%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU740^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n017.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 08:52:59 AM UTC 2026 % Result : Theorem 0.38s 0.61s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SEU740^2 : TPTP v9.2.1. Released v3.7.0. % 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n017.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 17:48:46 EDT 2026 % 0.17/0.36 % CPUTime : % 0.27/0.51 %----Proving TH0 % 0.38/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.61 % SZS status Theorem % 0.38/0.61 % SZS output start Proof % 0.38/0.61 ( % 0.38/0.61 (declare-sort $$unsorted 0) % 0.38/0.61 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.binintersectEL Bool) % 0.38/0.61 (declare-const tptp.binunionIL Bool) % 0.38/0.61 (declare-const tptp.binintersect (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.binunion (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.61 (define @t1 () (@var "B" $$unsorted)) % 0.38/0.61 (define @t2 () (@var "A" $$unsorted)) % 0.38/0.61 (define @t3 () (_ (_ tptp.binunion @t2) @t1)) % 0.38/0.61 (define @t4 () (@var "Xx" $$unsorted)) % 0.38/0.61 (define @t5 () (_ tptp.in @t4)) % 0.38/0.61 (define @t6 () (_ @t5 @t3)) % 0.38/0.61 (define @t7 () (_ @t5 @t2)) % 0.38/0.61 (define @t8 () (@list @t2 @t1 @t4)) % 0.38/0.61 (define @t9 () (forall @t8 (=> @t7 @t6))) % 0.38/0.61 (define @t10 () (= tptp.binunionIL @t9)) % 0.38/0.61 (define @t11 () (_ (_ tptp.binintersect @t2) @t1)) % 0.38/0.61 (define @t12 () (_ @t5 @t11)) % 0.38/0.61 (define @t13 () (forall @t8 (=> @t12 @t7))) % 0.38/0.61 (define @t14 () (= tptp.binintersectEL @t13)) % 0.38/0.61 (define @t15 () (@var "Z" $$unsorted)) % 0.38/0.61 (define @t16 () (@var "X" $$unsorted)) % 0.38/0.61 (define @t17 () (_ (_ tptp.binunion @t16) @t15)) % 0.38/0.61 (define @t18 () (_ @t5 @t17)) % 0.38/0.61 (define @t19 () (@var "Y" $$unsorted)) % 0.38/0.61 (define @t20 () (_ (_ tptp.binintersect @t16) @t19)) % 0.38/0.61 (define @t21 () (_ @t5 @t20)) % 0.38/0.61 (define @t22 () (=> @t21 @t18)) % 0.38/0.61 (define @t23 () (@list @t4)) % 0.38/0.61 (define @t24 () (forall @t23 (=> @t7 @t22))) % 0.38/0.61 (define @t25 () (_ tptp.powerset @t2)) % 0.38/0.61 (define @t26 () (_ tptp.in @t15)) % 0.38/0.61 (define @t27 () (_ @t26 @t25)) % 0.38/0.61 (define @t28 () (=> @t27 @t24)) % 0.38/0.61 (define @t29 () (@list @t15)) % 0.38/0.61 (define @t30 () (forall @t29 @t28)) % 0.38/0.61 (define @t31 () (_ tptp.in @t19)) % 0.38/0.61 (define @t32 () (_ @t31 @t25)) % 0.38/0.61 (define @t33 () (=> @t32 @t30)) % 0.38/0.61 (define @t34 () (@list @t19)) % 0.38/0.61 (define @t35 () (forall @t34 @t33)) % 0.38/0.61 (define @t36 () (_ tptp.in @t16)) % 0.38/0.61 (define @t37 () (_ @t36 @t25)) % 0.38/0.61 (define @t38 () (=> @t37 @t35)) % 0.38/0.61 (define @t39 () (@list @t2 @t16)) % 0.38/0.61 (define @t40 () (forall @t39 @t38)) % 0.38/0.61 (define @t41 () (=> tptp.binintersectEL @t40)) % 0.38/0.61 (define @t42 () (=> tptp.binunionIL @t41)) % 0.38/0.61 (define @t43 () (not @t42)) % 0.38/0.61 (define @t44 () (@var "BOUND_VARIABLE_7566" $$unsorted)) % 0.38/0.61 (define @t45 () (@var "BOUND_VARIABLE_7568" $$unsorted)) % 0.38/0.61 (define @t46 () (tptp.in @t45 (tptp.binunion @t16 @t44))) % 0.38/0.61 (define @t47 () (@var "BOUND_VARIABLE_7564" $$unsorted)) % 0.38/0.61 (define @t48 () (not (tptp.in @t45 (tptp.binintersect @t16 @t47)))) % 0.38/0.61 (define @t49 () (not (tptp.in @t45 @t2))) % 0.38/0.61 (define @t50 () (tptp.powerset @t2)) % 0.38/0.61 (define @t51 () (not (tptp.in @t44 @t50))) % 0.38/0.61 (define @t52 () (not (tptp.in @t47 @t50))) % 0.38/0.61 (define @t53 () (tptp.in @t16 @t50)) % 0.38/0.61 (define @t54 () (not @t53)) % 0.38/0.61 (define @t55 () (or @t54 @t52 @t51 @t49 @t48 @t46)) % 0.38/0.61 (define @t56 () (@list @t2 @t16 @t47 @t44 @t45)) % 0.38/0.61 (define @t57 () (forall @t56 @t55)) % 0.38/0.61 (define @t58 () (tptp.in @t4 @t2)) % 0.38/0.61 (define @t59 () (tptp.binintersect @t2 @t1)) % 0.38/0.61 (define @t60 () (tptp.in @t4 @t59)) % 0.38/0.61 (define @t61 () (not @t12)) % 0.38/0.61 (define @t62 () (or @t61 @t7)) % 0.38/0.61 (define @t63 () (=> tptp.binintersectEL @t57)) % 0.38/0.61 (define @t64 () (tptp.binunion @t2 @t1)) % 0.38/0.61 (define @t65 () (tptp.in @t4 @t64)) % 0.38/0.61 (define @t66 () (not @t7)) % 0.38/0.61 (define @t67 () (or @t66 @t6)) % 0.38/0.61 (define @t68 () (=> tptp.binunionIL @t63)) % 0.38/0.61 (define @t69 () (or @t52 @t51 @t49 @t48 @t46)) % 0.38/0.61 (define @t70 () (or @t54 @t69)) % 0.38/0.61 (define @t71 () (forall @t56 @t70)) % 0.38/0.61 (define @t72 () (@list @t47 @t44 @t45)) % 0.38/0.61 (define @t73 () (forall @t72 @t70)) % 0.38/0.61 (define @t74 () (forall @t72 @t69)) % 0.38/0.61 (define @t75 () (@var "BOUND_VARIABLE_7538" $$unsorted)) % 0.38/0.61 (define @t76 () (@var "BOUND_VARIABLE_7536" $$unsorted)) % 0.38/0.61 (define @t77 () (or @t54 @t74)) % 0.38/0.61 (define @t78 () (tptp.in @t75 (tptp.binunion @t16 @t76))) % 0.38/0.61 (define @t79 () (tptp.binintersect @t16 @t19)) % 0.38/0.61 (define @t80 () (not (tptp.in @t75 @t79))) % 0.38/0.61 (define @t81 () (not (tptp.in @t75 @t2))) % 0.38/0.61 (define @t82 () (not (tptp.in @t76 @t50))) % 0.38/0.61 (define @t83 () (tptp.in @t19 @t50)) % 0.38/0.61 (define @t84 () (not @t83)) % 0.38/0.61 (define @t85 () (or @t84 @t82 @t81 @t80 @t78)) % 0.38/0.61 (define @t86 () (@list @t19 @t76 @t75)) % 0.38/0.61 (define @t87 () (forall @t86 @t85)) % 0.38/0.61 (define @t88 () (not @t37)) % 0.38/0.61 (define @t89 () (or @t88 @t87)) % 0.38/0.61 (define @t90 () (or @t82 @t81 @t80 @t78)) % 0.38/0.61 (define @t91 () (or @t84 @t90)) % 0.38/0.61 (define @t92 () (forall @t86 @t91)) % 0.38/0.61 (define @t93 () (@list @t76 @t75)) % 0.38/0.61 (define @t94 () (forall @t93 @t91)) % 0.38/0.61 (define @t95 () (forall @t93 @t90)) % 0.38/0.61 (define @t96 () (@var "BOUND_VARIABLE_7513" $$unsorted)) % 0.38/0.61 (define @t97 () (or @t84 @t95)) % 0.38/0.61 (define @t98 () (tptp.binunion @t16 @t15)) % 0.38/0.61 (define @t99 () (tptp.in @t96 @t98)) % 0.38/0.61 (define @t100 () (not (tptp.in @t96 @t79))) % 0.38/0.61 (define @t101 () (not (tptp.in @t96 @t2))) % 0.38/0.61 (define @t102 () (tptp.in @t15 @t50)) % 0.38/0.61 (define @t103 () (not @t102)) % 0.38/0.61 (define @t104 () (or @t103 @t101 @t100 @t99)) % 0.38/0.61 (define @t105 () (@list @t15 @t96)) % 0.38/0.61 (define @t106 () (forall @t105 @t104)) % 0.38/0.61 (define @t107 () (not @t32)) % 0.38/0.61 (define @t108 () (or @t107 @t106)) % 0.38/0.61 (define @t109 () (or @t101 @t100 @t99)) % 0.38/0.61 (define @t110 () (or @t103 @t109)) % 0.38/0.61 (define @t111 () (forall @t105 @t110)) % 0.38/0.61 (define @t112 () (@list @t96)) % 0.38/0.61 (define @t113 () (forall @t112 @t110)) % 0.38/0.61 (define @t114 () (forall @t112 @t109)) % 0.38/0.61 (define @t115 () (or @t103 @t114)) % 0.38/0.61 (define @t116 () (tptp.in @t4 @t98)) % 0.38/0.61 (define @t117 () (tptp.in @t4 @t79)) % 0.38/0.61 (define @t118 () (forall @t23 (or (not @t58) (not @t117) @t116))) % 0.38/0.61 (define @t119 () (not @t27)) % 0.38/0.61 (define @t120 () (or @t119 @t118)) % 0.38/0.61 (define @t121 () (not @t21)) % 0.38/0.61 (define @t122 () (or @t66 @t121 @t18)) % 0.38/0.61 (define @t123 () (@quantifiers_skolemize @t57 2)) % 0.38/0.61 (define @t124 () (@quantifiers_skolemize @t57 1)) % 0.38/0.61 (define @t125 () (@quantifiers_skolemize @t57 4)) % 0.38/0.61 (define @t126 () (tptp.in @t125 (tptp.binintersect @t124 @t123))) % 0.38/0.61 (define @t127 () (@quantifiers_skolemize @t57 3)) % 0.38/0.61 (define @t128 () (tptp.in @t125 (tptp.binunion @t124 @t127))) % 0.38/0.61 (define @t129 () (not @t126)) % 0.38/0.61 (define @t130 () (@quantifiers_skolemize @t57 0)) % 0.38/0.61 (define @t131 () (tptp.powerset @t130)) % 0.38/0.61 (define @t132 () (or (not (tptp.in @t124 @t131)) (not (tptp.in @t123 @t131)) (not (tptp.in @t127 @t131)) (not (tptp.in @t125 @t130)) @t129 @t128)) % 0.38/0.61 (define @t133 () (@list true)) % 0.38/0.61 (define @t134 () (@list @t132)) % 0.38/0.61 (define @t135 () (tptp.in @t125 @t124)) % 0.38/0.61 (define @t136 () (not @t135)) % 0.38/0.61 (define @t137 () (or @t136 @t128)) % 0.38/0.61 (define @t138 () (or @t129 @t135)) % 0.38/0.61 (assume @p1 @t10) % 0.38/0.61 (assume @p2 @t14) % 0.38/0.61 (assume @p3 @t43) % 0.38/0.61 (assume @p4 true) % 0.38/0.61 (step @p5 :rule refl :args (@t57)) % 0.38/0.61 (step @p6 :rule refl :args (@t58)) % 0.38/0.61 (step @p7 :rule refl :args (@t7)) % 0.38/0.61 (step @p8 :rule cong :premises (@p7 @p6) :args ((= @t7 @t58))) % 0.38/0.61 (step @p9 :rule symm :premises (@p8)) % 0.38/0.61 (step @p10 :rule eq_resolve :premises (@p7 @p9)) % 0.38/0.61 (step @p11 :rule refl :args ((tptp.in @t4 @t11))) % 0.38/0.61 (step @p12 :rule refl :args (@t59)) % 0.38/0.61 (step @p13 :rule refl :args (@t4)) % 0.38/0.61 (step @p14 :rule cong :premises (@p13 @p12) :args (@t60)) % 0.38/0.61 (step @p15 :rule trans :premises (@p14 @p11)) % 0.38/0.61 (step @p16 :rule refl :args (@t5)) % 0.38/0.61 (step @p17 :rule ho_cong :premises (@p16 @p12)) % 0.38/0.61 (step @p18 :rule cong :premises (@p17 @p15) :args ((= (_ @t5 @t59) @t60))) % 0.38/0.61 (step @p19 :rule symm :premises (@p18)) % 0.38/0.61 (step @p20 :rule refl :args (@t12)) % 0.38/0.61 (step @p21 :rule eq_resolve :premises (@p20 @p19)) % 0.38/0.61 (step @p22 :rule refl :args (@t11)) % 0.38/0.61 (step @p23 :rule cong :premises (@p22 @p12) :args ((= @t11 @t59))) % 0.38/0.61 (step @p24 :rule symm :premises (@p23)) % 0.38/0.61 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 0.38/0.61 (step @p26 :rule ho_cong :premises (@p16 @p25)) % 0.38/0.61 (step @p27 :rule trans :premises (@p26 @p21)) % 0.38/0.61 (step @p28 :rule cong :premises (@p27) :args (@t61)) % 0.38/0.61 (step @p29 :rule nary_cong :premises (@p28 @p10) :args (@t62)) % 0.38/0.61 (step @p30 :rule cong :premises (@p29) :args ((forall @t8 @t62))) % 0.38/0.61 (step @p31 :rule bool-impl-elim :args (@t12 @t7)) % 0.38/0.61 (step @p32 :rule cong :premises (@p31) :args (@t13)) % 0.38/0.61 (step @p33 :rule trans :premises (@p32 @p30)) % 0.38/0.61 (step @p34 :rule refl :args (tptp.binintersectEL)) % 0.38/0.61 (step @p35 :rule cong :premises (@p34 @p33) :args (@t14)) % 0.38/0.61 (step @p36 :rule eq_resolve :premises (@p2 @p35)) % 0.38/0.61 (step @p37 :rule cong :premises (@p36 @p5) :args (@t63)) % 0.38/0.61 (step @p38 :rule refl :args ((tptp.in @t4 @t3))) % 0.38/0.61 (step @p39 :rule refl :args (@t64)) % 0.38/0.61 (step @p40 :rule cong :premises (@p13 @p39) :args (@t65)) % 0.38/0.61 (step @p41 :rule trans :premises (@p40 @p38)) % 0.38/0.61 (step @p42 :rule ho_cong :premises (@p16 @p39)) % 0.38/0.61 (step @p43 :rule cong :premises (@p42 @p41) :args ((= (_ @t5 @t64) @t65))) % 0.38/0.61 (step @p44 :rule symm :premises (@p43)) % 0.38/0.61 (step @p45 :rule refl :args (@t6)) % 0.38/0.61 (step @p46 :rule eq_resolve :premises (@p45 @p44)) % 0.38/0.61 (step @p47 :rule refl :args (@t3)) % 0.38/0.61 (step @p48 :rule cong :premises (@p47 @p39) :args ((= @t3 @t64))) % 0.38/0.61 (step @p49 :rule symm :premises (@p48)) % 0.38/0.61 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 0.38/0.61 (step @p51 :rule ho_cong :premises (@p16 @p50)) % 0.38/0.61 (step @p52 :rule trans :premises (@p51 @p46)) % 0.38/0.61 (step @p53 :rule cong :premises (@p10) :args (@t66)) % 0.38/0.61 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t67)) % 0.38/0.61 (step @p55 :rule cong :premises (@p54) :args ((forall @t8 @t67))) % 0.38/0.61 (step @p56 :rule bool-impl-elim :args (@t7 @t6)) % 0.38/0.61 (step @p57 :rule cong :premises (@p56) :args (@t9)) % 0.38/0.61 (step @p58 :rule trans :premises (@p57 @p55)) % 0.38/0.61 (step @p59 :rule refl :args (tptp.binunionIL)) % 0.38/0.61 (step @p60 :rule cong :premises (@p59 @p58) :args (@t10)) % 0.38/0.61 (step @p61 :rule eq_resolve :premises (@p1 @p60)) % 0.38/0.61 (step @p62 :rule cong :premises (@p61 @p37) :args (@t68)) % 0.38/0.61 (step @p63 :rule cong :premises (@p62) :args ((not @t68))) % 0.38/0.61 (step @p64 :rule aci_norm :args ((= @t70 @t55))) % 0.38/0.61 (step @p65 :rule cong :premises (@p64) :args (@t71)) % 0.38/0.61 (step @p66 :rule quant-merge-prenex :args ((= (forall @t39 @t73) @t71))) % 0.38/0.61 (step @p67 :rule alpha_equiv :args (@t74 (@list @t47 @t44 @t45) (@list @t19 @t76 @t75))) % 0.38/0.61 (step @p68 :rule refl :args (@t54)) % 0.38/0.61 (step @p69 :rule nary_cong :premises (@p68 @p67) :args (@t77)) % 0.38/0.61 (step @p70 :rule quant-miniscope-or :args ((= @t73 @t77))) % 0.38/0.61 (step @p71 :rule trans :premises (@p70 @p69)) % 0.38/0.61 (step @p72 :rule symm :premises (@p71)) % 0.38/0.61 (step @p73 :rule cong :premises (@p72) :args ((forall @t39 (or @t54 @t87)))) % 0.38/0.61 (step @p74 :rule trans :premises (@p73 @p66)) % 0.38/0.61 (step @p75 :rule trans :premises (@p74 @p65)) % 0.38/0.61 (step @p76 :rule refl :args (@t87)) % 0.38/0.61 (step @p77 :rule refl :args ((tptp.in @t16 @t25))) % 0.38/0.61 (step @p78 :rule refl :args (@t50)) % 0.38/0.61 (step @p79 :rule refl :args (@t16)) % 0.38/0.61 (step @p80 :rule cong :premises (@p79 @p78) :args (@t53)) % 0.38/0.61 (step @p81 :rule trans :premises (@p80 @p77)) % 0.38/0.61 (step @p82 :rule refl :args (@t36)) % 0.38/0.61 (step @p83 :rule ho_cong :premises (@p82 @p78)) % 0.38/0.61 (step @p84 :rule cong :premises (@p83 @p81) :args ((= (_ @t36 @t50) @t53))) % 0.38/0.61 (step @p85 :rule symm :premises (@p84)) % 0.38/0.61 (step @p86 :rule refl :args (@t37)) % 0.38/0.61 (step @p87 :rule eq_resolve :premises (@p86 @p85)) % 0.38/0.61 (step @p88 :rule refl :args (@t25)) % 0.38/0.61 (step @p89 :rule cong :premises (@p88 @p78) :args ((= @t25 @t50))) % 0.38/0.61 (step @p90 :rule symm :premises (@p89)) % 0.38/0.61 (step @p91 :rule eq_resolve :premises (@p88 @p90)) % 0.38/0.61 (step @p92 :rule ho_cong :premises (@p82 @p91)) % 0.38/0.61 (step @p93 :rule trans :premises (@p92 @p87)) % 0.38/0.61 (step @p94 :rule cong :premises (@p93) :args (@t88)) % 0.38/0.61 (step @p95 :rule nary_cong :premises (@p94 @p76) :args (@t89)) % 0.38/0.61 (step @p96 :rule cong :premises (@p95) :args ((forall @t39 @t89))) % 0.38/0.61 (step @p97 :rule trans :premises (@p96 @p75)) % 0.38/0.61 (step @p98 :rule bool-impl-elim :args (@t37 @t87)) % 0.38/0.61 (step @p99 :rule cong :premises (@p98) :args ((forall @t39 (=> @t37 @t87)))) % 0.38/0.61 (step @p100 :rule trans :premises (@p99 @p97)) % 0.38/0.61 (step @p101 :rule aci_norm :args ((= @t91 @t85))) % 0.38/0.61 (step @p102 :rule cong :premises (@p101) :args (@t92)) % 0.38/0.61 (step @p103 :rule quant-merge-prenex :args ((= (forall @t34 @t94) @t92))) % 0.38/0.61 (step @p104 :rule alpha_equiv :args (@t95 (@list @t76 @t75) (@list @t15 @t96))) % 0.38/0.61 (step @p105 :rule refl :args (@t84)) % 0.38/0.61 (step @p106 :rule nary_cong :premises (@p105 @p104) :args (@t97)) % 0.38/0.61 (step @p107 :rule quant-miniscope-or :args ((= @t94 @t97))) % 0.38/0.61 (step @p108 :rule trans :premises (@p107 @p106)) % 0.38/0.61 (step @p109 :rule symm :premises (@p108)) % 0.38/0.61 (step @p110 :rule cong :premises (@p109) :args ((forall @t34 (or @t84 @t106)))) % 0.38/0.61 (step @p111 :rule trans :premises (@p110 @p103)) % 0.38/0.61 (step @p112 :rule trans :premises (@p111 @p102)) % 0.38/0.61 (step @p113 :rule refl :args (@t106)) % 0.38/0.61 (step @p114 :rule refl :args ((tptp.in @t19 @t25))) % 0.38/0.61 (step @p115 :rule refl :args (@t19)) % 0.38/0.61 (step @p116 :rule cong :premises (@p115 @p78) :args (@t83)) % 0.38/0.61 (step @p117 :rule trans :premises (@p116 @p114)) % 0.38/0.61 (step @p118 :rule refl :args (@t31)) % 0.38/0.61 (step @p119 :rule ho_cong :premises (@p118 @p78)) % 0.38/0.61 (step @p120 :rule cong :premises (@p119 @p117) :args ((= (_ @t31 @t50) @t83))) % 0.38/0.61 (step @p121 :rule symm :premises (@p120)) % 0.38/0.61 (step @p122 :rule refl :args (@t32)) % 0.38/0.61 (step @p123 :rule eq_resolve :premises (@p122 @p121)) % 0.38/0.61 (step @p124 :rule ho_cong :premises (@p118 @p91)) % 0.38/0.61 (step @p125 :rule trans :premises (@p124 @p123)) % 0.38/0.61 (step @p126 :rule cong :premises (@p125) :args (@t107)) % 0.38/0.61 (step @p127 :rule nary_cong :premises (@p126 @p113) :args (@t108)) % 0.38/0.61 (step @p128 :rule cong :premises (@p127) :args ((forall @t34 @t108))) % 0.38/0.61 (step @p129 :rule trans :premises (@p128 @p112)) % 0.38/0.61 (step @p130 :rule bool-impl-elim :args (@t32 @t106)) % 0.38/0.61 (step @p131 :rule cong :premises (@p130) :args ((forall @t34 (=> @t32 @t106)))) % 0.38/0.61 (step @p132 :rule trans :premises (@p131 @p129)) % 0.38/0.61 (step @p133 :rule aci_norm :args ((= @t110 @t104))) % 0.38/0.61 (step @p134 :rule cong :premises (@p133) :args (@t111)) % 0.38/0.61 (step @p135 :rule quant-merge-prenex :args ((= (forall @t29 @t113) @t111))) % 0.38/0.61 (step @p136 :rule alpha_equiv :args (@t114 (@list @t96) (@list @t4))) % 0.38/0.61 (step @p137 :rule refl :args (@t103)) % 0.38/0.61 (step @p138 :rule nary_cong :premises (@p137 @p136) :args (@t115)) % 0.38/0.61 (step @p139 :rule quant-miniscope-or :args ((= @t113 @t115))) % 0.38/0.61 (step @p140 :rule trans :premises (@p139 @p138)) % 0.38/0.61 (step @p141 :rule symm :premises (@p140)) % 0.38/0.61 (step @p142 :rule cong :premises (@p141) :args ((forall @t29 (or @t103 @t118)))) % 0.38/0.61 (step @p143 :rule trans :premises (@p142 @p135)) % 0.38/0.61 (step @p144 :rule trans :premises (@p143 @p134)) % 0.38/0.61 (step @p145 :rule refl :args (@t118)) % 0.38/0.61 (step @p146 :rule refl :args ((tptp.in @t15 @t25))) % 0.38/0.61 (step @p147 :rule refl :args (@t15)) % 0.38/0.61 (step @p148 :rule cong :premises (@p147 @p78) :args (@t102)) % 0.38/0.61 (step @p149 :rule trans :premises (@p148 @p146)) % 0.38/0.61 (step @p150 :rule refl :args (@t26)) % 0.38/0.61 (step @p151 :rule ho_cong :premises (@p150 @p78)) % 0.38/0.61 (step @p152 :rule cong :premises (@p151 @p149) :args ((= (_ @t26 @t50) @t102))) % 0.38/0.61 (step @p153 :rule symm :premises (@p152)) % 0.38/0.61 (step @p154 :rule refl :args (@t27)) % 0.38/0.61 (step @p155 :rule eq_resolve :premises (@p154 @p153)) % 0.38/0.61 (step @p156 :rule ho_cong :premises (@p150 @p91)) % 0.38/0.61 (step @p157 :rule trans :premises (@p156 @p155)) % 0.38/0.61 (step @p158 :rule cong :premises (@p157) :args (@t119)) % 0.38/0.61 (step @p159 :rule nary_cong :premises (@p158 @p145) :args (@t120)) % 0.38/0.61 (step @p160 :rule cong :premises (@p159) :args ((forall @t29 @t120))) % 0.38/0.61 (step @p161 :rule trans :premises (@p160 @p144)) % 0.38/0.61 (step @p162 :rule bool-impl-elim :args (@t27 @t118)) % 0.38/0.61 (step @p163 :rule cong :premises (@p162) :args ((forall @t29 (=> @t27 @t118)))) % 0.38/0.61 (step @p164 :rule trans :premises (@p163 @p161)) % 0.38/0.61 (step @p165 :rule refl :args ((tptp.in @t4 @t17))) % 0.38/0.61 (step @p166 :rule refl :args (@t98)) % 0.38/0.61 (step @p167 :rule cong :premises (@p13 @p166) :args (@t116)) % 0.38/0.61 (step @p168 :rule trans :premises (@p167 @p165)) % 0.38/0.61 (step @p169 :rule ho_cong :premises (@p16 @p166)) % 0.38/0.61 (step @p170 :rule cong :premises (@p169 @p168) :args ((= (_ @t5 @t98) @t116))) % 0.38/0.61 (step @p171 :rule symm :premises (@p170)) % 0.38/0.61 (step @p172 :rule refl :args (@t18)) % 0.38/0.61 (step @p173 :rule eq_resolve :premises (@p172 @p171)) % 0.38/0.61 (step @p174 :rule refl :args (@t17)) % 0.38/0.61 (step @p175 :rule cong :premises (@p174 @p166) :args ((= @t17 @t98))) % 0.38/0.61 (step @p176 :rule symm :premises (@p175)) % 0.38/0.61 (step @p177 :rule eq_resolve :premises (@p174 @p176)) % 0.38/0.61 (step @p178 :rule ho_cong :premises (@p16 @p177)) % 0.38/0.61 (step @p179 :rule trans :premises (@p178 @p173)) % 0.38/0.61 (step @p180 :rule refl :args ((tptp.in @t4 @t20))) % 0.38/0.61 (step @p181 :rule refl :args (@t79)) % 0.38/0.61 (step @p182 :rule cong :premises (@p13 @p181) :args (@t117)) % 0.38/0.61 (step @p183 :rule trans :premises (@p182 @p180)) % 0.38/0.61 (step @p184 :rule ho_cong :premises (@p16 @p181)) % 0.38/0.61 (step @p185 :rule cong :premises (@p184 @p183) :args ((= (_ @t5 @t79) @t117))) % 0.38/0.61 (step @p186 :rule symm :premises (@p185)) % 0.38/0.61 (step @p187 :rule refl :args (@t21)) % 0.38/0.61 (step @p188 :rule eq_resolve :premises (@p187 @p186)) % 0.38/0.61 (step @p189 :rule refl :args (@t20)) % 0.38/0.61 (step @p190 :rule cong :premises (@p189 @p181) :args ((= @t20 @t79))) % 0.38/0.61 (step @p191 :rule symm :premises (@p190)) % 0.38/0.61 (step @p192 :rule eq_resolve :premises (@p189 @p191)) % 0.38/0.61 (step @p193 :rule ho_cong :premises (@p16 @p192)) % 0.38/0.61 (step @p194 :rule trans :premises (@p193 @p188)) % 0.38/0.61 (step @p195 :rule cong :premises (@p194) :args (@t121)) % 0.38/0.61 (step @p196 :rule nary_cong :premises (@p53 @p195 @p179) :args (@t122)) % 0.38/0.61 (step @p197 :rule cong :premises (@p196) :args ((forall @t23 @t122))) % 0.38/0.61 (step @p198 :rule aci_norm :args ((= (or @t66 (or @t121 @t18)) @t122))) % 0.38/0.61 (step @p199 :rule bool-impl-elim :args (@t21 @t18)) % 0.38/0.61 (step @p200 :rule refl :args (@t66)) % 0.38/0.61 (step @p201 :rule nary_cong :premises (@p200 @p199) :args ((or @t66 @t22))) % 0.38/0.61 (step @p202 :rule trans :premises (@p201 @p198)) % 0.38/0.61 (step @p203 :rule bool-impl-elim :args (@t7 @t22)) % 0.38/0.61 (step @p204 :rule trans :premises (@p203 @p202)) % 0.38/0.61 (step @p205 :rule cong :premises (@p204) :args (@t24)) % 0.38/0.61 (step @p206 :rule trans :premises (@p205 @p197)) % 