%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU961^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:53:35 AM UTC 2026 % Result : Theorem 0.39s 0.58s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU961^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n021.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 18:03:35 EDT 2026 % 0.17/0.35 % CPUTime : % 0.32/0.50 %----Proving TH0 % 0.39/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.58 % SZS status Theorem % 0.39/0.58 % SZS output start Proof % 0.39/0.58 ( % 0.39/0.58 (declare-sort $$unsorted 0) % 0.39/0.58 (define @t1 () (@var "Xk" (-> $$unsorted $$unsorted))) % 0.39/0.58 (define @t2 () (@var "Xp" (-> (-> $$unsorted $$unsorted) Bool))) % 0.39/0.58 (define @t3 () (_ @t2 @t1)) % 0.39/0.58 (define @t4 () (@var "Xx" $$unsorted)) % 0.39/0.58 (define @t5 () (@var "Xj_1" (-> $$unsorted $$unsorted))) % 0.39/0.58 (define @t6 () (_ @t5 @t4)) % 0.39/0.58 (define @t7 () (@var "Xj" (-> $$unsorted $$unsorted))) % 0.39/0.58 (define @t8 () (_ @t7 @t6)) % 0.39/0.58 (define @t9 () (@list @t4)) % 0.39/0.58 (define @t10 () (lambda @t9 @t8)) % 0.39/0.58 (define @t11 () (_ @t2 @t10)) % 0.39/0.58 (define @t12 () (_ @t2 @t5)) % 0.39/0.58 (define @t13 () (@list @t5)) % 0.39/0.58 (define @t14 () (forall @t13 (=> @t12 @t11))) % 0.39/0.58 (define @t15 () (_ @t2 @t7)) % 0.39/0.58 (define @t16 () (and @t15 @t14)) % 0.39/0.58 (define @t17 () (=> @t16 @t3)) % 0.39/0.58 (define @t18 () (@list @t2)) % 0.39/0.58 (define @t19 () (forall @t18 @t17)) % 0.39/0.58 (define @t20 () (_ @t7 @t4)) % 0.39/0.58 (define @t21 () (_ @t1 @t20)) % 0.39/0.58 (define @t22 () (lambda @t9 @t21)) % 0.39/0.58 (define @t23 () (_ @t2 @t22)) % 0.39/0.58 (define @t24 () (@var "Xj_0" (-> $$unsorted $$unsorted))) % 0.39/0.58 (define @t25 () (_ @t24 @t4)) % 0.39/0.58 (define @t26 () (_ @t7 @t25)) % 0.39/0.58 (define @t27 () (lambda @t9 @t26)) % 0.39/0.58 (define @t28 () (_ @t2 @t27)) % 0.39/0.58 (define @t29 () (_ @t2 @t24)) % 0.39/0.58 (define @t30 () (@list @t24)) % 0.39/0.58 (define @t31 () (forall @t30 (=> @t29 @t28))) % 0.39/0.58 (define @t32 () (and @t15 @t31)) % 0.39/0.58 (define @t33 () (=> @t32 @t23)) % 0.39/0.58 (define @t34 () (forall @t18 @t33)) % 0.39/0.58 (define @t35 () (=> @t34 @t19)) % 0.39/0.58 (define @t36 () (@list @t7 @t1)) % 0.39/0.58 (define @t37 () (forall @t36 @t35)) % 0.39/0.58 (define @t38 () (@var "Xg" (-> $$unsorted $$unsorted))) % 0.39/0.58 (define @t39 () (@var "Xf" (-> $$unsorted $$unsorted))) % 0.39/0.58 (define @t40 () (= @t39 @t38)) % 0.39/0.58 (define @t41 () (_ @t38 @t4)) % 0.39/0.58 (define @t42 () (_ @t39 @t4)) % 0.39/0.58 (define @t43 () (= @t42 @t41)) % 0.39/0.58 (define @t44 () (forall @t9 @t43)) % 0.39/0.58 (define @t45 () (=> @t44 @t40)) % 0.39/0.58 (define @t46 () (@list @t39 @t38)) % 0.39/0.58 (define @t47 () (forall @t46 @t45)) % 0.39/0.58 (define @t48 () (@var "Xb" $$unsorted)) % 0.39/0.58 (define @t49 () (@var "Xa" $$unsorted)) % 0.39/0.58 (define @t50 () (forall (@list @t49 @t48) (= @t49 @t48))) % 0.39/0.58 (define @t51 () (and @t50 @t47)) % 0.39/0.58 (define @t52 () (=> @t51 @t37)) % 0.39/0.58 (define @t53 () (not @t52)) % 0.39/0.58 (define @t54 () (@var "BOUND_VARIABLE_7536" (-> (-> $$unsorted $$unsorted) Bool))) % 0.39/0.58 (define @t55 () (_ @t54 @t1)) % 0.39/0.58 (define @t56 () (_ @t5 @t4)) % 0.39/0.58 (define @t57 () (_ @t7 @t56)) % 0.39/0.58 (define @t58 () (lambda @t9 @t57)) % 0.39/0.58 (define @t59 () (not (forall @t13 (or (not (_ @t54 @t5)) (_ @t54 @t58))))) % 0.39/0.58 (define @t60 () (not (_ @t54 @t7))) % 0.39/0.58 (define @t61 () (_ @t7 @t4)) % 0.39/0.58 (define @t62 () (_ @t1 @t61)) % 0.39/0.58 (define @t63 () (lambda @t9 @t62)) % 0.39/0.58 (define @t64 () (_ @t2 @t63)) % 0.39/0.58 (define @t65 () (_ @t24 @t4)) % 0.39/0.58 (define @t66 () (_ @t7 @t65)) % 0.39/0.58 (define @t67 () (lambda @t9 @t66)) % 0.39/0.58 (define @t68 () (_ @t2 @t67)) % 0.39/0.58 (define @t69 () (_ @t2 @t24)) % 0.39/0.58 (define @t70 () (not @t69)) % 0.39/0.58 (define @t71 () (forall @t30 (or @t70 @t68))) % 0.39/0.58 (define @t72 () (not @t71)) % 0.39/0.58 (define @t73 () (_ @t2 @t7)) % 0.39/0.58 (define @t74 () (not @t73)) % 0.39/0.58 (define @t75 () (forall @t18 (or @t74 @t72 @t64))) % 0.39/0.58 (define @t76 () (not @t75)) % 0.39/0.58 (define @t77 () (or @t76 @t60 @t59 @t55)) % 0.39/0.58 (define @t78 () (or @t60 @t59 @t55)) % 0.39/0.58 (define @t79 () (or @t76 @t78)) % 0.39/0.58 (define @t80 () (@list @t7 @t1 @t54)) % 0.39/0.58 (define @t81 () (forall @t80 @t79)) % 0.39/0.58 (define @t82 () (@list @t54)) % 0.39/0.58 (define @t83 () (forall @t82 @t79)) % 0.39/0.58 (define @t84 () (forall @t82 @t78)) % 0.39/0.58 (define @t85 () (or @t76 @t84)) % 0.39/0.58 (define @t86 () (_ @t2 @t1)) % 0.39/0.58 (define @t87 () (_ @t2 @t58)) % 0.39/0.58 (define @t88 () (_ @t2 @t5)) % 0.39/0.58 (define @t89 () (forall @t13 (or (not @t88) @t87))) % 0.39/0.58 (define @t90 () (not @t89)) % 0.39/0.58 (define @t91 () (forall @t18 (or @t74 @t90 @t86))) % 0.39/0.58 (define @t92 () (not @t15)) % 0.39/0.58 (define @t93 () (or @t92 @t90 @t3)) % 0.39/0.58 (define @t94 () (and @t15 @t89)) % 0.39/0.58 (define @t95 () (not @t12)) % 0.39/0.58 (define @t96 () (or @t95 @t11)) % 0.39/0.58 (define @t97 () (or @t92 @t72 @t23)) % 0.39/0.58 (define @t98 () (and @t15 @t71)) % 0.39/0.58 (define @t99 () (not @t29)) % 0.39/0.58 (define @t100 () (or @t99 @t28)) % 0.39/0.58 (define @t101 () (_ @t38 @t4)) % 0.39/0.58 (define @t102 () (_ @t39 @t4)) % 0.39/0.58 (define @t103 () (forall @t9 (= @t102 @t101))) % 0.39/0.58 (define @t104 () (forall @t80 @t77)) % 0.39/0.58 (define @t105 () (@quantifiers_skolemize @t104 1)) % 0.39/0.58 (define @t106 () (@quantifiers_skolemize @t104 2)) % 0.39/0.58 (define @t107 () (_ @t106 @t105)) % 