%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO300^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n010.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 09:12:23 AM UTC 2026 % Result : Theorem 168.76s 169.76s % Output : Proof 168.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO300^5 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n010.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 : Wed Jun 3 00:02:25 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.49 %----Proving TH0 % 168.76/169.76 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 168.76/169.76 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 168.76/169.76 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 168.76/169.76 --- Run --ho-elim --full-saturate-quant at 18s... % 168.76/169.76 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 168.76/169.76 % SZS status Theorem % 168.76/169.76 % SZS output start Proof % 168.76/169.76 ( % 168.76/169.76 (declare-sort $$unsorted 0) % 168.76/169.76 (define @t1 () (@var "X" (-> (-> $$unsorted $$unsorted) $$unsorted))) % 168.76/169.76 (define @t2 () (@var "V" $$unsorted)) % 168.76/169.76 (define @t3 () (lambda (@list @t2) @t2)) % 168.76/169.76 (define @t4 () (@var "U" (-> $$unsorted $$unsorted))) % 168.76/169.76 (define @t5 () (@list @t4)) % 168.76/169.76 (define @t6 () (@var "P" (-> (-> (-> $$unsorted $$unsorted) $$unsorted) (-> (-> $$unsorted $$unsorted) $$unsorted) Bool))) % 168.76/169.76 (define @t7 () (_ (_ @t6 (lambda @t5 (_ @t4 (_ @t1 @t3)))) @t1)) % 168.76/169.76 (define @t8 () (@var "Xz" (-> (-> $$unsorted $$unsorted) $$unsorted))) % 168.76/169.76 (define @t9 () (_ (_ @t6 @t8) @t8)) % 168.76/169.76 (define @t10 () (@list @t8)) % 168.76/169.76 (define @t11 () (forall @t10 @t9)) % 168.76/169.76 (define @t12 () (=> @t11 @t7)) % 168.76/169.76 (define @t13 () (@list @t1)) % 168.76/169.76 (define @t14 () (exists @t13 @t12)) % 168.76/169.76 (define @t15 () (@list @t6)) % 168.76/169.76 (define @t16 () (forall @t15 @t14)) % 168.76/169.76 (define @t17 () (not @t16)) % 168.76/169.76 (define @t18 () (@var "BOUND_VARIABLE_7558" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 168.76/169.76 (define @t19 () (@var "BOUND_VARIABLE_7556" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)))) % 168.76/169.76 (define @t20 () (@const 0 (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)) (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)))) % 168.76/169.76 (define @t21 () (@const 1 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)) (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted))))) % 168.76/169.76 (define @t22 () (@const 2 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)) (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted))) % 168.76/169.76 (define @t23 () (_ @t22 (_ @t21 @t20 @t19) @t18)) % 168.76/169.76 (define @t24 () (@const 3 (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 168.76/169.76 (define @t25 () (@const 4 (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted $$unsorted))) % 168.76/169.76 (define @t26 () (_ @t25 @t18 (_ @t22 @t19 @t24))) % 168.76/169.76 (define @t27 () (@list @t19 @t18)) % 168.76/169.76 (define @t28 () (forall @t27 (= @t23 @t26))) % 168.76/169.76 (define @t29 () (@const 5 (-> $$unsorted $$unsorted))) % 168.76/169.76 (define @t30 () (@var "BOUND_VARIABLE_7490" (-> (-> $$unsorted $$unsorted) $$unsorted))) % 168.76/169.76 (define @t31 () (@var "BOUND_VARIABLE_7491" (-> $$unsorted $$unsorted))) % 168.76/169.76 (define @t32 () (@const 6 (-> (-> (-> $$unsorted $$unsorted) $$unsorted) (-> $$unsorted $$unsorted) $$unsorted))) % 168.76/169.76 (define @t33 () (forall (@list @t30 @t31) (= (_ @t32 @t30 @t31) (_ @t31 (_ @t30 @t29))))) % 168.76/169.76 (define @t34 () (@const 7 (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)))) % 168.76/169.76 (define @t35 () (@var "BOUND_VARIABLE_7503" $$unsorted)) % 168.76/169.76 (define @t36 () (@list @t35)) % 168.76/169.76 (define @t37 () (forall @t36 (= @t35 (_ @t29 @t35)))) % 168.76/169.76 (define @t38 () (_ @t22 @t34 @t24)) % 168.76/169.76 (define @t39 () (@var "y" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)))) % 168.76/169.76 (define @t40 () (@var "x" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)))) % 168.76/169.76 (define @t41 () (@var "z" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 168.76/169.76 (define @t42 () (@list @t41)) % 168.76/169.76 (define @t43 () (_ @t21 @t20 @t34)) % 168.76/169.76 (define @t44 () (_ @t21 @t20 @t43)) % 168.76/169.76 (define @t45 () (@var "BOUND_VARIABLE_7516" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)))) % 168.76/169.76 (define @t46 () (_ @t21 @t20 @t45)) % 168.76/169.76 (define @t47 () (@var "BOUND_VARIABLE_7526" (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)) Bool)))) % 168.76/169.76 (define @t48 () (@const 8 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)) Bool)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)) (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)) Bool))))) % 168.76/169.76 (define @t49 () (@const 9 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)) Bool)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)) Bool))) % 168.76/169.76 (define @t50 () (@list @t45)) % 168.76/169.76 (define @t51 () (@var "BOUND_VARIABLE_7539" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted)))) % 168.76/169.76 (define @t52 () (@list @t51)) % 168.76/169.76 (define @t53 () (forall (@list @t47) (or (not (forall @t52 (_ @t49 (_ @t48 @t47 @t51) @t51))) (not (forall @t50 (not (_ @t49 (_ @t48 @t47 @t46) @t45))))))) % 168.76/169.76 (define @t54 () (@var "BOUND_VARIABLE_7444" (-> (-> $$unsorted $$unsorted) $$unsorted))) % 168.76/169.76 (define @t55 () (@list @t54)) % 168.76/169.76 (define @t56 () (_ @t6 @t8 @t8)) % 168.76/169.76 (define @t57 () (forall @t10 @t56)) % 168.76/169.76 (define @t58 () (not @t57)) % 168.76/169.76 (define @t59 () (not (forall @t15 (or @t58 (not (forall @t55 (not (_ @t6 (_ @t32 @t54) @t54)))))))) % 168.76/169.76 (define @t60 () (_ @t54 @t3)) % 168.76/169.76 (define @t61 () (_ @t4 @t60)) % 168.76/169.76 (define @t62 () (lambda @t5 @t61)) % 168.76/169.76 (define @t63 () (_ @t6 @t62 @t54)) % 168.76/169.76 (define @t64 () (forall @t55 (not @t63))) % 168.76/169.76 (define @t65 () (_ @t54 @t3)) % 168.76/169.76 (define @t66 () (_ @t4 @t65)) % 168.76/169.76 (define @t67 () (lambda @t5 @t66)) % 168.76/169.76 (define @t68 () (_ (_ @t6 @t67) @t54)) % 168.76/169.76 (define @t69 () (not @t68)) % 168.76/169.76 (define @t70 () (forall @t55 @t69)) % 168.76/169.76 (define @t71 () (not @t7)) % 168.76/169.76 (define @t72 () (forall @t13 @t71)) % 168.76/169.76 (define @t73 () (forall @t13 @t57)) % 168.76/169.76 (define @t74 () (and @t73 @t72)) % 168.76/169.76 (define @t75 () (=> @t57 @t7)) % 168.76/169.76 (define @t76 () (forall @t13 (not @t75))) % 168.76/169.76 (define @t77 () (not @t76)) % 168.76/169.76 (define @t78 () (@quantifiers_skolemize @t53 0)) % 168.76/169.76 (define @t79 () (forall @t52 (_ @t49 (_ @t48 @t78 @t51) @t51))) % 168.76/169.76 (define @t80 () (forall @t50 (not (_ @t49 (_ @t48 @t78 @t46) @t45)))) % 168.76/169.76 (define @t81 () (not @t80)) % 168.76/169.76 (define @t82 () (not @t79)) % 168.76/169.76 (define @t83 () (or @t82 @t81)) % 168.76/169.76 (define @t84 () (@list true)) % 168.76/169.76 (define @t85 () (@list @t83)) % 168.76/169.76 (define @t86 () (= @t43 @t44)) % 168.76/169.76 (define @t87 () (not @t86)) % 168.76/169.76 (define @t88 () (_ @t48 @t78 @t44)) % 168.76/169.76 (define @t89 () (_ @t49 @t88 @t44)) % 168.76/169.76 (define @t90 () (not @t89)) % 168.76/169.76 (define @t91 () (_ @t49 @t88 @t43)) % 168.76/169.76 (define @t92 () (not @t91)) % 168.76/169.76 (define @t93 () (and @t92 @t86 @t89)) % 168.76/169.76 (define @t94 () (@list true false)) % 168.76/169.76 (define @t95 () (forall @t42 (= (_ @t22 @t43 @t41) (_ @t22 @t44 @t41)))) % 168.76/169.76 (define @t96 () (not @t95)) % 168.76/169.76 (define @t97 () (or @t96 @t86)) % 168.76/169.76 (define @t98 () (@quantifiers_skolemize @t95 0)) % 168.76/169.76 (define @t99 () (_ @t22 @t44 @t98)) % 168.76/169.76 (define @t100 () (_ @t22 @t43 @t98)) % 168.76/169.76 (define @t101 () (= @t100 @t99)) % 168.76/169.76 (define @t102 () (not @t101)) % 168.76/169.76 (define @t103 () (_ @t25 @t98 @t38)) % 168.76/169.76 (define @t104 () (forall @t27 (= @t26 @t23))) % 168.76/169.76 (define @t105 () (= @t103 @t100)) % 168.76/169.76 (define @t106 () (@list @t34 @t98)) % 168.76/169.76 (define @t107 () (= @t100 @t103)) % 168.76/169.76 (define @t108 () (@list false)) % 168.76/169.76 (define @t109 () (@list @t104)) % 168.76/169.76 (define @t110 () (_ @t22 @t43 @t24)) % 168.76/169.76 (define @t111 () (_ @t25 @t98 @t110)) % 168.76/169.76 (define @t112 () (= @t111 @t99)) % 168.76/169.76 (define @t113 () (= @t99 @t111)) % 168.76/169.76 (define @t114 () (not @t113)) % 168.76/169.76 (define @t115 () (not @t107)) % 168.76/169.76 (define @t116 () (_ @t25 @t24 @t38)) % 168.76/169.76 (define @t117 () (= @t38 @t116)) % 168.76/169.76 (define @t118 () (not @t117)) % 168.76/169.76 (define @t119 () (= @t116 @t110)) % 168.76/169.76 (define @t120 () (not @t119)) % 168.76/169.76 (define @t121 () (and @t114 @t113)) % 168.76/169.76 (assume @p1 @t17) % 168.76/169.76 (assume @p2 true) % 168.76/169.76 (step @p3 :rule eq-symm :args (@t23 @t26)) % 168.76/169.76 (step @p4 :rule cong :premises (@p3) :args (@t28)) % 168.76/169.76 ; WARNING: add trust step for TRUST % 168.76/169.76 ; trust TRUST PREPROCESS_HO_ELIM % 168.76/169.76 (step @p5 :rule