%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET066^1 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n013.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 08:47:13 AM UTC 2026 % Result : Theorem 0.38s 0.58s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET066^1 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n013.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 14:50:00 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.51 %----Proving TH0 % 0.38/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.58 % SZS status Theorem % 0.38/0.58 % SZS output start Proof % 0.38/0.58 ( % 0.38/0.58 (declare-sort $$unsorted 0) % 0.38/0.58 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.38/0.58 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.38/0.58 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.38/0.58 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.38/0.58 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.38/0.58 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.38/0.58 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.38/0.58 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.38/0.58 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.38/0.58 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.38/0.58 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.38/0.58 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.38/0.58 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.38/0.58 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.38/0.58 (define @t1 () (@var "X" $$unsorted)) % 0.38/0.58 (define @t2 () (@var "Y" $$unsorted)) % 0.38/0.58 (define @t3 () (= (_ (_ tptp.unord_pair @t1) @t2) (_ (_ tptp.unord_pair @t2) @t1))) % 0.38/0.58 (define @t4 () (@list @t1 @t2)) % 0.38/0.58 (define @t5 () (forall @t4 @t3)) % 0.38/0.58 (define @t6 () (not @t5)) % 0.38/0.58 (define @t7 () (@var "M" (-> $$unsorted Bool))) % 0.38/0.58 (define @t8 () (lambda (@list @t1 @t7) (_ @t7 @t1))) % 0.38/0.58 (define @t9 () (lambda (@list @t1) false)) % 0.38/0.58 (define @t10 () (@var "U" $$unsorted)) % 0.38/0.58 (define @t11 () (= @t10 @t1)) % 0.38/0.58 (define @t12 () (or @t11 (= @t10 @t2))) % 0.38/0.58 (define @t13 () (@list @t1 @t2 @t10)) % 0.38/0.58 (define @t14 () (lambda @t13 @t12)) % 0.38/0.58 (define @t15 () (lambda (@list @t1 @t10) @t11)) % 0.38/0.58 (define @t16 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.58 (define @t17 () (_ @t16 @t10)) % 0.38/0.58 (define @t18 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.58 (define @t19 () (_ @t18 @t10)) % 0.38/0.58 (define @t20 () (@list @t18 @t16 @t10)) % 0.38/0.58 (define @t21 () (lambda @t20 (or @t19 @t17))) % 0.38/0.58 (define @t22 () (not @t19)) % 0.38/0.58 (define @t23 () (and @t19 (not @t17))) % 0.38/0.58 (define @t24 () (lambda @t20 (or @t23 (and @t22 @t17)))) % 0.38/0.58 (define @t25 () (and @t19 @t17)) % 0.38/0.58 (define @t26 () (lambda @t20 @t25)) % 0.38/0.58 (define @t27 () (lambda @t20 @t23)) % 0.38/0.58 (define @t28 () (lambda (@list @t18 @t10) @t22)) % 0.38/0.58 (define @t29 () (@list @t18 @t16)) % 0.38/0.58 (define @t30 () (lambda @t29 (= (_ (_ tptp.intersection @t18) @t16) tptp.emptyset))) % 0.38/0.58 (define @t31 () (@list @t10)) % 0.38/0.58 (define @t32 () (lambda @t29 (forall @t31 (=> @t19 @t17)))) % 0.38/0.58 (define @t33 () (exists @t31 @t25)) % 0.38/0.58 (define @t34 () (lambda @t29 @t33)) % 0.38/0.58 (define @t35 () (lambda @t29 (not @t33))) % 0.38/0.58 (define @t36 () (= @t2 @t10)) % 0.38/0.58 (define @t37 () (or @t36 @t11)) % 0.38/0.58 (define @t38 () (lambda @t31 @t37)) % 0.38/0.58 (define @t39 () (@var "BOUND_VARIABLE_7632" $$unsorted)) % 0.38/0.58 (define @t40 () (= @t10 @t39)) % 0.38/0.58 (define @t41 () (lambda (@list @t39 @t10) (or @t36 @t40))) % 0.38/0.58 (define @t42 () (= @t1 @t10)) % 0.38/0.58 (define @t43 () (@list @t1 @t39 @t10)) % 0.38/0.58 (define @t44 () (or @t42 (= @t39 @t10))) % 0.38/0.58 (define @t45 () (or @t42 @t36)) % 0.38/0.58 (define @t46 () (lambda @t13 @t45)) % 0.38/0.58 (define @t47 () (lambda @t31 @t45)) % 0.38/0.58 (define @t48 () (lambda (@list @t2 @t10) @t45)) % 0.38/0.58 (define @t49 () (_ @t46 @t1)) % 0.38/0.58 (define @t50 () (= (_ @t49 @t2) (_ (_ @t46 @t2) @t1))) % 0.38/0.58 (define @t51 () (forall @t4 @t50)) % 0.38/0.58 (define @t52 () (forall @t4 (= @t47 (lambda @t31 (or @t36 @t42))))) % 0.38/0.58 (define @t53 () (@quantifiers_skolemize @t52 1)) % 0.38/0.58 (define @t54 () (= @t10 @t53)) % 0.38/0.58 (define @t55 () (@quantifiers_skolemize @t52 0)) % 0.38/0.58 (define @t56 () (= @t10 @t55)) % 0.38/0.58 (define @t57 () (lambda @t31 (or @t56 @t54))) % 0.38/0.58 (define @t58 () (@purify @t57)) % 0.38/0.58 (define @t59 () (lambda @t31 (or @t54 @t56))) % 0.38/0.58 (define @t60 () (@purify @t59)) % 0.38/0.58 (define @t61 () (= @t60 @t58)) % 0.38/0.58 (define @t62 () (not @t61)) % 0.38/0.58 (define @t63 () (not @t52)) % 0.38/0.58 (define @t64 () (= @t57 @t59)) % 0.38/0.58 (define @t65 () (not @t64)) % 0.38/0.58 (define @t66 () (= @t55 @t10)) % 0.38/0.58 (define @t67 () (= @t53 @t10)) % 0.38/0.58 (define @t68 () (or @t67 @t66)) % 0.38/0.58 (define @t69 () (lambda @t31 @t68)) % 0.38/0.58 (define @t70 () (or @t66 @t67)) % 0.38/0.58 (define @t71 () (lambda @t31 @t70)) % 0.38/0.58 (define @t72 () (= @t71 @t69)) % 0.38/0.58 (define @t73 () (not @t72)) % 0.38/0.58 (define @t74 () (@list true)) % 0.38/0.58 (define @t75 () (@const 0 $$unsorted)) % 0.38/0.58 (define @t76 () (= @t55 @t75)) % 0.38/0.58 (define @t77 () (= @t53 @t75)) % 0.38/0.58 (define @t78 () (or @t77 @t76)) % 0.38/0.58 (define @t79 () (or @t76 @t77)) % 0.38/0.58 (define @t80 () (= @t79 @t78)) % 0.38/0.58 (define @t81 () (= @t75 @t53)) % 0.38/0.58 (define @t82 () (= @t75 @t55)) % 0.38/0.58 (define @t83 () (or @t82 @t81)) % 0.38/0.58 (define @t84 () (_ @t57 @t75)) % 0.38/0.58 (define @t85 () (_ @t58 @t75)) % 0.38/0.58 (define @t86 () (or @t81 @t82)) % 0.38/0.58 (define @t87 () (_ @t59 @t75)) % 0.38/0.58 (define @t88 () (_ @t60 @t75)) % 0.38/0.58 (define @t89 () (= @t88 @t85)) % 0.38/0.58 (define @t90 () (not @t89)) % 0.38/0.58 (define @t91 () (or @t61 @t90)) % 0.38/0.58 (define @t92 () (@list true false false)) % 0.38/0.58 (define @t93 () (@list @t80 @t78 @t79)) % 0.38/0.58 (define @t94 () (not @t79)) % 0.38/0.58 (define @t95 () (@list true true)) % 0.38/0.58 (define @t96 () (@list @t76 @t77)) % 0.38/0.58 (define @t97 () (not @t78)) % 0.38/0.58 (assume @p1 @t6) % 0.38/0.58 (assume @p2 true) % 0.38/0.58 (step @p3 (= tptp.in @t8) :rule refl :args (@t8)) % 0.38/0.58 (step @p4 (= tptp.is_a @t8) :rule refl :args (@t8)) % 0.38/0.58 (step @p5 (= tptp.emptyset @t9) :rule refl :args (@t9)) % 0.38/0.58 (step @p6 (= tptp.unord_pair @t14) :rule refl :args (@t14)) % 0.38/0.58 (step @p7 (= tptp.singleton @t15) :rule refl :args (@t15)) % 0.38/0.58 (step @p8 (= tptp.union @t21) :rule refl :args (@t21)) % 0.38/0.58 (step @p9 (= tptp.excl_union @t24) :rule refl :args (@t24)) % 0.38/0.58 (step @p10 (= tptp.intersection @t26) :rule refl :args (@t26)) % 0.38/0.58 (step @p11 (= tptp.setminus @t27) :rule refl :args (@t27)) % 0.38/0.58 (step @p12 (= tptp.complement @t28) :rule refl :args (@t28)) % 0.38/0.58 (step @p13 (= tptp.disjoint @t30) :rule refl :args (@t30)) % 0.38/0.58 (step @p14 (= tptp.subset @t32) :rule refl :args (@t32)) % 0.38/0.58 (step @p15 (= tptp.meets @t34) :rule refl :args (@t34)) % 0.38/0.58 (step @p16 (= tptp.misses @t35) :rule refl :args (@t35)) % 0.38/0.58 (step @p17 :rule eq-symm :args (@t10 @t1)) % 0.38/0.58 (step @p18 :rule refl :args (@t36)) % 0.38/0.58 (step @p19 :rule nary_cong :premises (@p18 @p17) :args (@t37)) % 0.38/0.58 (step @p20 :rule cong :premises (@p19) :args (@t38)) % 0.38/0.58 (step @p21 :rule beta-reduce :args ((= (_ @t41 @t1) @t38))) % 0.38/0.58 (step @p22 :rule trans :premises (@p21 @p20)) % 0.38/0.58 (step @p23 :rule refl :args (@t1)) % 0.38/0.58 (step @p24 :rule beta-reduce :args ((= (_ (lambda @t43 (or @t42 @t40)) @t2) @t41))) % 0.38/0.58 (step @p25 :rule refl :args (@t2)) % 0.38/0.58 (step @p26 :rule eq-symm :args (@t39 @t10)) % 0.38/0.58 (step @p27 :rule refl :args (@t42)) % 0.38/0.58 (step @p28 :rule nary_cong :premises (@p27 @p26) :args (@t44)) % 0.38/0.58 (step @p29 :rule cong :premises (@p28) :args ((lambda @t43 @t44))) % 0.38/0.58 (step @p30 :rule ho_cong :premises (@p29 @p25)) % 0.38/0.58 (step @p31 :rule trans :premises (@p30 @p24)) % 0.38/0.58 (step @p32 :rule refl :args (@t2)) % 0.38/0.58 (step @p33 :rule alpha_equiv :args (@t46 (@list @t2) (@list @t39))) % 0.38/0.58 (step @p34 :rule ho_cong :premises (@p33 @p32)) % 0.38/0.58 (step @p35 :rule trans :premises (@p34 @p31)) % 0.38/0.58 (step @p36 :rule ho_cong :premises (@p35 @p23)) % 0.38/0.58 (step @p37 :rule trans :premises (@p36 @p22)) % 0.38/0.58 (step @p38 :rule beta-reduce :args ((= (_ @t48 @t2) @t47))) % 0.38/0.58 (step @p39 :rule beta-reduce :args ((= @t49 @t48))) % 0.38/0.58 (step @p40 :rule ho_cong :premises (@p39 @p25)) % 0.38/0.58 (step @p41 :rule trans :premises (@p40 @p38)) % 0.38/0.58 (step @p42 :rule cong :premises (@p41 @p37) :args (@t50)) % 0.38/0.58 (step @p43 :rule cong :premises (@p42) :args (@t51)) % 0.38/0.58 (step @p44 :rule cong :premises (@p43) :args ((not @t51))) % 0.38/0.58 (step @p45 :rule eq-symm :args (@t10 @t2)) % 0.38/0.58 (step @p46 :rule nary_cong :premises (@p17 @p45) :args (@t12)) % 0.38/0.58 (step @p47 :rule cong :premises (@p46) :args (@t14)) % 0.38/0.58 (step @p48 :rule trans :premises (@p6 @p47)) % 0.38/0.58 (step @p49 :rule ho_cong :premises (@p48 @p25)) % 0.38/0.58 (step @p50 :rule ho_cong :premises (@p49 @p23)) % 0.38/0.58 (step @p51 :rule ho_cong :premises (@p48 @p23)) % 0.38/0.58 (step @p52 :rule ho_cong :premises (@p51 @p25)) % 0.38/0.58 (step @p53 :rule cong :premises (@p52 @p50) :args (@t3)) % 0.38/0.58 (step @p54 :rule cong :premises (@p53) :args (@t5)) % 0.38/0.58 (step @p55 :rule cong :premises (@p54) :args (@t6)) % 0.38/0.58 (step @p56 :rule trans :premises (@p55 @p44)) % 0.38/0.58 (step @p57 :rule eq_resolve :premises (@p1 @p56)) % 0.38/0.58 (step @p58 :rule refl :args (@t62)) % 0.38/0.58 (step @p59 :rule bool-double-not-elim :args (@t52)) % 0.38/0.58 (step @p60 :rule nary_cong :premises (@p59 @p58) :args ((or (not @t63) @t62))) % 0.38/0.58 (step @p61 :rule eq-symm :args (@t58 @t60)) % 0.38/0.58 (step @p62 :rule eq-refl :args (@t59)) % 0.38/0.58 (step @p63 :rule skolem_intro :args (@t60)) % 0.38/0.58 (step @p64 :rule refl :args (@t59)) % 0.38/0.58 (step @p65 :rule cong :premises (@p64 @p63) :args ((= @t59 @t60))) % 0.38/0.58 (step @p66 :rule trans :premises (@p65 @p62)) % 0.38/0.58 (step @p67 :rule true_elim :premises (@p66)) % 0.38/0.58 (step @p68 :rule eq-refl :args (@t57)) % 0.38/0.58 (step @p69 :rule skolem_intro :args (@t58)) % 0.38/0.58 (step @p70 :rule refl :args (@t57)) % 0.38/0.58 (step @p71 :rule cong :premises (@p70 @p69) :args ((= @t57 @t58))) % 0.38/0.58 (step @p72 :rule trans :premises (@p71 @p68)) % 0.38/0.58 (step @p73 :rule true_elim :premises (@p72)) % 0.38/0.58 (step @p74 :rule cong :premises (@p73 @p67) :args (@t64)) % 0.38/0.58 (step @p75 :rule trans :premises (@p74 @p61)) % 0.38/0.58 (step @p76 :rule cong :premises (@p75) :args (@t65)) % 0.38/0.58 (step @p77 :rule refl :args (@t63)) % 0.38/0.58 (step @p78 :rule cong :premises (@p77 @p76) :args ((=> @t63 @t65))) % 0.38/0.58 (step @p79 :rule eq-symm :args (@t55 @t10)) % 0.38/0.58 (step @p80 :rule eq-symm :args (@t53 @t10)) % 0.38/0.58 (step @p81 :rule nary_cong :premises (@p80 @p79) :args (@t68)) % 0.38/0.58 (step @p82 :rule cong :premises (@p81) :args (@t69)) % 0.38/0.58 (step @p83 :rule nary_cong :premises (@p79 @p80) :args (@t70)) % 0.38/0.58 (step @p84 :rule cong :premises (@p83) :args (@t71)) % 0.38/0.58 (step @p85 :rule cong :premises (@p84 @p82) :args (@t72)) % 0.38/0.58 (step @p86 :rule cong :premises (@p85) :args (@t73)) % 0.38/0.58 (step @p87 :rule cong :premises (@p77 @p86) :args ((=> @t63 @t73))) % 0.38/0.58 (step @p88 :rule trans :premises (@p87 @p78)) % 0.38/0.58 (assume-push @p149 @t63) % 0.38/0.58 (step @p90 :rule skolemize :premises (@p57)) % 0.38/0.58 (step-pop @p150 :rule scope :premises (@p90)) % 0.38/0.58 (step @p91 :rule process_scope :premises (@p150) :args (@t73)) % 0.38/0.58 (step @p93 :rule eq_resolve :premises (@p91 @p88)) % 0.38/0.58 (step @p94 :rule implies_elim :premises (@p93)) % 0.38/0.58 (step @p95 :rule eq_resolve :premises (@p94 @p60)) % 0.38/0.58 (step @p96 :rule chain_m_resolution :premises (@p95 @p57) :args (@t62 @t74 (@list @t52))) % 0.38/0.58 (step @p97 :rule aci_norm :args (@t80)) % 0.38/0.58 (step @p98 :rule symm :premises (@p97)) % 0.38/0.58 (step @p99 :rule cong :premises (@p98 @p97) :args ((= @t78 @t79))) % 0.38/0.58 (step @p100 :rule eq-refl :args (@t79)) % 0.38/0.58 (step @p101 :rule refl :args (@t79)) % 0.38/0.58 (step @p102 :rule eq-symm :args (@t75 @t53)) % 0.38/0.58 (step @p103 :rule eq-symm :args (@t75 @t55)) % 0.38/0.58 (step @p104 :rule nary_cong :premises (@p103 @p102) :args (@t83)) % 0.38/0.58 (step @p105 :rule beta-reduce :args ((= @t84 @t83))) % 