%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET096^1 : 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 : n009.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 08:47:22 AM UTC 2026 % Result : Theorem 0.39s 0.57s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET096^1 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n009.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 14:52:29 EDT 2026 % 0.18/0.34 % CPUTime : % 0.32/0.49 %----Proving TH0 % 0.39/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.57 % SZS status Theorem % 0.39/0.57 % SZS output start Proof % 0.39/0.57 ( % 0.39/0.57 (declare-sort $$unsorted 0) % 0.39/0.57 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.39/0.57 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.39/0.57 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.39/0.57 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.39/0.57 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.39/0.57 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.39/0.57 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.39/0.57 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.39/0.57 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.39/0.57 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.39/0.57 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.39/0.57 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.39/0.57 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.39/0.57 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.39/0.57 (define @t1 () (@var "Y" $$unsorted)) % 0.39/0.57 (define @t2 () (_ tptp.singleton @t1)) % 0.39/0.57 (define @t3 () (@var "X" (-> $$unsorted Bool))) % 0.39/0.57 (define @t4 () (= @t3 @t2)) % 0.39/0.57 (define @t5 () (= @t3 tptp.emptyset)) % 0.39/0.57 (define @t6 () (or @t5 @t4)) % 0.39/0.57 (define @t7 () (=> (_ (_ tptp.subset @t3) @t2) @t6)) % 0.39/0.57 (define @t8 () (@list @t3 @t1)) % 0.39/0.57 (define @t9 () (forall @t8 @t7)) % 0.39/0.57 (define @t10 () (not @t9)) % 0.39/0.57 (define @t11 () (@var "X" $$unsorted)) % 0.39/0.57 (define @t12 () (@var "M" (-> $$unsorted Bool))) % 0.39/0.57 (define @t13 () (lambda (@list @t11 @t12) (_ @t12 @t11))) % 0.39/0.57 (define @t14 () (lambda (@list @t11) false)) % 0.39/0.57 (define @t15 () (@var "U" $$unsorted)) % 0.39/0.57 (define @t16 () (= @t15 @t11)) % 0.39/0.57 (define @t17 () (lambda (@list @t11 @t1 @t15) (or @t16 (= @t15 @t1)))) % 0.39/0.57 (define @t18 () (@list @t11 @t15)) % 0.39/0.57 (define @t19 () (lambda @t18 @t16)) % 0.39/0.57 (define @t20 () (@var "Y" (-> $$unsorted Bool))) % 0.39/0.57 (define @t21 () (_ @t20 @t15)) % 0.39/0.57 (define @t22 () (_ @t3 @t15)) % 0.39/0.57 (define @t23 () (@list @t3 @t20 @t15)) % 0.39/0.57 (define @t24 () (lambda @t23 (or @t22 @t21))) % 0.39/0.57 (define @t25 () (not @t22)) % 0.39/0.57 (define @t26 () (and @t22 (not @t21))) % 0.39/0.57 (define @t27 () (lambda @t23 (or @t26 (and @t25 @t21)))) % 0.39/0.57 (define @t28 () (and @t22 @t21)) % 0.39/0.57 (define @t29 () (lambda @t23 @t28)) % 0.39/0.57 (define @t30 () (lambda @t23 @t26)) % 0.39/0.57 (define @t31 () (lambda (@list @t3 @t15) @t25)) % 0.39/0.57 (define @t32 () (@list @t3 @t20)) % 0.39/0.57 (define @t33 () (lambda @t32 (= (_ (_ tptp.intersection @t3) @t20) tptp.emptyset))) % 0.39/0.57 (define @t34 () (@list @t15)) % 0.39/0.57 (define @t35 () (forall @t34 (=> @t22 @t21))) % 0.39/0.57 (define @t36 () (lambda @t32 @t35)) % 0.39/0.57 (define @t37 () (exists @t34 @t28)) % 0.39/0.57 (define @t38 () (lambda @t32 @t37)) % 0.39/0.57 (define @t39 () (lambda @t32 (not @t37))) % 0.39/0.57 (define @t40 () (= @t1 @t15)) % 0.39/0.57 (define @t41 () (lambda @t34 @t40)) % 0.39/0.57 (define @t42 () (= @t3 @t41)) % 0.39/0.57 (define @t43 () (@var "BOUND_VARIABLE_7703" $$unsorted)) % 0.39/0.57 (define @t44 () (lambda (@list @t43) false)) % 0.39/0.57 (define @t45 () (= @t3 @t44)) % 0.39/0.57 (define @t46 () (_ @t3 @t15)) % 0.39/0.57 (define @t47 () (not @t46)) % 0.39/0.57 (define @t48 () (forall @t34 (or @t47 @t40))) % 0.39/0.57 (define @t49 () (not @t48)) % 0.39/0.57 (define @t50 () (or @t49 @t45 @t42)) % 0.39/0.57 (define @t51 () (or @t45 @t42)) % 0.39/0.57 (define @t52 () (_ (lambda @t18 (= @t11 @t15)) @t1)) % 0.39/0.57 (define @t53 () (= @t3 @t52)) % 0.39/0.57 (define @t54 () (= @t3 @t14)) % 0.39/0.57 (define @t55 () (or @t54 @t53)) % 0.39/0.57 (define @t56 () (_ @t41 @t15)) % 0.39/0.57 (define @t57 () (or @t47 @t56)) % 0.39/0.57 (define @t58 () (forall @t34 @t57)) % 0.39/0.57 (define @t59 () (_ @t20 @t15)) % 0.39/0.57 (define @t60 () (forall @t34 (or @t47 @t59))) % 0.39/0.57 (define @t61 () (lambda (@list @t20) @t60)) % 0.39/0.57 (define @t62 () (_ (lambda @t32 @t60) @t3)) % 0.39/0.57 (define @t63 () (=> (_ @t62 @t52) @t55)) % 0.39/0.57 (define @t64 () (forall @t8 @t63)) % 0.39/0.57 (define @t65 () (or @t25 @t21)) % 0.39/0.57 (define @t66 () (forall @t8 @t50)) % 0.39/0.57 (define @t67 () (@quantifiers_skolemize @t66 1)) % 0.39/0.57 (define @t68 () (= @t15 @t67)) % 0.39/0.57 (define @t69 () (lambda @t34 @t68)) % 0.39/0.57 (define @t70 () (@purify @t69)) % 0.39/0.57 (define @t71 () (@quantifiers_skolemize @t66 0)) % 0.39/0.57 (define @t72 () (= @t71 @t70)) % 0.39/0.57 (define @t73 () (@purify @t44)) % 0.39/0.57 (define @t74 () (= @t71 @t73)) % 0.39/0.57 (define @t75 () (not (_ @t71 @t15))) % 0.39/0.57 (define @t76 () (forall @t34 (or @t75 @t68))) % 0.39/0.57 (define @t77 () (not @t76)) % 0.39/0.57 (define @t78 () (or @t77 @t74 @t72)) % 0.39/0.57 (define @t79 () (not @t78)) % 0.39/0.57 (define @t80 () (not @t66)) % 0.39/0.57 (define @t81 () (= @t71 @t69)) % 0.39/0.57 (define @t82 () (= @t44 @t71)) % 0.39/0.57 (define @t83 () (or @t77 @t82 @t81)) % 0.39/0.57 (define @t84 () (not @t83)) % 0.39/0.57 (define @t85 () (= @t67 @t15)) % 0.39/0.57 (define @t86 () (lambda @t34 @t85)) % 0.39/0.57 (define @t87 () (= @t71 @t86)) % 0.39/0.57 (define @t88 () (or @t75 @t85)) % 0.39/0.57 (define @t89 () (forall @t34 @t88)) % 0.39/0.57 (define @t90 () (not @t89)) % 0.39/0.57 (define @t91 () (or @t90 (= @t71 @t44) @t87)) % 0.39/0.57 (define @t92 () (not @t91)) % 0.39/0.57 (define @t93 () (@list true)) % 0.39/0.57 (define @t94 () (@list @t78)) % 0.39/0.57 (define @t95 () (@const 0 $$unsorted)) % 0.39/0.57 (define @t96 () (= @t67 @t95)) % 0.39/0.57 (define @t97 () (= @t95 @t67)) % 0.39/0.57 (define @t98 () (_ @t69 @t95)) % 0.39/0.57 (define @t99 () (_ @t70 @t95)) % 0.39/0.57 (define @t100 () (_ @t71 @t95)) % 0.39/0.57 (define @t101 () (= @t100 @t99)) % 0.39/0.57 (define @t102 () (not @t101)) % 0.39/0.57 (define @t103 () (or @t72 @t102)) % 0.39/0.57 (define @t104 () (= @t100 @t96)) % 0.39/0.57 (define @t105 () (not @t100)) % 0.39/0.57 (define @t106 () (or @t105 @t97)) % 0.39/0.57 (define @t107 () (or @t105 @t96)) % 0.39/0.57 (define @t108 () (@list false)) % 0.39/0.57 (define @t109 () (@list @t76)) % 0.39/0.57 (define @t110 () (@const 1 $$unsorted)) % 0.39/0.57 (define @t111 () (_ @t71 @t110)) % 0.39/0.57 (define @t112 () (not @t111)) % 0.39/0.57 (define @t113 () (or @t112 (= @t110 @t67))) % 0.39/0.57 (define @t114 () (= @t67 @t110)) % 0.39/0.57 (define @t115 () (or @t112 @t114)) % 0.39/0.57 (define @t116 () (_ @t44 @t110)) % 0.39/0.57 (define @t117 () (_ @t73 @t110)) % 0.39/0.57 (define @t118 () (= @t111 @t117)) % 0.39/0.57 (define @t119 () (not @t118)) % 0.39/0.57 (define @t120 () (or @t74 @t119)) % 0.39/0.57 (assume @p1 @t10) % 0.39/0.57 (assume @p2 true) % 0.39/0.57 (step @p3 (= tptp.in @t13) :rule refl :args (@t13)) % 0.39/0.57 (step @p4 (= tptp.is_a @t13) :rule refl :args (@t13)) % 0.39/0.57 (step @p5 (= tptp.emptyset @t14) :rule refl :args (@t14)) % 0.39/0.57 (step @p6 (= tptp.unord_pair @t17) :rule refl :args (@t17)) % 0.39/0.57 (step @p7 (= tptp.singleton @t19) :rule refl :args (@t19)) % 0.39/0.57 (step @p8 (= tptp.union @t24) :rule refl :args (@t24)) % 0.39/0.57 (step @p9 (= tptp.excl_union @t27) :rule refl :args (@t27)) % 0.39/0.57 (step @p10 (= tptp.intersection @t29) :rule refl :args (@t29)) % 0.39/0.57 (step @p11 (= tptp.setminus @t30) :rule refl :args (@t30)) % 0.39/0.57 (step @p12 (= tptp.complement @t31) :rule refl :args (@t31)) % 0.39/0.57 (step @p13 (= tptp.disjoint @t33) :rule refl :args (@t33)) % 0.39/0.57 (step @p14 (= tptp.subset @t36) :rule refl :args (@t36)) % 0.39/0.57 (step @p15 (= tptp.meets @t38) :rule refl :args (@t38)) % 0.39/0.57 (step @p16 (= tptp.misses @t39) :rule refl :args (@t39)) % 0.39/0.57 (step @p17 :rule evaluate :args ((= true false))) % 0.39/0.57 (step @p18 :rule aci_norm :args ((= (or @t49 @t51) @t50))) % 0.39/0.57 (step @p19 :rule bool-impl-elim :args (@t48 @t51)) % 0.39/0.57 (step @p20 :rule trans :premises (@p19 @p18)) % 0.39/0.57 (step @p21 :rule cong :premises (@p20) :args ((forall @t8 (=> @t48 @t51)))) % 0.39/0.57 (step @p22 :rule beta-reduce :args ((= @t52 @t41))) % 0.39/0.57 (step @p23 :rule refl :args (@t3)) % 0.39/0.57 (step @p24 :rule cong :premises (@p23 @p22) :args (@t53)) % 0.39/0.57 (step @p25 :rule refl :args (@t44)) % 0.39/0.57 (step @p26 :rule symm :premises (@p25)) % 0.39/0.57 (step @p27 :rule alpha_equiv :args (@t14 (@list @t11) (@list @t43))) % 0.39/0.57 (step @p28 :rule trans :premises (@p27 @p26)) % 0.39/0.57 (step @p29 :rule cong :premises (@p23 @p28) :args (@t54)) % 0.39/0.57 (step @p30 :rule nary_cong :premises (@p29 @p24) :args (@t55)) % 0.39/0.57 (step @p31 :rule beta-reduce :args ((= @t56 @t40))) % 0.39/0.57 (step @p32 :rule refl :args (@t47)) % 0.39/0.57 (step @p33 :rule nary_cong :premises (@p32 @p31) :args (@t57)) % 0.39/0.57 (step @p34 :rule cong :premises (@p33) :args (@t58)) % 0.39/0.57 (step @p35 :rule beta-reduce :args ((= (_ @t61 @t41) @t58))) % 0.39/0.57 (step @p36 :rule trans :premises (@p35 @p34)) % 0.39/0.57 (step @p37 :rule beta-reduce :args ((= @t62 @t61))) % 0.39/0.57 (step @p38 :rule ho_cong :premises (@p37 @p22)) % 0.39/0.57 (step @p39 :rule trans :premises (@p38 @p36)) % 0.39/0.57 (step @p40 :rule cong :premises (@p39 @p30) :args (@t63)) % 0.39/0.57 (step @p41 :rule cong :premises (@p40) :args (@t64)) % 0.39/0.57 (step @p42 :rule trans :premises (@p41 @p21)) % 0.39/0.57 (step @p43 :rule cong :premises (@p42) :args ((not @t64))) % 0.39/0.57 (step @p44 :rule refl :args (@t1)) % 0.39/0.57 (step @p45 :rule eq-symm :args (@t15 @t11)) % 0.39/0.57 (step @p46 :rule cong :premises (@p45) :args (@t19)) % 0.39/0.57 (step @p47 :rule trans :premises (@p7 @p46)) % 0.39/0.57 (step @p48 :rule ho_cong :premises (@p47 @p44)) % 0.39/0.57 (step @p49 :rule cong :premises (@p23 @p48) :args (@t4)) % 0.39/0.57 (step @p50 :rule cong :premises (@p23 @p5) :args (@t5)) % 0.39/0.57 (step @p51 :rule nary_cong :premises (@p50 @p49) :args (@t6)) % 0.39/0.57 (step @p52 :rule refl :args (@t59)) % 0.39/0.57 (step @p53 :rule refl :args (@t21)) % 0.39/0.57 (step @p54 :rule cong :premises (@p53 @p52) :args ((= @t21 @t59))) % 0.39/0.57 (step @p55 :rule symm :premises (@p54)) % 0.39/0.57 (step @p56 :rule eq_resolve :premises (@p53 @p55)) % 0.39/0.57 (step @p57 :rule refl :args (@t46)) % 0.39/0.57 (step @p58 :rule refl :args (@t22)) % 0.39/0.57 (step @p59 :rule cong :premises (@p58 @p57) :args ((= @t22 @t46))) % 0.39/0.57 (step @p60 :rule symm :premises (@p59)) % 0.39/0.57 (step @p61 :rule eq_resolve :premises (@p58 @p60)) % 0.39/0.57 (step @p62 :rule cong :premises (@p61) :args (@t25)) % 0.39/0.57 (step @p63 :rule nary_cong :premises (@p62 @p56) :args (@t65)) % 0.39/0.57 (step @p64 :rule cong :premises (@p63) :args ((forall @t34 @t65))) % 0.39/0.57 (step @p65 :rule bool-impl-elim :args (@t22 @t21)) % 0.39/0.57 (step @p66 :rule cong :premises (@p65) :args (@t35)) % 0.39/0.57 (step @p67 :rule trans :premises (@p66 @p64)) % 0.39/0.57 (step @p68 :rule cong :premises (@p67) :args (@t36)) % 0.39/0.57 (step @p69 :rule trans :premises (@p14 @p68)) % 0.39/0.57 (step @p70 :rule ho_cong :premises (@p69 @p23)) % 0.39/0.57 (step @p71 :rule ho_cong :premises (@p70 @p48)) % 0.39/0.57 (step @p72 :rule cong :premises (@p71 @p51) :args (@t7)) % 0.39/0.57 (step @p73 :rule cong :premises (@p72) :args (@t9)) % 0.39/0.57 (step @p74 :rule cong :premises (@p73) :args (@t10)) % 0.39/0.57 (step @p75 :rule trans :premises (@p74 @p43)) % 0.39/0.57 (step @p76 :rule eq_resolve :premises (@p1 @p75)) % 0.39/0.57 (step @p77 :rule refl :args (@t79)) % 0.39/0.57 (step @p78 :rule bool-double-not-elim :args (@t66)) % 0.39/0.57 (step @p79 :rule nary_cong :premises (@p78 @p77) :args ((or (not @t80) @t79))) % 0.39/0.57 (step @p80 :rule eq-refl :args (@t69)) % 0.39/0.57 (step @p81 :rule skolem_intro :args (@t70)) % 0.39/0.57 (step @p82 :rule refl :args (@t69)) % 0.39/0.57 (step @p83 :rule cong :premises (@p82 @p81) :args ((= @t69 @t70))) % 0.39/0.57 (step @p84 :rule trans :premises (@p83 @p80)) % 0.39/0.57 (step @p85 :rule true_elim :premises (@p84)) % 0.39/0.57 (step @p86 :rule refl :args (@t71)) % 0.39/0.57 (step @p87 :rule cong :premises (@p86 @p85) :args (@t81)) % 0.39/0.57 (step @p88 :rule eq-symm :args (@t73 @t71)) % 0.39/0.57 (step @p89 :rule eq-refl :args (@t44)) % 0.39/0.57 (step @p90 :rule refl :args (@t44)) % 0.39/0.57 (step @p91 :rule cong :premises (@p90 @p26) :args ((= @t44 @t44))) % 0.39/0.57 (step @p92 :rule trans :premises (@p91 @p89)) % 0.39/0.57 (step @p93 :rule skolem_intro :args (@t73)) % 0.39/0.57 (step @p94 :rule cong :premises (@p90 @p93) :args ((= @t44 @t73))) % 0.39/0.57 (step @p95 :rule trans :premises (@p94 @p92)) % 0.39/0.57 (step @p96 :rule true_elim :premises (@p95)) % 0.39/0.57 (step @p97 :rule cong :premises (@p96 @p86) :args (@t82)) % 0.39/0.57 (step @p98 :rule trans :premises (@p97 @p88)) % 0.39/0.57 (step @p99 :rule refl :args (@t77)) % 0.39/0.57 (step @p100 :rule nary_cong :premises (@p99 @p98 @p87) :args (@t83)) % 0.39/0.57 (step @p101 :rule cong :premises (@p100) :args (@t84)) % 0.39/0.57 (step @p102 :rule refl :args (@t80)) % 0.39/0.57 (step @p103 :rule cong :premises (@p102 @p101) :args ((=> @t80 @t84))) % 0.39/0.57 (step @p104 :rule eq-symm :args (@t67 @t15)) % 0.39/0.57 (step @p105 :rule cong :premises (@p104) :args (@t86)) % 0.39/0.57 (step @p106 :rule cong :premises (@p86 @p105) :args (@t87)) % 0.39/0.57 (step @p107 :rule eq-symm :args (@t71 @t44)) % 0.39/0.57 (step @p108 :rule refl :args (@t75)) % 0.39/0.57 (step @p109 :rule nary_cong :premises (@p108 @p104) :args (@t88)) % 0.39/0.57 (step @p110 :rule cong :premises (@p109) :args (@t89)) % 0.39/0.57 (step @p111 :rule cong :premises (@p110) :args (@t90)) % 0.39/0.57 (step @p112 :rule nary_cong :premises (@p111 @p107 @p106) :args (@t91)) % 0.39/0.57 (step @p113 :rule cong :premises (@p112) :args (@t92)) % 0.39/0.57 (step @p114 :rule cong :premises (@p102 @p113) :args ((=> @t80 @t92))) % 0.39/0.57 (step @p115 :rule trans :premises (@p114 @p103)) % 0.39/0.57 (assume-push @p217 @t80) % 0.39/0.57 (step @p117 :rule skolemize :premises (@p76)) % 0.39/0.57 (step-pop @p218 :rule scope :premises (@p117)) % 0.39/0.57 (step @p118 :rule process_scope :premises (@p218) :args (@t92)) % 0.39/0.57 (step @p120 :rule eq_resolve :premises (@p118 @p115)) % 0.39/0.57 (step @p121 :rule implies_elim :premises (@p120)) % 0.39/0.57 (step @p122 :rule eq_resolve :premises (@p121 @p79)) % 0.39/0.57 (step @p123 :rule chain_m_resolution :premises (@p122 @p76) :args (@t79 @t93 (@list @t66))) % 0.39/0.57 (step @p124 :rule cnf_or_neg :args (@t78 2)) % 0.39/0.57 (step @p125 :rule chain_m_resolution :premises (@p124 @p123) :args ((not @t72) @t93 @t94)) % 0.39/0.57 (step @p126 :rule eq-refl :args (@t96)) % 0.39/0.57 (step @p127 :rule refl :args (@t96)) % 0.39/0.57 (step @p128 :rule eq-symm :args (@t95 @t67)) % 0.39/0.57 (step @p129 :rule beta-reduce :args ((= @t98 @t97))) % 0.39/0.57 (step @p130 :rule trans :premises (@p129 @p128)) % 0.39/0.57 (step @p131 :rule cong :premises (@p130 @p127) :args ((= @t98 @t96))) % 0.39/0.57 (step @p132 :rule trans :premises (@p131 @p126)) % 0.39/0.57 (step @p133 :rule refl :args (@t95)) % 0.39/0.57 (step @p134 :rule ho_cong :premises (@p81 @p133)) % 0.39/0.57 (step @p135 :rule cong :premises (@p134 @p127) :args ((= @t99 @t96))) % 0.39/0.57 (step @p136 :rule trans :premises (@p135 @p132)) % 0.39/0.57 (step @p137 :rule true_elim :premises (@p136)) % 0.39/0.57 (step @p138 :rule refl :args (@t100)) % 0.39/0.57 (step @p139 :rule cong :premises (@p138 @p137) :args (@t101)) % 0.39/0.57 (step @p140 :rule cong :premises (@p139) :args (@t102)) % 0.39/0.57 (step @p141 :rule refl :args (@t72)) % 0.39/0.57 (step @p142 :rule nary_cong :premises (@p141 @p140) :args (@t103)) % 0.39/0.57 ; WARNING: add trust step for TRUST % 0.39/0.57 ; trust TRUST