :rule quant-unused-vars :args ((= (forall @t38 true) true))) % 0.40/0.58 (step @p36 :rule bool-or-taut :args (false @t68 false false)) % 0.40/0.58 (step @p37 :rule refl :args (@t69)) % 0.40/0.58 (step @p38 :rule bool-double-not-elim :args (@t68)) % 0.40/0.58 (step @p39 :rule nary_cong :premises (@p38 @p37) :args ((or (not @t69) @t69))) % 0.40/0.58 (step @p40 :rule bool-impl-elim :args (@t69 @t69)) % 0.40/0.58 (step @p41 :rule trans :premises (@p40 @p39)) % 0.40/0.58 (step @p42 :rule trans :premises (@p41 @p36)) % 0.40/0.58 (step @p43 :rule cong :premises (@p42) :args ((forall @t38 (=> @t69 @t69)))) % 0.40/0.58 (step @p44 :rule trans :premises (@p43 @p35)) % 0.40/0.58 (step @p45 :rule refl :args (@t66)) % 0.40/0.58 (step @p46 :rule refl :args (@t67)) % 0.40/0.58 (step @p47 :rule refl :args (@t35)) % 0.40/0.58 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t35 @t67))) % 0.40/0.58 (step @p49 :rule symm :premises (@p48)) % 0.40/0.58 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 0.40/0.58 (step @p51 :rule cong :premises (@p50) :args (@t70)) % 0.40/0.58 (step @p52 :rule nary_cong :premises (@p51 @p45) :args (@t71)) % 0.40/0.58 (step @p53 :rule cong :premises (@p52) :args ((forall @t7 @t71))) % 0.40/0.58 (step @p54 :rule bool-and-de-morgan :args (@t35 @t65 true)) % 0.40/0.58 (step @p55 :rule cong :premises (@p54) :args (@t73)) % 0.40/0.58 (step @p56 :rule trans :premises (@p55 @p53)) % 0.40/0.58 (step @p57 :rule cong :premises (@p56) :args (@t74)) % 0.40/0.58 (step @p58 :rule exists-elim :args ((= (exists @t7 @t72) @t74))) % 0.40/0.58 (step @p59 :rule trans :premises (@p58 @p57)) % 0.40/0.58 (step @p60 :rule refl :args (@t33)) % 0.40/0.58 (step @p61 :rule refl :args (@t64)) % 0.40/0.58 (step @p62 :rule refl :args (@t39)) % 0.40/0.58 (step @p63 :rule cong :premises (@p62 @p61) :args ((= @t39 @t64))) % 0.40/0.58 (step @p64 :rule symm :premises (@p63)) % 0.40/0.58 (step @p65 :rule eq_resolve :premises (@p62 @p64)) % 0.40/0.58 (step @p66 :rule cong :premises (@p65) :args (@t75)) % 0.40/0.58 (step @p67 :rule nary_cong :premises (@p66 @p60) :args (@t76)) % 0.40/0.58 (step @p68 :rule cong :premises (@p67) :args ((forall @t21 @t76))) % 0.40/0.58 (step @p69 :rule bool-impl-elim :args (@t39 @t33)) % 0.40/0.58 (step @p70 :rule cong :premises (@p69) :args (@t42)) % 0.40/0.58 (step @p71 :rule trans :premises (@p70 @p68)) % 0.40/0.58 (step @p72 :rule refl :args (@t35)) % 0.40/0.58 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t43)) % 0.40/0.58 (step @p74 :rule cong :premises (@p73) :args (@t44)) % 0.40/0.58 (step @p75 :rule trans :premises (@p74 @p59)) % 0.40/0.58 (step @p76 :rule refl :args (@t33)) % 0.40/0.58 (step @p77 :rule beta-reduce :args ((= @t77 @t39))) % 0.40/0.58 (step @p78 :rule cong :premises (@p77) :args (@t78)) % 0.40/0.58 (step @p79 :rule nary_cong :premises (@p78 @p76) :args (@t79)) % 0.40/0.58 (step @p80 :rule