trust :premises () :args ((= @t33 @t28))) % 168.76/169.76 (step @p6 :rule trans :premises (@p5 @p4)) % 168.76/169.76 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 168.76/169.76 (step @p7 :rule trust :premises () :args (@t33)) % 168.76/169.76 (step @p8 :rule eq_resolve :premises (@p7 @p6)) % 168.76/169.76 (step @p9 :rule instantiate :premises (@p8) :args ((@list @t34 @t24))) % 168.76/169.76 ; trust TRUST PREPROCESS_HO_ELIM % 168.76/169.76 (step @p10 :rule trust :premises () :args ((= @t37 (forall @t36 (= @t35 (_ @t25 @t24 @t35)))))) % 168.76/169.76 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 168.76/169.76 (step @p11 :rule trust :premises () :args (@t37)) % 168.76/169.76 (step @p12 :rule eq_resolve :premises (@p11 @p10)) % 168.76/169.76 (step @p13 :rule instantiate :premises (@p12) :args ((@list @t38))) % 168.76/169.76 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 168.76/169.76 (step @p14 :rule trust :premises () :args ((forall (@list @t40 @t39) (or (not (forall @t42 (= (_ @t22 @t40 @t41) (_ @t22 @t39 @t41)))) (= @t40 @t39))))) % 168.76/169.76 (step @p15 :rule instantiate :premises (@p14) :args ((@list @t43 @t44))) % 168.76/169.76 ; trust TRUST PREPROCESS_HO_ELIM % 168.76/169.76 (step @p16 :rule trust :premises () :args ((= @t59 (not @t53)))) % 168.76/169.76 ; trust TRUST PREPROCESS_HO_ELIM % 168.76/169.76 (step @p17 :rule trust :premises () :args ((= (not (forall @t15 (or @t58 (not @t64)))) @t59))) % 168.76/169.76 (step @p18 :rule bool-and-de-morgan :args (@t57 @t64 true)) % 168.76/169.76 (step @p19 :rule cong :premises (@p18) :args ((forall @t15 (not (and @t57 @t64))))) % 168.76/169.76 (step @p20 :rule refl :args ((_ @t6 @t67 @t54))) % 168.76/169.76 (step @p21 :rule refl :args (@t54)) % 168.76/169.76 (step @p22 :rule refl :args ((_ @t4 @t65))) % 168.76/169.76 (step @p23 :rule refl :args (@t60)) % 168.76/169.76 (step @p24 :rule cong :premises (@p23) :args (@t61)) % 168.76/169.76 (step @p25 :rule trans :premises (@p24 @p22)) % 168.76/169.76 (step @p26 :rule cong :premises (@p25) :args (@t62)) % 168.76/169.76 (step @p27 :rule cong :premises (@p26 @p21) :args (@t63)) % 168.76/169.76 (step @p28 :rule trans :premises (@p27 @p20)) % 168.76/169.76 (step @p29 :rule refl :args (@t6)) % 168.76/169.76 (step @p30 :rule ho_cong :premises (@p29 @p26)) % 168.76/169.76 (step @p31 :rule ho_cong :premises (@p30 @p21)) % 168.76/169.76 (step @p32 :rule cong :premises (@p31 @p28) :args ((= (_ (_ @t6 @t62) @t54) @t63))) % 168.76/169.76 (step @p33 :rule symm :premises (@p32)) % 168.76/169.76 (step @p34 :rule refl :args (@t68)) % 168.76/169.76 (step @p35 :rule eq_resolve :premises (@p34 @p33)) % 168.76/169.76 (step @p36 :rule refl :args (@t4)) % 168.76/169.76 (step @p37 :rule ho_cong :premises (@p36 @p23)) % 168.76/169.76 (step @p38 :rule cong :premises (@p37 @p25) :args ((= (_ @t4 @t60) @t61))) % 168.76/169.76 (step @p39 :rule symm :premises (@p38)) % 168.76/169.76 (step @p40 :rule refl :args (@t66)) % 168.76/169.76 (step @p41 :rule eq_resolve :premises (@p40 @p39)) % 168.76/169.76 (step @p42 :rule refl :args (@t65)) % 168.76/169.76 (step @p43 :rule cong :premises (@p42 @p23) :args ((= @t65 @t60))) % 168.76/169.76 (step @p44 :rule symm :premises (@p43)) % 168.76/169.76 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 168.76/169.76 (step @p46 :rule ho_cong :premises (@p36 @p45)) % 168.76/169.76 (step @p47 :rule trans :premises (@p46 @p41)) % 168.76/169.76 (step @p48 :rule cong :premises (@p47) :args (@t67)) % 168.76/169.76 (step @p49 :rule ho_cong :premises (@p29 @p48)) % 168.76/169.76 (step @p50 :rule ho_cong :premises (@p49 @p21)) % 168.76/169.76 (step @p51 :rule trans :premises (@p50 @p35)) % 168.76/169.76 (step @p52 :rule cong :premises (@p51) :args (@t69)) % 168.76/169.76 (step @p53 :rule cong :premises (@p52) :args (@t70)) % 168.76/169.76 (step @p54 :rule refl :args (@t57)) % 168.76/169.76 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((and @t57 @t70))) % 168.76/169.76 (step @p56 :rule alpha_equiv :args (@t72 (@list @t1) (@list @t54))) % 168.76/169.76 (step @p57 :rule quant-unused-vars :args ((= @t73 @t57))) % 168.76/169.76 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t74)) % 168.76/169.76 (step @p59 :rule quant-miniscope-and :args ((= (forall @t13 (and @t57 @t71)) @t74))) % 168.76/169.76 (step @p60 :rule trans :premises (@p59 @p58)) % 168.76/169.76 (step @p61 :rule trans :premises (@p60 @p55)) % 168.76/169.76 (step @p62 :rule bool-implies-de-morgan :args (@t57 @t7)) % 168.76/169.76 (step @p63 :rule cong :premises (@p62) :args (@t76)) % 168.76/169.76 (step @p64 :rule trans :premises (@p63 @p61)) % 168.76/169.76 (step @p65 :rule cong :premises (@p64) :args (@t77)) % 168.76/169.76 (step @p66 :rule exists-elim :args ((= (exists @t13 @t75) @t77))) % 168.76/169.76 (step @p67 :rule trans :premises (@p66 @p65)) % 168.76/169.76 (step @p68 :rule refl :args (@t7)) % 168.76/169.76 (step @p69 :rule refl :args (@t56)) % 168.76/169.76 (step @p70 :rule refl :args (@t9)) % 168.76/169.76 (step @p71 :rule cong :premises (@p70 @p69) :args ((= @t9 @t56))) % 168.76/169.76 (step @p72 :rule symm :premises (@p71)) % 168.76/169.76 (step @p73 :rule eq_resolve :premises (@p70 @p72)) % 168.76/169.76 (step @p74 :rule cong :premises (@p73) :args (@t11)) % 168.76/169.76 (step @p75 :rule cong :premises (@p74 @p68) :args (@t12)) % 168.76/169.76 (step @p76 :rule cong :premises (@p75) :args (@t14)) % 168.76/169.76 (step @p77 :rule trans :premises (@p76 @p67)) % 168.76/169.76 (step @p78 :rule cong :premises (@p77) :args (@t16)) % 168.76/169.76 (step @p79 :rule trans :premises (@p78 @p19)) % 168.76/169.76 (step @p80 :rule cong :premises (@p79) :args (@t17)) % 168.76/169.76 (step @p81 :rule trans :premises (@p80 @p17 @p16)) % 168.76/169.76 (step @p82 :rule eq_resolve :premises (@p1 @p81)) % 168.76/169.76 (step @p83 :rule skolemize :premises (@p82)) % 168.76/169.76 (step @p84 :rule bool-double-not-elim :args (@t79)) % 168.76/169.76 (step @p85 :rule refl :args (@t83)) % 168.76/169.76 (step @p86 :rule nary_cong :premises (@p85 @p84) :args ((or @t83 (not @t82)))) % 168.76/169.76 (step @p87 :rule cnf_or_neg :args (@t83 0)) % 168.76/169.76 (step @p88 :rule eq_resolve :premises (@p87 @p86)) % 168.76/169.76 (step @p89 :rule reordering :premises (@p88) :args ((or @t79 @t83))) % 168.76/169.76 (step @p90 :rule chain_m_resolution :premises (@p89 @p83) :args (@t79 @t84 @t85)) % 168.76/169.76 (step @p91 :rule instantiate :premises (@p90) :args ((@list @t44))) % 168.76/169.76 (step @p92 :rule bool-double-not-elim :args (@t80)) % 168.76/169.76 (step @p93 :rule nary_cong :premises (@p85 @p92) :args ((or @t83 (not @t81)))) % 168.76/169.76 (step @p94 :rule cnf_or_neg :args (@t83 1)) % 168.76/169.76 (step @p95 :rule eq_resolve :premises (@p94 @p93)) % 168.76/169.76 (step @p96 :rule reordering :premises (@p95) :args ((or @t80 @t83))) % 168.76/169.76 (step @p97 :rule chain_m_resolution :premises (@p96 @p83) :args (@t80 @t84 @t85)) % 168.76/169.76 (step @p98 :rule instantiate :premises (@p97) :args ((@list @t43))) % 168.76/169.76 (step @p99 :rule refl :args (@t87)) % 168.76/169.76 (step @p100 :rule refl :args (@t90)) % 168.76/169.76 (step @p101 :rule bool-double-not-elim :args (@t91)) % 168.76/169.76 (step @p102 :rule nary_cong :premises (@p101 @p100 @p99) :args ((or (not @t92) @t90 @t87))) % 168.76/169.76 (assume-push @p227 @t92) % 168.76/169.76 (assume-push @p228 @t86) % 168.76/169.76 (assume-push @p229 @t89) % 168.76/169.76 (step @p106 :rule evaluate :args ((= true false))) % 168.76/169.76 (step @p107 :rule false_intro :premises (@p98)) % 168.76/169.76 (step @p108 :rule symm :premises (@p228)) % 168.76/169.76 (step @p109 :rule refl :args (@t88)) % 168.76/169.76 (step @p110 :rule cong :premises (@p109 @p108) :args (@t89)) % 168.76/169.76 (step @p111 :rule true_intro :premises (@p91)) % 168.76/169.76 (step @p112 :rule symm :premises (@p111)) % 168.76/169.76 (step @p113 :rule trans :premises (@p112 @p110 @p107)) % 168.76/169.76 (step @p114 false :rule eq_resolve :premises (@p113 @p106)) % 168.76/169.76 (step-pop @p230 :rule scope :premises (@p114)) % 168.76/169.76 (step-pop @p231 :rule scope :premises (@p230)) % 168.76/169.76 (step-pop @p232 :rule scope :premises (@p231)) % 168.76/169.76 (step @p115 :rule process_scope :premises (@p232) :args (false)) % 168.76/169.76 (assume-push @p233 @t92) % 168.76/169.76 (assume-push @p234 @t89) % 168.76/169.76 (assume-push @p235 @t86) % 168.76/169.76 (step @p122 :rule and_intro :premises (@p98 @p235 @p91)) % 168.76/169.76 (step-pop @p236 :rule scope :premises (@p122)) % 168.76/169.76 (step-pop @p237 :rule scope :premises (@p236)) % 168.76/169.76 (step-pop @p238 :rule scope :premises (@p237)) % 168.76/169.76 (step @p123 :rule process_scope :premises (@p238) :args (@t93)) % 168.76/169.76 (step @p127 :rule implies_elim :premises (@p123)) % 168.76/169.76 (step @p128 :rule resolution :premises (@p127 @p115) :args (true @t93)) % 168.76/169.76 (step @p129 :rule not_and :premises (@p128)) % 168.76/169.76 (step @p130 :rule eq_resolve :premises (@p129 @p102)) % 168.76/169.76 (step @p131 :rule chain_m_resolution :premises (@p130 @p98 @p91) :args (@t87 @t94 (@list @t91 @t89))) % 168.76/169.76 (step @p132 :rule cnf_or_pos :args (@t97)) % 168.76/169.76 (step @p133 :rule reordering :premises (@p132) :args ((or @t96 @t86 (not @t97)))) % 168.76/169.76 (step @p134 :rule chain_m_resolution :premises (@p133 @p131 @p15) :args (@t96 @t94 (@list @t86 @t97))) % 168.76/169.76 (step @p135 :rule refl :args (@t102)) % 168.76/169.76 (step @p136 :rule bool-double-not-elim :args (@t95)) % 168.76/169.76 (step @p137 :rule nary_cong :premises (@p136 @p135) :args ((or (not @t96) @t102))) % 168.76/169.76 (assume-push @p239 @t96) % 168.76/169.76 (step @p139 :rule skolemize :premises (@p239)) % 168.76/169.76 (step-pop @p240 :rule scope :premises (@p139)) % 168.76/169.76 (step @p140 :rule process_scope :premises (@p240) :args (@t102)) % 168.76/169.76 (step @p142 :rule implies_elim :premises (@p140)) % 168.76/169.76 (step @p143 :rule eq_resolve :premises (@p142 @p137)) % 168.76/169.76 (step @p144 :rule chain_m_resolution :premises (@p143 @p134) :args (@t102 @t84 (@list @t95))) % 168.76/169.76 (step @p145 :rule eq-symm :args (@t103 @t100)) % 168.76/169.76 (step @p146 :rule refl :args (@t104)) % 168.76/169.76 (step @p147 :rule cong :premises (@p146 @p145) :args ((=> @t104 @t105))) % 168.76/169.76 (assume-push @p241 @t104) % 168.76/169.76 (step @p149 :rule instantiate :premises (@p8) :args (@t106)) % 168.76/169.76 (step-pop @p242 :rule scope :premises (@p149)) % 168.76/169.76 (step @p150 :rule process_scope :premises (@p242) :args (@t105)) % 168.76/169.76 (step @p152 :rule eq_resolve :premises (@p150 @p147)) % 168.76/169.76 (step @p153 :rule implies_elim :premises (@p152)) % 168.76/169.76 (step @p154 :rule chain_m_resolution :premises (@p153 @p8) :args (@t107 @t108 @t109)) % 168.76/169.76 (step @p155 :rule eq-symm :args (@t111 @t99)) % 168.76/169.76 (step @p156 :rule cong :premises (@p146 @p155) :args ((=> @t104 @t112))) % 168.76/169.76 (assume-push @p243 @t104) % 168.76/169.76 (step @p158 :rule instantiate :premises (@p8) :args ((@list @t43 @t98))) % 168.76/169.76 (step-pop @p244 :rule scope :premises (@p158)) % 168.76/169.77 (step @p159 :rule process_scope :premises (@p244) :args (@t112)) % 168.76/169.77 (step @p161 :rule eq_resolve :premises (@p159 @p156)) % 168.76/169.77 (step @p162 :rule implies_elim :premises (@p161)) % 168.76/169.77 (step @p163 :rule chain_m_resolution :premises (@p162 @p8) :args (@t113 @t108 @t109)) % 168.76/169.77 (step @p164 :rule refl :args (@t114)) % 168.76/169.77 (step @p165 :rule refl :args (@t115)) % 168.76/169.77 (step @p166 :rule bool-double-not-elim :args (@t101)) % 168.76/169.77 (step @p167 :rule refl :args (@t118)) % 168.76/169.77 (step @p168 :rule refl :args (@t120)) % 168.76/169.77 (step @p169 :rule nary_cong :premises (@p168 @p167 @p166 @p165 @p164) :args ((or @t120 @t118 (not @t102) @t115 @t114))) % 168.76/169.77 (assume-push @p245 @t114) % 168.76/169.77 (assume-push @p246 @t113) % 168.76/169.77 (step @p172 :rule evaluate :args ((= false true))) % 168.76/169.77 (step @p173 :rule true_intro :premises (@p163)) % 168.76/169.77 (step @p174 :rule false_intro :premises (@p245)) % 168.76/169.77 (step @p175 :rule symm :premises (@p174)) % 168.76/169.77 (step @p176 :rule trans :premises (@p175 @p173)) % 168.76/169.77 (step @p177 false :rule eq_resolve :premises (@p176 @p172)) % 168.76/169.77 (step-pop @p247 :rule scope :premises (@p177)) % 168.76/169.77 (step-pop @p248 :rule scope :premises (@p247)) % 168.76/169.77 (step @p178 :rule process_scope :premises (@p248) :args (false)) % 168.76/169.77 (assume-push @p249 @t119) % 