%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV064^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : 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 08:55:24 AM UTC 2026 % Result : Theorem 0.85s 1.04s % Output : Proof 0.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV064^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n017.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 18:09:46 EDT 2026 % 0.16/0.35 % CPUTime : % 0.27/0.50 %----Proving TH0 % 0.85/1.04 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.85/1.04 % SZS status Theorem % 0.85/1.04 % SZS output start Proof % 0.85/1.04 ( % 0.85/1.04 (declare-sort $$unsorted 0) % 0.85/1.04 (define @t1 () (@var "Xw_2" $$unsorted)) % 0.85/1.04 (define @t2 () (@var "Xz" (-> $$unsorted Bool))) % 0.85/1.04 (define @t3 () (@var "Xx" (-> $$unsorted Bool))) % 0.85/1.04 (define @t4 () (@var "Xr_28" (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool))) % 0.85/1.04 (define @t5 () (_ @t4 @t3)) % 0.85/1.04 (define @t6 () (_ (_ @t5 @t2) @t1)) % 0.85/1.04 (define @t7 () (@var "Xr_27" (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool))) % 0.85/1.04 (define @t8 () (_ @t7 @t3)) % 0.85/1.04 (define @t9 () (_ (_ @t8 @t2) @t1)) % 0.85/1.04 (define @t10 () (or @t9 @t6)) % 0.85/1.04 (define @t11 () (@list @t1)) % 0.85/1.04 (define @t12 () (forall @t11 @t10)) % 0.85/1.04 (define @t13 () (@var "Xy" (-> $$unsorted Bool))) % 0.85/1.04 (define @t14 () (_ (_ (_ @t4 @t13) @t2) @t1)) % 0.85/1.04 (define @t15 () (_ (_ (_ @t7 @t13) @t2) @t1)) % 0.85/1.04 (define @t16 () (or @t15 @t14)) % 0.85/1.04 (define @t17 () (forall @t11 @t16)) % 0.85/1.04 (define @t18 () (_ (_ @t5 @t13) @t1)) % 0.85/1.04 (define @t19 () (_ (_ @t8 @t13) @t1)) % 0.85/1.04 (define @t20 () (or @t19 @t18)) % 0.85/1.04 (define @t21 () (forall @t11 @t20)) % 0.85/1.04 (define @t22 () (and @t21 @t17)) % 0.85/1.04 (define @t23 () (=> @t22 @t12)) % 0.85/1.04 (define @t24 () (@list @t3 @t13 @t2)) % 0.85/1.04 (define @t25 () (forall @t24 @t23)) % 0.85/1.04 (define @t26 () (_ (_ @t5 @t3) @t1)) % 0.85/1.04 (define @t27 () (_ (_ @t8 @t3) @t1)) % 0.85/1.04 (define @t28 () (or @t27 @t26)) % 0.85/1.04 (define @t29 () (@list @t3 @t1)) % 0.85/1.04 (define @t30 () (forall @t29 @t28)) % 0.85/1.04 (define @t31 () (@var "Xx" $$unsorted)) % 0.85/1.04 (define @t32 () (@list @t31)) % 0.85/1.04 (define @t33 () (lambda @t32 false)) % 0.85/1.04 (define @t34 () (lambda @t32 true)) % 0.85/1.04 (define @t35 () (or (_ (_ (_ @t7 @t34) @t33) @t1) (_ (_ (_ @t4 @t34) @t33) @t1))) % 0.85/1.04 (define @t36 () (forall @t11 @t35)) % 0.85/1.04 (define @t37 () (not @t36)) % 0.85/1.04 (define @t38 () (and @t37 @t30 @t25)) % 0.85/1.04 (define @t39 () (@list @t4 @t7)) % 0.85/1.04 (define @t40 () (exists @t39 @t38)) % 0.85/1.04 (define @t41 () (not @t40)) % 0.85/1.04 (define @t42 () (@var "BOUND_VARIABLE_7528" $$unsorted)) % 0.85/1.04 (define @t43 () (@var "BOUND_VARIABLE_7662" $$unsorted)) % 0.85/1.04 (define @t44 () (lambda (@list @t43) false)) % 0.85/1.04 (define @t45 () (@var "BOUND_VARIABLE_7666" $$unsorted)) % 0.85/1.04 (define @t46 () (lambda (@list @t45) true)) % 0.85/1.04 (define @t47 () (_ @t4 @t46 @t44 @t42)) % 0.85/1.04 (define @t48 () (_ @t7 @t46 @t44 @t42)) % 0.85/1.04 (define @t49 () (@var "BOUND_VARIABLE_7509" $$unsorted)) % 0.85/1.04 (define @t50 () (_ @t4 @t3 @t2 @t49)) % 0.85/1.04 (define @t51 () (_ @t7 @t3 @t2 @t49)) % 0.85/1.04 (define @t52 () (_ @t4 @t13 @t2 @t1)) % 0.85/1.04 (define @t53 () (_ @t7 @t13 @t2 @t1)) % 0.85/1.04 (define @t54 () (forall @t11 (or @t53 @t52))) % 0.85/1.04 (define @t55 () (not @t54)) % 0.85/1.04 (define @t56 () (_ @t4 @t3 @t13 @t1)) % 0.85/1.04 (define @t57 () (_ @t7 @t3 @t13 @t1)) % 0.85/1.04 (define @t58 () (forall @t11 (or @t57 @t56))) % 