%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PUZ081^3 : TPTP v9.2.1. Released v3.6.0. % 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 08:44:10 AM UTC 2026 % Result : Theorem 0.42s 0.59s % Output : Proof 0.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PUZ081^3 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n010.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 13:17:40 EDT 2026 % 0.17/0.35 % CPUTime : % 0.34/0.50 %----Proving TH0 % 0.42/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.42/0.59 % SZS status Theorem % 0.42/0.59 % SZS output start Proof % 0.42/0.59 ( % 0.42/0.59 (declare-sort $$unsorted 0) % 0.42/0.59 (declare-const tptp.zoey $$unsorted) % 0.42/0.59 (declare-const tptp.mel $$unsorted) % 0.42/0.59 (declare-const tptp.says (-> $$unsorted Bool Bool)) % 0.42/0.59 (declare-const tptp.knight (-> $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.knave (-> $$unsorted Bool)) % 0.42/0.59 (define @t1 () (@var "P" $$unsorted)) % 0.42/0.59 (define @t2 () (_ tptp.knave @t1)) % 0.42/0.59 (define @t3 () (_ tptp.knight @t1)) % 0.42/0.59 (define @t4 () (@list @t1)) % 0.42/0.59 (define @t5 () (forall @t4 (xor @t3 @t2))) % 0.42/0.59 (define @t6 () (@var "S" Bool)) % 0.42/0.59 (define @t7 () (_ (_ tptp.says @t1) @t6)) % 0.42/0.59 (define @t8 () (and @t3 @t7)) % 0.42/0.59 (define @t9 () (@list @t1 @t6)) % 0.42/0.59 (define @t10 () (forall @t9 (=> @t8 @t6))) % 0.42/0.59 (define @t11 () (not @t6)) % 0.42/0.59 (define @t12 () (and @t2 @t7)) % 0.42/0.59 (define @t13 () (forall @t9 (=> @t12 @t11))) % 0.42/0.59 (define @t14 () (_ tptp.knave tptp.mel)) % 0.42/0.59 (define @t15 () (_ tptp.says tptp.zoey)) % 0.42/0.59 (define @t16 () (not @t14)) % 0.42/0.59 (define @t17 () (_ tptp.knave tptp.zoey)) % 0.42/0.59 (define @t18 () (not @t17)) % 0.42/0.59 (define @t19 () (and @t18 @t16)) % 0.42/0.59 (define @t20 () (_ tptp.says tptp.mel)) % 0.42/0.59 (define @t21 () (@var "Knave" $$unsorted)) % 0.42/0.59 (define @t22 () (_ tptp.knave @t21)) % 0.42/0.59 (define @t23 () (@var "Knight" $$unsorted)) % 0.42/0.59 (define @t24 () (_ tptp.knight @t23)) % 0.42/0.59 (define @t25 () (and @t24 @t22)) % 0.42/0.59 (define @t26 () (@list @t23 @t21)) % 0.42/0.59 (define @t27 () (exists @t26 @t25)) % 0.42/0.59 (define @t28 () (not @t27)) % 0.42/0.59 (define @t29 () (@purify @t19)) % 0.42/0.59 (define @t30 () (tptp.says tptp.mel @t29)) % 0.42/0.59 (define @t31 () (_ @t20 @t29)) % 0.42/0.59 (define @t32 () (= @t19 @t29)) % 0.42/0.59 (define @t33 () (@purify false)) % 0.42/0.59 (define @t34 () (not (tptp.says @t1 false))) % 0.42/0.59 (define @t35 () (tptp.knight @t1)) % 0.42/0.59 (define @t36 () (not @t35)) % 0.42/0.59 (define @t37 () (or @t36 @t34)) % 0.42/0.59 (define @t38 () (or @t36 @t34 false)) % 0.42/0.59 (define @t39 () (tptp.says @t1 @t6)) % 0.42/0.59 (define @t40 () (not @t39)) % 0.42/0.59 (define @t41 () (@list @t6)) % 0.42/0.59 (define @t42 () (or @t6 @t36 @t40 @t6)) % 0.42/0.59 (define @t43 () (or @t36 @t40 @t6)) % 0.42/0.59 (define @t44 () (forall @t41 @t43)) % 0.42/0.59 (define @t45 () (forall @t4 @t44)) % 0.42/0.59 (define @t46 () (not @t7)) % 0.42/0.59 (define @t47 () (not @t3)) % 0.42/0.59 (define @t48 () (or @t47 @t46 @t6)) % 0.42/0.59 (define @t49 () (not @t33)) % 0.42/0.59 (define @t50 () (tptp.says tptp.mel false)) % 0.42/0.59 (define @t51 () (not @t50)) % 0.42/0.59 (define @t52 () (tptp.knight tptp.mel)) % 0.42/0.59 (define @t53 () (not @t52)) % 0.42/0.59 (define @t54 () (or @t53 @t51)) % 0.42/0.59 (define @t55 () (forall @t4 @t37)) % 0.42/0.59 (define @t56 () (@list tptp.mel)) % 0.42/0.59 (define @t57 () (tptp.says tptp.mel @t33)) % 0.42/0.59 (define @t58 () (not @t57)) % 0.42/0.59 (define @t59 () (or @t53 @t58)) % 0.42/0.59 (define @t60 () (@list false)) % 0.42/0.59 (define @t61 () (@list @t55)) % 0.42/0.59 (define @t62 () (tptp.knave @t1)) % 0.42/0.59 (define @t63 () (= @t2 @t47)) % 0.42/0.59 (define @t64 () (tptp.knave tptp.mel)) % 0.42/0.59 (define @t65 () (@purify @t14)) % 0.42/0.59 (define @t66 () (= @t14 @t65)) % 0.42/0.59 (define @t67 () (not @t65)) % 0.42/0.59 (define @t68 () (tptp.says tptp.zoey @t65)) % 0.42/0.59 (define @t69 () (_ @t15 @t65)) % 0.42/0.59 (define @t70 () (@purify true)) % 0.42/0.59 (define @t71 () (tptp.says tptp.zoey @t70)) % 0.42/0.59 (define @t72 () (and @t65 @t68 @t70)) % 0.42/0.59 (define @t73 () (not @t68)) % 0.42/0.59 (define @t74 () (not (tptp.says @t1 true))) % 0.42/0.59 (define @t75 () (not @t62)) % 0.42/0.59 (define @t76 () (or @t75 @t74)) % 0.42/0.59 (define @t77 () (not true)) % 0.42/0.59 (define @t78 () (or @t75 @t74 @t77)) % 0.42/0.59 (define @t79 () (or @t11 @t75 @t40 @t11)) % 0.42/0.59 (define @t80 () (or @t75 @t40 @t11)) % 0.42/0.59 (define @t81 () (forall @t41 @t80)) % 0.42/0.59 (define @t82 () (forall @t4 @t81)) % 0.42/0.59 (define @t83 () (not @t2)) % 0.42/0.59 (define @t84 () (or @t83 @t46 @t11)) % 0.42/0.59 (define @t85 () (tptp.says tptp.zoey true)) % 0.42/0.59 (define @t86 () (not @t85)) % 0.42/0.59 (define @t87 () (tptp.knave tptp.zoey)) % 0.42/0.59 (define @t88 () (not @t87)) % 0.42/0.59 (define @t89 () (or @t88 @t86)) % 0.42/0.59 (define @t90 () (forall @t4 @t76)) % 0.42/0.59 (define @t91 () (@list tptp.zoey)) % 0.42/0.59 (define @t92 () (not @t71)) % 0.42/0.59 (define @t93 () (or @t88 @t92)) % 0.42/0.59 (define @t94 () (tptp.knight tptp.zoey)) % 0.42/0.59 (define @t95 () (not @t94)) % 0.42/0.59 (define @t96 () (= @t87 @t95)) % 0.42/0.59 (define @t97 () (not @t96)) % 0.42/0.59 (define @t98 () (tptp.knight @t23)) % 0.42/0.59 (define @t99 () (@list @t23)) % 0.42/0.59 (define @t100 () (forall @t99 (not @t98))) % 0.42/0.59 (define @t101 () (tptp.knave @t21)) % 0.42/0.59 (define @t102 () (@list @t21)) % 0.42/0.59 (define @t103 () (forall @t102 (not @t101))) % 0.42/0.59 (define @t104 () (not @t22)) % 0.42/0.59 (define @t105 () (forall @t102 @t104)) % 0.42/0.59 (define @t106 () (not @t24)) % 0.42/0.59 (define @t107 () (forall @t99 @t106)) % 0.42/0.59 (define @t108 () (or @t107 @t105)) % 0.42/0.59 (define @t109 () (forall @t26 (not @t25))) % 0.42/0.59 (define @t110 () (not @t109)) % 0.42/0.59 (define @t111 () (not @t64)) % 0.42/0.59 (define @t112 () (@list true)) % 0.42/0.59 (define @t113 () (= @t64 @t53)) % 0.42/0.59 (define @t114 () (not @t113)) % 0.42/0.59 (define @t115 () (@list true false)) % 0.42/0.59 (define @t116 () (@list false false)) % 0.42/0.59 (define @t117 () (tptp.says tptp.zoey false)) % 0.42/0.59 (define @t118 () (not @t117)) % 0.42/0.59 (define @t119 () (or @t95 @t118)) % 0.42/0.59 (define @t120 () (tptp.says tptp.zoey @t33)) % 0.42/0.59 (define @t121 () (not @t120)) % 0.42/0.59 (define @t122 () (or @t95 @t121)) % 0.42/0.59 (define @t123 () (not @t49)) % 0.42/0.59 (define @t124 () (and @t68 @t67 @t49)) % 0.42/0.59 (define @t125 () (and @t88 @t111)) % 0.42/0.59 (define @t126 () (not @t125)) % 0.42/0.59 (define @t127 () (not @t29)) % 0.42/0.59 (define @t128 () (not @t30)) % 0.42/0.59 (define @t129 () (and @t58 @t49 @t127 @t30)) % 0.42/0.59 (assume @p1 @t5) % 0.42/0.59 (assume @p2 @t10) % 0.42/0.59 (assume @p3 @t13) % 0.42/0.59 (assume @p4 (_ @t15 @t14)) % 0.42/0.59 (assume @p5 (_ @t20 @t19)) % 0.42/0.59 (assume @p6 @t28) % 0.42/0.59 (assume @p7 true) % 0.42/0.59 (step @p8 :rule refl :args (@t30)) % 0.42/0.59 (step @p9 :rule refl :args (@t31)) % 0.42/0.59 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t31 @t30))) % 0.42/0.59 (step @p11 :rule symm :premises (@p10)) % 0.42/0.59 (step @p12 :rule eq_resolve :premises (@p9 @p11)) % 0.42/0.59 (step @p13 :rule eq-refl :args (@t19)) % 0.42/0.59 (step @p14 :rule skolem_intro :args (@t29)) % 0.42/0.59 (step @p15 :rule refl :args (@t19)) % 0.42/0.59 (step @p16 :rule cong :premises (@p15 @p14) :args (@t32)) % 0.42/0.59 (step @p17 :rule trans :premises (@p16 @p13)) % 0.42/0.59 (step @p18 :rule true_elim :premises (@p17)) % 0.42/0.59 (step @p19 :rule refl :args (@t20)) % 0.42/0.59 (step @p20 :rule ho_cong :premises (@p19 @p18)) % 0.42/0.59 (step @p21 :rule trans :premises (@p20 @p12)) % 0.42/0.59 (step @p22 :rule eq_resolve :premises (@p5 @p21)) % 0.42/0.59 (step @p23 :rule bool-eq-false :args (@t33)) % 0.42/0.59 (step @p24 :rule skolem_intro :args (@t33)) % 0.42/0.59 (step @p25 :rule eq_resolve :premises (@p24 @p23)) % 0.42/0.59 (step @p26 :rule aci_norm :args ((= @t38 @t37))) % 0.42/0.59 (step @p27 :rule cong :premises (@p26) :args ((forall @t4 @t38))) % 0.42/0.59 (step @p28 :rule quant-var-elim-eq :args ((= (forall @t41 (or (not (= @t6 false)) @t36 @t40 @t6)) @t38))) % 0.42/0.59 (step @p29 :rule refl :args (@t6)) % 0.42/0.59 (step @p30 :rule refl :args (@t40)) % 0.42/0.59 (step @p31 :rule refl :args (@t36)) % 0.42/0.59 (step @p32 :rule bool-eq-false :args (@t6)) % 0.42/0.59 (step @p33 :rule symm :premises (@p32)) % 0.42/0.59 (step @p34 :rule cong :premises (@p33) :args ((not @t11))) % 0.42/0.59 (step @p35 :rule bool-double-not-elim :args (@t6)) % 0.42/0.59 (step @p36 :rule symm :premises (@p35)) % 0.42/0.59 (step @p37 :rule trans :premises (@p36 @p34)) % 0.42/0.59 (step @p38 :rule nary_cong :premises (@p37 @p31 @p30 @p29) :args (@t42)) % 0.42/0.59 (step @p39 :rule aci_norm :args ((= @t43 @t42))) % 0.42/0.59 (step @p40 :rule trans :premises (@p39 @p38)) % 0.42/0.59 (step @p41 :rule cong :premises (@p40) :args (@t44)) % 0.42/0.59 (step @p42 :rule trans :premises (@p41 @p28)) % 0.42/0.59 (step @p43 :rule cong :premises (@p42) :args (@t45)) % 0.42/0.59 (step @p44 :rule quant-merge-prenex :args ((= @t45 (forall @t9 @t43)))) % 0.42/0.59 (step @p45 :rule symm :premises (@p44)) % 0.42/0.59 (step @p46 :rule trans :premises (@p45 @p43)) % 0.42/0.59 (step @p47 :rule trans :premises (@p46 @p27)) % 0.42/0.59 (step @p48 :rule refl :args (@t39)) % 0.42/0.59 (step @p49 :rule refl :args (@t7)) % 0.42/0.59 (step @p50 :rule cong :premises (@p49 @p48) :args ((= @t7 @t39))) % 0.42/0.59 (step @p51 :rule symm :premises (@p50)) % 0.42/0.59 (step @p52 :rule eq_resolve :premises (@p49 @p51)) % 0.42/0.59 (step @p53 :rule cong :premises (@p52) :args (@t46)) % 0.42/0.59 (step @p54 :rule refl :args (@t35)) % 0.42/0.59 (step @p55 :rule refl :args (@t3)) % 0.42/0.59 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t3 @t35))) % 0.42/0.59 (step @p57 :rule symm :premises (@p56)) % 0.42/0.59 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 0.42/0.59 (step @p59 :rule cong :premises (@p58) :args (@t47)) % 0.42/0.59 (step @p60 :rule nary_cong :premises (@p59 @p53 @p29) :args (@t48)) % 0.42/0.59 (step @p61 :rule cong :premises (@p60) :args ((forall @t9 @t48))) % 0.42/0.59 (step @p62 :rule trans :premises (@p61 @p47)) % 0.42/0.59 (step @p63 :rule aci_norm :args ((= (or (or @t47 @t46) @t6) @t48))) % 0.42/0.59 (step @p64 :rule bool-and-de-morgan :args (@t3 @t7 true)) % 0.42/0.59 (step @p65 :rule nary_cong :premises (@p64 @p29) :args ((or (not @t8) @t6))) % 0.42/0.59 (step @p66 :rule trans :premises (@p65 @p63)) % 0.42/0.59 (step @p67 :rule bool-impl-elim :args (@t8 @t6)) % 0.42/0.59 (step @p68 :rule trans :premises (@p67 @p66)) % 0.42/0.59 (step @p69 :rule cong :premises (@p68) :args (@t10)) % 0.42/0.59 (step @p70 :rule trans :premises (@p69 @p62)) % 0.42/0.59 (step @p71 :rule eq_resolve :premises (@p2 @p70)) % 0.42/0.59 (step @p72 :rule evaluate :args ((not false))) % 0.42/0.59 (step @p73 :rule cong :premises (@p24) :args (@t49)) % 0.42/0.59 (step @p74 :rule bool-eq-false :args (@t33)) % 0.42/0.59 (step @p75 :rule eq-symm :args (false @t33)) % 0.42/0.59 (step @p76 :rule trans :premises (@p75 @p74)) % 0.42/0.59 (step @p77 :rule trans :premises (@p76 @p73 @p72)) % 0.42/0.59 (step @p78 :rule true_elim :premises (@p77)) % 0.42/0.59 (step @p79 :rule refl :args (tptp.mel)) % 0.42/0.59 (step @p80 :rule cong :premises (@p79 @p78) :args (@t50)) % 0.42/0.59 (step @p81 :rule cong :premises (@p80) :args (@t51)) % 0.42/0.59 (step @p82 :rule refl :args (@t53)) % 0.42/0.59 (step @p83 :rule nary_cong :premises (@p82 @p81) :args (@t54)) % 0.42/0.59 (step @p84 :rule refl :args (@t55)) % 0.42/0.59 (step @p85 :rule cong :premises (@p84 @p83) :args ((=> @t55 @t54))) % 0.42/0.59 (assume-push @p388 @t55) % 0.42/0.59 (step @p87 :rule instantiate :premises (@p71) :args (@t56)) % 0.42/0.59 (step-pop @p389 :rule scope :premises (@p87)) % 0.42/0.59 (step @p88 :rule process_scope :premises (@p389) :args (@t54)) % 0.42/0.59 (step @p90 :rule eq_resolve :premises (@p88 @p85)) % 0.42/0.59 (step @p91 :rule implies_elim :premises (@p90)) % 0.42/0.59 (step @p92 :rule chain_m_resolution :premises (@p91 @p71) :args (@t59 @t60 @t61)) % 0.42/0.59 (step @p93 :rule refl :args (@t62)) % 0.42/0.59 (step @p94 :rule refl :args (@t2)) % 0.42/0.59 (step @p95 :rule cong :premises (@p94 @p93) :args ((= @t2 @t62))) % 0.42/0.59 (step @p96 :rule symm :premises (@p95)) % 0.42/0.59 (step @p97 :rule eq_resolve :premises (@p94 @p96)) % 0.42/0.59 (step @p98 :rule cong :premises (@p97 @p59) :args (@t63)) % 0.42/0.59 (step @p99 :rule cong :premises (@p98) :args ((forall @t4 @t63))) % 0.42/0.59 (step @p100 :rule eq-symm :args (@t47 @t2)) % 0.42/0.59 (step @p101 :rule cong :premises (@p100) :args ((forall @t4 (= @t47 @t2)))) % 0.42/0.59 (step @p102 :rule trans :premises (@p101 @p99)) % 0.42/0.59 (step @p103 :rule bool-xor-elim :args (@t3 @t2)) % 0.42/0.59 (step @p104 :rule cong :premises (@p103) :args (@t5)) % 0.42/0.59 (step @p105 :rule trans :premises (@p104 @p102)) % 0.42/0.59 (step @p106 :rule eq_resolve :premises (@p1 @p105)) % 0.42/0.59 (step @p107 :rule instantiate :premises (@p106) :args (@t56)) % 0.42/0.59 (step @p108 :rule eq-symm :args (@t64 @t65)) % 0.42/0.59 (step @p109 :rule refl :args (@t65)) % 0.42/0.59 (step @p110 :rule refl :args (@t64)) % 0.42/0.59 (step @p111 :rule refl :args (@t14)) % 0.42/0.59 (step @p112 :rule cong :premises (@p111 @p110) :args ((= @t14 @t64))) % 0.42/0.59 (step @p113 :rule symm :premises (@p112)) % 0.42/0.59 (step @p114 :rule eq_resolve :premises (@p111 @p113)) % 0.42/0.59 (step @p115 :rule cong :premises (@p114 @p109) :args (@t66)) % 0.42/0.59 (step @p116 :rule trans :premises (@p115 @p108)) % 0.42/0.59 (step @p117 :rule eq-symm :args (@t65 @t14)) % 0.42/0.59 (step @p118 :rule trans :premises (@p117 @p116)) % 0.42/0.59 (step @p119 :rule skolem_intro :args (@t65)) % 0.42/0.59 (step @p120 :rule eq_resolve :premises (@p119 @p118)) % 0.42/0.59 (step @p121 :rule equiv_elim1 :premises (@p120)) % 0.42/0.59 (step @p122 :rule reordering :premises (@p121) :args ((or @t64 @t67))) % 0.42/0.59 (step @p123 :rule refl :args (@t68)) % 0.42/0.59 (step @p124 :rule refl :args (@t69)) % 0.42/0.59 (step @p125 :rule cong :premises (@p124 @p123) :args ((= @t69 @t68))) % 0.42/0.59 (step @p126 :rule symm :premises (@p125)) % 0.42/0.59 (step @p127 :rule eq_resolve :premises (@p124 @p126)) % 0.42/0.59 (step @p128 :rule eq-refl :args (@t14)) % 0.42/0.59 (step @p129 :rule refl :args (@t14)) % 0.42/0.59 (step @p130 :rule cong :premises (@p129 @p119) :args (@t66)) % 0.42/0.59 (step @p131 :rule trans :premises (@p130 @p128)) % 0.42/0.59 (step @p132 :rule true_elim :premises (@p131)) % 0.42/0.59 (step @p133 :rule refl :args (@t15)) % 0.42/0.59 (step @p134 :rule ho_cong :premises (@p133 @p132)) % 0.42/0.59 (step @p135 :rule trans :premises (@p134 @p127)) % 0.42/0.59 (step @p136 :rule eq_resolve :premises (@p4 @p135)) % 0.42/0.59 (step @p137 :rule bool-eq-true :args (@t70)) % 0.42/0.59 (step @p138 :rule skolem_intro :args (@t70)) % 0.42/0.59 (step @p139 :rule eq_resolve :premises (@p138 @p137)) % 0.42/0.59 (assume-push @p390 @t65) % 0.42/0.59 (assume-push @p391 @t68) % 0.42/0.59 (assume-push @p392 @t70) % 0.42/0.59 (assume-push @p393 @t68) % 0.42/0.59 (assume-push @p394 @t65) % 0.42/0.59 (assume-push @p395 @t70) % 0.42/0.59 (step @p146 :rule true_intro :premises (@p136)) % 0.42/0.59 (step @p147 :rule true_intro :premises (@p390)) % 0.42/0.59 (step @p148 :rule symm :premises (@p147)) % 0.42/0.59 (step @p149 :rule trans :premises (@p138 @p148)) % 0.42/0.59 (step @p150 :rule refl :args (tptp.zoey)) % 0.42/0.59 (step @p151 :rule cong :premises (@p150 @p149) :args (@t71)) % 0.42/0.59 (step @p152 :rule trans :premises (@p151 @p146)) % 0.42/0.59 (step @p153 :rule true_elim :premises (@p152)) % 0.42/0.59 (step-pop @p396 :rule scope :premises (@p153)) % 0.42/0.59 (step-pop @p397 :rule