%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO538^1 : TPTP v9.2.1. Released 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 : n006.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 09:13:05 AM UTC 2026 % Result : Theorem 0.45s 0.64s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYO538^1 : TPTP v9.2.1. Released v5.2.0. % 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 : n006.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 : Wed Jun 3 00:19:34 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.51 %----Proving TH0 % 0.45/0.64 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.45/0.64 % SZS status Theorem % 0.45/0.64 % SZS output start Proof % 0.45/0.64 ( % 0.45/0.64 (declare-sort $$unsorted 0) % 0.45/0.64 (declare-const tptp.eps (-> (-> $$unsorted Bool) $$unsorted)) % 0.45/0.64 (define tptp.if () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "B" Bool))) (let ((_let_4 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_4 _let_1) (_ tptp.eps (lambda (@list _let_2) (or (and _let_3 (= _let_2 _let_4)) (and (not _let_3) (= _let_2 _let_1))))))))))) % 0.45/0.64 (define @t1 () (@var "P" (-> $$unsorted Bool))) % 0.45/0.64 (define @t2 () (_ tptp.eps @t1)) % 0.45/0.64 (define @t3 () (_ @t1 @t2)) % 0.45/0.64 (define @t4 () (@var "X" $$unsorted)) % 0.45/0.64 (define @t5 () (_ @t1 @t4)) % 0.45/0.64 (define @t6 () (@list @t4)) % 0.45/0.64 (define @t7 () (exists @t6 @t5)) % 0.45/0.64 (define @t8 () (=> @t7 @t3)) % 0.45/0.64 (define @t9 () (@list @t1)) % 0.45/0.64 (define @t10 () (forall @t9 @t8)) % 0.45/0.64 (define @t11 () (@var "Y" $$unsorted)) % 0.45/0.64 (define @t12 () (= (_ (_ (_ tptp.if false) @t4) @t11) @t11)) % 0.45/0.64 (define @t13 () (= (_ (_ (_ tptp.if true) @t4) @t11) @t4)) % 0.45/0.64 (define @t14 () (and @t13 @t12)) % 0.45/0.64 (define @t15 () (@list @t4 @t11)) % 0.45/0.64 (define @t16 () (forall @t15 @t14)) % 0.45/0.64 (define @t17 () (not @t16)) % 0.45/0.64 (define @t18 () (@var "Z" $$unsorted)) % 0.45/0.64 (define @t19 () (@var "B" Bool)) % 0.45/0.64 (define @t20 () (not @t19)) % 0.45/0.64 (define @t21 () (and @t20 (= @t18 @t11))) % 0.45/0.64 (define @t22 () (and @t19 (= @t18 @t4))) % 0.45/0.64 (define @t23 () (or @t22 @t21)) % 0.45/0.64 (define @t24 () (@list @t18)) % 0.45/0.64 (define @t25 () (lambda @t24 @t23)) % 0.45/0.64 (define @t26 () (@list @t19 @t4 @t11)) % 0.45/0.64 (define @t27 () (lambda @t26 (_ tptp.eps @t25))) % 0.45/0.64 (define @t28 () (@var "BOUND_VARIABLE_14839" $$unsorted)) % 0.45/0.64 (define @t29 () (@var "BOUND_VARIABLE_7539" $$unsorted)) % 0.45/0.64 (define @t30 () (lambda @t24 (= @t18 @t29))) % 0.45/0.64 (define @t31 () (tptp.eps @t30)) % 0.45/0.64 (define @t32 () (@list @t29)) % 0.45/0.64 (define @t33 () (forall @t32 (= @t29 @t31))) % 0.45/0.64 (define @t34 () (@quantifiers_skolemize @t33 0)) % 0.45/0.64 (define @t35 () (@list @t28)) % 0.45/0.64 (define @t36 () (lambda @t35 (= @t34 @t28))) % 0.45/0.64 (define @t37 () (@purify @t36)) % 0.45/0.64 (define @t38 () (lambda @t24 (= @t18 @t34))) % 0.45/0.64 (define @t39 () (@purify @t38)) % 0.45/0.64 (define @t40 () (= @t39 @t37)) % 0.45/0.64 (define @t41 () (not true)) % 0.45/0.64 (define @t42 () (@const 0 $$unsorted)) % 0.45/0.64 (define @t43 () (= @t34 @t42)) % 