%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET171^3 : 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 : n023.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 08:47:34 AM UTC 2026 % Result : Theorem 0.37s 0.56s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET171^3 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n023.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 15:07:28 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.37/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.56 % SZS status Theorem % 0.37/0.56 % SZS output start Proof % 0.37/0.56 ( % 0.37/0.56 (declare-sort $$unsorted 0) % 0.37/0.56 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.37/0.56 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.37/0.56 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.37/0.56 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.37/0.56 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.37/0.56 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.37/0.56 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.37/0.56 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.37/0.56 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.37/0.56 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.56 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.37/0.56 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.37/0.56 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.37/0.56 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.37/0.56 (define @t1 () (@var "C" (-> $$unsorted Bool))) % 0.37/0.56 (define @t2 () (@var "A" (-> $$unsorted Bool))) % 0.37/0.56 (define @t3 () (_ tptp.union @t2)) % 0.37/0.56 (define @t4 () (@var "B" (-> $$unsorted Bool))) % 0.37/0.56 (define @t5 () (= (_ @t3 (_ (_ tptp.intersection @t4) @t1)) (_ (_ tptp.intersection (_ @t3 @t4)) (_ @t3 @t1)))) % 0.37/0.56 (define @t6 () (@list @t2 @t4 @t1)) % 0.37/0.56 (define @t7 () (forall @t6 @t5)) % 0.37/0.56 (define @t8 () (not @t7)) % 0.37/0.56 (define @t9 () (@var "X" $$unsorted)) % 0.37/0.56 (define @t10 () (@var "M" (-> $$unsorted Bool))) % 0.37/0.56 (define @t11 () (lambda (@list @t9 @t10) (_ @t10 @t9))) % 0.37/0.56 (define @t12 () (lambda (@list @t9) false)) % 0.37/0.56 (define @t13 () (@var "Y" $$unsorted)) % 0.37/0.56 (define @t14 () (@var "U" $$unsorted)) % 0.37/0.56 (define @t15 () (= @t14 @t9)) % 0.37/0.56 (define @t16 () (lambda (@list @t9 @t13 @t14) (or @t15 (= @t14 @t13)))) % 0.37/0.56 (define @t17 () (lambda (@list @t9 @t14) @t15)) % 0.37/0.56 (define @t18 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.56 (define @t19 () (_ @t18 @t14)) % 0.37/0.56 (define @t20 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.56 (define @t21 () (_ @t20 @t14)) % 0.37/0.56 (define @t22 () (@list @t20 @t18 @t14)) % 0.37/0.56 (define @t23 () (lambda @t22 (or @t21 @t19))) % 0.37/0.56 (define @t24 () (not @t21)) % 0.37/0.56 (define @t25 () (and @t21 (not @t19))) % 0.37/0.56 (define @t26 () (lambda @t22 (or @t25 (and @t24 @t19)))) % 0.37/0.56 (define @t27 () (and @t21 @t19)) % 0.37/0.56 (define @t28 () (lambda @t22 @t27)) % 0.37/0.56 (define @t29 () (lambda @t22 @t25)) % 0.37/0.56 (define @t30 () (lambda (@list @t20 @t14) @t24)) % 0.37/0.56 (define @t31 () (@list @t20 @t18)) % 0.37/0.56 (define @t32 () (lambda @t31 (= (_ (_ tptp.intersection @t20) @t18) tptp.emptyset))) % 0.37/0.56 (define @t33 () (@list @t14)) % 0.37/0.56 (define @t34 () (lambda @t31 (forall @t33 (=> @t21 @t19)))) % 0.37/0.56 (define @t35 () (exists @t33 @t27)) % 0.37/0.56 (define @t36 () (lambda @t31 @t35)) % 0.37/0.56 (define @t37 () (lambda @t31 (not @t35))) % 0.37/0.56 (define @t38 () (_ @t1 @t14)) % 0.37/0.56 (define @t39 () (_ @t1 @t14)) % 0.37/0.56 (define @t40 () (_ @t2 @t14)) % 0.37/0.56 (define @t41 () (_ @t2 @t14)) % 0.37/0.56 (define @t42 () (or @t41 @t39)) % 0.37/0.56 (define @t43 () (_ @t4 @t14)) % 0.37/0.56 (define @t44 () (_ @t4 @t14)) % 0.37/0.56 (define @t45 () (or @t41 @t44)) % 0.37/0.56 (define @t46 () (and @t45 @t42)) % 0.37/0.56 (define @t47 () (lambda @t33 @t46)) % 0.37/0.56 (define @t48 () (and @t44 @t39)) % 0.37/0.56 (define @t49 () (or @t41 @t48)) % 0.37/0.56 (define @t50 () (lambda @t33 @t49)) % 0.37/0.56 (define @t51 () (= @t50 @t47)) % 0.37/0.56 (define @t52 () (lambda @t33 @t42)) % 0.37/0.56 (define @t53 () (_ @t52 @t14)) % 0.37/0.56 (define @t54 () (and @t45 @t53)) % 0.37/0.56 (define @t55 () (lambda @t33 @t54)) % 0.37/0.56 (define @t56 () (@list @t18 @t14)) % 0.37/0.56 (define @t57 () (lambda @t56 (or @t41 @t19))) % 0.37/0.56 (define @t58 () (_ @t23 @t2)) % 0.37/0.56 (define @t59 () (lambda @t33 @t45)) % 0.37/0.56 (define @t60 () (_ @t59 @t14)) % 0.37/0.56 (define @t61 () (and @t60 @t19)) % 0.37/0.56 (define @t62 () (lambda @t56 @t61)) % 0.37/0.56 (define @t63 () (lambda @t33 @t48)) % 0.37/0.56 (define @t64 () (_ @t63 @t14)) % 0.37/0.56 (define @t65 () (or @t41 @t64)) % 0.37/0.56 (define @t66 () (lambda @t33 @t65)) % 0.37/0.56 (define @t67 () (lambda @t56 (and @t44 @t19))) % 0.37/0.56 (define @t68 () (_ @t28 @t4)) % 0.37/0.56 (define @t69 () (= (_ @t58 (_ @t68 @t1)) (_ (_ @t28 (_ @t58 @t4)) (_ @t58 @t1)))) % 0.37/0.56 (define @t70 () (forall @t6 @t69)) % 0.37/0.56 (define @t71 () (forall @t6 (= (lambda @t33 (or @t40 (and @t43 @t38))) (lambda @t33 (and (or @t40 @t43) (or @t40 @t38)))))) % 0.37/0.56 (define @t72 () (@quantifiers_skolemize @t71 2)) % 0.37/0.56 (define @t73 () (_ @t72 @t14)) % 0.37/0.56 (define @t74 () (@quantifiers_skolemize @t71 1)) % 0.37/0.56 (define @t75 () (_ @t74 @t14)) % 0.37/0.56 (define @t76 () (@quantifiers_skolemize @t71 0)) % 0.37/0.56 (define @t77 () (_ @t76 @t14)) % 0.37/0.56 (define @t78 () (lambda @t33 (or @t77 (and @t75 @t73)))) % 0.37/0.56 (define @t79 () (@purify @t78)) % 0.37/0.56 (define @t80 () (lambda @t33 (and (or @t77 @t75) (or @t77 @t73)))) % 0.37/0.56 (define @t81 () (@purify @t80)) % 0.37/0.56 (define @t82 () (= @t81 @t79)) % 0.37/0.56 (define @t83 () (not @t82)) % 0.37/0.56 (define @t84 () (not @t71)) % 0.37/0.56 (define @t85 () (= @t78 @t80)) % 0.37/0.56 (define @t86 () (not @t85)) % 0.37/0.56 (define @t87 () (@list true)) % 0.37/0.56 (define @t88 () (@const 0 $$unsorted)) % 0.37/0.56 (define @t89 () (_ @t72 @t88)) % 0.37/0.56 (define @t90 () (_ @t76 @t88)) % 0.37/0.56 (define @t91 () (or @t90 @t89)) % 0.37/0.56 (define @t92 () (_ @t74 @t88)) % 0.37/0.56 (define @t93 () (or @t90 @t92)) % 0.37/0.56 (define @t94 () (and @t93 @t91)) % 0.37/0.56 (define @t95 () (and @t92 @t89)) % 0.37/0.56 (define @t96 () (or @t90 @t95)) % 0.37/0.56 (define @t97 () (= (_ @t78 @t88) @t96)) % 0.37/0.56 (define @t98 () (_ @t79 @t88)) % 0.37/0.56 (define @t99 () (= (_ @t80 @t88) @t94)) % 0.37/0.56 (define @t100 () (_ @t81 @t88)) % 0.37/0.56 (define @t101 () (= @t100 @t98)) % 0.37/0.56 (define @t102 () (not @t101)) % 0.37/0.56 (define @t103 () (or @t82 @t102)) % 0.37/0.56 (define @t104 () (= @t96 @t94)) % 0.37/0.56 (define @t105 () (not @t95)) % 0.37/0.56 (define @t106 () (not @t96)) % 0.37/0.56 (define @t107 () (not @t94)) % 0.37/0.56 (define @t108 () (not @t92)) % 0.37/0.56 (define @t109 () (@list true true)) % 0.37/0.56 (define @t110 () (not @t93)) % 0.37/0.56 (assume @p1 @t8) % 0.37/0.56 (assume @p2 true) % 0.37/0.56 (step @p3 (= tptp.in @t11) :rule refl :args (@t11)) % 0.37/0.56 (step @p4 (= tptp.is_a @t11) :rule refl :args (@t11)) % 0.37/0.56 (step @p5 (= tptp.emptyset @t12) :rule refl :args (@t12)) % 0.37/0.56 (step @p6 (= tptp.unord_pair @t16) :rule refl :args (@t16)) % 0.37/0.56 (step @p7 (= tptp.singleton @t17) :rule refl :args (@t17)) % 0.37/0.56 (step @p8 (= tptp.union @t23) :rule refl :args (@t23)) % 0.37/0.56 (step @p9 (= tptp.excl_union @t26) :rule refl :args (@t26)) % 0.37/0.56 (step @p10 (= tptp.intersection @t28) :rule refl :args (@t28)) % 0.37/0.56 (step @p11 (= tptp.setminus @t29) :rule refl :args (@t29)) % 0.37/0.56 (step @p12 (= tptp.complement @t30) :rule refl :args (@t30)) % 0.37/0.56 (step @p13 (= tptp.disjoint @t32) :rule refl :args (@t32)) % 0.37/0.56 (step @p14 (= tptp.subset @t34) :rule refl :args (@t34)) % 0.37/0.56 (step @p15 (= tptp.meets @t36) :rule refl :args (@t36)) % 0.37/0.56 (step @p16 (= tptp.misses @t37) :rule refl :args (@t37)) % 0.37/0.56 (step @p17 :rule refl :args (@t38)) % 0.37/0.56 (step @p18 :rule refl :args (@t39)) % 0.37/0.56 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t39 @t38))) % 0.37/0.56 (step @p20 :rule symm :premises (@p19)) % 0.37/0.56 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.37/0.56 (step @p22 :rule refl :args (@t40)) % 0.37/0.56 (step @p23 :rule refl :args (@t41)) % 0.37/0.56 (step @p24 :rule cong :premises (@p23 @p22) :args ((= @t41 @t40))) % 0.37/0.56 (step @p25 :rule symm :premises (@p24)) % 0.37/0.56 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 0.37/0.56 (step @p27 :rule nary_cong :premises (@p26 @p21) :args (@t42)) % 0.37/0.56 (step @p28 :rule refl :args (@t43)) % 0.37/0.56 (step @p29 :rule refl :args (@t44)) % 0.37/0.56 (step @p30 :rule cong :premises (@p29 @p28) :args ((= @t44 @t43))) % 0.37/0.56 (step @p31 :rule symm :premises (@p30)) % 0.37/0.56 (step @p32 :rule eq_resolve :premises (@p29 @p31)) % 0.37/0.56 (step @p33 :rule nary_cong :premises (@p26 @p32) :args (@t45)) % 0.37/0.56 (step @p34 :rule nary_cong :premises (@p33 @p27) :args (@t46)) % 0.37/0.56 (step @p35 :rule cong :premises (@p34) :args (@t47)) % 0.37/0.56 (step @p36 :rule nary_cong :premises (@p32 @p21) :args (@t48)) % 0.37/0.56 (step @p37 :rule nary_cong :premises (@p26 @p36) :args (@t49)) % 0.37/0.56 (step @p38 :rule cong :premises (@p37) :args (@t50)) % 0.37/0.56 (step @p39 :rule cong :premises (@p38 @p35) :args (@t51)) % 0.37/0.56 (step @p40 :rule cong :premises (@p39) :args ((forall @t6 @t51))) % 0.37/0.56 (step @p41 :rule beta-reduce :args ((= @t53 @t42))) % 0.37/0.56 (step @p42 :rule refl :args (@t45)) % 0.37/0.56 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t54)) % 0.37/0.56 (step @p44 :rule cong :premises (@p43) :args (@t55)) % 0.37/0.56 (step @p45 :rule beta-reduce :args ((= (_ (lambda @t56 (and @t45 @t19)) @t52) @t55))) % 0.37/0.56 (step @p46 :rule trans :premises (@p45 @p44)) % 0.37/0.56 (step @p47 :rule beta-reduce :args ((= (_ @t57 @t1) @t52))) % 0.37/0.56 (step @p48 :rule refl :args (@t1)) % 0.37/0.56 (step @p49 :rule beta-reduce :args ((= @t58 @t57))) % 0.37/0.56 (step @p50 :rule ho_cong :premises (@p49 @p48)) % 0.37/0.56 (step @p51 :rule trans :premises (@p50 @p47)) % 0.37/0.56 (step @p52 :rule refl :args (@t19)) % 0.37/0.56 (step @p53 :rule beta-reduce :args ((= @t60 @t45))) % 0.37/0.56 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t61)) % 0.37/0.56 (step @p55 :rule cong :premises (@p54) :args (@t62)) % 0.37/0.56 (step @p56 :rule beta-reduce :args ((= (_ @t28 @t59) @t62))) % 0.37/0.56 (step @p57 :rule trans :premises (@p56 @p55)) % 0.37/0.56 (step @p58 :rule beta-reduce :args ((= (_ @t57 @t4) @t59))) % 0.37/0.56 (step @p59 :rule refl :args (@t4)) % 0.37/0.56 (step @p60 :rule ho_cong :premises (@p49 @p59)) % 0.37/0.56 (step @p61 :rule trans :premises (@p60 @p58)) % 0.37/0.56 (step @p62 :rule refl :args (@t28)) % 0.37/0.56 (step @p63 :rule ho_cong :premises (@p62 @p61)) % 0.37/0.56 (step @p64 :rule trans :premises (@p63 @p57)) % 0.37/0.56 (step @p65 :rule ho_cong :premises (@p64 @p51)) % 0.37/0.56 (step @p66 :rule trans :premises (@p65 @p46)) % 0.37/0.56 (step @p67 :rule beta-reduce :args ((= @t64 @t48))) % 0.37/0.56 (step @p68 :rule refl :args (@t41)) % 0.37/0.56 (step @p69 :rule nary_cong :premises (@p68 @p67) :args (@t65)) % 0.37/0.56 (step @p70 :rule cong :premises (@p69) :args (@t66)) % 0.37/0.56 (step @p71 :rule beta-reduce :args ((= (_ @t57 @t63) @t66))) % 0.37/0.56 (step @p72 :rule trans :premises (@p71 @p70)) % 0.37/0.56 (step @p73 :rule beta-reduce :args ((= (_ @t67 @t1) @t63))) % 0.37/0.56 (step @p74 :rule beta-reduce :args ((= @t68 @t67))) % 0.37/0.56 (step @p75 :rule ho_cong :premises (@p74 @p48)) % 0.37/0.56 (step @p76 :rule trans :premises (@p75 @p73)) % 0.37/0.56 (step @p77 :rule ho_cong :premises (@p49 @p76)) % 0.37/0.56 (step @p78 :rule trans :premises (@p77 @p72)) % 0.37/0.56 (step @p79 :rule cong :premises (@p78 @p66) :args (@t69)) % 0.37/0.56 (step @p80 :rule cong :premises (@p79) :args (@t70)) % 0.37/0.56 (step @p81 :rule trans :premises (@p80 @p40)) % 0.37/0.56 (step @p82 :rule cong :premises (@p81) :args ((not @t70))) % 0.37/0.56 (step @p83 :rule refl :args (@t2)) % 0.37/0.56 (step @p84 :rule ho_cong :premises (@p8 @p83)) % 0.37/0.56 (step @p85 :rule ho_cong :premises (@p84 @p48)) % 0.37/0.56 (step @p86 :rule ho_cong :premises (@p84 @p59)) % 0.37/0.56 (step @p87 :rule ho_cong :premises (@p10 @p86)) % 0.37/0.56 (step @p88 :rule ho_cong :premises (@p87 @p85)) % 0.37/0.56 (step @p89 :rule ho_cong :premises (@p10 @p59)) % 0.37/0.56 (step @p90 :rule ho_cong :premises (@p89 @p48)) % 0.37/0.56 (step @p91 :rule ho_cong :premises (@p84 @p90)) % 0.37/0.56 (step @p92 :rule cong :premises (@p91 @p88) :args (@t5)) % 0.37/0.56 (step @p93 :rule cong :premises (@p92) :args (@t7)) % 0.37/0.56 (step @p94 :rule cong :premises (@p93) :args (@t8)) % 0.37/0.56 (step @p95 :rule trans :premises (@p94 @p82)) % 0.37/0.56 (step @p96 :rule eq_resolve :premises (@p1 @p95)) % 0.37/0.56 (step @p97 :rule refl :args (@t83)) % 0.37/0.56 (step @p98 :rule bool-double-not-elim :args (@t71)) % 0.37/0.56 (step @p99 :rule nary_cong :premises (@p98 @p97) :args ((or (not @t84) @t83))) % 0.37/0.56 (step @p100 :rule eq-symm :args (@t79 @t81)) % 0.37/0.56 (step @p101 :rule eq-refl :args (@t80)) % 0.37/0.56 (step @p102 :rule skolem_intro :args (@t81)) % 0.37/0.56 (step @p103 :rule refl :args (@t80)) % 0.37/0.56 (step @p104 :rule cong :premises (@p103 @p102) :args ((= @t80 @t81))) % 0.37/0.56 (step @p105 :rule trans :premises (@p104 @p101)) % 0.37/0.56 (step @p106 :rule true_elim :premises (@p105)) % 0.37/0.56 (step @p107 :rule eq-refl :args (@t78)) % 0.37/0.56 (step @p108 :rule skolem_intro :args (@t79)) % 0.37/0.56 (step @p109 :rule refl :args (@t78)) % 0.37/0.56 (step @p110 :rule cong :premises (@p109 @p108) :args ((= @t78 @t79))) % 0.37/0.56 (step @p111 :rule trans :premises (@p110 @p107)) % 0.37/0.56 (step @p112 :rule true_elim :premises (@p111)) % 0.37/0.56 (step @p113 :rule cong :premises (@p112 @p106) :args (@t85)) % 0.37/0.56 (step @p114 :rule trans :premises (@p113 @p100)) % 0.37/0.56 (step @p115 :rule cong :premises (@p114) :args (@t86)) % 0.37/0.56 (step @p116 :rule refl :args (@t84)) % 0.37/0.56 (step @p117 :rule cong :premises (@p116 @p115) :args ((=> @t84 @t86))) % 0.37/0.56 (assume-push @p188 @t84) % 0.37/0.56 (step @p119 :rule skolemize :premises (@p96)) % 0.37/0.56 (step-pop @p189 :rule scope :premises (@p119)) % 0.37/0.56 (step @p120 :rule process_scope :premises (@p189) :args (@t86)) % 0.37/0.56 (step @p122 :rule eq_resolve :premises (@p120 @p117)) % 0.37/0.56 (step @p123 :rule implies_elim :premises (@p122)) % 0.37/0.56 (step @p124 :rule eq_resolve :premises (@p123 @p99)) % 0.37/0.56 (step @p125 :rule chain_m_resolution :premises (@p124 @p96) :args (@t83 @t87 (@list @t71))) % 0.37/0.56 (step @p126 :rule eq-symm :args (@t94 @t96)) % 0.37/0.56 (step @p127 :rule eq-refl :args (@t96)) % 0.37/0.56 (step @p128 :rule refl :args (@t96)) % 0.37/0.56 (step @p129 :rule beta-reduce :args (@t97)) % 0.37/0.56 (step @p130 :rule cong :premises (@p129 @p128) :args (@t97)) % 0.37/0.56 (step @p131 :rule trans :premises (@p130 @p127)) % 0.37/0.56 (step @p132 :rule refl :args (@t88)) % 0.37/0.56 (step @p133 :rule ho_cong :premises (@p108 @p132)) % 0.37/0.56 (step @p134 :rule cong :premises (@p133 @p128) :args ((= @t98 @t96))) % 0.37/0.56 (step @p135 :rule trans :premises (@p134 @p131)) % 0.37/0.56 (step @p136 :rule true_elim :premises (@p135)) % 0.37/0.56 (step @p137 :rule eq-refl :args (@t94)) % 0.37/0.56 (step @p138 :rule refl :args (@t94)) % 0.37/0.56 (step @p139 :rule beta-reduce :args (@t99)) % 0.37/0.56 (step @p140 :rule cong :premises (@p139 @p138) :args (@t99)) % 0.37/0.56 (step @p141 :rule trans :premises (@p140 @p137)) % 0.37/0.56 (step @p142 :rule ho_cong :premises (@p102 @p132)) % 0.37/0.56 (step @p143 :rule cong :premises (@p142 @p138) :args ((= @t100 @t94))) % 0.37/0.56 (step @p144 :rule trans :premises (@p143 @p141)) % 0.37/0.56 (step @p145 :rule true_elim :premises (@p144)) % 0.37/0.56 (step @p146 :rule cong :premises (@p145 @p136) :args (@t101)) % 0.37/0.56 (step @p147 :rule trans :premises (@p146 @p126)) % 0.37/0.56 (step @p148 :rule cong :premises (@p147) :args (@t102)) % 0.37/0.56 (step @p149 :rule refl :args (@t82)) % 0.37/0.56 (step @p150 :rule nary_cong :premises (@p149 @p148) :args (@t103)) % 0.37/0.56 ; WARNING: add trust step for TRUST % 0.37/0.56 ; trust TRUST THEORY_LEMMA % 0.37/0.56 (step @p151 :rule trust :premises () :args (@t103)) % 0.37/0.56 (step @p152 :rule eq_resolve :premises (@p151 @p150)) % 0.37/0.56 (step @p153 :rule chain_m_resolution :premises (@p152 @p125) :args ((not @t104) @t87 (@list @t82))) % 0.37/0.56 (step @p154 :rule cnf_and_pos :args (@t95 1)) % 0.37/0.56 (step @p155 :rule reordering :premises (@p154) :args ((or @t89 @t105))) % 0.37/0.56 (step @p156 :rule cnf_or_neg :args (@t96 0)) % 0.37/0.56 (step @p157 :rule cnf_or_neg :args (@t93 0)) % 0.37/0.56 (step @p158 :rule cnf_or_neg :args (@t91 0)) % 0.37/0.56 (step @p159 :rule cnf_equiv_neg2 :args (@t104)) % 0.37/0.56 (step @p160 :rule cnf_and_neg :args (@t94)) % 0.37/0.56 (step @p161 :rule chain_m_resolution :premises (@p160 @p159 @p153 @p158 @p157 @p156) :args ((not @t90) (@list true true false false false) (@list @t94 @t104 @t91 @t93 @t96))) % 0.37/0.56 (step @p162 :rule cnf_or_pos :args (@t91)) % 0.37/0.56 (step @p163 :rule reordering :premises (@p162) :args ((or @t90 @t89 (not @t91)))) % 0.37/0.56 (step @p164 :rule cnf_or_pos :args (@t96)) % 0.37/0.56 (step @p165 :rule reordering :premises (@p164) :args ((or @t90 @t95 @t106))) % 0.37/0.56 (step @p166 :rule cnf_and_pos :args (@t94 1)) % 0.37/0.56 (step @p167 :rule reordering :premises (@p166) :args ((or @t91 @t107))) % 0.37/0.56 (step @p168 :rule cnf_equiv_neg1 :args (@t104)) % 0.37/0.56 (step @p169 :rule reordering :premises (@p168) :args ((or @t96 @t94 @t104))) % 0.37/0.56 (step @p170 :rule chain_m_resolution :premises (@p169 @p153 @p167 @p165 @p161 @p163 @p161 @p155) :args (@t89 (@list true true true true true true true) (@list @t104 @t94 @t96 @t90 @t91 @t90 @t95))) % 0.37/0.56 (step @p171 :rule cnf_or_neg :args (@t93 1)) % 0.37/0.56 (step @p172 :rule cnf_and_neg :args (@t95)) % 0.37/0.56 (step @p173 :rule cnf_or_neg :args (@t91 1)) % 0.37/0.56 (step @p174 :rule cnf_or_neg :args (@t96 1)) % 0.37/0.56 (step @p175 :rule chain_m_resolution :premises (@p159 @p153 @p160 @p174 @p173 @p172 @p171) :args ((or @t108 (not @t89)) (@list true false false false false false) (@list @t104 @t94 @t96 @t91 @t95 @t93))) % 0.37/0.56 (step @p176 :rule chain_m_resolution :premises (@p175 @p170) :args (@t108 (@list false) (@list @t89))) % 0.37/0.56 (step @p177 :rule cnf_and_pos :args (@t95 0)) % 0.37/0.56 (step @p178 :rule reordering :premises (@p177) :args ((or @t92 @t105))) % 0.37/0.56 (step @p179 :rule chain_m_resolution :premises (@p178 @p176) :args (@t105 @t87 (@list @t92))) % 0.37/0.56 (step @p180 :rule chain_m_resolution :premises (@p165 @p161 @p179) :args (@t106 @t109 (@list @t90 @t95))) % 0.37/0.56 (step @p181 :rule cnf_or_pos :args (@t93)) % 0.37/0.56 (step @p182 :rule reordering :premises (@p181) :args ((or @t90 @t92 @t110))) % 0.37/0.56 (step @p183 :rule chain_m_resolution :premises (@p182 @p161 @p176) :args (@t110 @t109 (@list @t90 @t92))) % 0.37/0.56 (step @p184 :rule cnf_and_pos :args (@t94 0)) % 0.37/0.56 (step @p185 :rule reordering :premises (@p184) :args ((or @t93 @t107))) % 0.37/0.56 (step @p186 :rule chain_m_resolution :premises (@p185 @p183) :args (@t107 @t87 (@list @t93))) % 0.37/0.56 (step @p187 false :rule chain_m_resolution :premises (@p169 @p186 @p180 @p153) :args (false (@list true true true) (@list @t94 @t96 @t104))) % 0.37/0.56 ) % 0.37/0.56 % SZS output end Proof % 0.37/0.56 % cvc5 exiting %------------------------------------------------------------------------------