0.39/0.58 (define @t108 () (@quantifiers_skolemize @t104 0)) % 0.39/0.58 (define @t109 () (_ @t106 @t108)) % 0.39/0.58 (define @t110 () (not @t109)) % 0.39/0.58 (define @t111 () (or (not (forall @t18 (or (not (_ @t2 @t108)) (not (forall @t30 (or @t70 (_ @t2 (lambda @t9 (_ @t108 @t65)))))) (_ @t2 (lambda @t9 (_ @t105 (_ @t108 @t4))))))) @t110 (not (forall @t13 (or (not (_ @t106 @t5)) (_ @t106 (lambda @t9 (_ @t108 @t56)))))) @t107)) % 0.39/0.58 (define @t112 () (not @t107)) % 0.39/0.58 (define @t113 () (@list true)) % 0.39/0.58 (define @t114 () (@list @t111)) % 0.39/0.58 (define @t115 () (= @t108 @t105)) % 0.39/0.58 (define @t116 () (not @t115)) % 0.39/0.58 (define @t117 () (and @t109 @t115 @t112)) % 0.39/0.58 (define @t118 () (@const 0 $$unsorted)) % 0.39/0.58 (define @t119 () (_ @t105 @t118)) % 0.39/0.58 (define @t120 () (_ @t108 @t118)) % 0.39/0.58 (define @t121 () (= @t120 @t119)) % 0.39/0.58 (define @t122 () (not @t121)) % 0.39/0.58 (define @t123 () (= @t119 @t120)) % 0.39/0.58 (assume @p1 @t53) % 0.39/0.58 (assume @p2 true) % 0.39/0.58 (step @p3 :rule aci_norm :args ((= @t79 @t77))) % 0.39/0.58 (step @p4 :rule cong :premises (@p3) :args (@t81)) % 0.39/0.58 (step @p5 :rule quant-merge-prenex :args ((= (forall @t36 @t83) @t81))) % 0.39/0.58 (step @p6 :rule alpha_equiv :args (@t84 (@list @t54) (@list @t2))) % 0.39/0.58 (step @p7 :rule refl :args (@t76)) % 0.39/0.58 (step @p8 :rule nary_cong :premises (@p7 @p6) :args (@t85)) % 0.39/0.58 (step @p9 :rule quant-miniscope-or :args ((= @t83 @t85))) % 0.39/0.58 (step @p10 :rule trans :premises (@p9 @p8)) % 0.39/0.58 (step @p11 :rule symm :premises (@p10)) % 0.39/0.58 (step @p12 :rule cong :premises (@p11) :args ((forall @t36 (or @t76 @t91)))) % 0.39/0.58 (step @p13 :rule trans :premises (@p12 @p5)) % 0.39/0.58 (step @p14 :rule trans :premises (@p13 @p4)) % 0.39/0.58 (step @p15 :rule bool-impl-elim :args (@t75 @t91)) % 0.39/0.58 (step @p16 :rule cong :premises (@p15) :args ((forall @t36 (=> @t75 @t91)))) % 0.39/0.58 (step @p17 :rule trans :premises (@p16 @p14)) % 0.39/0.58 (step @p18 :rule refl :args (@t86)) % 0.39/0.58 (step @p19 :rule refl :args (@t3)) % 0.39/0.58 (step @p20 :rule cong :premises (@p19 @p18) :args ((= @t3 @t86))) % 0.39/0.58 (step @p21 :rule symm :premises (@p20)) % 0.39/0.58 (step @p22 :rule eq_resolve :premises (@p19 @p21)) % 0.39/0.58 (step @p23 :rule refl :args (@t90)) % 0.39/0.58 (step @p24 :rule refl :args (@t73)) % 0.39/0.58 (step @p25 :rule refl :args (@t15)) % 0.39/0.58 (step @p26 :rule cong :premises (@p25 @p24) :args ((= @t15 @t73))) % 0.39/0.58 (step @p27 :rule symm :premises (@p26)) % 0.39/0.58 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 0.39/0.58 (step @p29 :rule cong :premises (@p28) :args (@t92)) % 0.39/0.58 (step @p30 :rule nary_cong :premises (@p29 @p23 @p22) :args (@t93)) % 0.39/0.58 (step @p31 :rule cong :premises (@p30) :args ((forall @t18 @t93))) % 0.39/0.58 (step @p32 :rule aci_norm :args ((= (or (or @t92 @t90) @t3) @t93))) % 0.39/0.58 (step @p33 :rule bool-and-de-morgan :args (@t15 @t89 true)) % 0.39/0.58 (step @p34 :rule nary_cong :premises (@p33 @p19) :args ((or (not @t94) @t3))) % 0.39/0.58 (step @p35 :rule trans :premises (@p34 @p32)) % 0.39/0.58 (step @p36 :rule bool-impl-elim :args (@t94 @t3)) % 0.39/0.58 (step @p37 :rule trans :premises (@p36 @p35)) % 0.39/0.58 (step @p38 :rule cong :premises (@p37) :args ((forall @t18 (=> @t94 @t3)))) % 0.39/0.58 (step @p39 :rule trans :premises (@p38 @p31)) % 0.39/0.58 (step @p40 :rule refl :args (@t3)) % 0.39/0.58 (step @p41 :rule refl :args ((_ @t2 @t10))) % 0.39/0.58 (step @p42 :rule refl :args ((_ @t7 @t6))) % 0.39/0.58 (step @p43 :rule refl :args (@t56)) % 0.39/0.58 (step @p44 :rule cong :premises (@p43) :args (@t57)) % 0.39/0.58 (step @p45 :rule trans :premises (@p44 @p42)) % 0.39/0.58 (step @p46 :rule cong :premises (@p45) :args (@t58)) % 0.39/0.58 (step @p47 :rule cong :premises (@p46) :args (@t87)) % 0.39/0.58 (step @p48 :rule trans :premises (@p47 @p41)) % 0.39/0.58 (step @p49 :rule refl :args (@t2)) % 0.39/0.58 (step @p50 :rule ho_cong :premises (@p49 @p46)) % 0.39/0.58 (step @p51 :rule cong :premises (@p50 @p48) :args ((= (_ @t2 @t58) @t87))) % 0.39/0.58 (step @p52 :rule symm :premises (@p51)) % 0.39/0.58 (step @p53 :rule refl :args (@t11)) % 0.39/0.58 (step @p54 :rule eq_resolve :premises (@p53 @p52)) % 0.39/0.58 (step @p55 :rule refl :args (@t7)) % 0.39/0.58 (step @p56 :rule ho_cong :premises (@p55 @p43)) % 0.39/0.58 (step @p57 :rule cong :premises (@p56 @p45) :args ((= (_ @t7 @t56) @t57))) % 0.39/0.58 (step @p58 :rule symm :premises (@p57)) % 0.39/0.58 (step @p59 :rule refl :args (@t8)) % 0.39/0.58 (step @p60 :rule eq_resolve :premises (@p59 @p58)) % 0.39/0.58 (step @p61 :rule refl :args (@t6)) % 0.39/0.58 (step @p62 :rule cong :premises (@p61 @p43) :args ((= @t6 @t56))) % 0.39/0.58 (step @p63 :rule symm :premises (@p62)) % 0.39/0.58 (step @p64 :rule eq_resolve :premises (@p61 @p63)) % 0.39/0.58 (step @p65 :rule ho_cong :premises (@p55 @p64)) % 0.39/0.58 (step @p66 :rule trans :premises (@p65 @p60)) % 0.39/0.58 (step @p67 :rule cong :premises (@p66) :args (@t10)) % 0.39/0.58 (step @p68 :rule ho_cong :premises (@p49 @p67)) % 0.39/0.58 (step @p69 :rule trans :premises (@p68 @p54)) % 0.39/0.58 (step @p70 :rule refl :args (@t88)) % 0.39/0.58 (step @p71 :rule refl :args (@t12)) % 0.39/0.58 (step @p72 :rule cong :premises (@p71 @p70) :args ((= @t12 @t88))) % 0.39/0.58 (step @p73 :rule symm :premises (@p72)) % 0.39/0.58 (step @p74 :rule eq_resolve :premises (@p71 @p73)) % 0.39/0.58 (step @p75 :rule cong :premises (@p74) :args (@t95)) % 0.39/0.58 (step @p76 :rule nary_cong :premises (@p75 @p69) :args (@t96)) % 0.39/0.58 (step @p77 :rule cong :premises (@p76) :args ((forall @t13 @t96))) % 0.39/0.58 (step @p78 :rule bool-impl-elim :args (@t12 @t11)) % 0.39/0.58 (step @p79 :rule cong :premises (@p78) :args (@t14)) % 0.39/0.58 (step @p80 :rule trans :premises (@p79 @p77)) % 0.39/0.58 (step @p81 :rule refl :args (@t15)) % 0.39/0.58 (step @p82 :rule nary_cong :premises (@p81 @p80) :args (@t16)) % 0.39/0.58 (step @p83 :rule cong :premises (@p82 @p40) :args (@t17)) % 0.39/0.58 (step @p84 :rule cong :premises (@p83) :args (@t19)) % 0.39/0.58 (step @p85 :rule trans :premises (@p84 @p39)) % 0.39/0.58 (step @p86 :rule refl :args ((_ @t2 @t22))) % 0.39/0.58 (step @p87 :rule refl :args ((_ @t1 @t20))) % 0.39/0.58 (step @p88 :rule refl :args (@t61)) % 0.39/0.58 (step @p89 :rule cong :premises (@p88) :args (@t62)) % 0.39/0.58 (step @p90 :rule trans :premises (@p89 @p87)) % 0.39/0.58 (step @p91 :rule cong :premises (@p90) :args (@t63)) % 0.39/0.58 (step @p92 :rule cong :premises (@p91) :args (@t64)) % 0.39/0.58 (step @p93 :rule trans :premises (@p92 @p86)) % 0.39/0.58 (step @p94 :rule ho_cong :premises (@p49 @p91)) % 0.39/0.58 (step @p95 :rule cong :premises (@p94 @p93) :args ((= (_ @t2 @t63) @t64))) % 0.39/0.58 (step @p96 :rule symm :premises (@p95)) % 0.39/0.58 (step @p97 :rule refl :args (@t23)) % 0.39/0.58 (step @p98 :rule eq_resolve :premises (@p97 @p96)) % 0.39/0.58 (step @p99 :rule refl :args (@t1)) % 0.39/0.58 (step @p100 :rule ho_cong :premises (@p99 @p88)) % 0.39/0.58 (step @p101 :rule cong :premises (@p100 @p90) :args ((= (_ @t1 @t61) @t62))) % 0.39/0.58 (step @p102 :rule symm :premises (@p101)) % 0.39/0.58 (step @p103 :rule refl :args (@t21)) % 0.39/0.58 (step @p104 :rule eq_resolve :premises (@p103 @p102)) % 0.39/0.58 (step @p105 :rule refl :args (@t20)) % 0.39/0.58 (step @p106 :rule cong :premises (@p105 @p88) :args ((= @t20 @t61))) % 0.39/0.58 (step @p107 :rule symm :premises (@p106)) % 0.39/0.58 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 0.39/0.58 (step @p109 :rule ho_cong :premises (@p99 @p108)) % 0.39/0.58 (step @p110 :rule trans :premises (@p109 @p104)) % 0.39/0.58 (step @p111 :rule cong :premises (@p110) :args (@t22)) % 0.39/0.58 (step @p112 :rule ho_cong :premises (@p49 @p111)) % 0.39/0.58 (step @p113 :rule trans :premises (@p112 @p98)) % 0.39/0.58 (step @p114 :rule refl :args (@t72)) % 0.39/0.58 (step @p115 :rule nary_cong :premises (@p29 @p114 @p113) :args (@t97)) % 0.39/0.58 (step @p116 :rule cong :premises (@p115) :args ((forall @t18 @t97))) % 0.39/0.58 (step @p117 :rule aci_norm :args ((= (or (or @t92 @t72) @t23) @t97))) % 0.39/0.58 (step @p118 :rule bool-and-de-morgan :args (@t15 @t71 true)) % 0.39/0.58 (step @p119 :rule nary_cong :premises (@p118 @p97) :args ((or (not @t98) @t23))) % 0.39/0.58 (step @p120 :rule trans :premises (@p119 @p117)) % 0.39/0.58 (step @p121 :rule bool-impl-elim :args (@t98 @t23)) % 0.39/0.58 (step @p122 :rule trans :premises (@p121 @p120)) % 0.39/0.58 (step @p123 :rule cong :premises (@p122) :args ((forall @t18 (=> @t98 @t23)))) % 0.39/0.58 (step @p124 :rule trans :premises (@p123 @p116)) % 0.39/0.58 (step @p125 :rule refl :args (@t23)) % 0.39/0.58 (step @p126 :rule refl :args ((_ @t2 @t27))) % 0.39/0.58 (step @p127 :rule refl :args ((_ @t7 @t25))) % 0.39/0.58 (step @p128 :rule refl :args (@t65)) % 0.39/0.58 (step @p129 :rule cong :premises (@p128) :args (@t66)) % 0.39/0.58 (step @p130 :rule trans :premises (@p129 @p127)) % 0.39/0.58 (step @p131 :rule cong :premises (@p130) :args (@t67)) % 0.39/0.58 (step @p132 :rule cong :premises (@p131) :args (@t68)) % 0.39/0.58 (step @p133 :rule trans :premises (@p132 @p126)) % 0.39/0.58 (step @p134 :rule ho_cong :premises (@p49 @p131)) % 0.39/0.58 (step @p135 :rule cong :premises (@p134 @p133) :args ((= (_ @t2 @t67) @t68))) % 0.39/0.58 (step @p136 :rule symm :premises (@p135)) % 0.39/0.58 (step @p137 :rule refl :args (@t28)) % 0.39/0.58 (step @p138 :rule eq_resolve :premises (@p137 @p136)) % 0.39/0.58 (step @p139 :rule ho_cong :premises (@p55 @p128)) % 0.39/0.58 (step @p140 :rule cong :premises (@p139 @p130) :args ((= (_ @t7 @t65) @t66))) % 0.39/0.58 (step @p141 :rule symm :premises (@p140)) % 0.39/0.58 (step @p142 :rule refl :args (@t26)) % 0.39/0.58 (step @p143 :rule eq_resolve :premises (@p142 @p141)) % 0.39/0.58 (step @p144 :rule refl :args (@t25)) % 0.39/0.58 (step @p145 :rule cong :premises (@p144 @p128) :args ((= @t25 @t65))) % 0.39/0.58 (step @p146 :rule symm :premises (@p145)) % 0.39/0.58 (step @p147 :rule eq_resolve :premises (@p144 @p146)) % 0.39/0.58 (step @p148 :rule ho_cong :premises (@p55 @p147)) % 0.39/0.58 (step @p149 :rule trans :premises (@p148 @p143)) % 0.39/0.58 (step @p150 :rule cong :premises (@p149) :args (@t27)) % 0.39/0.58 (step @p151 :rule ho_cong :premises (@p49 @p150)) % 0.39/0.58 (step @p152 :rule trans :premises (@p151 @p138)) % 0.39/0.58 (step @p153 :rule refl :args (@t69)) % 0.39/0.58 (step @p154 :rule refl :args (@t29)) % 0.39/0.58 (step @p155 :rule cong :premises (@p154 @p153) :args ((= @t29 @t69))) % 0.39/0.58 (step @p156 :rule symm :premises (@p155)) % 0.39/0.58 (step @p157 :rule eq_resolve :premises (@p154 @p156)) % 0.39/0.58 (step @p158 :rule cong :premises (@p157) :args (@t99)) % 0.39/0.58 (step @p159 :rule nary_cong :premises (@p158 @p152) :args (@t100)) % 0.39/0.58 (step @p160 :rule cong :premises (@p159) :args ((forall @t30 @t100))) % 0.39/0.58 (step @p161 :rule bool-impl-elim :args (@t29 @t28)) % 0.39/0.58 (step @p162 :rule cong :premises (@p161) :args (@t31)) % 0.39/0.58 (step @p163 :rule trans :premises (@p162 @p160)) % 0.39/0.58 (step @p164 :rule nary_cong :premises (@p81 @p163) :args (@t32)) % 0.39/0.58 (step @p165 :rule cong :premises (@p164 @p125) :args (@t33)) % 0.39/0.58 (step @p166 :rule cong :premises (@p165) :args (@t34)) % 0.39/0.58 (step @p167 :rule