168.76/169.77 (assume-push @p250 @t117) % 168.76/169.77 (assume-push @p251 @t102) % 168.76/169.77 (assume-push @p252 @t107) % 168.76/169.77 (assume-push @p253 @t113) % 168.76/169.77 (assume-push @p254 @t107) % 168.76/169.77 (assume-push @p255 @t117) % 168.76/169.77 (assume-push @p256 @t119) % 168.76/169.77 (assume-push @p257 @t102) % 168.76/169.77 (step @p190 :rule bool-eq-false :args (@t113)) % 168.76/169.77 (step @p191 :rule symm :premises (@p190)) % 168.76/169.77 (step @p192 :rule cong :premises (@p155) :args ((not @t112))) % 168.76/169.77 (step @p193 :rule bool-eq-false :args (@t112)) % 168.76/169.77 (step @p194 :rule trans :premises (@p193 @p192)) % 168.76/169.77 (step @p195 :rule trans :premises (@p194 @p191)) % 168.76/169.77 (step @p196 :rule false_intro :premises (@p251)) % 168.76/169.77 (step @p197 :rule refl :args (@t99)) % 168.76/169.77 (step @p149 :rule instantiate :premises (@p8) :args (@t106)) % 168.76/169.77 (step @p198 :rule symm :premises (@p13)) % 168.76/169.77 (step @p199 :rule symm :premises (@p9)) % 168.76/169.77 (step @p200 :rule trans :premises (@p199 @p198)) % 168.76/169.77 (step @p201 :rule refl :args (@t98)) % 168.76/169.77 (step @p202 :rule cong :premises (@p201 @p200) :args (@t111)) % 168.76/169.77 (step @p203 :rule trans :premises (@p202 @p149)) % 168.76/169.77 (step @p204 :rule cong :premises (@p203 @p197) :args (@t112)) % 168.76/169.77 (step @p205 :rule trans :premises (@p204 @p196)) % 168.76/169.77 (step @p206 :rule eq_resolve :premises (@p205 @p195)) % 168.76/169.77 (step @p207 :rule false_elim :premises (@p206)) % 168.76/169.77 (step-pop @p258 :rule scope :premises (@p207)) % 168.76/169.77 (step-pop @p259 :rule scope :premises (@p258)) % 168.76/169.77 (step-pop @p260 :rule scope :premises (@p259)) % 168.76/169.77 (step-pop @p261 :rule scope :premises (@p260)) % 168.76/169.77 (step @p208 :rule process_scope :premises (@p261) :args (@t114)) % 168.76/169.77 (step @p213 :rule and_intro :premises (@p154 @p13 @p9 @p251)) % 168.76/169.77 (step @p214 :rule modus_ponens :premises (@p213 @p208)) % 168.76/169.77 (step @p215 :rule and_intro :premises (@p214 @p163)) % 168.76/169.77 (step-pop @p262 :rule scope :premises (@p215)) % 168.76/169.77 (step-pop @p263 :rule scope :premises (@p262)) % 168.76/169.77 (step-pop @p264 :rule scope :premises (@p263)) % 168.76/169.77 (step-pop @p265 :rule scope :premises (@p264)) % 168.76/169.77 (step-pop @p266 :rule scope :premises (@p265)) % 168.76/169.77 (step @p216 :rule process_scope :premises (@p266) :args (@t121)) % 168.76/169.77 (step @p222 :rule implies_elim :premises (@p216)) % 168.76/169.77 (step @p223 :rule resolution :premises (@p222 @p178) :args (true @t121)) % 168.76/169.77 (step @p224 :rule not_and :premises (@p223)) % 168.76/169.77 (step @p225 :rule eq_resolve :premises (@p224 @p169)) % 168.76/169.77 (step @p226 false :rule chain_m_resolution :premises (@p225 @p163 @p154 @p144 @p13 @p9) :args (false (@list false false true false false) (@list @t113 @t107 @t101 @t117 @t119))) % 168.76/169.77 ) % 168.76/169.77 % SZS output end Proof % 168.76/169.77 % cvc5 exiting %------------------------------------------------------------------------------