cong :premises (@p79) :args (@t80)) % 0.40/0.58 (step @p81 :rule trans :premises (@p80 @p68)) % 0.40/0.58 (step @p82 :rule cong :premises (@p81) :args (@t81)) % 0.40/0.58 (step @p83 :rule beta-reduce :args ((= @t82 @t35))) % 0.40/0.58 (step @p84 :rule cong :premises (@p83) :args (@t83)) % 0.40/0.58 (step @p85 :rule nary_cong :premises (@p84 @p82) :args (@t84)) % 0.40/0.58 (step @p86 :rule cong :premises (@p85) :args (@t85)) % 0.40/0.58 (step @p87 :rule trans :premises (@p86 @p53)) % 0.40/0.58 (step @p88 :rule cong :premises (@p87) :args (@t86)) % 0.40/0.58 (step @p89 :rule beta-reduce :args ((= @t87 @t86))) % 0.40/0.58 (step @p90 :rule trans :premises (@p89 @p88)) % 0.40/0.58 (step @p91 :rule cong :premises (@p90 @p75) :args (@t88)) % 0.40/0.58 (step @p92 :rule cong :premises (@p91) :args (@t89)) % 0.40/0.58 (step @p93 :rule trans :premises (@p92 @p44)) % 0.40/0.58 (step @p94 :rule refl :args (tptp.dsetconstrER)) % 0.40/0.58 (step @p95 :rule cong :premises (@p94 @p93) :args (@t90)) % 0.40/0.58 (step @p96 :rule trans :premises (@p95 @p34)) % 0.40/0.58 (step @p97 :rule refl :args (tptp.dsetconstrEL)) % 0.40/0.58 (step @p98 :rule cong :premises (@p97 @p96) :args (@t91)) % 0.40/0.58 (step @p99 :rule trans :premises (@p98 @p33)) % 0.40/0.58 (step @p100 :rule refl :args (tptp.dsetconstrI)) % 0.40/0.58 (step @p101 :rule cong :premises (@p100 @p99) :args (@t92)) % 0.40/0.58 (step @p102 :rule trans :premises (@p101 @p32)) % 0.40/0.58 (step @p103 :rule refl :args (tptp.descrp)) % 0.40/0.58 (step @p104 :rule cong :premises (@p103 @p102) :args (@t93)) % 0.40/0.58 (step @p105 :rule trans :premises (@p104 @p31)) % 0.40/0.58 (step @p106 :rule refl :args (tptp.wellorderingAx)) % 0.40/0.58 (step @p107 :rule cong :premises (@p106 @p105) :args (@t94)) % 0.40/0.58 (step @p108 :rule trans :premises (@p107 @p30)) % 0.40/0.58 (step @p109 :rule refl :args (tptp.foundationAx)) % 0.40/0.58 (step @p110 :rule cong :premises (@p109 @p108) :args (@t95)) % 0.40/0.58 (step @p111 :rule trans :premises (@p110 @p29)) % 0.40/0.58 (step @p112 :rule refl :args (tptp.replAx)) % 0.40/0.58 (step @p113 :rule cong :premises (@p112 @p111) :args (@t96)) % 0.40/0.58 (step @p114 :rule trans :premises (@p113 @p28)) % 0.40/0.58 (step @p115 :rule refl :args (tptp.omegaIndAx)) % 0.40/0.58 (step @p116 :rule cong :premises (@p115 @p114) :args (@t97)) % 0.40/0.58 (step @p117 :rule trans :premises (@p116 @p27)) % 0.40/0.58 (step @p118 :rule refl :args (tptp.omegaSAx)) % 0.40/0.58 (step @p119 :rule cong :premises (@p118 @p117) :args (@t98)) % 0.40/0.58 (step @p120 :rule trans :premises (@p119 @p26)) % 0.40/0.58 (step @p121 :rule refl :args (tptp.omega0Ax)) % 0.40/0.58 (step @p122 :rule cong :premises (@p121 @p120) :args (@t99)) % 0.40/0.58 (step @p123 :rule trans :premises (@p122 @p25)) % 0.40/0.58 (step @p124 :rule refl :args (tptp.setunionAx)) % 0.40/0.58 (step @p125 :rule cong :premises (@p124 @p123) :args (@t100)) % 0.40/0.58 (step @p126 :rule trans :premises (@p125 @p24)) % 0.40/0.58 (step @p127 :rule refl :args (tptp.powersetAx)) % 0.40/0.58 (step @p128 :rule cong :premises (@p127 @p126) :args (@t101)) % 0.40/0.58 (step @p129 :rule trans :premises (@p128 @p23)) % 0.40/0.58 (step @p130 :rule refl :args (tptp.setadjoinAx)) % 0.40/0.58 (step @p131 :rule cong :premises (@p130 @p129) :args (@t102)) % 0.40/0.58 (step @p132 :rule trans :premises (@p131 @p22)) % 0.40/0.58 (step @p133 :rule refl :args (tptp.emptysetAx)) % 0.40/0.58 (step @p134 :rule cong :premises (@p133 @p132) :args (@t103)) % 0.40/0.58 (step @p135 :rule trans :premises (@p134 @p21)) % 0.40/0.58 (step @p136 :rule refl :args (tptp.setextAx)) % 0.40/0.58 (step @p137 :rule cong :premises (@p136 @p135) :args (@t104)) % 0.40/0.58 (step @p138 :rule trans :premises (@p137 @p20)) % 0.40/0.58 (step @p139 :rule cong :premises (@p138) :args ((not @t104))) % 0.40/0.58 (step @p140 :rule trans :premises (@p139 @p19)) % 0.40/0.58 (step @p141 :rule refl :args (@t44)) % 0.40/0.58 (step @p142 :rule refl :args (@t36)) % 0.40/0.58 (step @p143 :rule cong :premises (@p75) :args (@t63)) % 0.40/0.58 (step @p144 :rule trans :premises (@p18 @p143)) % 0.40/0.58 (step @p145 :rule ho_cong :premises (@p144 @p142)) % 0.40/0.58 (step @p146 :rule cong :premises (@p145 @p141) :args (@t45)) % 0.40/0.58 (step @p147 :rule cong :premises (@p146) :args (@t46)) % 0.40/0.58 (step @p148 :rule cong :premises (@p94 @p147) :args (@t47)) % 0.40/0.58 (step @p149 :rule cong :premises (@p97 @p148) :args (@t48)) % 0.40/0.58 (step @p150 :rule cong :premises (@p100 @p149) :args (@t49)) % 0.40/0.58 (step @p151 :rule cong :premises (@p103 @p150) :args (@t50)) % 0.40/0.58 (step @p152 :rule cong :premises (@p106 @p151) :args (@t51)) % 0.40/0.58 (step @p153 :rule cong :premises (@p109 @p152) :args (@t52)) % 0.40/0.58 (step @p154 :rule cong :premises (@p112 @p153) :args (@t53)) % 0.40/0.58 (step @p155 :rule cong :premises (@p115 @p154) :args (@t54)) % 0.40/0.58 (step @p156 :rule cong :premises (@p118 @p155) :args (@t55)) % 0.40/0.58 (step @p157 :rule cong :premises (@p121 @p156) :args (@t56)) % 0.40/0.58 (step @p158 :rule cong :premises (@p124 @p157) :args (@t57)) % 0.40/0.58 (step @p159 :rule cong :premises (@p127 @p158) :args (@t58)) % 0.40/0.58 (step @p160 :rule cong :premises (@p130 @p159) :args (@t59)) % 0.40/0.58 (step @p161 :rule cong :premises (@p133 @p160) :args (@t60)) % 0.40/0.58 (step @p162 :rule cong :premises (@p136 @p161) :args (@t61)) % 0.40/0.58 (step @p163 :rule cong :premises (@p162) :args (@t62)) % 0.40/0.58 (step @p164 :rule trans :premises (@p163 @p140)) % 0.40/0.58 (step @p165 false :rule eq_resolve :premises (@p16 @p164)) % 0.40/0.58 ) % 0.40/0.58 % SZS output end Proof % 0.40/0.58 % cvc5 exiting %------------------------------------------------------------------------------