0.38/0.58 (step @p106 :rule trans :premises (@p105 @p104)) % 0.38/0.58 (step @p107 :rule cong :premises (@p106 @p101) :args ((= @t84 @t79))) % 0.38/0.58 (step @p108 :rule trans :premises (@p107 @p100)) % 0.38/0.58 (step @p109 :rule refl :args (@t75)) % 0.38/0.58 (step @p110 :rule ho_cong :premises (@p69 @p109)) % 0.38/0.58 (step @p111 :rule cong :premises (@p110 @p101) :args ((= @t85 @t79))) % 0.38/0.58 (step @p112 :rule trans :premises (@p111 @p108)) % 0.38/0.58 (step @p113 :rule true_elim :premises (@p112)) % 0.38/0.58 (step @p114 :rule eq-refl :args (@t78)) % 0.38/0.58 (step @p115 :rule refl :args (@t78)) % 0.38/0.58 (step @p116 :rule nary_cong :premises (@p102 @p103) :args (@t86)) % 0.38/0.58 (step @p117 :rule beta-reduce :args ((= @t87 @t86))) % 0.38/0.58 (step @p118 :rule trans :premises (@p117 @p116)) % 0.38/0.58 (step @p119 :rule cong :premises (@p118 @p115) :args ((= @t87 @t78))) % 0.38/0.58 (step @p120 :rule trans :premises (@p119 @p114)) % 0.38/0.58 (step @p121 :rule ho_cong :premises (@p63 @p109)) % 0.38/0.58 (step @p122 :rule cong :premises (@p121 @p115) :args ((= @t88 @t78))) % 0.38/0.58 (step @p123 :rule trans :premises (@p122 @p120)) % 0.38/0.58 (step @p124 :rule true_elim :premises (@p123)) % 0.38/0.58 (step @p125 :rule cong :premises (@p124 @p113) :args (@t89)) % 0.38/0.58 (step @p126 :rule trans :premises (@p125 @p99)) % 0.38/0.58 (step @p127 :rule cong :premises (@p126) :args (@t90)) % 0.38/0.58 (step @p128 :rule refl :args (@t61)) % 0.38/0.58 (step @p129 :rule nary_cong :premises (@p128 @p127) :args (@t91)) % 0.38/0.58 ; WARNING: add trust step for TRUST % 0.38/0.58 ; trust TRUST THEORY_LEMMA % 0.38/0.58 (step @p130 :rule trust :premises () :args (@t91)) % 0.38/0.58 (step @p131 :rule eq_resolve :premises (@p130 @p129)) % 0.38/0.58 (step @p132 :rule chain_m_resolution :premises (@p131 @p96) :args ((not @t80) @t74 (@list @t61))) % 0.38/0.58 (step @p133 :rule cnf_or_neg :args (@t79 1)) % 0.38/0.58 (step @p134 :rule cnf_or_neg :args (@t78 0)) % 0.38/0.58 (step @p135 :rule cnf_equiv_neg2 :args (@t80)) % 0.38/0.58 (step @p136 :rule chain_m_resolution :premises (@p135 @p132 @p134 @p133) :args ((not @t77) @t92 @t93)) % 0.38/0.58 (step @p137 :rule cnf_or_neg :args (@t79 0)) % 0.38/0.58 (step @p138 :rule cnf_or_neg :args (@t78 1)) % 0.38/0.58 (step @p139 :rule chain_m_resolution :premises (@p135 @p132 @p138 @p137) :args ((not @t76) @t92 @t93)) % 0.38/0.58 (step @p140 :rule cnf_or_pos :args (@t79)) % 0.38/0.58 (step @p141 :rule reordering :premises (@p140) :args ((or @t76 @t77 @t94))) % 0.38/0.58 (step @p142 :rule chain_m_resolution :premises (@p141 @p139 @p136) :args (@t94 @t95 @t96)) % 0.38/0.58 (step @p143 :rule cnf_or_pos :args (@t78)) % 0.38/0.58 (step @p144 :rule reordering :premises (@p143) :args ((or @t76 @t77 @t97))) % 0.38/0.58 (step @p145 :rule chain_m_resolution :premises (@p144 @p139 @p136) :args (@t97 @t95 @t96)) % 0.38/0.58 (step @p146 :rule cnf_equiv_neg1 :args (@t80)) % 0.38/0.58 (step @p147 :rule reordering :premises (@p146) :args ((or @t79 @t78 @t80))) % 0.38/0.58 (step @p148 false :rule chain_m_resolution :premises (@p147 @p145 @p142 @p132) :args (false (@list true true true) (@list @t78 @t79 @t80))) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------