trans :premises (@p166 @p124)) % 0.39/0.58 (step @p168 :rule cong :premises (@p167 @p85) :args (@t35)) % 0.39/0.58 (step @p169 :rule cong :premises (@p168) :args (@t37)) % 0.39/0.58 (step @p170 :rule trans :premises (@p169 @p17)) % 0.39/0.58 (step @p171 :rule bool-impl-elim :args (@t103 @t40)) % 0.39/0.58 (step @p172 :rule cong :premises (@p171) :args ((forall @t46 (=> @t103 @t40)))) % 0.39/0.58 (step @p173 :rule refl :args (@t40)) % 0.39/0.58 (step @p174 :rule refl :args (@t101)) % 0.39/0.58 (step @p175 :rule refl :args (@t41)) % 0.39/0.58 (step @p176 :rule cong :premises (@p175 @p174) :args ((= @t41 @t101))) % 0.39/0.58 (step @p177 :rule symm :premises (@p176)) % 0.39/0.58 (step @p178 :rule eq_resolve :premises (@p175 @p177)) % 0.39/0.58 (step @p179 :rule refl :args (@t102)) % 0.39/0.58 (step @p180 :rule refl :args (@t42)) % 0.39/0.58 (step @p181 :rule cong :premises (@p180 @p179) :args ((= @t42 @t102))) % 0.39/0.58 (step @p182 :rule symm :premises (@p181)) % 0.39/0.58 (step @p183 :rule eq_resolve :premises (@p180 @p182)) % 0.39/0.58 (step @p184 :rule cong :premises (@p183 @p178) :args (@t43)) % 0.39/0.58 (step @p185 :rule cong :premises (@p184) :args (@t44)) % 0.39/0.58 (step @p186 :rule cong :premises (@p185 @p173) :args (@t45)) % 0.39/0.58 (step @p187 :rule cong :premises (@p186) :args (@t47)) % 0.39/0.58 (step @p188 :rule trans :premises (@p187 @p172)) % 0.39/0.58 (step @p189 :rule refl :args (@t50)) % 0.39/0.58 (step @p190 :rule nary_cong :premises (@p189 @p188) :args (@t51)) % 0.39/0.58 (step @p191 :rule cong :premises (@p190 @p170) :args (@t52)) % 0.39/0.58 (step @p192 :rule cong :premises (@p191) :args (@t53)) % 0.39/0.58 (step @p193 :rule eq_resolve :premises (@p1 @p192)) % 0.39/0.58 (step @p194 :rule not_implies_elim1 :premises (@p193)) % 0.39/0.58 (step @p195 :rule and_elim :premises (@p194) :args (0)) % 0.39/0.58 (step @p196 :rule not_implies_elim2 :premises (@p193)) % 0.39/0.58 (step @p197 :rule skolemize :premises (@p196)) % 0.39/0.58 (step @p198 :rule cnf_or_neg :args (@t111 3)) % 0.39/0.58 (step @p199 :rule chain_m_resolution :premises (@p198 @p197) :args (@t112 @t113 @t114)) % 0.39/0.58 (step @p200 :rule bool-double-not-elim :args (@t109)) % 0.39/0.58 (step @p201 :rule refl :args (@t111)) % 0.39/0.58 (step @p202 :rule nary_cong :premises (@p201 @p200) :args ((or @t111 (not @t110)))) % 0.39/0.58 (step @p203 :rule cnf_or_neg :args (@t111 1)) % 0.39/0.58 (step @p204 :rule eq_resolve :premises (@p203 @p202)) % 0.39/0.58 (step @p205 :rule reordering :premises (@p204) :args ((or @t109 @t111))) % 0.39/0.58 (step @p206 :rule chain_m_resolution :premises (@p205 @p197) :args (@t109 @t113 @t114)) % 0.39/0.58 (step @p207 :rule refl :args (@t116)) % 0.39/0.58 (step @p208 :rule bool-double-not-elim :args (@t107)) % 0.39/0.58 (step @p209 :rule refl :args (@t110)) % 0.39/0.58 (step @p210 :rule nary_cong :premises (@p209 @p208 @p207) :args ((or @t110 (not @t112) @t116))) % 0.39/0.58 (assume-push @p250 @t109) % 0.39/0.58 (assume-push @p251 @t115) % 0.39/0.58 (assume-push @p252 @t112) % 0.39/0.58 (step @p214 :rule evaluate :args ((= false true))) % 0.39/0.58 (step @p215 :rule true_intro :premises (@p206)) % 0.39/0.58 (step @p216 :rule symm :premises (@p251)) % 0.39/0.58 (step @p217 :rule cong :premises (@p216) :args (@t107)) % 0.39/0.58 (step @p218 :rule false_intro :premises (@p199)) % 0.39/0.58 (step @p219 :rule symm :premises (@p218)) % 0.39/0.58 (step @p220 :rule trans :premises (@p219 @p217 @p215)) % 0.39/0.58 (step @p221 false :rule eq_resolve :premises (@p220 @p214)) % 0.39/0.58 (step-pop @p253 :rule scope :premises (@p221)) % 0.39/0.58 (step-pop @p254 :rule scope :premises (@p253)) % 0.39/0.58 (step-pop @p255 :rule scope :premises (@p254)) % 0.39/0.58 (step @p222 :rule process_scope :premises (@p255) :args (false)) % 0.39/0.58 (assume-push @p256 @t109) % 0.39/0.58 (assume-push @p257 @t112) % 0.39/0.58 (assume-push @p258 @t115) % 0.39/0.58 (step @p229 :rule and_intro :premises (@p206 @p258 @p199)) % 0.39/0.58 (step-pop @p259 :rule scope :premises (@p229)) % 0.39/0.58 (step-pop @p260 :rule scope :premises (@p259)) % 0.39/0.58 (step-pop @p261 :rule scope :premises (@p260)) % 0.39/0.58 (step @p230 :rule process_scope :premises (@p261) :args (@t117)) % 0.39/0.58 (step @p234 :rule implies_elim :premises (@p230)) % 0.39/0.58 (step @p235 :rule resolution :premises (@p234 @p222) :args (true @t117)) % 0.39/0.58 (step @p236 :rule not_and :premises (@p235)) % 0.39/0.58 (step @p237 :rule eq_resolve :premises (@p236 @p210)) % 0.39/0.58 (step @p238 :rule chain_m_resolution :premises (@p237 @p206 @p199) :args (@t116 (@list false true) (@list @t109 @t107))) % 0.39/0.58 ; WARNING: add trust step for TRUST % 0.39/0.58 ; trust TRUST THEORY_LEMMA % 0.39/0.58 (step @p239 :rule trust :premises () :args ((or @t115 @t122))) % 0.39/0.58 (step @p240 :rule chain_m_resolution :premises (@p239 @p238) :args (@t122 @t113 (@list @t115))) % 0.39/0.58 (step @p241 :rule eq-symm :args (@t119 @t120)) % 0.39/0.59 (step @p242 :rule cong :premises (@p189 @p241) :args ((=> @t50 @t123))) % 0.39/0.59 (assume-push @p262 @t50) % 0.39/0.59 (step @p244 :rule instantiate :premises (@p195) :args ((@list @t119 @t120))) % 0.39/0.59 (step-pop @p263 :rule scope :premises (@p244)) % 0.39/0.59 (step @p245 :rule process_scope :premises (@p263) :args (@t123)) % 0.39/0.59 (step @p247 :rule eq_resolve :premises (@p245 @p242)) % 0.39/0.59 (step @p248 :rule implies_elim :premises (@p247)) % 0.39/0.59 (step @p249 false :rule chain_m_resolution :premises (@p248 @p240 @p195) :args (false (@list true false) (@list @t121 @t50))) % 0.39/0.59 ) % 0.39/0.59 % SZS output end Proof % 0.39/0.59 % cvc5 exiting %------------------------------------------------------------------------------