scope :premises (@p396)) % 0.42/0.59 (step-pop @p398 :rule scope :premises (@p397)) % 0.42/0.59 (step @p154 :rule process_scope :premises (@p398) :args (@t71)) % 0.42/0.59 (step @p158 :rule and_intro :premises (@p136 @p390 @p139)) % 0.42/0.59 (step @p159 :rule modus_ponens :premises (@p158 @p154)) % 0.42/0.59 (step-pop @p399 :rule scope :premises (@p159)) % 0.42/0.59 (step-pop @p400 :rule scope :premises (@p399)) % 0.42/0.59 (step-pop @p401 :rule scope :premises (@p400)) % 0.42/0.59 (step @p160 :rule process_scope :premises (@p401) :args (@t71)) % 0.42/0.59 (step @p164 :rule implies_elim :premises (@p160)) % 0.42/0.59 (step @p165 :rule cnf_and_neg :args (@t72)) % 0.42/0.59 (step @p166 :rule resolution :premises (@p165 @p164) :args (true @t72)) % 0.42/0.59 (step @p167 :rule reordering :premises (@p166) :args ((or @t73 @t67 (not @t70) @t71))) % 0.42/0.59 (step @p168 :rule aci_norm :args ((= (or @t75 @t74 false) @t76))) % 0.42/0.59 (step @p169 :rule evaluate :args (@t77)) % 0.42/0.59 (step @p170 :rule refl :args (@t74)) % 0.42/0.59 (step @p171 :rule refl :args (@t75)) % 0.42/0.59 (step @p172 :rule nary_cong :premises (@p171 @p170 @p169) :args (@t78)) % 0.42/0.59 (step @p173 :rule trans :premises (@p172 @p168)) % 0.42/0.59 (step @p174 :rule cong :premises (@p173) :args ((forall @t4 @t78))) % 0.42/0.59 (step @p175 :rule quant-var-elim-eq :args ((= (forall @t41 (or (not (= @t6 true)) @t75 @t40 @t11)) @t78))) % 0.42/0.59 (step @p176 :rule refl :args (@t11)) % 0.42/0.59 (step @p177 :rule refl :args (@t75)) % 0.42/0.59 (step @p178 :rule bool-eq-true :args (@t6)) % 0.42/0.59 (step @p179 :rule symm :premises (@p178)) % 0.42/0.59 (step @p180 :rule cong :premises (@p179) :args (@t11)) % 0.42/0.59 (step @p181 :rule nary_cong :premises (@p180 @p177 @p30 @p176) :args (@t79)) % 0.42/0.59 (step @p182 :rule aci_norm :args ((= @t80 @t79))) % 0.42/0.59 (step @p183 :rule trans :premises (@p182 @p181)) % 0.42/0.59 (step @p184 :rule cong :premises (@p183) :args (@t81)) % 0.42/0.59 (step @p185 :rule trans :premises (@p184 @p175)) % 0.42/0.59 (step @p186 :rule cong :premises (@p185) :args (@t82)) % 0.42/0.59 (step @p187 :rule quant-merge-prenex :args ((= @t82 (forall @t9 @t80)))) % 0.42/0.59 (step @p188 :rule symm :premises (@p187)) % 0.42/0.59 (step @p189 :rule trans :premises (@p188 @p186)) % 0.42/0.59 (step @p190 :rule trans :premises (@p189 @p174)) % 0.42/0.59 (step @p191 :rule cong :premises (@p97) :args (@t83)) % 0.42/0.59 (step @p192 :rule nary_cong :premises (@p191 @p53 @p176) :args (@t84)) % 0.42/0.59 (step @p193 :rule cong :premises (@p192) :args ((forall @t9 @t84))) % 0.42/0.59 (step @p194 :rule trans :premises (@p193 @p190)) % 0.42/0.59 (step @p195 :rule aci_norm :args ((= (or (or @t83 @t46) @t11) @t84))) % 0.42/0.59 (step @p196 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 0.42/0.59 (step @p197 :rule nary_cong :premises (@p196 @p176) :args ((or (not @t12) @t11))) % 0.42/0.59 (step @p198 :rule trans :premises (@p197 @p195)) % 0.42/0.59 (step @p199 :rule bool-impl-elim :args (@t12 @t11)) % 0.42/0.59 (step @p200 :rule trans :premises (@p199 @p198)) % 0.42/0.59 (step @p201 :rule cong :premises (@p200) :args (@t13)) % 0.42/0.59 (step @p202 :rule trans :premises (@p201 @p194)) % 0.42/0.59 (step @p203 :rule eq_resolve :premises (@p3 @p202)) % 0.42/0.59 (step @p204 :rule symm :premises (@p138)) % 0.42/0.59 (step @p150 :rule refl :args (tptp.zoey)) % 0.42/0.59 (step @p205 :rule cong :premises (@p150 @p204) :args (@t85)) % 0.42/0.59 (step @p206 :rule cong :premises (@p205) :args (@t86)) % 0.42/0.59 (step @p207 :rule refl :args (@t88)) % 0.42/0.59 (step @p208 :rule nary_cong :premises (@p207 @p206) :args (@t89)) % 0.42/0.59 (step @p209 :rule refl :args (@t90)) % 0.42/0.59 (step @p210 :rule cong :premises (@p209 @p208) :args ((=> @t90 @t89))) % 0.42/0.59 (assume-push @p402 @t90) % 0.42/0.59 (step @p212 :rule instantiate :premises (@p203) :args (@t91)) % 0.42/0.59 (step-pop @p403 :rule scope :premises (@p212)) % 0.42/0.59 (step @p213 :rule process_scope :premises (@p403) :args (@t89)) % 0.42/0.59 (step @p215 :rule eq_resolve :premises (@p213 @p210)) % 0.42/0.59 (step @p216 :rule implies_elim :premises (@p215)) % 0.42/0.59 (step @p217 :rule chain_m_resolution :premises (@p216 @p203) :args (@t93 @t60 (@list @t90))) % 0.42/0.59 (step @p218 :rule cnf_or_pos :args (@t93)) % 0.42/0.59 (step @p219 :rule reordering :premises (@p218) :args ((or @t88 @t92 (not @t93)))) % 0.42/0.59 (step @p220 :rule instantiate :premises (@p106) :args (@t91)) % 0.42/0.59 (step @p221 :rule bool-double-not-elim :args (@t94)) % 0.42/0.59 (step @p222 :rule refl :args (@t87)) % 0.42/0.59 (step @p223 :rule refl :args (@t97)) % 0.42/0.59 (step @p224 :rule nary_cong :premises (@p223 @p222 @p221) :args ((or @t97 @t87 (not @t95)))) % 0.42/0.59 (step @p225 :rule cnf_equiv_pos2 :args (@t96)) % 0.42/0.59 (step @p226 :rule eq_resolve :premises (@p225 @p224)) % 0.42/0.59 (step @p227 :rule reordering :premises (@p226) :args ((or @t87 @t94 @t97))) % 0.42/0.59 (assume-push @p404 @t100) % 0.42/0.59 (step @p229 :rule instantiate :premises (@p404) :args (@t91)) % 0.42/0.59 (step-pop @p405 :rule scope :premises (@p229)) % 0.42/0.59 (step @p230 :rule process_scope :premises (@p405) :args (@t95)) % 0.42/0.59 (step @p232 :rule implies_elim :premises (@p230)) % 0.42/0.59 (step @p233 :rule bool-double-not-elim :args ((or @t100 @t103))) % 0.42/0.59 (step @p234 :rule refl :args (@t101)) % 0.42/0.59 (step @p235 :rule refl :args (@t22)) % 0.42/0.59 (step @p236 :rule cong :premises (@p235 @p234) :args ((= @t22 @t101))) % 0.42/0.59 (step @p237 :rule symm :premises (@p236)) % 0.42/0.59 (step @p238 :rule eq_resolve :premises (@p235 @p237)) % 0.42/0.59 (step @p239 :rule cong :premises (@p238) :args (@t104)) % 0.42/0.59 (step @p240 :rule cong :premises (@p239) :args (@t105)) % 0.42/0.59 (step @p241 :rule refl :args (@t98)) % 0.42/0.59 (step @p242 :rule refl :args (@t24)) % 0.42/0.59 (step @p243 :rule cong :premises (@p242 @p241) :args ((= @t24 @t98))) % 0.42/0.59 (step @p244 :rule symm :premises (@p243)) % 0.42/0.59 (step @p245 :rule eq_resolve :premises (@p242 @p244)) % 0.42/0.59 (step @p246 :rule cong :premises (@p245) :args (@t106)) % 0.42/0.59 (step @p247 :rule cong :premises (@p246) :args (@t107)) % 0.42/0.59 (step @p248 :rule nary_cong :premises (@p247 @p240) :args (@t108)) % 0.42/0.59 (step @p249 :rule quant-miniscope-or :args ((= (forall @t26 (or @t106 @t104)) @t108))) % 0.42/0.59 (step @p250 :rule trans :premises (@p249 @p248)) % 0.42/0.59 (step @p251 :rule bool-and-de-morgan :args (@t24 @t22 true)) % 0.42/0.59 (step @p252 :rule cong :premises (@p251) :args (@t109)) % 0.42/0.59 (step @p253 :rule trans :premises (@p252 @p250)) % 0.42/0.59 (step @p254 :rule cong :premises (@p253) :args (@t110)) % 0.42/0.59 (step @p255 :rule exists-elim :args ((= @t27 @t110))) % 0.42/0.59 (step @p256 :rule trans :premises (@p255 @p254)) % 0.42/0.59 (step @p257 :rule cong :premises (@p256) :args (@t28)) % 0.42/0.59 (step @p258 :rule trans :premises (@p257 @p233)) % 0.42/0.59 (step @p259 :rule eq_resolve :premises (@p6 @p258)) % 0.42/0.59 (assume-push @p406 @t103) % 0.42/0.59 (step @p261 :rule instantiate :premises (@p406) :args (@t56)) % 0.42/0.59 (step-pop @p407 :rule scope :premises (@p261)) % 0.42/0.59 (step @p262 :rule process_scope :premises (@p407) :args (@t111)) % 0.42/0.59 (step @p264 :rule implies_elim :premises (@p262)) % 0.42/0.59 (step @p265 :rule reordering :premises (@p264) :args ((or @t111 (not @t103)))) % 0.42/0.59 (step @p266 :rule chain_m_resolution :premises (@p265 @p259 @p232 @p227 @p220 @p219 @p217 @p167 @p139 @p136 @p122) :args (@t67 (@list false true false false true false false false false false) (@list @t103 @t100 @t94 @t96 @t87 @t93 @t71 @t70 @t68 @t64))) % 0.42/0.59 (step @p267 :rule equiv_elim2 :premises (@p120)) % 0.42/0.59 (step @p268 :rule chain_m_resolution :premises (@p267 @p266) :args (@t111 @t112 (@list @t65))) % 0.42/0.59 (step @p269 :rule bool-double-not-elim :args (@t52)) % 0.42/0.59 (step @p270 :rule refl :args (@t64)) % 0.42/0.59 (step @p271 :rule refl :args (@t114)) % 