0.45/0.64 (define @t44 () (= (_ @t36 @t42) @t43)) % 0.45/0.64 (define @t45 () (_ @t37 @t42)) % 0.45/0.64 (define @t46 () (_ @t38 @t42)) % 0.45/0.64 (define @t47 () (_ @t39 @t42)) % 0.45/0.64 (define @t48 () (= @t47 @t45)) % 0.45/0.64 (define @t49 () (not @t48)) % 0.45/0.64 (define @t50 () (or @t40 @t49)) % 0.45/0.64 (define @t51 () (tptp.eps @t37)) % 0.45/0.64 (define @t52 () (tptp.eps @t1)) % 0.45/0.64 (define @t53 () (_ @t1 @t52)) % 0.45/0.64 (define @t54 () (@var "BOUND_VARIABLE_7481" $$unsorted)) % 0.45/0.64 (define @t55 () (not (_ @t1 @t54))) % 0.45/0.64 (define @t56 () (or @t55 @t53)) % 0.45/0.64 (define @t57 () (forall (@list @t1 @t54) @t56)) % 0.45/0.64 (define @t58 () (@list @t54)) % 0.45/0.64 (define @t59 () (forall @t58 @t56)) % 0.45/0.64 (define @t60 () (forall @t58 @t55)) % 0.45/0.64 (define @t61 () (or @t60 @t53)) % 0.45/0.64 (define @t62 () (_ @t1 @t4)) % 0.45/0.64 (define @t63 () (forall @t6 (not @t62))) % 0.45/0.64 (define @t64 () (or @t63 @t3)) % 0.45/0.64 (define @t65 () (not @t63)) % 0.45/0.64 (define @t66 () (not @t5)) % 0.45/0.64 (define @t67 () (forall @t6 @t66)) % 0.45/0.64 (define @t68 () (not @t67)) % 0.45/0.64 (define @t69 () (tptp.eps @t36)) % 0.45/0.64 (define @t70 () (= @t34 @t69)) % 0.45/0.64 (define @t71 () (lambda @t35 (= @t28 @t34))) % 0.45/0.64 (define @t72 () (tptp.eps @t71)) % 0.45/0.64 (define @t73 () (_ @t71 @t72)) % 0.45/0.64 (define @t74 () (_ @t71 @t34)) % 0.45/0.64 (define @t75 () (not @t74)) % 0.45/0.64 (define @t76 () (or @t75 @t73)) % 0.45/0.64 (define @t77 () (@list false)) % 0.45/0.64 (define @t78 () (= @t34 (tptp.eps @t39))) % 0.45/0.64 (define @t79 () (not @t78)) % 0.45/0.64 (define @t80 () (not @t33)) % 0.45/0.64 (define @t81 () (tptp.eps @t38)) % 0.45/0.64 (define @t82 () (= @t34 @t81)) % 0.45/0.64 (define @t83 () (not @t82)) % 0.45/0.64 (define @t84 () (@var "BOUND_VARIABLE_7609" $$unsorted)) % 0.45/0.64 (define @t85 () (@var "BOUND_VARIABLE_7610" $$unsorted)) % 0.45/0.64 (define @t86 () (@list @t84 @t85)) % 0.45/0.64 (define @t87 () (@var "BOUND_VARIABLE_7551" $$unsorted)) % 0.45/0.64 (define @t88 () (lambda @t24 (= @t18 @t87))) % 0.45/0.64 (define @t89 () (tptp.eps @t88)) % 0.45/0.64 (define @t90 () (@list @t87)) % 0.45/0.64 (define @t91 () (forall @t90 (= @t87 @t89))) % 0.45/0.64 (define @t92 () (_ tptp.eps @t88)) % 0.45/0.64 (define @t93 () (= @t87 @t92)) % 0.45/0.64 (define @t94 () (forall @t90 @t93)) % 0.45/0.64 (define @t95 () (@var "BOUND_VARIABLE_7549" $$unsorted)) % 0.45/0.64 (define @t96 () (@list @t95 @t87)) % 0.45/0.64 (define @t97 () (lambda @t24 (= @t87 @t18))) % 0.45/0.64 (define @t98 () (= @t87 (_ tptp.eps @t97))) % 0.45/0.64 (define @t99 () (forall @t96 @t98)) % 0.45/0.64 (define @t100 () (_ tptp.eps @t30)) % 0.45/0.64 (define @t101 () (= @t29 @t100)) % 0.45/0.64 (define @t102 () (forall @t32 @t101)) % 0.45/0.64 (define @t103 () (@var "BOUND_VARIABLE_7541" $$unsorted)) % 0.45/0.64 (define @t104 () (@list @t29 @t103)) % 0.45/0.64 (define @t105 () (lambda @t24 (= @t29 @t18))) % 0.45/0.64 (define @t106 () (= @t29 (_ tptp.eps @t105))) % 0.45/0.64 (define @t107 () (forall @t104 @t106)) % 0.45/0.64 (define @t108 () (= @t11 @t18)) % 0.45/0.64 (define @t109 () (_ tptp.eps (lambda @t24 @t108))) % 0.45/0.64 (define @t110 () (= @t11 @t109)) % 0.45/0.64 (define @t111 () (forall @t15 @t110)) % 0.45/0.64 (define @t112 () (@list @t4 @t11)) % 0.45/0.64 (define @t113 () (= @t4 @t18)) % 0.45/0.64 (define @t114 () (_ tptp.eps (lambda @t24 @t113))) % 0.45/0.64 (define @t115 () (= @t4 @t114)) % 0.45/0.64 (define @t116 () (forall @t15 @t115)) % 0.45/0.64 (define @t117 () (and @t116 @t111)) % 0.45/0.64 (define @t118 () (@list @t11)) % 0.45/0.64 (define @t119 () (lambda @t118 @t109)) % 0.45/0.64 (define @t120 () (not false)) % 0.45/0.64 (define @t121 () (and @t120 @t108)) % 0.45/0.64 (define @t122 () (and false @t113)) % 0.45/0.64 (define @t123 () (or @t122 @t121)) % 0.45/0.64 (define @t124 () (lambda @t24 @t123)) % 0.45/0.64 (define @t125 () (lambda @t15 (_ tptp.eps @t124))) % 0.45/0.64 (define @t126 () (lambda @t26 (_ tptp.eps (lambda @t24 (or (and @t19 @t113) (and @t20 @t108)))))) % 0.45/0.64 (define @t127 () (_ @t126 false)) % 0.45/0.64 (define @t128 () (= (_ (_ @t127 @t4) @t11) @t11)) % 0.45/0.64 (define @t129 () (lambda @t118 @t114)) % 0.45/0.64 (define @t130 () (and @t41 @t108)) % 0.45/0.64 (define @t131 () (and true @t113)) % 0.45/0.64 (define @t132 () (or @t131 @t130)) % 0.45/0.64 (define @t133 () (lambda @t24 @t132)) % 0.45/0.64 (define @t134 () (lambda @t15 (_ tptp.eps @t133))) % 0.45/0.64 (define @t135 () (_ @t126 true)) % 0.45/0.64 (define @t136 () (= (_ (_ @t135 @t4) @t11) @t4)) % 0.45/0.64 (define @t137 () (and @t136 @t128)) % 0.45/0.64 (define @t138 () (forall @t15 @t137)) % 0.45/0.64 (assume @p1 @t10) % 0.45/0.64 (assume @p2 @t17) % 0.45/0.64 (assume @p3 true) % 0.45/0.64 (step @p4 (= tptp.if @t27) :rule refl :args (@t27)) % 0.45/0.64 (step @p5 :rule aci_norm :args ((= (or @t40 false) @t40))) % 0.45/0.64 (step @p6 :rule evaluate :args (@t41)) % 0.45/0.64 (step @p7 :rule eq-refl :args (@t43)) % 0.45/0.64 (step @p8 :rule refl :args (@t43)) % 0.45/0.64 (step @p9 :rule beta-reduce :args (@t44)) % 0.45/0.64 (step @p10 :rule cong :premises (@p9 @p8) :args (@t44)) % 0.45/0.64 (step @p11 :rule trans :premises (@p10 @p7)) % 0.45/0.64 (step @p12 :rule refl :args (@t42)) % 0.45/0.64 (step @p13 :rule skolem_intro :args (@t37)) % 0.45/0.64 (step @p14 :rule ho_cong :premises (@p13 @p12)) % 0.45/0.64 (step @p15 :rule cong :premises (@p14 @p8) :args ((= @t45 @t43))) % 0.45/0.64 (step @p16 :rule trans :premises (@p15 @p11)) % 0.45/0.64 (step @p17 :rule true_elim :premises (@p16)) % 0.45/0.64 (step @p18 :rule eq-symm :args (@t42 @t34)) % 0.45/0.64 (step @p19 :rule beta-reduce :args ((= @t46 (= @t42 @t34)))) % 0.45/0.64 (step @p20 :rule trans :premises (@p19 @p18)) % 0.45/0.64 (step @p21 :rule cong :premises (@p8 @p20) :args ((= @t43 @t46))) % 0.45/0.64 (step @p22 :rule trans :premises (@p21 @p7)) % 0.45/0.64 (step @p23 :rule eq-symm :args (@t46 @t43)) % 0.45/0.64 (step @p24 :rule trans :premises (@p23 @p22)) % 0.45/0.64 (step @p25 :rule skolem_intro :args (@t39)) % 0.45/0.64 (step @p26 :rule ho_cong :premises (@p25 @p12)) % 0.45/0.64 (step @p27 :rule cong :premises (@p26 @p8) :args ((= @t47 @t43))) % 0.45/0.64 (step @p28 :rule trans :premises (@p27 @p24)) % 0.45/0.64 (step @p29 :rule true_elim :premises (@p28)) % 0.45/0.64 (step @p30 :rule cong :premises (@p29 @p17) :args (@t48)) % 0.45/0.64 (step @p31 :rule trans :premises (@p30 @p7)) % 0.45/0.64 (step @p32 :rule cong :premises (@p31) :args (@t49)) % 0.45/0.64 (step @p33 :rule trans :premises (@p32 @p6)) % 0.45/0.64 (step @p34 :rule refl :args (@t40)) % 0.45/0.64 (step @p35 :rule nary_cong :premises (@p34 @p33) :args (@t50)) % 0.45/0.64 (step @p36 :rule trans :premises (@p35 @p5)) % 0.45/0.64 ; WARNING: add trust step for TRUST % 0.45/0.64 ; trust TRUST THEORY_LEMMA % 0.45/0.64 (step @p37 :rule trust :premises () :args (@t50)) % 0.45/0.64 (step @p38 :rule eq_resolve :premises (@p37 @p36)) % 0.45/0.64 (step @p39 :rule symm :premises (@p38)) % 0.45/0.64 (step @p40 :rule cong :premises (@p39) :args (@t51)) % 0.45/0.64 (step @p41 :rule quant-merge-prenex :args ((= (forall @t9 @t59) @t57))) % 0.45/0.64 (step @p42 :rule refl :args (@t53)) % 0.45/0.64 (step @p43 :rule alpha_equiv :args (@t60 (@list @t54) (@list @t4))) % 0.45/0.64 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t61)) % 0.45/0.64 (step @p45 :rule quant-miniscope-or :args ((= @t59 @t61))) % 0.45/0.64 (step @p46 :rule trans :premises (@p45 @p44)) % 0.45/0.64 (step @p47 :rule symm :premises (@p46)) % 0.45/0.64 (step @p48 :rule cong :premises (@p47) :args ((forall @t9 (or @t63 @t53)))) % 0.45/0.64 (step @p49 :rule trans :premises (@p48 @p41)) % 0.45/0.64 (step @p50 :rule refl :args ((_ @t1 @t2))) % 0.45/0.64 (step @p51 :rule refl :args (@t52)) % 0.45/0.64 (step @p52 :rule cong :premises (@p51) :args (@t53)) % 0.45/0.64 (step @p53 :rule trans :premises (@p52 @p50)) % 0.45/0.64 (step @p54 :rule refl :args (@t1)) % 0.45/0.64 (step @p55 :rule ho_cong :premises (@p54 @p51)) % 0.45/0.64 (step @p56 :rule cong :premises (@p55 @p53) :args ((= (_ @t1 @t52) @t53))) % 0.45/0.64 (step @p57 :rule symm :premises (@p56)) % 0.45/0.64 (step @p58 :rule refl :args (@t3)) % 0.45/0.64 (step @p59 :rule eq_resolve :premises (@p58 @p57)) % 0.45/0.64 (step @p60 :rule refl :args (@t2)) % 0.45/0.64 (step @p61 :rule cong :premises (@p60 @p51) :args ((= @t2 @t52))) % 0.45/0.64 (step @p62 :rule symm :premises (@p61)) % 0.45/0.64 (step @p63 :rule eq_resolve :premises (@p60 @p62)) % 0.45/0.64 (step @p64 :rule ho_cong :premises (@p54 @p63)) % 0.45/0.64 (step @p65 :rule trans :premises (@p64 @p59)) % 0.45/0.64 (step @p66 :rule refl :args (@t63)) % 0.45/0.64 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t64)) % 0.45/0.64 (step @p68 :rule cong :premises (@p67) :args ((forall @t9 @t64))) % 0.45/0.64 (step @p69 :rule trans :premises (@p68 @p49)) % 0.45/0.64 (step @p70 :rule bool-double-not-elim :args (@t63)) % 0.45/0.64 (step @p71 :rule nary_cong :premises (@p70 @p58) :args ((or (not @t65) @t3))) % 0.45/0.64 (step @p72 :rule bool-impl-elim :args (@t65 @t3)) % 0.45/0.64 (step @p73 :rule trans :premises (@p72 @p71)) % 0.45/0.64 (step @p74 :rule cong :premises (@p73) :args ((forall @t9 (=> @t65 @t3)))) % 0.45/0.64 (step @p75 :rule trans :premises (@p74 @p69)) % 0.45/0.64 (step @p76 :rule refl :args (@t3)) % 0.45/0.64 (step @p77 :rule refl :args (@t62)) % 0.45/0.64 (step @p78 :rule refl :args (@t5)) % 0.45/0.64 (step @p79 :rule cong :premises (@p78 @p77) :args ((= @t5 @t62))) % 0.45/0.64 (step @p80 :rule symm :premises (@p79)) % 0.45/0.64 (step @p81 :rule eq_resolve :premises (@p78 @p80)) % 0.45/0.64 (step @p82 :rule cong :premises (@p81) :args (@t66)) % 0.45/0.64 (step @p83 :rule cong :premises (@p82) :args (@t67)) % 0.45/0.64 (step @p84 :rule cong :premises (@p83) :args (@t68)) % 0.45/0.64 (step @p85 :rule exists-elim :args ((= @t7 @t68))) % 0.45/0.64 (step @p86 :rule trans :premises (@p85 @p84)) % 0.45/0.64 (step @p87 :rule cong :premises (@p86 @p76) :args (@t8)) % 0.45/0.64 (step @p88 :rule cong :premises (@p87) :args (@t10)) % 0.45/0.64 (step @p89 :rule trans :premises (@p88 @p75)) % 0.45/0.64 (step @p90 :rule eq_resolve :premises (@p1 @p89)) % 0.45/0.64 (step @p91 :rule eq-refl :args (@t36)) % 0.45/0.64 (step @p92 :rule refl :args (@t36)) % 0.45/0.64 (step @p93 :rule cong :premises (@p92 @p13) :args ((= @t36 @t37))) % 0.45/0.64 (step @p94 :rule trans :premises (@p93 @p91)) % 0.45/0.64 (step @p95 :rule true_elim :premises (@p94)) % 0.45/0.64 (step @p96 :rule cong :premises (@p95) :args (@t69)) % 0.45/0.64 (step @p97 :rule refl :args (@t34)) % 0.45/0.64 (step @p98 :rule cong :premises (@p97 @p96) :args (@t70)) % 0.45/0.64 (step @p99 :rule refl :args (@t57)) % 0.45/0.64 (step @p100 :rule cong :premises (@p99 @p98) :args ((=> @t57 @t70))) % 0.45/0.64 (step @p101 :rule aci_norm :args ((= (or false @t70) @t70))) % 0.45/0.64 (step @p102 :rule eq-symm :args (@t69 @t34)) % 0.45/0.64 (step @p103 :rule beta-reduce :args ((= (_ @t71 @t69) (= @t69 @t34)))) % 0.45/0.64 (step @p104 :rule trans :premises (@p103 @p102)) % 0.45/0.64 (step @p105 :rule eq-symm :args (@t28 @t34)) % 0.45/0.64 (step @p106 :rule cong :premises (@p105) :args (@t71)) % 0.45/0.64 (step @p107 :rule cong :premises (@p106) :args (@t72)) % 0.45/0.64 (step @p108 :rule cong :premises (@p107) :args (@t73)) % 0.45/0.64 (step @p109 :rule trans :premises (@p108 @p104)) % 0.45/0.64 (step @p110 :rule eq-refl :args (@t34)) % 0.45/0.64 (step @p111 :rule beta-reduce :args ((= @t74 (= @t34 @t34)))) % 0.45/0.64 (step @p112 :rule trans :premises (@p111 @p110)) % 0.45/0.64 (step @p113 :rule cong :premises (@p112) :args (@t75)) % 0.45/0.64 (step @p114 :rule trans :premises (@p113 @p6)) % 0.45/0.64 (step @p115 :rule nary_cong :premises (@p114 @p109) :args (@t76)) % 0.45/0.64 (step @p116 :rule trans :premises (@p115 @p101)) % 0.45/0.64 (step @p117 :rule cong :premises (@p99 @p116) :args ((=> @t57 @t76))) % 0.45/0.64 (assume-push @p274 @t57) % 0.45/0.64 (step @p119 :rule instantiate :premises (@p90) :args ((@list @t71 @t34))) % 0.45/0.64 (step-pop @p275 :rule scope :premises (@p119)) % 0.45/0.64 (step @p120 :rule process_scope :premises (@p275) :args (@t76)) % 0.45/0.64 (step @p122 :rule eq_resolve :premises (@p120 @p117)) % 0.45/0.64 (step @p123 :rule eq_resolve :premises (@p122 @p100)) % 0.45/0.64 (step @p124 :rule implies_elim :premises (@p123)) % 0.45/0.64 (step @p125 :rule chain_m_resolution :premises (@p124 @p90) :args ((= @t34 @t51) @t77 (@list @t57))) % 0.45/0.64 (step @p126 :rule trans :premises (@p125 @p40)) % 0.45/0.64 (step @p127 :rule refl :args (@t79)) % 0.45/0.64 (step @p128 :rule bool-double-not-elim :args (@t33)) % 0.45/0.64 (step @p129 :rule nary_cong :premises (@p128 @p127) :args ((or (not @t80) @t79))) % 0.45/0.64 (step @p130 :rule eq-refl :args (@t38)) % 0.45/0.64 (step @p131 :rule refl :args (@t38)) % 0.45/0.64 (step @p132 :rule cong :premises (@p131 @p25) :args ((= @t38 @t39))) % 0.45/0.64 (step @p133 :rule trans :premises (@p132 @p130)) % 0.45/0.64 (step @p134 :rule true_elim :premises (@p133)) % 0.45/0.64 (step @p135 :rule cong :premises (@p134) :args (@t81)) % 0.45/0.64 (step @p136 :rule cong :premises (@p97 @p135) :args (@t82)) % 0.45/0.64 (step @p137 :rule cong :premises (@p136) :args (@t83)) % 0.45/0.64 (step @p138 :rule refl :args (@t80)) % 0.45/0.64 (step @p139 :rule cong :premises (@p138 @p137) :args ((=> @t80 @t83))) % 0.45/0.64 (assume-push @p276 @t80) % 0.45/0.64 (step @p141 :rule skolemize :premises (@p276)) % 0.45/0.64 (step-pop @p277 :rule scope :premises (@p141)) % 0.45/0.64 (step @p142 :rule process_scope :premises (@p277) :args (@t83)) % 0.45/0.64 (step @p144 :rule eq_resolve :premises (@p142 @p139)) % 0.45/0.64 (step @p145 :rule implies_elim :premises (@p144)) % 0.45/0.64 (step @p146 :rule eq_resolve :premises (@p145 @p129)) % 0.45/0.64 (step @p147 :rule chain_m_resolution :premises (@p146 @p126) :args (@t33 @t77 (@list @t78))) % 0.45/0.64 (step @p148 :rule alpha_equiv :args ((forall (@list @t84) (= @t84 (tptp.eps (lambda (@list @t85) (= @t85 @t84))))) @t86 (@list @t87 @t18))) % 0.45/0.64 (step @p149 :rule alpha_equiv :args (@t33 (@list @t29 @t18) @t86)) % 0.45/0.64 (step @p150 :rule trans :premises (@p149 @p148)) % 0.45/0.64 (step @p151 :rule equiv_elim1 :premises (@p150)) % 0.45/0.64 (step @p152 :rule reordering :premises (@p151) :args ((or @t91 @t80))) % 0.45/0.64 (step @p153 :rule chain_m_resolution :premises (@p152 @p147) :args (@t91 @t77 (@list @t33))) % 0.45/0.64 (step @p154 :rule refl :args (@t89)) % 0.45/0.64 (step @p155 :rule refl :args (@t92)) % 0.45/0.64 (step @p156 :rule cong :premises (@p155 @p154) :args ((= @t92 @t89))) % 0.45/0.64 (step @p157 :rule symm :premises (@p156)) % 0.45/0.64 (step @p158 :rule eq_resolve :premises (@p155 @p157)) % 0.45/0.64 (step @p159 :rule refl :args (@t87)) % 0.45/0.64 (step @p160 :rule cong :premises (@p159 @p158) :args (@t93)) % 0.45/0.64 (step @p161 :rule cong :premises (@p160) :args (@t94)) % 0.45/0.64 (step @p162 :rule quant-unused-vars :args ((= (forall @t96 @t93) @t94))) % 0.45/0.64 (step @p163 :rule trans :premises (@p162 @p161)) % 0.45/0.64 (step @p164 :rule eq-symm :args (@t87 @t18)) % 0.45/0.64 (step @p165 :rule cong :premises (@p164) :args (@t97)) % 0.45/0.64 (step @p166 :rule refl :args (tptp.eps)) % 0.45/0.64 (step @p167 :rule ho_cong :premises (@p166 @p165)) % 0.45/0.64 (step @p168 :rule refl :args (@t87)) % 0.45/0.64 (step @p169 :rule cong :premises (@p168 @p167) :args (@t98)) % 0.45/0.64 (step @p170 :rule cong :premises (@p169) :args (@t99)) % 0.45/0.64 (step @p171 :rule trans :premises (@p170 @p163)) % 0.45/0.64 (step @p172 :rule refl :args (@t31)) % 0.45/0.64 (step @p173 :rule refl :args (@t100)) % 0.45/0.64 (step @p174 :rule cong :premises (@p173 @p172) :args ((= @t100 @t31))) % 0.45/0.64 (step @p175 :rule symm :premises (@p174)) % 0.45/0.64 (step @p176 :rule eq_resolve :premises (@p173 @p175)) % 0.45/0.64 (step @p177 :rule refl :args (@t29)) % 0.45/0.64 (step @p178 :rule cong :premises (@p177 @p176) :args (@t101)) % 0.45/0.64 (step @p179 :rule cong :premises (@p178) :args (@t102)) % 0.45/0.64 (step @p180 :rule quant-unused-vars :args ((= (forall @t104 @t101) @t102))) % 0.45/0.64 (step @p181 :rule trans :premises (@p180 @p179)) % 0.45/0.64 (step @p182 :rule eq-symm :args (@t29 @t18)) % 0.45/0.64 (step @p183 :rule cong :premises (@p182) :args (@t105)) % 0.45/0.64 (step @p184 :rule ho_cong :premises (@p166 @p183)) % 0.45/0.64 (step @p185 :rule refl :args (@t29)) % 0.45/0.64 (step @p186 :rule cong :premises (@p185 @p184) :args (@t106)) % 0.45/0.64 (step @p187 :rule cong :premises (@p186) :args (@t107)) % 0.45/0.64 (step @p188 :rule trans :premises (@p187 @p181)) % 0.45/0.64 (step @p189 :rule nary_cong :premises (@p188 @p171) :args ((and @t107 @t99))) % 0.45/0.64 (step @p190 :rule alpha_equiv :args (@t111 @t112 (@list @t95 @t87))) % 0.45/0.64 (step @p191 :rule alpha_equiv :args (@t116 @t112 (@list @t29 @t103))) % 0.45/0.64 (step @p192 :rule nary_cong :premises (@p191 @p190) :args (@t117)) % 0.45/0.64 (step @p193 :rule quant-miniscope-and :args ((= (forall @t15 (and @t115 @t110)) @t117))) % 0.45/0.64 (step @p194 :rule trans :premises (@p193 @p192)) % 0.45/0.64 (step @p195 :rule trans :premises (@p194 @p189)) % 0.45/0.64 (step @p196 :rule eq-symm :args (@t109 @t11)) % 0.45/0.64 (step @p197 :rule refl :args (@t11)) % 0.45/0.64 (step @p198 :rule beta-reduce :args ((= (_ @t119 @t11) @t109))) % 0.45/0.64 (step @p199 :rule beta-reduce :args ((= (_ (lambda @t15 @t109) @t4) @t119))) % 0.45/0.64 (step @p200 :rule refl :args (@t4)) % 0.45/0.64 (step @p201 :rule aci_norm :args ((= (or false @t108) @t108))) % 0.45/0.64 (step @p202 :rule aci_norm :args ((= (and true @t108) @t108))) % 0.45/0.64 (step @p203 :rule refl :args (@t108)) % 0.45/0.64 (step @p204 :rule evaluate :args (@t120)) % 0.45/0.64 (step @p205 :rule nary_cong :premises (@p204 @p203) :args (@t121)) % 0.45/0.64 (step @p206 :rule trans :premises (@p205 @p202)) % 0.45/0.64 (step @p207 :rule absorb :args ((= @t122 false))) % 0.45/0.64 (step @p208 :rule nary_cong :premises (@p207 @p206) :args (@t123)) % 0.45/0.64 (step @p209 :rule trans :premises (@p208 @p201)) % 0.45/0.64 (step @p210 :rule cong :premises (@p209) :args (@t124)) % 0.45/0.64 (step @p211 :rule ho_cong :premises (@p166 @p210)) % 0.45/0.64 (step @p212 :rule cong :premises (@p211) :args (@t125)) % 0.45/0.64 (step @p213 :rule beta-reduce :args ((= @t127 @t125))) % 0.45/0.64 (step @p214 :rule trans :premises (@p213 @p212)) % 0.45/0.64 (step @p215 :rule ho_cong :premises (@p214 @p200)) % 0.45/0.64 (step @p216 :rule trans :premises (@p215 @p199)) % 0.45/0.64 (step @p217 :rule ho_cong :premises (@p216 @p197)) % 0.45/0.64 (step @p218 :rule trans :premises (@p217 @p198)) % 0.45/0.64 (step @p219 :rule cong :premises (@p218 @p197) :args (@t128)) % 0.45/0.64 (step @p220 :rule trans :premises (@p219 @p196)) % 0.45/0.64 (step @p221 :rule eq-symm :args (@t114 @t4)) % 0.45/0.64 (step @p222 :rule beta-reduce :args ((= (_ @t129 @t11) @t114))) % 0.45/0.64 (step @p223 :rule beta-reduce :args ((= (_ (lambda @t15 @t114) @t4) @t129))) % 0.45/0.64 (step @p224 :rule aci_norm :args ((= (or @t113 false) @t113))) % 0.45/0.64 (step @p225 :rule absorb :args ((= (and false @t108) false))) % 0.45/0.64 (step @p226 :rule nary_cong :premises (@p6 @p203) :args (@t130)) % 0.45/0.64 (step @p227 :rule