%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET014^4 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n014.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 08:46:56 AM UTC 2026 % Result : Theorem 0.35s 0.58s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET014^4 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n014.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 14:40:43 EDT 2026 % 0.16/0.35 % CPUTime : % 0.35/0.51 %----Proving TH0 % 0.35/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.35/0.58 % SZS status Theorem % 0.35/0.58 % SZS output start Proof % 0.35/0.58 ( % 0.35/0.58 (declare-sort $$unsorted 0) % 0.35/0.58 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.35/0.58 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.35/0.58 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.35/0.58 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.35/0.58 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.35/0.58 (define tptp.union () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.35/0.58 (define tptp.excl_union () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.35/0.58 (define tptp.intersection () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.35/0.58 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.35/0.58 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.35/0.58 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.35/0.58 (define tptp.subset () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (forall (@list _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.35/0.58 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.35/0.58 (define tptp.misses () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (not (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))))) % 0.35/0.58 (define @t1 () (@var "A" (-> $$unsorted Bool))) % 0.35/0.58 (define @t2 () (@var "Y" (-> $$unsorted Bool))) % 0.35/0.58 (define @t3 () (@var "X" (-> $$unsorted Bool))) % 0.35/0.58 (define @t4 () (and (_ (_ tptp.subset @t3) @t1) (_ (_ tptp.subset @t2) @t1))) % 0.35/0.58 (define @t5 () (=> @t4 (_ (_ tptp.subset (_ (_ tptp.union @t3) @t2)) @t1))) % 0.35/0.58 (define @t6 () (@list @t3 @t2 @t1)) % 0.35/0.58 (define @t7 () (forall @t6 @t5)) % 0.35/0.58 (define @t8 () (not @t7)) % 0.35/0.58 (define @t9 () (@var "X" $$unsorted)) % 0.35/0.58 (define @t10 () (@var "M" (-> $$unsorted Bool))) % 0.35/0.58 (define @t11 () (lambda (@list @t9 @t10) (_ @t10 @t9))) % 0.35/0.58 (define @t12 () (lambda (@list @t9) false)) % 0.35/0.58 (define @t13 () (@var "Y" $$unsorted)) % 0.35/0.58 (define @t14 () (@var "U" $$unsorted)) % 0.35/0.58 (define @t15 () (= @t14 @t9)) % 0.35/0.58 (define @t16 () (lambda (@list @t9 @t13 @t14) (or @t15 (= @t14 @t13)))) % 0.35/0.58 (define @t17 () (lambda (@list @t9 @t14) @t15)) % 0.35/0.58 (define @t18 () (_ @t2 @t14)) % 0.35/0.58 (define @t19 () (_ @t3 @t14)) % 0.35/0.58 (define @t20 () (or @t19 @t18)) % 0.35/0.58 (define @t21 () (@list @t3 @t2 @t14)) % 0.35/0.58 (define @t22 () (lambda @t21 @t20)) % 0.35/0.58 (define @t23 () (not @t19)) % 0.35/0.58 (define @t24 () (not @t18)) % 0.35/0.58 (define @t25 () (and @t19 @t24)) % 0.35/0.58 (define @t26 () (lambda @t21 (or @t25 (and @t23 @t18)))) % 0.35/0.58 (define @t27 () (and @t19 @t18)) % 0.35/0.58 (define @t28 () (lambda @t21 @t27)) % 0.35/0.58 (define @t29 () (lambda @t21 @t25)) % 0.35/0.58 (define @t30 () (lambda (@list @t3 @t14) @t23)) % 0.35/0.58 (define @t31 () (@list @t3 @t2)) % 0.35/0.58 (define @t32 () (lambda @t31 (= (_ (_ tptp.intersection @t3) @t2) tptp.emptyset))) % 0.35/0.58 (define @t33 () (@list @t14)) % 0.35/0.58 (define @t34 () (forall @t33 (=> @t19 @t18))) % 0.35/0.58 (define @t35 () (lambda @t31 @t34)) % 0.35/0.58 (define @t36 () (exists @t33 @t27)) % 0.35/0.58 (define @t37 () (lambda @t31 @t36)) % 0.35/0.58 (define @t38 () (lambda @t31 (not @t36))) % 0.35/0.58 (define @t39 () (@var "BOUND_VARIABLE_7702" $$unsorted)) % 0.35/0.58 (define @t40 () (_ @t1 @t39)) % 0.35/0.58 (define @t41 () (and (not (_ @t3 @t39)) (not (_ @t2 @t39)))) % 0.35/0.58 (define @t42 () (_ @t1 @t14)) % 0.35/0.58 (define @t43 () (_ @t2 @t14)) % 0.35/0.58 (define @t44 () (not @t43)) % 0.35/0.58 (define @t45 () (forall @t33 (or @t44 @t42))) % 0.35/0.58 (define @t46 () (not @t45)) % 0.35/0.58 (define @t47 () (_ @t3 @t14)) % 0.35/0.58 (define @t48 () (not @t47)) % 0.35/0.58 (define @t49 () (forall @t33 (or @t48 @t42))) % 0.35/0.58 (define @t50 () (not @t49)) % 0.35/0.58 (define @t51 () (or @t50 @t46 @t41 @t40)) % 0.35/0.58 (define @t52 () (or @t41 @t40)) % 0.35/0.58 (define @t53 () (or @t50 @t46 @t52)) % 0.35/0.58 (define @t54 () (@list @t3 @t2 @t1 @t39)) % 0.35/0.58 (define @t55 () (forall @t54 @t53)) % 0.35/0.58 (define @t56 () (@list @t39)) % 0.35/0.58 (define @t57 () (forall @t56 @t53)) % 0.35/0.58 (define @t58 () (forall @t56 @t52)) % 0.35/0.58 (define @t59 () (or @t50 @t46 @t58)) % 0.35/0.58 (define @t60 () (and @t48 @t44)) % 0.35/0.58 (define @t61 () (forall @t33 (or @t60 @t42))) % 0.35/0.58 (define @t62 () (or @t50 @t46 @t61)) % 0.35/0.58 (define @t63 () (and @t49 @t45)) % 0.35/0.58 (define @t64 () (@var "BOUND_VARIABLE_7666" (-> $$unsorted Bool))) % 0.35/0.58 (define @t65 () (_ @t64 @t14)) % 0.35/0.58 (define @t66 () (@list @t64)) % 0.35/0.58 (define @t67 () (and @t23 @t24)) % 0.35/0.58 (define @t68 () (or @t67 @t65)) % 0.35/0.58 (define @t69 () (or (not @t20) @t65)) % 0.35/0.58 (define @t70 () (lambda @t33 @t20)) % 0.35/0.58 (define @t71 () (_ @t70 @t14)) % 0.35/0.58 (define @t72 () (not @t71)) % 0.35/0.58 (define @t73 () (or @t72 @t65)) % 0.35/0.58 (define @t74 () (forall @t33 @t73)) % 0.35/0.58 (define @t75 () (lambda @t66 @t74)) % 0.35/0.58 (define @t76 () (forall @t33 (or @t48 @t43))) % 0.35/0.58 (define @t77 () (lambda @t31 @t76)) % 0.35/0.58 (define @t78 () (@list @t2)) % 0.35/0.58 (define @t79 () (lambda (@list @t2 @t14) @t20)) % 0.35/0.58 (define @t80 () (_ @t22 @t3)) % 0.35/0.58 (define @t81 () (@var "BOUND_VARIABLE_7645" (-> $$unsorted Bool))) % 0.35/0.58 (define @t82 () (_ @t81 @t14)) % 0.35/0.58 (define @t83 () (lambda (@list @t81) (forall @t33 (or @t44 @t82)))) % 0.35/0.58 (define @t84 () (lambda (@list @t2) @t76)) % 0.35/0.58 (define @t85 () (_ @t77 @t3)) % 0.35/0.58 (define @t86 () (and (_ @t85 @t1) (_ (_ @t77 @t2) @t1))) % 