%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV181^5 : TPTP v9.2.1. Bugfixed v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n004.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 08:55:34 AM UTC 2026 % Result : Theorem 0.43s 0.63s % Output : Proof 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV181^5 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 18:17:37 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.49 %----Proving TH0 % 0.43/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.43/0.63 % SZS status Theorem % 0.43/0.63 % SZS output start Proof % 0.43/0.63 ( % 0.43/0.63 (declare-sort $$unsorted 0) % 0.43/0.63 (define tptp.cD_FOR_X5309 () (let ((_let_1 (@var "Xt" (-> $$unsorted Bool)))) (let ((_let_2 (@var "Xh" (-> (-> $$unsorted Bool) $$unsorted)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@var "Xz" $$unsorted))) (lambda (@list _let_2 _let_4) (exists (@list _let_1) (and (not (_ _let_1 _let_3)) (= _let_4 _let_3))))))))) % 0.43/0.63 (define @t1 () (@var "Xh" (-> (-> $$unsorted Bool) $$unsorted))) % 0.43/0.63 (define @t2 () (_ tptp.cD_FOR_X5309 @t1)) % 0.43/0.63 (define @t3 () (not (_ @t2 (_ @t1 @t2)))) % 0.43/0.63 (define @t4 () (@var "Xq" (-> $$unsorted Bool))) % 0.43/0.63 (define @t5 () (@var "Xp" (-> $$unsorted Bool))) % 0.43/0.63 (define @t6 () (= @t5 @t4)) % 0.43/0.63 (define @t7 () (_ @t1 @t4)) % 0.43/0.63 (define @t8 () (_ @t1 @t5)) % 0.43/0.63 (define @t9 () (= @t8 @t7)) % 0.43/0.63 (define @t10 () (@list @t5 @t4)) % 0.43/0.63 (define @t11 () (forall @t10 (=> @t9 @t6))) % 0.43/0.63 (define @t12 () (=> @t11 @t3)) % 0.43/0.63 (define @t13 () (@list @t1)) % 0.43/0.63 (define @t14 () (forall @t13 @t12)) % 0.43/0.63 (define @t15 () (not @t14)) % 0.43/0.63 (define @t16 () (@var "Xt" (-> $$unsorted Bool))) % 0.43/0.63 (define @t17 () (_ @t1 @t16)) % 0.43/0.63 (define @t18 () (@var "Xz" $$unsorted)) % 0.43/0.63 (define @t19 () (= @t18 @t17)) % 0.43/0.63 (define @t20 () (_ @t16 @t17)) % 0.43/0.63 (define @t21 () (not @t20)) % 0.43/0.63 (define @t22 () (and @t21 @t19)) % 0.43/0.63 (define @t23 () (@list @t16)) % 0.43/0.63 (define @t24 () (exists @t23 @t22)) % 0.43/0.63 (define @t25 () (@list @t1 @t18)) % 0.43/0.63 (define @t26 () (lambda @t25 @t24)) % 0.43/0.63 (define @t27 () (@var "BOUND_VARIABLE_7493" (-> $$unsorted Bool))) % 0.43/0.63 (define @t28 () (@var "BOUND_VARIABLE_7521" (-> $$unsorted Bool))) % 0.43/0.63 (define @t29 () (_ @t1 @t28)) % 0.43/0.63 (define @t30 () (_ @t1 @t27)) % 0.43/0.63 (define @t31 () (= @t18 @t30)) % 0.43/0.63 (define @t32 () (not @t31)) % 0.43/0.63 (define @t33 () (_ @t27 @t30)) % 0.43/0.63 (define @t34 () (or @t33 @t32)) % 0.43/0.63 (define @t35 () (@list @t27)) % 0.43/0.63 (define @t36 () (forall @t35 @t34)) % 0.43/0.63 (define @t37 () (not @t36)) % 0.43/0.63 (define @t38 () (@list @t18)) % 0.43/0.63 (define @t39 () (lambda @t38 @t37)) % 0.43/0.63 (define @t40 () (_ @t1 @t39)) % 0.43/0.63 (define @t41 () (_ @t28 @t29)) % 0.43/0.63 (define @t42 () (_ @t1 @t4)) % 0.43/0.63 (define @t43 () (_ @t1 @t5)) % 0.43/0.63 (define @t44 () (forall @t10 (or (not (= @t43 @t42)) @t6))) % 0.43/0.63 (define @t45 () (not @t44)) % 0.43/0.63 (define @t46 () (@list @t1 @t28)) % 0.43/0.63 (define @t47 () (forall @t46 (or @t45 @t41 (not (= @t40 @t29))))) % 0.43/0.63 (define @t48 () (@quantifiers_skolemize @t47 0)) % 0.43/0.63 (define @t49 () (_ @t48 @t27)) % 0.43/0.63 (define @t50 () (_ @t27 @t49)) % 0.43/0.63 (define @t51 () (not (forall @t35 (or @t50 (not (= @t18 @t49)))))) % 0.43/0.63 (define @t52 () (lambda @t38 @t51)) % 0.43/0.63 (define @t53 () (@purify @t52)) % 0.43/0.63 (define @t54 () (_ @t53 @t18)) % 0.43/0.63 (define @t55 () (_ @t52 @t18)) % 0.43/0.63 (define @t56 () (= @t54 @t55)) % 0.43/0.63 (define @t57 () (forall @t38 @t56)) % 0.43/0.63 (define @t58 () (_ @t48 @t53)) % 0.43/0.63 (define @t59 () (forall @t35 (or @t50 (not (= @t49 @t58))))) % 0.43/0.63 (define @t60 () (not @t59)) % 0.43/0.63 (define @t61 () (_ @t53 @t58)) % 0.43/0.63 (define @t62 () (not (= @t58 @t49))) % 0.43/0.63 (define @t63 () (or @t50 @t62)) % 0.43/0.63 (define @t64 () (forall @t35 @t63)) % 0.43/0.63 (define @t65 () (not @t64)) % 0.43/0.63 (define @t66 () (= @t65 @t61)) % 0.43/0.63 (define @t67 () (forall @t38 (= @t51 @t54))) % 0.43/0.63 (define @t68 () (= @t61 @t60)) % 0.43/0.63 (define @t69 () (not (= @t29 @t40))) % 0.43/0.63 (define @t70 () (or @t45 @t41 @t69)) % 0.43/0.63 (define @t71 () (or @t41 @t69)) % 0.43/0.63 (define @t72 () (or @t45 @t71)) % 0.43/0.63 (define @t73 () (forall @t46 @t72)) % 0.43/0.63 (define @t74 () (@list @t28)) % 0.43/0.63 (define @t75 () (forall @t74 @t72)) % 0.43/0.63 (define @t76 () (forall @t74 @t71)) % 0.43/0.63 (define @t77 () (@list @t16)) % 0.43/0.63 (define @t78 () (or @t45 @t76)) % 0.43/0.63 (define @t79 () (_ @t1 @t16)) % 0.43/0.63 (define @t80 () (_ @t16 @t79)) % 0.43/0.63 (define @t81 () (forall @t23 (or @t80 (not (= @t79 @t40))))) % 0.43/0.63 (define @t82 () (_ @t1 @t27)) % 0.43/0.63 (define @t83 () (lambda @t38 (not (forall @t35 (or (_ @t27 @t82) (not (= @t18 @t82))))))) % 0.43/0.63 (define @t84 () (_ @t1 @t39)) % 0.43/0.63 (define @t85 () (= @t79 @t84)) % 0.43/0.63 (define @t86 () (not @t85)) % 0.43/0.63 (define @t87 () (or @t80 @t86)) % 0.43/0.63 (define @t88 () (forall @t23 (or @t80 (not (= @t18 @t79))))) % 0.43/0.63 (define @t89 () (not @t88)) % 0.43/0.63 (define @t90 () (lambda @t38 @t89)) % 0.43/0.63 (define @t91 () (_ @t1 @t90)) % 0.43/0.63 (define @t92 () (= @t79 @t91)) % 0.43/0.63 (define @t93 () (not @t92)) % 0.43/0.63 (define @t94 () (or @t80 @t93)) % 0.43/0.63 (define @t95 () (not (= @t91 @t79))) % 0.43/0.63 (define @t96 () (or @t80 @t95)) % 0.43/0.63 (define @t97 () (forall @t23 @t96)) % 0.43/0.63 (define @t98 () (not @t97)) % 0.43/0.63 (define @t99 () (_ (lambda @t25 @t89) @t1)) % 0.43/0.63 (define @t100 () (not (_ @t99 (_ @t1 @t99)))) % 0.43/0.63 (define @t101 () (not @t9)) % 0.43/0.63 (define @t102 () (or @t101 @t6)) % 0.43/0.63 (define @t103 () (=> @t11 @t100)) % 0.43/0.63 (define @t104 () (forall @t13 @t103)) % 0.43/0.63 (define @t105 () (not @t19)) % 0.43/0.63 (define @t106 () (or @t20 @t105)) % 0.43/0.63 (define @t107 () (forall @t23 (not @t22))) % 0.43/0.63 (define @t108 () (not @t107)) % 0.43/0.63 (define @t109 () (@quantifiers_skolemize @t47 1)) % 0.43/0.63 (define @t110 () (_ @t48 @t109)) % 0.43/0.63 (define @t111 () (= @t110 @t58)) % 0.43/0.63 (define @t112 () (not @t111)) % 0.43/0.63 (define @t113 () (_ @t109 @t110)) % 0.43/0.63 (define @t114 () (forall @t10 (or (not (= (_ @t48 @t5) (_ @t48 @t4))) @t6))) % 0.43/0.63 (define @t115 () (not @t114)) % 0.43/0.63 (define @t116 () (or @t115 @t113 @t112)) % 0.43/0.63 (define @t117 () (not @t116)) % 0.43/0.63 (define @t118 () (not @t47)) % 0.43/0.63 (define @t119 () (_ @t48 @t52)) % 0.43/0.63 (define @t120 () (= @t110 @t119)) % 0.43/0.63 (define @t121 () (not @t120)) % 0.43/0.63 (define @t122 () (or @t115 @t113 @t121)) % 0.43/0.63 (define @t123 () (not @t122)) % 0.43/0.63 (define @t124 () (not (= @t119 @t110))) % 0.43/0.63 (define @t125 () (or @t115 @t113 @t124)) % 0.43/0.63 (define @t126 () (not @t125)) % 0.43/0.63 (define @t127 () (@list true)) % 0.43/0.63 (define @t128 () (@list @t116)) % 0.43/0.63 (define @t129 () (= @t109 @t53)) % 0.43/0.63 (define @t130 () (or @t112 @t129)) % 0.43/0.63 (define @t131 () (not @t68)) % 0.43/0.63 (define @t132 () (@list true false)) % 0.43/0.63 (define @t133 () (or @t113 @t112)) % 0.43/0.63 (define @t134 () (not @t133)) % 0.43/0.63 (assume @p1 @t15) % 0.43/0.63 (assume @p2 true) % 0.43/0.63 (step @p3 (= tptp.cD_FOR_X5309 @t26) :rule refl :args (@t26)) % 0.43/0.63 (step @p4 :rule eq-symm :args (@t54 @t51)) % 0.43/0.63 (step @p5 :rule beta-reduce :args ((= @t55 @t51))) % 0.43/0.63 (step @p6 :rule refl :args (@t54)) % 0.43/0.63 (step @p7 :rule cong :premises (@p6 @p5) :args (@t56)) % 0.43/0.63 (step @p8 :rule trans :premises (@p7 @p4)) % 0.43/0.63 (step @p9 :rule cong :premises (@p8) :args (@t57)) % 0.43/0.63 (step @p10 :rule quant-unused-vars :args ((= (forall @t38 true) true))) % 0.43/0.63 (step @p11 :rule eq-refl :args (@t55)) % 0.43/0.63 (step @p12 :rule cong :premises (@p11) :args ((forall @t38 (= @t55 @t55)))) % 0.43/0.63 (step @p13 :rule trans :premises (@p12 @p10)) % 0.43/0.63 (step @p14 :rule refl :args (@t55)) % 0.43/0.63 (step @p15 :rule refl :args (@t18)) % 0.43/0.63 (step @p16 :rule skolem_intro :args (@t53)) % 0.43/0.63 (step @p17 :rule ho_cong :premises (@p16 @p15)) % 0.43/0.64 (step @p18 :rule cong :premises (@p17 @p14) :args (@t56)) % 0.43/0.64 (step @p19 :rule cong :premises (@p18) :args (@t57)) % 0.43/0.64 (step @p20 :rule trans :premises (@p19 @p13)) % 0.43/0.64 (step @p21 :rule true_elim :premises (@p20)) % 0.43/0.64 (step @p22 :rule eq_resolve :premises (@p21 @p9)) % 0.43/0.64 (step @p23 :rule eq-symm :args (@t60 @t61)) % 0.43/0.64 (step @p24 :rule refl :args (@t61)) % 0.43/0.64 (step @p25 :rule eq-symm :args (@t58 @t49)) % 0.43/0.64 (step @p26 :rule cong :premises (@p25) :args (@t62)) % 0.43/0.64 (step @p27 :rule refl :args (@t50)) % 0.43/0.64 (step @p28 :rule nary_cong :premises (@p27 @p26) :args (@t63)) % 0.43/0.64 (step @p29 :rule cong :premises (@p28) :args (@t64)) % 0.43/0.64 (step @p30 :rule cong :premises (@p29) :args (@t65)) % 0.43/0.64 (step @p31 :rule cong :premises (@p30 @p24) :args (@t66)) % 0.43/0.64 (step @p32 :rule trans :premises (@p31 @p23)) % 0.43/0.64 (step @p33 :rule refl :args (@t67)) % 0.43/0.64 (step @p34 :rule cong :premises (@p33 @p32) :args ((=> @t67 @t66))) % 0.43/0.64 (assume-push @p252 @t67) % 0.43/0.64 (step @p36 :rule instantiate :premises (@p22) :args ((@list @t58))) % 0.43/0.64 (step-pop @p253 :rule scope :premises (@p36)) % 0.43/0.64 (step @p37 :rule process_scope :premises (@p253) :args (@t66)) % 0.43/0.64 (step @p39 :rule eq_resolve :premises (@p37 @p34)) % 0.43/0.64 (step @p40 :rule implies_elim :premises (@p39)) % 0.43/0.64 (step @p41 :rule chain_m_resolution :premises (@p40 @p22) :args (@t68 (@list false) (@list @t67))) % 0.43/0.64 (step @p42 :rule eq-symm :args (@t29 @t40)) % 0.43/0.64 (step @p43 :rule cong :premises (@p42) :args (@t69)) % 0.43/0.64 (step @p44 :rule refl :args (@t41)) % 0.43/0.64 (step @p45 :rule refl :args (@t45)) % 0.43/0.64 (step @p46 :rule nary_cong :premises (@p45 @p44 @p43) :args (@t70)) % 0.43/0.64 (step @p47 :rule aci_norm :args ((= @t72 @t70))) % 0.43/0.64 (step @p48 :rule trans :premises (@p47 @p46)) % 0.43/0.64 (step @p49 :rule cong :premises (@p48) :args (@t73)) % 0.43/0.64 (step @p50 :rule quant-merge-prenex :args ((= (forall @t13 @t75) @t73))) % 0.43/0.64 (step @p51 :rule alpha_equiv :args (@t76 (@list @t28) @t77)) % 0.43/0.64 (step @p52 :rule refl :args (@t45)) % 0.43/0.64 (step @p53 :rule nary_cong :premises (@p52 @p51) :args (@t78)) % 0.43/0.64 (step @p54 :rule quant-miniscope-or :args ((= @t75 @t78))) % 0.43/0.64 (step @p55 :rule trans :premises (@p54 @p53)) % 0.43/0.64 (step @p56 :rule symm :premises (@p55)) % 0.43/0.64 (step @p57 :rule cong :premises (@p56) :args ((forall @t13 (or @t45 @t81)))) % 0.43/0.64 (step @p58 :rule trans :premises (@p57 @p50)) % 0.43/0.64 (step @p59 :rule trans :premises (@p58 @p49)) % 0.43/0.64 (step @p60 :rule bool-impl-elim :args (@t44 @t81)) % 0.43/0.64 (step @p61 :rule cong :premises (@p60) :args ((forall @t13 (=> @t44 @t81)))) % 0.43/0.64 (step @p62 :rule trans :premises (@p61 @p59)) % 0.43/0.64 (step @p63 :rule bool-double-not-elim :args (@t81)) % 0.43/0.64 (step @p64 :rule refl :args ((_ @t1 @t83))) % 0.43/0.64 (step @p65 :rule refl :args (@t30)) % 0.43/0.64 (step @p66 :rule refl :args (@t18)) % 0.43/0.64 (step @p67 :rule cong :premises (@p66 @p65) :args (@t31)) % 0.43/0.64 (step @p68 :rule cong :premises (@p67) :args (@t32)) % 0.43/0.64 (step @p69 :rule refl :args ((_ @t27 @t82))) % 0.43/0.64 (step @p70 :rule cong :premises (@p65) :args (@t33)) % 0.43/0.64 (step @p71 :rule trans :premises (@p70 @p69)) % 0.43/0.64 (step @p72 :rule nary_cong :premises (@p71 @p68) :args (@t34)) % 0.43/0.64 (step @p73 :rule cong :premises (@p72) :args (@t36)) % 0.43/0.64 (step @p74 :rule cong :premises (@p73) :args (@t37)) % 0.43/0.64 (step @p75 :rule cong :premises (@p74) :args (@t39)) % 0.43/0.64 (step @p76 :rule cong :premises (@p75) :args (@t40)) % 0.43/0.64 (step @p77 :rule trans :premises (@p76 @p64)) % 0.43/0.64 (step @p78 :rule refl :args (@t1)) % 0.43/0.64 (step @p79 :rule ho_cong :premises (@p78 @p75)) % 0.43/0.64 (step @p80 :rule cong :premises (@p79 @p77) :args ((= @t84 @t40))) % 0.43/0.64 (step @p81 :rule symm :premises (@p80)) % 0.43/0.64 (step @p82 :rule refl :args ((_ @t1 @t83))) % 0.43/0.64 (step @p83 :rule eq_resolve :premises (@p82 @p81)) % 0.43/0.64 (step @p84 :rule refl :args (@t79)) % 0.43/0.64 (step @p85 :rule cong :premises (@p84 @p83) :args (@t85)) % 0.43/0.64 (step @p86 :rule cong :premises (@p85) :args (@t86)) % 0.43/0.64 (step @p87 :rule refl :args (@t80)) % 0.43/0.64 (step @p88 :rule nary_cong :premises (@p87 @p86) :args (@t87)) % 0.43/0.64 (step @p89 :rule cong :premises (@p88) :args ((forall @t23 @t87))) % 0.43/0.64 (step @p90 :rule alpha_equiv :args (@t88 @t77 (@list @t27))) % 0.43/0.64 (step @p91 :rule cong :premises (@p90) :args (@t89)) % 0.43/0.64 (step @p92 :rule cong :premises (@p91) :args (@t90)) % 0.43/0.64 (step @p93 :rule ho_cong :premises (@p78 @p92)) % 0.43/0.64 (step @p94 :rule cong :premises (@p84 @p93) :args (@t92)) % 0.43/0.64 (step @p95 :rule cong :premises (@p94) :args (@t93)) % 0.43/0.64 (step @p96 :rule nary_cong :premises (@p87 @p95) :args (@t94)) % 0.43/0.64 (step @p97 :rule cong :premises (@p96) :args ((forall @t23 @t94))) % 0.43/0.64 (step @p98 :rule trans :premises (@p97 @p89)) % 0.43/0.64 (step @p99 :rule eq-symm :args (@t91 @t79)) % 0.43/0.64 (step @p100 :rule cong :premises (@p99) :args (@t95)) % 0.43/0.64 (step @p101 :rule refl :args (@t80)) % 0.43/0.64 (step @p102 :rule nary_cong :premises (@p101 @p100) :args (@t96)) % 0.43/0.64 (step @p103 :rule cong :premises (@p102) :args (@t97)) % 0.43/0.64 (step @p104 :rule trans :premises (@p103 @p98)) % 0.43/0.64 (step @p105 :rule cong :premises (@p104) :args (@t98)) % 0.43/0.64 (step @p106 :rule beta-reduce :args ((= (_ @t90 @t91) @t98))) % 0.43/0.64 (step @p107 :rule trans :premises (@p106 @p105)) % 0.43/0.64 (step @p108 :rule beta-reduce :args ((= @t99 @t90))) % 0.43/0.64 (step @p109 :rule refl :args (@t1)) % 0.43/0.64 (step @p110 :rule ho_cong :premises (@p109 @p108)) % 0.43/0.64 (step @p111 :rule ho_cong :premises (@p108 @p110)) % 0.43/0.64 (step @p112 :rule trans :premises (@p111 @p107)) % 0.43/0.64 (step @p113 :rule cong :premises (@p112) :args (@t100)) % 0.43/0.64 (step @p114 :rule trans :premises (@p113 @p63)) % 0.43/0.64 (step @p115 :rule refl :args (@t6)) % 0.43/0.64 (step @p116 :rule refl :args (@t42)) % 0.43/0.64 (step @p117 :rule refl :args (@t7)) % 0.43/0.64 (step @p118 :rule cong :premises (@p117 @p116) :args ((= @t7 @t42))) % 0.43/0.64 (step @p119 :rule symm :premises (@p118)) % 0.43/0.64 (step @p120 :rule eq_resolve :premises (@p117 @p119)) % 0.43/0.64 (step @p121 :rule refl :args (@t43)) % 0.43/0.64 (step @p122 :rule refl :args (@t8)) % 0.43/0.64 (step @p123 :rule cong :premises (@p122 @p121) :args ((= @t8 @t43))) % 0.43/0.64 (step @p124 :rule symm :premises (@p123)) % 0.43/0.64 (step @p125 :rule eq_resolve :premises (@p122 @p124)) % 0.43/0.64 (step @p126 :rule cong :premises (@p125 @p120) :args (@t9)) % 0.43/0.64 (step @p127 :rule cong :premises (@p126) :args (@t101)) % 0.43/0.64 (step @p128 :rule nary_cong :premises (@p127 @p115) :args (@t102)) % 0.43/0.64 (step @p129 :rule cong :premises (@p128) :args ((forall @t10 @t102))) % 0.43/0.64 (step @p130 :rule bool-impl-elim :args (@t9 @t6)) % 0.43/0.64 (step @p131 :rule cong :premises (@p130) :args (@t11)) % 0.43/0.64 (step @p132 :rule trans :premises (@p131 @p129)) % 0.43/0.64 (step @p133 :rule cong :premises (@p132 @p114) :args (@t103)) % 0.43/0.64 (step @p134 :rule cong :premises (@p133) :args (@t104)) % 0.43/0.64 (step @p135 :rule trans :premises (@p134 @p62)) % 0.43/0.64 (step @p136 :rule cong :premises (@p135) :args ((not @t104))) % 0.43/0.64 (step @p137 :rule refl :args (@t79)) % 0.43/0.64 (step @p138 :rule refl :args (@t17)) % 0.43/0.64 (step @p139 :rule cong :premises (@p138 @p137) :args ((= @t17 @t79))) % 0.43/0.64 (step @p140 :rule symm :premises (@p139)) % 0.43/0.64 (step @p141 :rule eq_resolve :premises (@p138 @p140)) % 0.43/0.64 (step @p142 :rule cong :premises (@p66 @p141) :args (@t19)) % 0.43/0.64 (step @p143 :rule cong :premises (@p142) :args (@t105)) % 0.43/0.64 (step @p144 :rule refl :args ((_ @t16 @t17))) % 0.43/0.64 (step @p145 :rule cong :premises (@p137) :args (@t80)) % 0.43/0.64 (step @p146 :rule trans :premises (@p145 @p144)) % 0.43/0.64 (step @p147 :rule refl :args (@t16)) % 0.43/0.64 (step @p148 :rule ho_cong :premises (@p147 @p137)) % 0.43/0.64 (step @p149 :rule cong :premises (@p148 @p146) :args ((= (_ @t16 @t79) @t80))) % 0.43/0.64 (step @p150 :rule symm :premises (@p149)) % 0.43/0.64 (step @p151 :rule refl :args (@t20)) % 0.43/0.64 (step @p152 :rule eq_resolve :premises (@p151 @p150)) % 0.43/0.64 (step @p153 :rule ho_cong :premises (@p147 @p141)) % 0.43/0.64 (step @p154 :rule trans :premises (@p153 @p152)) % 0.43/0.64 (step @p155 :rule nary_cong :premises (@p154 @p143) :args (@t106)) % 0.43/0.64 (step @p156 :rule cong :premises (@p155) :args ((forall @t23 @t106))) % 0.43/0.64 (step @p157 :rule refl :args (@t105)) % 0.43/0.64 (step @p158 :rule bool-double-not-elim :args (@t20)) % 0.43/0.64 (step @p159 :rule nary_cong :premises (@p158 @p157) :args ((or (not @t21) @t105))) % 0.43/0.64 (step @p160 :rule bool-and-de-morgan :args (@t21 @t19 true)) % 0.43/0.64 (step @p161 :rule trans :premises (@p160 @p159)) % 0.43/0.64 (step @p162 :rule cong :premises (@p161) :args (@t107)) % 0.43/0.64 (step @p163 :rule trans :premises (@p162 @p156)) % 0.43/0.64 (step @p164 :rule cong :premises (@p163) :args (@t108)) % 0.43/0.64 (step @p165 :rule exists-elim :args ((= @t24 @t108))) % 0.43/0.64 (step @p166 :rule trans :premises (@p165 @p164)) % 0.43/0.64 (step @p167 :rule cong :premises (@p166) :args (@t26)) % 0.43/0.64 (step @p168 :rule trans :premises (@p3 @p167)) % 0.43/0.64 (step @p169 :rule ho_cong :premises (@p168 @p109)) % 0.43/0.64 (step @p170 :rule ho_cong :premises (@p109 @p169)) % 0.43/0.64 (step @p171 :rule ho_cong :premises (@p169 @p170)) % 0.43/0.64 (step @p172 :rule cong :premises (@p171) :args (@t3)) % 0.43/0.64 (step @p173 :rule refl :args (@t11)) % 0.43/0.64 (step @p174 :rule cong :premises (@p173 @p172) :args (@t12)) % 0.43/0.64 (step @p175 :rule cong :premises (@p174) :args (@t14)) % 0.43/0.64 (step @p176 :rule cong :premises (@p175) :args (@t15)) % 0.43/0.64 (step @p177 :rule trans :premises (@p176 @p136)) % 0.43/0.64 (step @p178 :rule eq_resolve :premises (@p1 @p177)) % 0.43/0.64 (step @p179 :rule refl :args (@t117)) % 0.43/0.64 (step @p180 :rule bool-double-not-elim :args (@t47)) % 0.43/0.64 (step @p181 :rule nary_cong :premises (@p180 @p179) :args ((or (not @t118) @t117))) % 0.43/0.64 (step @p182 :rule eq-refl :args (@t52)) % 0.43/0.64 (step @p183 :rule refl :args (@t52)) % 0.43/0.64 (step @p184 :rule cong :premises (@p183 @p16) :args ((= @t52 @t53))) % 0.43/0.64 (step @p185 :rule trans :premises (@p184 @p182)) % 0.43/0.64 (step @p186 :rule true_elim :premises (@p185)) % 0.43/0.64 (step @p187 :rule cong :premises (@p186) :args (@t119)) % 0.43/0.64 (step @p188 :rule refl :args (@t110)) % 0.43/0.64 (step @p189 :rule cong :premises (@p188 @p187) :args (@t120)) % 0.43/0.64 (step @p190 :rule cong :premises (@p189) :args (@t121)) % 0.43/0.64 (step @p191 :rule refl :args (@t113)) % 0.43/0.64 (step @p192 :rule refl :args (@t115)) % 0.43/0.64 (step @p193 :rule nary_cong :premises (@p192 @p191 @p190) :args (@t122)) % 0.43/0.64 (step @p194 :rule cong :premises (@p193) :args (@t123)) % 0.43/0.64 (step @p195 :rule refl :args (@t118)) % 0.43/0.64 (step @p196 :rule cong :premises (@p195 @p194) :args ((=> @t118 @t123))) % 0.43/0.64 (step @p197 :rule eq-symm :args (@t119 @t110)) % 0.43/0.64 (step @p198 :rule cong :premises (@p197) :args (@t124)) % 0.43/0.64 (step @p199 :rule nary_cong :premises (@p192 @p191 @p198) :args (@t125)) % 0.43/0.64 (step @p200 :rule cong :premises (@p199) :args (@t126)) % 0.43/0.64 (step @p201 :rule cong :premises (@p195 @p200) :args ((=> @t118 @t126))) % 0.43/0.64 (step @p202 :rule trans :premises (@p201 @p196)) % 0.43/0.64 (assume-push @p254 @t118) % 0.43/0.64 (step @p204 :rule skolemize :premises (@p178)) % 0.43/0.64 (step-pop @p255 :rule scope :premises (@p204)) % 0.43/0.64 (step @p205 :rule process_scope :premises (@p255) :args (@t126)) % 0.43/0.64 (step @p207 :rule eq_resolve :premises (@p205 @p202)) % 0.43/0.64 (step @p208 :rule implies_elim :premises (@p207)) % 0.43/0.64 (step @p209 :rule eq_resolve :premises (@p208 @p181)) % 0.43/0.64 (step @p210 :rule chain_m_resolution :premises (@p209 @p178) :args (@t117 @t127 (@list @t47))) % 0.43/0.64 (step @p211 :rule cnf_or_neg :args (@t116 1)) % 0.43/0.64 (step @p212 :rule chain_m_resolution :premises (@p211 @p210) :args ((not @t113) @t127 @t128)) % 0.43/0.64 (step @p213 :rule false_intro :premises (@p212)) % 0.43/0.64 (step @p214 :rule bool-double-not-elim :args (@t111)) % 0.43/0.64 (step @p215 :rule refl :args (@t116)) % 0.43/0.64 (step @p216 :rule nary_cong :premises (@p215 @p214) :args ((or @t116 (not @t112)))) % 0.43/0.64 (step @p217 :rule cnf_or_neg :args (@t116 2)) % 0.43/0.64 (step @p218 :rule eq_resolve :premises (@p217 @p216)) % 0.43/0.64 (step @p219 :rule reordering :premises (@p218) :args ((or @t111 @t116))) % 0.43/0.64 (step @p220 :rule chain_m_resolution :premises (@p219 @p210) :args (@t111 @t127 @t128)) % 0.43/0.64 (step @p221 :rule symm :premises (@p220)) % 0.43/0.64 (step @p222 :rule bool-double-not-elim :args (@t114)) % 0.43/0.64 (step @p223 :rule nary_cong :premises (@p215 @p222) :args ((or @t116 (not @t115)))) % 0.43/0.64 (step @p224 :rule cnf_or_neg :args (@t116 0)) % 0.43/0.64 (step @p225 :rule eq_resolve :premises (@p224 @p223)) % 0.43/0.64 (step @p226 :rule reordering :premises (@p225) :args ((or @t114 @t116))) % 0.43/0.64 (step @p227 :rule chain_m_resolution :premises (@p226 @p210) :args (@t114 @t127 @t128)) % 0.43/0.64 (step @p228 :rule instantiate :premises (@p227) :args ((@list @t109 @t53))) % 0.43/0.64 (step @p229 :rule cnf_or_pos :args (@t130)) % 0.43/0.64 (step @p230 :rule reordering :premises (@p229) :args ((or @t112 @t129 (not @t130)))) % 0.43/0.64 (step @p231 :rule chain_m_resolution :premises (@p230 @p220 @p228) :args (@t129 (@list false false) (@list @t111 @t130))) % 0.43/0.64 (step @p232 :rule symm :premises (@p231)) % 0.43/0.64 (step @p233 :rule ho_cong :premises (@p232 @p221)) % 0.43/0.64 (step @p234 :rule trans :premises (@p233 @p213)) % 0.43/0.64 (step @p235 :rule false_elim :premises (@p234)) % 0.43/0.64 (step @p236 :rule bool-double-not-elim :args (@t59)) % 0.43/0.64 (step @p237 :rule refl :args (@t131)) % 0.43/0.64 (step @p238 :rule nary_cong :premises (@p237 @p24 @p236) :args ((or @t131 @t61 (not @t60)))) % 0.43/0.64 (step @p239 :rule cnf_equiv_pos2 :args (@t68)) % 0.43/0.64 (step @p240 :rule eq_resolve :premises (@p239 @p238)) % 0.43/0.64 (step @p241 :rule reordering :premises (@p240) :args ((or @t61 @t59 @t131))) % 0.43/0.64 (step @p242 :rule chain_m_resolution :premises (@p241 @p235 @p41) :args (@t59 @t132 (@list @t61 @t68))) % 0.43/0.64 (step @p243 :rule cnf_or_pos :args (@t133)) % 0.43/0.64 (step @p244 :rule reordering :premises (@p243) :args ((or @t113 @t112 @t134))) % 0.43/0.64 (step @p245 :rule chain_m_resolution :premises (@p244 @p212 @p220) :args (@t134 @t132 (@list @t113 @t111))) % 0.43/0.64 (assume-push @p256 @t59) % 0.43/0.64 (step @p247 :rule instantiate :premises (@p242) :args ((@list @t109))) % 0.43/0.64 (step-pop @p257 :rule scope :premises (@p247)) % 0.43/0.64 (step @p248 :rule process_scope :premises (@p257) :args (@t133)) % 0.43/0.64 (step @p250 :rule implies_elim :premises (@p248)) % 0.43/0.64 (step @p251 false :rule chain_m_resolution :premises (@p250 @p245 @p242) :args (false @t132 (@list @t133 @t59))) % 0.43/0.64 ) % 0.43/0.64 % SZS output end Proof % 0.43/0.64 % cvc5 exiting %------------------------------------------------------------------------------