THEORY_LEMMA % 0.39/0.57 (step @p143 :rule trust :premises () :args (@t103)) % 0.39/0.57 (step @p144 :rule eq_resolve :premises (@p143 @p142)) % 0.39/0.57 (step @p145 :rule chain_m_resolution :premises (@p144 @p125) :args ((not @t104) @t93 (@list @t72))) % 0.39/0.57 (step @p146 :rule cnf_equiv_neg2 :args (@t104)) % 0.39/0.57 (step @p147 :rule bool-double-not-elim :args (@t76)) % 0.39/0.57 (step @p148 :rule refl :args (@t78)) % 0.39/0.57 (step @p149 :rule nary_cong :premises (@p148 @p147) :args ((or @t78 (not @t77)))) % 0.39/0.57 (step @p150 :rule cnf_or_neg :args (@t78 0)) % 0.39/0.57 (step @p151 :rule eq_resolve :premises (@p150 @p149)) % 0.39/0.57 (step @p152 :rule reordering :premises (@p151) :args ((or @t76 @t78))) % 0.39/0.57 (step @p153 :rule chain_m_resolution :premises (@p152 @p123) :args (@t76 @t93 @t94)) % 0.39/0.57 (step @p154 :rule refl :args (@t105)) % 0.39/0.57 (step @p155 :rule nary_cong :premises (@p154 @p128) :args (@t106)) % 0.39/0.57 (step @p156 :rule refl :args (@t76)) % 0.39/0.57 (step @p157 :rule cong :premises (@p156 @p155) :args ((=> @t76 @t106))) % 0.39/0.57 (assume-push @p219 @t76) % 0.39/0.57 (step @p159 :rule instantiate :premises (@p153) :args ((@list @t95))) % 0.39/0.57 (step-pop @p220 :rule scope :premises (@p159)) % 0.39/0.57 (step @p160 :rule process_scope :premises (@p220) :args (@t106)) % 0.39/0.57 (step @p162 :rule eq_resolve :premises (@p160 @p157)) % 0.39/0.57 (step @p163 :rule implies_elim :premises (@p162)) % 0.39/0.57 (step @p164 :rule chain_m_resolution :premises (@p163 @p153) :args (@t107 @t108 @t109)) % 0.39/0.57 (step @p165 :rule cnf_or_pos :args (@t107)) % 0.39/0.57 (step @p166 :rule reordering :premises (@p165) :args ((or @t96 @t105 (not @t107)))) % 0.39/0.57 (step @p167 :rule chain_m_resolution :premises (@p166 @p164 @p146 @p145) :args (@t105 (@list false true true) (@list @t107 @t96 @t104))) % 0.39/0.57 (step @p168 :rule false_intro :premises (@p167)) % 0.39/0.57 (step @p169 :rule cnf_equiv_neg1 :args (@t104)) % 0.39/0.57 (step @p170 :rule reordering :premises (@p169) :args ((or @t100 @t96 @t104))) % 0.39/0.57 (step @p171 :rule chain_m_resolution :premises (@p170 @p167 @p145) :args (@t96 (@list true true) (@list @t100 @t104))) % 0.39/0.57 (step @p172 :rule eq-symm :args (@t110 @t67)) % 0.39/0.57 (step @p173 :rule refl :args (@t112)) % 0.39/0.57 (step @p174 :rule nary_cong :premises (@p173 @p172) :args (@t113)) % 0.39/0.57 (step @p175 :rule cong :premises (@p156 @p174) :args ((=> @t76 @t113))) % 0.39/0.57 (assume-push @p221 @t76) % 0.39/0.57 (step @p177 :rule instantiate :premises (@p153) :args ((@list @t110))) % 0.39/0.57 (step-pop @p222 :rule scope :premises (@p177)) % 0.39/0.57 (step @p178 :rule process_scope :premises (@p222) :args (@t113)) % 