0.35/0.58 (define @t87 () (=> @t86 (_ (_ @t77 (_ @t80 @t2)) @t1))) % 0.35/0.58 (define @t88 () (forall @t6 @t87)) % 0.35/0.58 (define @t89 () (or @t23 @t18)) % 0.35/0.58 (define @t90 () (forall @t54 @t51)) % 0.35/0.58 (define @t91 () (@quantifiers_skolemize @t90 2)) % 0.35/0.58 (define @t92 () (_ @t91 @t14)) % 0.35/0.58 (define @t93 () (@quantifiers_skolemize @t90 1)) % 0.35/0.58 (define @t94 () (forall @t33 (or (not (_ @t93 @t14)) @t92))) % 0.35/0.58 (define @t95 () (@quantifiers_skolemize @t90 3)) % 0.35/0.58 (define @t96 () (_ @t91 @t95)) % 0.35/0.58 (define @t97 () (_ @t93 @t95)) % 0.35/0.58 (define @t98 () (not @t97)) % 0.35/0.58 (define @t99 () (@quantifiers_skolemize @t90 0)) % 0.35/0.58 (define @t100 () (_ @t99 @t95)) % 0.35/0.58 (define @t101 () (not @t100)) % 0.35/0.58 (define @t102 () (and @t101 @t98)) % 0.35/0.58 (define @t103 () (not @t94)) % 0.35/0.58 (define @t104 () (forall @t33 (or (not (_ @t99 @t14)) @t92))) % 0.35/0.58 (define @t105 () (not @t104)) % 0.35/0.58 (define @t106 () (or @t105 @t103 @t102 @t96)) % 0.35/0.58 (define @t107 () (@list true)) % 0.35/0.58 (define @t108 () (@list @t106)) % 0.35/0.58 (define @t109 () (@list @t95)) % 0.35/0.58 (define @t110 () (or @t101 @t96)) % 0.35/0.58 (define @t111 () (@list true false)) % 0.35/0.58 (define @t112 () (or @t98 @t96)) % 0.35/0.58 (define @t113 () (not @t112)) % 0.35/0.58 (assume @p1 @t8) % 0.35/0.58 (assume @p2 true) % 0.35/0.58 (step @p3 (= tptp.in @t11) :rule refl :args (@t11)) % 0.35/0.58 (step @p4 (= tptp.is_a @t11) :rule refl :args (@t11)) % 0.35/0.58 (step @p5 (= tptp.emptyset @t12) :rule refl :args (@t12)) % 0.35/0.58 (step @p6 (= tptp.unord_pair @t16) :rule refl :args (@t16)) % 0.35/0.58 (step @p7 (= tptp.singleton @t17) :rule refl :args (@t17)) % 0.35/0.58 (step @p8 (= tptp.union @t22) :rule refl :args (@t22)) % 0.35/0.58 (step @p9 (= tptp.excl_union @t26) :rule refl :args (@t26)) % 0.35/0.58 (step @p10 (= tptp.intersection @t28) :rule refl :args (@t28)) % 0.35/0.58 (step @p11 (= tptp.setminus @t29) :rule refl :args (@t29)) % 0.35/0.58 (step @p12 (= tptp.complement @t30) :rule refl :args (@t30)) % 0.35/0.58 (step @p13 (= tptp.disjoint @t32) :rule refl :args (@t32)) % 0.35/0.58 (step @p14 (= tptp.subset @t35) :rule refl :args (@t35)) % 0.35/0.58 (step @p15 (= tptp.meets @t37) :rule refl :args (@t37)) % 0.35/0.58 (step @p16 (= tptp.misses @t38) :rule refl :args (@t38)) % 0.35/0.58 (step @p17 :rule aci_norm :args ((= @t53 @t51))) % 0.35/0.58 (step @p18 :rule cong :premises (@p17) :args (@t55)) % 0.35/0.58 (step @p19 :rule quant-merge-prenex :args ((= (forall @t6 @t57) @t55))) % 0.35/0.58 (step @p20 :rule alpha_equiv :args (@t58 (@list @t39) (@list @t14))) % 0.35/0.58 (step @p21 :rule refl :args (@t46)) % 0.35/0.58 (step @p22 :rule refl :args (@t50)) % 0.35/0.58 (step @p23 :rule nary_cong :premises (@p22 @p21 @p20) :args (@t59)) % 0.35/0.58 (step @p24 :rule quant-miniscope-or :args ((= @t57 @t59))) % 0.35/0.58 (step @p25 :rule trans :premises (@p24 @p23)) % 0.35/0.58 (step @p26 :rule symm :premises (@p25)) % 0.35/0.58 (step @p27 :rule cong :premises (@p26) :args ((forall @t6 @t62))) % 0.35/0.58 (step @p28 :rule trans :premises (@p27 @p19)) % 0.35/0.58 (step @p29 :rule trans :premises (@p28 @p18)) % 0.35/0.58 (step @p30 :rule aci_norm :args ((= (or (or @t50 @t46) @t61) @t62))) % 0.35/0.58 (step @p31 :rule refl :args (@t61)) % 0.35/0.58 (step @p32 :rule bool-and-de-morgan :args (@t49 @t45 true)) % 0.35/0.58 (step @p33 :rule nary_cong :premises (@p32 @p31) :args ((or (not @t63) @t61))) % 0.35/0.58 (step @p34 :rule trans :premises (@p33 @p30)) % 0.35/0.58 (step @p35 :rule bool-impl-elim :args (@t63 @t61)) % 0.35/0.58 (step @p36 :rule trans :premises (@p35 @p34)) % 0.35/0.58 (step @p37 :rule cong :premises (@p36) :args ((forall @t6 (=> @t63 @t61)))) % 0.35/0.58 (step @p38 :rule trans :premises (@p37 @p29)) % 0.35/0.58 (step @p39 :rule beta-reduce :args ((= (_ (lambda @t66 (forall @t33 (or @t60 @t65))) @t1) @t61))) % 0.35/0.58 (step @p40 :rule refl :args (@t1)) % 0.35/0.58 (step @p41 :rule refl :args (@t65)) % 0.35/0.58 (step @p42 :rule refl :args (@t43)) % 0.35/0.58 (step @p43 :rule refl :args (@t18)) % 0.35/0.58 (step @p44 :rule cong :premises (@p43 @p42) :args ((= @t18 @t43))) % 0.35/0.58 (step @p45 :rule symm :premises (@p44)) % 0.35/0.58 (step @p46 :rule eq_resolve :premises (@p43 @p45)) % 0.35/0.58 (step @p47 :rule cong :premises (@p46) :args (@t24)) % 0.35/0.58 (step @p48 :rule refl :args (@t47)) % 0.35/0.58 (step @p49 :rule refl :args (@t19)) % 0.35/0.58 (step @p50 :rule cong :premises (@p49 @p48) :args ((= @t19 @t47))) % 0.35/0.58 (step @p51 :rule symm :premises (@p50)) % 0.35/0.58 (step @p52 :rule eq_resolve :premises (@p49 @p51)) % 0.35/0.58 (step @p53 :rule cong :premises (@p52) :args (@t23)) % 0.35/0.58 (step @p54 :rule nary_cong :premises (@p53 @p47) :args (@t67)) % 0.35/0.58 (step @p55 :rule nary_cong :premises (@p54 @p41) :args (@t68)) % 0.35/0.58 (step @p56 :rule cong :premises (@p55) :args ((forall @t33 @t68))) % 0.35/0.58 (step @p57 :rule bool-or-de-morgan :args (@t19 @t18 false)) % 0.35/0.58 (step @p58 :rule nary_cong :premises (@p57 @p41) :args (@t69)) % 0.35/0.58 (step @p59 :rule cong :premises (@p58) :args ((forall @t33 @t69))) % 0.35/0.58 (step @p60 :rule trans :premises (@p59 @p56)) % 0.35/0.58 (step @p61 :rule refl :args (@t65)) % 0.35/0.58 (step @p62 :rule beta-reduce :args ((= @t71 @t20))) % 0.35/0.58 (step @p63 :rule cong :premises (@p62) :args (@t72)) % 0.35/0.58 (step @p64 :rule nary_cong :premises (@p63 @p61) :args (@t73)) % 0.35/0.58 (step @p65 :rule cong :premises (@p64) :args (@t74)) % 0.35/0.58 (step @p66 :rule trans :premises (@p65 @p60)) % 0.35/0.58 (step @p67 :rule cong :premises (@p66) :args (@t75)) % 0.35/0.58 (step @p68 :rule beta-reduce :args ((= (_ (lambda (@list @t3 @t64) (forall @t33 (or @t48 @t65))) @t70) @t75))) % 0.35/0.58 (step @p69 :rule trans :premises (@p68 @p67)) % 0.35/0.58 (step @p70 :rule refl :args (@t70)) % 0.35/0.58 (step @p71 :rule alpha_equiv :args (@t77 @t78 (@list @t64))) % 0.35/0.58 (step @p72 :rule ho_cong :premises (@p71 @p70)) % 0.35/0.58 (step @p73 :rule trans :premises (@p72 @p69)) % 0.35/0.58 (step @p74 :rule beta-reduce :args ((= (_ @t79 @t2) @t70))) % 0.35/0.58 (step @p75 :rule refl :args (@t2)) % 