trans :premises (@p226 @p225)) % 0.45/0.64 (step @p228 :rule aci_norm :args ((= @t131 @t113))) % 0.45/0.64 (step @p229 :rule nary_cong :premises (@p228 @p227) :args (@t132)) % 0.45/0.64 (step @p230 :rule trans :premises (@p229 @p224)) % 0.45/0.64 (step @p231 :rule cong :premises (@p230) :args (@t133)) % 0.45/0.64 (step @p232 :rule ho_cong :premises (@p166 @p231)) % 0.45/0.64 (step @p233 :rule cong :premises (@p232) :args (@t134)) % 0.45/0.64 (step @p234 :rule beta-reduce :args ((= @t135 @t134))) % 0.45/0.64 (step @p235 :rule trans :premises (@p234 @p233)) % 0.45/0.64 (step @p236 :rule ho_cong :premises (@p235 @p200)) % 0.45/0.64 (step @p237 :rule trans :premises (@p236 @p223)) % 0.45/0.64 (step @p238 :rule ho_cong :premises (@p237 @p197)) % 0.45/0.64 (step @p239 :rule trans :premises (@p238 @p222)) % 0.45/0.64 (step @p240 :rule cong :premises (@p239 @p200) :args (@t136)) % 0.45/0.64 (step @p241 :rule trans :premises (@p240 @p221)) % 0.45/0.64 (step @p242 :rule nary_cong :premises (@p241 @p220) :args (@t137)) % 0.45/0.64 (step @p243 :rule cong :premises (@p242) :args (@t138)) % 0.45/0.64 (step @p244 :rule trans :premises (@p243 @p195)) % 0.45/0.64 (step @p245 :rule cong :premises (@p244) :args ((not @t138))) % 0.45/0.64 (step @p246 :rule refl :args (false)) % 0.45/0.64 (step @p247 :rule eq-symm :args (@t18 @t11)) % 0.45/0.64 (step @p248 :rule refl :args (@t20)) % 0.45/0.64 (step @p249 :rule nary_cong :premises (@p248 @p247) :args (@t21)) % 0.45/0.64 (step @p250 :rule eq-symm :args (@t18 @t4)) % 0.45/0.64 (step @p251 :rule refl :args (@t19)) % 0.45/0.64 (step @p252 :rule nary_cong :premises (@p251 @p250) :args (@t22)) % 0.45/0.64 (step @p253 :rule nary_cong :premises (@p252 @p249) :args (@t23)) % 0.45/0.64 (step @p254 :rule cong :premises (@p253) :args (@t25)) % 0.45/0.64 (step @p255 :rule ho_cong :premises (@p166 @p254)) % 0.45/0.64 (step @p256 :rule cong :premises (@p255) :args (@t27)) % 0.45/0.64 (step @p257 :rule trans :premises (@p4 @p256)) % 0.45/0.64 (step @p258 :rule ho_cong :premises (@p257 @p246)) % 0.45/0.64 (step @p259 :rule ho_cong :premises (@p258 @p200)) % 0.45/0.64 (step @p260 :rule ho_cong :premises (@p259 @p197)) % 0.45/0.64 (step @p261 :rule cong :premises (@p260 @p197) :args (@t12)) % 0.45/0.64 (step @p262 :rule refl :args (true)) % 0.45/0.64 (step @p263 :rule ho_cong :premises (@p257 @p262)) % 0.45/0.64 (step @p264 :rule ho_cong :premises (@p263 @p200)) % 0.45/0.64 (step @p265 :rule ho_cong :premises (@p264 @p197)) % 0.45/0.64 (step @p266 :rule cong :premises (@p265 @p200) :args (@t13)) % 0.45/0.64 (step @p267 :rule nary_cong :premises (@p266 @p261) :args (@t14)) % 0.45/0.64 (step @p268 :rule cong :premises (@p267) :args (@t16)) % 0.45/0.64 (step @p269 :rule cong :premises (@p268) :args (@t17)) % 0.45/0.64 (step @p270 :rule trans :premises (@p269 @p245)) % 0.45/0.64 (step @p271 :rule eq_resolve :premises (@p2 @p270)) % 0.45/0.64 (step @p272 :rule not_and :premises (@p271)) % 0.45/0.64 (step @p273 false :rule chain_m_resolution :premises (@p272 @p153 @p147) :args (false (@list false false) (@list @t91 @t33))) % 0.45/0.64 ) % 0.45/0.64 % SZS output end Proof % 0.45/0.64 % cvc5 exiting %------------------------------------------------------------------------------