0.38/0.61 (step @p207 :rule refl :args (@t27)) % 0.38/0.61 (step @p208 :rule cong :premises (@p207 @p206) :args (@t28)) % 0.38/0.61 (step @p209 :rule cong :premises (@p208) :args (@t30)) % 0.38/0.61 (step @p210 :rule trans :premises (@p209 @p164)) % 0.38/0.61 (step @p211 :rule refl :args (@t32)) % 0.38/0.61 (step @p212 :rule cong :premises (@p211 @p210) :args (@t33)) % 0.38/0.61 (step @p213 :rule cong :premises (@p212) :args (@t35)) % 0.38/0.61 (step @p214 :rule trans :premises (@p213 @p132)) % 0.38/0.61 (step @p215 :rule refl :args (@t37)) % 0.38/0.61 (step @p216 :rule cong :premises (@p215 @p214) :args (@t38)) % 0.38/0.61 (step @p217 :rule cong :premises (@p216) :args (@t40)) % 0.38/0.61 (step @p218 :rule trans :premises (@p217 @p100)) % 0.38/0.61 (step @p219 :rule cong :premises (@p34 @p218) :args (@t41)) % 0.38/0.61 (step @p220 :rule cong :premises (@p59 @p219) :args (@t42)) % 0.38/0.61 (step @p221 :rule cong :premises (@p220) :args (@t43)) % 0.38/0.61 (step @p222 :rule trans :premises (@p221 @p63)) % 0.38/0.61 (step @p223 :rule eq_resolve :premises (@p3 @p222)) % 0.38/0.61 (step @p224 :rule not_implies_elim2 :premises (@p223)) % 0.38/0.61 (step @p225 :rule not_implies_elim2 :premises (@p224)) % 0.38/0.61 (step @p226 :rule skolemize :premises (@p225)) % 0.38/0.61 (step @p227 :rule bool-double-not-elim :args (@t126)) % 0.38/0.61 (step @p228 :rule refl :args (@t132)) % 0.38/0.61 (step @p229 :rule nary_cong :premises (@p228 @p227) :args ((or @t132 (not @t129)))) % 0.38/0.61 (step @p230 :rule cnf_or_neg :args (@t132 4)) % 0.38/0.61 (step @p231 :rule eq_resolve :premises (@p230 @p229)) % 0.38/0.61 (step @p232 :rule reordering :premises (@p231) :args ((or @t126 @t132))) % 0.38/0.61 (step @p233 :rule chain_m_resolution :premises (@p232 @p226) :args (@t126 @t133 @t134)) % 0.38/0.61 (step @p234 :rule not_implies_elim1 :premises (@p224)) % 0.38/0.61 (step @p235 :rule instantiate :premises (@p234) :args ((@list @t124 @t123 @t125))) % 0.38/0.61 (step @p236 :rule not_implies_elim1 :premises (@p223)) % 0.38/0.61 (step @p237 :rule instantiate :premises (@p236) :args ((@list @t124 @t127 @t125))) % 0.38/0.61 (step @p238 :rule cnf_or_neg :args (@t132 5)) % 0.38/0.61 (step @p239 :rule chain_m_resolution :premises (@p238 @p226) :args ((not @t128) @t133 @t134)) % 0.38/0.61 (step @p240 :rule cnf_or_pos :args (@t137)) % 0.38/0.61 (step @p241 :rule reordering :premises (@p240) :args ((or @t128 @t136 (not @t137)))) % 0.38/0.61 (step @p242 :rule chain_m_resolution :premises (@p241 @p239 @p237) :args (@t136 (@list true false) (@list @t128 @t137))) % 0.38/0.61 (step @p243 :rule cnf_or_pos :args (@t138)) % 0.38/0.61 (step @p244 :rule reordering :premises (@p243) :args ((or @t129 @t135 (not @t138)))) % 0.38/0.61 (step @p245 false :rule chain_m_resolution :premises (@p244 @p242 @p235 @p233) :args (false (@list true false false) (@list @t135 @t138 @t126))) % 0.38/0.61 ) % 0.38/0.61 % SZS output end Proof % 0.38/0.61 % cvc5 exiting %------------------------------------------------------------------------------