0.35/0.58 (step @p76 :rule beta-reduce :args ((= @t80 @t79))) % 0.35/0.58 (step @p77 :rule ho_cong :premises (@p76 @p75)) % 0.35/0.58 (step @p78 :rule trans :premises (@p77 @p74)) % 0.35/0.58 (step @p79 :rule refl :args (@t77)) % 0.35/0.58 (step @p80 :rule ho_cong :premises (@p79 @p78)) % 0.35/0.58 (step @p81 :rule trans :premises (@p80 @p73)) % 0.35/0.58 (step @p82 :rule ho_cong :premises (@p81 @p40)) % 0.35/0.58 (step @p83 :rule trans :premises (@p82 @p39)) % 0.35/0.58 (step @p84 :rule beta-reduce :args ((= (_ @t83 @t1) @t45))) % 0.35/0.58 (step @p85 :rule beta-reduce :args ((= (_ (lambda (@list @t3 @t81) (forall @t33 (or @t48 @t82))) @t2) @t83))) % 0.35/0.58 (step @p86 :rule refl :args (@t2)) % 0.35/0.58 (step @p87 :rule alpha_equiv :args (@t77 @t78 (@list @t81))) % 0.35/0.58 (step @p88 :rule ho_cong :premises (@p87 @p86)) % 0.35/0.58 (step @p89 :rule trans :premises (@p88 @p85)) % 0.35/0.58 (step @p90 :rule ho_cong :premises (@p89 @p40)) % 0.35/0.58 (step @p91 :rule trans :premises (@p90 @p84)) % 0.35/0.58 (step @p92 :rule beta-reduce :args ((= (_ @t84 @t1) @t49))) % 0.35/0.58 (step @p93 :rule beta-reduce :args ((= @t85 @t84))) % 0.35/0.58 (step @p94 :rule ho_cong :premises (@p93 @p40)) % 0.35/0.58 (step @p95 :rule trans :premises (@p94 @p92)) % 0.35/0.58 (step @p96 :rule nary_cong :premises (@p95 @p91) :args (@t86)) % 0.35/0.58 (step @p97 :rule cong :premises (@p96 @p83) :args (@t87)) % 0.35/0.58 (step @p98 :rule cong :premises (@p97) :args (@t88)) % 0.35/0.58 (step @p99 :rule trans :premises (@p98 @p38)) % 0.35/0.58 (step @p100 :rule cong :premises (@p99) :args ((not @t88))) % 0.35/0.58 (step @p101 :rule refl :args (@t3)) % 0.35/0.58 (step @p102 :rule ho_cong :premises (@p8 @p101)) % 0.35/0.58 (step @p103 :rule ho_cong :premises (@p102 @p75)) % 0.35/0.58 (step @p104 :rule nary_cong :premises (@p53 @p46) :args (@t89)) % 0.35/0.58 (step @p105 :rule cong :premises (@p104) :args ((forall @t33 @t89))) % 0.35/0.58 (step @p106 :rule bool-impl-elim :args (@t19 @t18)) % 0.35/0.58 (step @p107 :rule cong :premises (@p106) :args (@t34)) % 0.35/0.58 (step @p108 :rule trans :premises (@p107 @p105)) % 0.35/0.58 (step @p109 :rule cong :premises (@p108) :args (@t35)) % 0.35/0.58 (step @p110 :rule trans :premises (@p14 @p109)) % 0.35/0.58 (step @p111 :rule ho_cong :premises (@p110 @p103)) % 0.35/0.58 (step @p112 :rule ho_cong :premises (@p111 @p40)) % 0.35/0.58 (step @p113 :rule ho_cong :premises (@p110 @p75)) % 0.35/0.58 (step @p114 :rule ho_cong :premises (@p113 @p40)) % 0.35/0.58 (step @p115 :rule ho_cong :premises (@p110 @p101)) % 0.35/0.58 (step @p116 :rule ho_cong :premises (@p115 @p40)) % 0.35/0.58 (step @p117 :rule nary_cong :premises (@p116 @p114) :args (@t4)) % 0.35/0.58 (step @p118 :rule cong :premises (@p117 @p112) :args (@t5)) % 0.35/0.58 (step @p119 :rule cong :premises (@p118) :args (@t7)) % 0.35/0.58 (step @p120 :rule cong :premises (@p119) :args (@t8)) % 0.35/0.58 (step @p121 :rule trans :premises (@p120 @p100)) % 0.35/0.58 (step @p122 :rule eq_resolve :premises (@p1 @p121)) % 0.35/0.58 (step @p123 :rule skolemize :premises (@p122)) % 0.35/0.58 (step @p124 :rule