0.39/0.57 (step @p180 :rule eq_resolve :premises (@p178 @p175)) % 0.39/0.57 (step @p181 :rule implies_elim :premises (@p180)) % 0.39/0.57 (step @p182 :rule chain_m_resolution :premises (@p181 @p153) :args (@t115 @t108 @t109)) % 0.39/0.57 (step @p183 :rule cnf_or_neg :args (@t78 1)) % 0.39/0.57 (step @p184 :rule chain_m_resolution :premises (@p183 @p123) :args ((not @t74) @t93 @t94)) % 0.39/0.57 (step @p185 :rule bool-double-not-elim :args (@t111)) % 0.39/0.57 (step @p186 :rule bool-eq-false :args (@t111)) % 0.39/0.57 (step @p187 :rule evaluate :args ((not false))) % 0.39/0.57 (step @p188 :rule beta-reduce :args ((= @t116 false))) % 0.39/0.57 (step @p189 :rule cong :premises (@p188) :args ((not @t116))) % 0.39/0.57 (step @p190 :rule trans :premises (@p189 @p187)) % 0.39/0.57 (step @p191 :rule refl :args (@t110)) % 0.39/0.57 (step @p192 :rule ho_cong :premises (@p93 @p191)) % 0.39/0.57 (step @p193 :rule cong :premises (@p192) :args ((not @t117))) % 0.39/0.57 (step @p194 :rule bool-eq-false :args (@t117)) % 0.39/0.57 (step @p195 :rule trans :premises (@p194 @p193 @p190)) % 0.39/0.57 (step @p196 :rule true_elim :premises (@p195)) % 0.39/0.57 (step @p197 :rule refl :args (@t111)) % 0.39/0.57 (step @p198 :rule cong :premises (@p197 @p196) :args (@t118)) % 0.39/0.57 (step @p199 :rule trans :premises (@p198 @p186)) % 0.39/0.57 (step @p200 :rule cong :premises (@p199) :args (@t119)) % 0.39/0.57 (step @p201 :rule trans :premises (@p200 @p185)) % 0.39/0.57 (step @p202 :rule refl :args (@t74)) % 0.39/0.57 (step @p203 :rule nary_cong :premises (@p202 @p201) :args (@t120)) % 0.39/0.57 ; trust TRUST THEORY_LEMMA % 0.39/0.57 (step @p204 :rule trust :premises () :args (@t120)) % 0.39/0.57 (step @p205 :rule eq_resolve :premises (@p204 @p203)) % 0.39/0.57 (step @p206 :rule chain_m_resolution :premises (@p205 @p184) :args (@t111 @t93 (@list @t74))) % 0.39/0.57 (step @p207 :rule cnf_or_pos :args (@t115)) % 0.39/0.57 (step @p208 :rule reordering :premises (@p207) :args ((or @t112 @t114 (not @t115)))) % 0.39/0.57 (step @p209 :rule chain_m_resolution :premises (@p208 @p206 @p182) :args (@t114 (@list false false) (@list @t111 @t115))) % 0.39/0.57 (step @p210 :rule symm :premises (@p209)) % 0.39/0.57 (step @p211 :rule trans :premises (@p210 @p171)) % 0.39/0.57 (step @p212 :rule cong :premises (@p211) :args (@t111)) % 0.39/0.57 (step @p213 :rule true_intro :premises (@p206)) % 0.39/0.57 (step @p214 :rule symm :premises (@p213)) % 0.39/0.57 (step @p215 :rule trans :premises (@p214 @p212 @p168)) % 0.39/0.57 (step @p216 false :rule eq_resolve :premises (@p215 @p17)) % 0.39/0.57 ) % 0.39/0.57 % SZS output end Proof % 0.39/0.57 % cvc5 exiting %------------------------------------------------------------------------------