0.42/0.59 (step @p272 :rule nary_cong :premises (@p271 @p270 @p269) :args ((or @t114 @t64 (not @t53)))) % 0.42/0.59 (step @p273 :rule cnf_equiv_pos2 :args (@t113)) % 0.42/0.59 (step @p274 :rule eq_resolve :premises (@p273 @p272)) % 0.42/0.59 (step @p275 :rule reordering :premises (@p274) :args ((or @t64 @t52 @t114))) % 0.42/0.59 (step @p276 :rule chain_m_resolution :premises (@p275 @p268 @p107) :args (@t52 @t115 (@list @t64 @t113))) % 0.42/0.59 (step @p277 :rule cnf_or_pos :args (@t59)) % 0.42/0.59 (step @p278 :rule reordering :premises (@p277) :args ((or @t53 @t58 (not @t59)))) % 0.42/0.59 (step @p279 :rule chain_m_resolution :premises (@p278 @p276 @p92) :args (@t58 @t116 (@list @t52 @t59))) % 0.42/0.59 (step @p280 :rule cong :premises (@p150 @p78) :args (@t117)) % 0.42/0.59 (step @p281 :rule cong :premises (@p280) :args (@t118)) % 0.42/0.59 (step @p282 :rule refl :args (@t95)) % 0.42/0.59 (step @p283 :rule nary_cong :premises (@p282 @p281) :args (@t119)) % 0.42/0.59 (step @p284 :rule cong :premises (@p84 @p283) :args ((=> @t55 @t119))) % 0.42/0.59 (assume-push @p408 @t55) % 0.42/0.59 (step @p286 :rule instantiate :premises (@p71) :args (@t91)) % 0.42/0.59 (step-pop @p409 :rule scope :premises (@p286)) % 0.42/0.59 (step @p287 :rule process_scope :premises (@p409) :args (@t119)) % 0.42/0.59 (step @p289 :rule eq_resolve :premises (@p287 @p284)) % 0.42/0.59 (step @p290 :rule implies_elim :premises (@p289)) % 0.42/0.59 (step @p291 :rule chain_m_resolution :premises (@p290 @p71) :args (@t122 @t60 @t61)) % 0.42/0.59 (step @p292 :rule refl :args (@t120)) % 0.42/0.59 (step @p293 :rule bool-double-not-elim :args (@t33)) % 0.42/0.59 (step @p294 :rule bool-double-not-elim :args (@t65)) % 0.42/0.59 (step @p295 :rule refl :args (@t73)) % 0.42/0.59 (step @p296 :rule nary_cong :premises (@p295 @p294 @p293 @p292) :args ((or @t73 (not @t67) @t123 @t120))) % 0.42/0.59 (assume-push @p410 @t68) % 0.42/0.59 (assume-push @p411 @t67) % 0.42/0.59 (assume-push @p412 @t49) % 0.42/0.59 (assume-push @p413 @t68) % 0.42/0.59 (assume-push @p414 @t67) % 0.42/0.59 (assume-push @p415 @t49) % 0.42/0.59 (step @p146 :rule true_intro :premises (@p136)) % 0.42/0.59 (step @p303 :rule false_intro :premises (@p411)) % 0.42/0.59 (step @p304 :rule symm :premises (@p303)) % 0.42/0.59 (step @p305 :rule trans :premises (@p24 @p304)) % 0.42/0.59 (step @p306 :rule cong :premises (@p150 @p305) :args (@t120)) % 0.42/0.59 (step @p307 :rule trans :premises (@p306 @p146)) % 0.42/0.59 (step @p308 :rule true_elim :premises (@p307)) % 0.42/0.59 (step-pop @p416 :rule scope :premises (@p308)) % 0.42/0.59 (step-pop @p417 :rule scope :premises (@p416)) % 0.42/0.59 (step-pop @p418 :rule scope :premises (@p417)) % 0.42/0.59 (step @p309 :rule process_scope :premises (@p418) :args (@t120)) % 0.42/0.59 (step @p313 :rule and_intro :premises (@p136 @p411 @p25)) % 0.42/0.59 (step @p314 :rule modus_ponens :premises (@p313 @p309)) % 0.42/0.59 (step-pop @p419 :rule scope :premises (@p314)) % 0.42/0.59 (step-pop @p420 :rule scope :premises (@p419)) % 0.42/0.59 (step-pop @p421 :rule scope :premises (@p420)) % 0.42/0.59 (step @p315 :rule process_scope :premises (@p421) :args (@t120)) % 0.42/0.59 (step @p319 :rule implies_elim :premises (@p315)) % 0.42/0.59 (step @p320 :rule cnf_and_neg :args (@t124)) % 0.42/0.59 (step @p321 :rule resolution :premises (@p320 @p319) :args (true @t124)) % 0.42/0.59 (step @p322 :rule eq_resolve :premises (@p321 @p296)) % 0.42/0.59 (step @p323 :rule reordering :premises (@p322) :args ((or @t65 @t73 @t33 @t120))) % 0.42/0.59 (step @p324 :rule chain_m_resolution :premises (@p323 @p266 @p136 @p25) :args (@t120 (@list true false true) (@list @t65 @t68 @t33))) % 0.42/0.59 (step @p325 :rule cnf_or_pos :args (@t122)) % 0.42/0.59 (step @p326 :rule reordering :premises (@p325) :args ((or @t95 @t121 (not @t122)))) % 0.42/0.59 (step @p327 :rule chain_m_resolution :premises (@p326 @p324 @p291) :args (@t95 @t116 (@list @t120 @t122))) % 0.42/0.59 (step @p328 :rule chain_m_resolution :premises (@p227 @p327 @p220) :args (@t87 @t115 (@list @t94 @t96))) % 0.42/0.59 (step @p329 :rule cnf_and_pos :args (@t125 0)) % 0.42/0.59 (step @p330 :rule reordering :premises (@p329) :args ((or @t88 @t126))) % 0.42/0.59 (step @p331 :rule chain_m_resolution :premises (@p330 @p328) :args (@t126 @t60 (@list @t87))) % 0.42/0.59 (step @p332 :rule eq-symm :args (@t125 @t29)) % 0.42/0.59 (step @p333 :rule refl :args (@t29)) % 0.42/0.59 (step @p334 :rule cong :premises (@p114) :args (@t16)) % 0.42/0.59 (step @p335 :rule refl :args (@t87)) % 0.42/0.59 (step @p336 :rule refl :args (@t17)) % 0.42/0.59 (step @p337 :rule cong :premises (@p336 @p335) :args ((= @t17 @t87))) % 0.42/0.59 (step @p338 :rule symm :premises (@p337)) % 0.42/0.59 (step @p339 :rule eq_resolve :premises (@p336 @p338)) % 0.42/0.59 (step @p340 :rule cong :premises (@p339) :args (@t18)) % 0.42/0.59 (step @p341 :rule nary_cong :premises (@p340 @p334) :args (@t19)) % 0.42/0.59 (step @p342 :rule cong :premises (@p341 @p333) :args (@t32)) % 0.42/0.59 (step @p343 :rule trans :premises (@p342 @p332)) % 0.42/0.59 (step @p344 :rule eq-symm :args (@t29 @t19)) % 0.42/0.59 (step @p345 :rule trans :premises (@p344 @p343)) % 0.42/0.59 (step @p346 :rule eq_resolve :premises (@p14 @p345)) % 0.42/0.59 (step @p347 :rule equiv_elim1 :premises (@p346)) % 0.42/0.59 (step @p348 :rule reordering :premises (@p347) :args ((or @t125 @t127))) % 0.42/0.59 (step @p349 :rule chain_m_resolution :premises (@p348 @p331) :args (@t127 @t112 (@list @t125))) % 0.42/0.59 (step @p350 :rule bool-double-not-elim :args (@t57)) % 0.42/0.59 (step @p351 :rule bool-double-not-elim :args (@t29)) % 0.42/0.59 (step @p352 :rule refl :args (@t128)) % 0.42/0.59 (step @p353 :rule nary_cong :premises (@p352 @p351 @p350 @p293) :args ((or @t128 (not @t127) (not @t58) @t123))) % 0.42/0.59 (assume-push @p422 @t58) % 0.42/0.59 (assume-push @p423 @t49) % 0.42/0.59 (assume-push @p424 @t127) % 0.42/0.59 (assume-push @p425 @t30) % 0.42/0.59 (step @p358 :rule evaluate :args ((= true false))) % 0.42/0.59 (step @p359 :rule false_intro :premises (@p422)) % 0.42/0.59 (step @p360 :rule false_intro :premises (@p424)) % 0.42/0.59 (step @p361 :rule trans :premises (@p360 @p78)) % 0.42/0.59 (step @p362 :rule cong :premises (@p79 @p361) :args (@t30)) % 0.42/0.59 (step @p363 :rule true_intro :premises (@p22)) % 0.42/0.59 (step @p364 :rule symm :premises (@p363)) % 0.42/0.59 (step @p365 :rule trans :premises (@p364 @p362 @p359)) % 0.42/0.59 (step @p366 false :rule eq_resolve :premises (@p365 @p358)) % 0.42/0.59 (step-pop @p426 :rule scope :premises (@p366)) % 0.42/0.59 (step-pop @p427 :rule scope :premises (@p426)) % 0.42/0.59 (step-pop @p428 :rule scope :premises (@p427)) % 0.42/0.59 (step-pop @p429 :rule scope :premises (@p428)) % 0.42/0.59 (step @p367 :rule process_scope :premises (@p429) :args (false)) % 0.42/0.59 (assume-push @p430 @t30) % 0.42/0.59 (assume-push @p431 @t127) % 0.42/0.59 (assume-push @p432 @t58) % 0.42/0.59 (assume-push @p433 @t49) % 0.42/0.59 (step @p376 :rule and_intro :premises (@p432 @p25 @p431 @p22)) % 0.42/0.59 (step-pop @p434 :rule scope :premises (@p376)) % 0.42/0.59 (step-pop @p435 :rule scope :premises (@p434)) % 0.42/0.59 (step-pop @p436 :rule scope :premises (@p435)) % 0.42/0.59 (step-pop @p437 :rule scope :premises (@p436)) % 0.42/0.59 (step @p377 :rule process_scope :premises (@p437) :args (@t129)) % 0.42/0.59 (step @p382 :rule implies_elim :premises (@p377)) % 0.42/0.59 (step @p383 :rule resolution :premises (@p382 @p367) :args (true @t129)) % 0.42/0.59 (step @p384 :rule not_and :premises (@p383)) % 0.42/0.59 (step @p385 :rule eq_resolve :premises (@p384 @p353)) % 0.42/0.59 (step @p386 :rule reordering :premises (@p385) :args ((or @t29 @t128 @t33 @t57))) % 0.42/0.59 (step @p387 false :rule chain_m_resolution :premises (@p386 @p349 @p279 @p25 @p22) :args (false (@list true true true false) (@list @t29 @t57 @t33 @t30))) % 0.42/0.59 ) % 0.42/0.59 % SZS output end Proof % 0.42/0.59 % cvc5 exiting %------------------------------------------------------------------------------