bool-double-not-elim :args (@t94)) % 0.35/0.58 (step @p125 :rule refl :args (@t106)) % 0.35/0.58 (step @p126 :rule nary_cong :premises (@p125 @p124) :args ((or @t106 (not @t103)))) % 0.35/0.58 (step @p127 :rule cnf_or_neg :args (@t106 1)) % 0.35/0.58 (step @p128 :rule eq_resolve :premises (@p127 @p126)) % 0.35/0.58 (step @p129 :rule reordering :premises (@p128) :args ((or @t94 @t106))) % 0.35/0.58 (step @p130 :rule chain_m_resolution :premises (@p129 @p123) :args (@t94 @t107 @t108)) % 0.35/0.58 (step @p131 :rule cnf_or_neg :args (@t106 3)) % 0.35/0.58 (step @p132 :rule chain_m_resolution :premises (@p131 @p123) :args ((not @t96) @t107 @t108)) % 0.35/0.58 (step @p133 :rule cnf_or_neg :args (@t106 2)) % 0.35/0.58 (step @p134 :rule chain_m_resolution :premises (@p133 @p123) :args ((not @t102) @t107 @t108)) % 0.35/0.58 (step @p135 :rule bool-double-not-elim :args (@t104)) % 0.35/0.58 (step @p136 :rule nary_cong :premises (@p125 @p135) :args ((or @t106 (not @t105)))) % 0.35/0.58 (step @p137 :rule cnf_or_neg :args (@t106 0)) % 0.35/0.58 (step @p138 :rule eq_resolve :premises (@p137 @p136)) % 0.35/0.58 (step @p139 :rule reordering :premises (@p138) :args ((or @t104 @t106))) % 0.35/0.58 (step @p140 :rule chain_m_resolution :premises (@p139 @p123) :args (@t104 @t107 @t108)) % 0.35/0.58 (step @p141 :rule instantiate :premises (@p140) :args (@t109)) % 0.35/0.58 (step @p142 :rule cnf_or_pos :args (@t110)) % 0.35/0.58 (step @p143 :rule reordering :premises (@p142) :args ((or @t101 @t96 (not @t110)))) % 0.35/0.58 (step @p144 :rule chain_m_resolution :premises (@p143 @p132 @p141) :args (@t101 @t111 (@list @t96 @t110))) % 0.35/0.58 (step @p145 :rule bool-double-not-elim :args (@t97)) % 0.35/0.58 (step @p146 :rule bool-double-not-elim :args (@t100)) % 0.35/0.58 (step @p147 :rule refl :args (@t102)) % 0.35/0.58 (step @p148 :rule nary_cong :premises (@p147 @p146 @p145) :args ((or @t102 (not @t101) (not @t98)))) % 0.35/0.58 (step @p149 :rule cnf_and_neg :args (@t102)) % 0.35/0.58 (step @p150 :rule eq_resolve :premises (@p149 @p148)) % 0.35/0.58 (step @p151 :rule reordering :premises (@p150) :args ((or @t100 @t97 @t102))) % 0.35/0.58 (step @p152 :rule chain_m_resolution :premises (@p151 @p144 @p134) :args (@t97 (@list true true) (@list @t100 @t102))) % 0.35/0.58 (step @p153 :rule cnf_or_pos :args (@t112)) % 0.35/0.58 (step @p154 :rule reordering :premises (@p153) :args ((or @t98 @t96 @t113))) % 0.35/0.58 (step @p155 :rule chain_m_resolution :premises (@p154 @p152 @p132) :args (@t113 (@list false true) (@list @t97 @t96))) % 0.35/0.59 (assume-push @p162 @t94) % 0.35/0.59 (step @p157 :rule instantiate :premises (@p130) :args (@t109)) % 0.35/0.59 (step-pop @p163 :rule scope :premises (@p157)) % 0.35/0.59 (step @p158 :rule process_scope :premises (@p163) :args (@t112)) % 0.35/0.59 (step @p160 :rule implies_elim :premises (@p158)) % 0.35/0.59 (step @p161 false :rule chain_m_resolution :premises (@p160 @p155 @p130) :args (false @t111 (@list @t112 @t94))) % 0.35/0.59 ) % 0.35/0.59 % SZS output end Proof % 0.35/0.59 % cvc5 exiting %------------------------------------------------------------------------------