0.85/1.04 (define @t59 () (not @t58)) % 0.85/1.04 (define @t60 () (or @t59 @t55 @t51 @t50)) % 0.85/1.04 (define @t61 () (@list @t3 @t13 @t2 @t49)) % 0.85/1.04 (define @t62 () (forall @t61 @t60)) % 0.85/1.04 (define @t63 () (not @t62)) % 0.85/1.04 (define @t64 () (_ @t4 @t3 @t3 @t1)) % 0.85/1.04 (define @t65 () (_ @t7 @t3 @t3 @t1)) % 0.85/1.04 (define @t66 () (forall @t29 (or @t65 @t64))) % 0.85/1.04 (define @t67 () (not @t66)) % 0.85/1.04 (define @t68 () (or @t67 @t63 @t48 @t47)) % 0.85/1.04 (define @t69 () (@list @t4 @t7 @t42)) % 0.85/1.04 (define @t70 () (forall @t69 @t68)) % 0.85/1.04 (define @t71 () (or @t48 @t47)) % 0.85/1.04 (define @t72 () (or @t71 @t67 @t63)) % 0.85/1.04 (define @t73 () (forall @t69 @t72)) % 0.85/1.04 (define @t74 () (@list @t42)) % 0.85/1.04 (define @t75 () (forall @t74 @t72)) % 0.85/1.04 (define @t76 () (forall @t74 @t71)) % 0.85/1.04 (define @t77 () (@list @t1)) % 0.85/1.04 (define @t78 () (or @t76 @t67 @t63)) % 0.85/1.04 (define @t79 () (_ @t4 @t46 @t44 @t1)) % 0.85/1.04 (define @t80 () (_ @t7 @t46 @t44 @t1)) % 0.85/1.04 (define @t81 () (forall @t11 (or @t80 @t79))) % 0.85/1.04 (define @t82 () (not @t81)) % 0.85/1.04 (define @t83 () (not @t82)) % 0.85/1.04 (define @t84 () (or @t83 @t67 @t63)) % 0.85/1.04 (define @t85 () (and @t82 @t66 @t62)) % 0.85/1.04 (define @t86 () (forall @t39 (not @t85))) % 0.85/1.04 (define @t87 () (not @t86)) % 0.85/1.04 (define @t88 () (or @t51 @t50)) % 0.85/1.04 (define @t89 () (or @t59 @t55 @t88)) % 0.85/1.04 (define @t90 () (forall @t61 @t89)) % 0.85/1.04 (define @t91 () (@list @t49)) % 0.85/1.04 (define @t92 () (forall @t91 @t89)) % 0.85/1.04 (define @t93 () (forall @t91 @t88)) % 0.85/1.04 (define @t94 () (or @t59 @t55 @t93)) % 0.85/1.04 (define @t95 () (_ @t4 @t3 @t2 @t1)) % 0.85/1.04 (define @t96 () (_ @t7 @t3 @t2 @t1)) % 0.85/1.04 (define @t97 () (forall @t11 (or @t96 @t95))) % 0.85/1.04 (define @t98 () (or @t59 @t55 @t97)) % 0.85/1.04 (define @t99 () (and @t58 @t54)) % 0.85/1.04 (define @t100 () (_ (_ (_ @t4 @t46) @t44) @t1)) % 0.85/1.04 (define @t101 () (_ (_ (_ @t7 @t46) @t44) @t1)) % 0.85/1.04 (define @t102 () (or @t101 @t100)) % 0.85/1.04 (define @t103 () (@list @t31)) % 0.85/1.04 (define @t104 () (= @t46 @t44)) % 0.85/1.04 (define @t105 () (@purify (as @$$unsorted_0 $$unsorted))) % 0.85/1.04 (define @t106 () (@var "BOUND_VARIABLE_38553" (-> $$unsorted Bool))) % 0.85/1.04 (define @t107 () (@var "BOUND_VARIABLE_38552" (-> $$unsorted Bool))) % 0.85/1.04 (define @t108 () (lambda (@list @t107 @t106 (@var "BOUND_VARIABLE_38554" $$unsorted)) (= @t107 @t106))) % 0.85/1.04 (define @t109 () (_ @t108 @t46 @t44 @t105)) % 0.85/1.04 (define @t110 () (lambda (@list (@var "BOUND_VARIABLE_38774" (-> $$unsorted Bool)) (@var "BOUND_VARIABLE_38775" (-> $$unsorted Bool)) (@var "BOUND_VARIABLE_38776" $$unsorted)) false)) % 0.85/1.04 (define @t111 () (_ @t110 @t46 @t44 @t105)) % 0.85/1.04 (define @t112 () (@list @t13 @t2)) % 0.85/1.04 (define @t113 () (= @t13 @t2)) % 0.85/1.04 (define @t114 () (not @t113)) % 0.85/1.04 (define @t115 () (or @t114 @t113)) % 0.85/1.04 (define @t116 () (not (= @t13 @t13))) % 0.85/1.04 (define @t117 () (or @t116 @t114 @t113)) % 0.85/1.04 (define @t118 () (= @t3 @t2)) % 0.85/1.04 (define @t119 () (= @t3 @t13)) % 0.85/1.04 (define @t120 () (not @t119)) % 0.85/1.04 (define @t121 () (or @t120 @t120 @t114 @t118)) % 0.85/1.04 (define @t122 () (@list @t3)) % 0.85/1.04 (define @t123 () (or @t120 @t114 @t118)) % 0.85/1.04 (define @t124 () (forall @t122 @t123)) % 0.85/1.04 (define @t125 () (forall @t112 @t124)) % 0.85/1.04 (define @t126 () (forall (@list @t13 @t2 @t3) @t123)) % 0.85/1.04 (define @t127 () (forall @t24 @t123)) % 0.85/1.04 (define @t128 () (_ @t108 @t3 @t2 @t49)) % 0.85/1.04 (define @t129 () (_ @t110 @t3 @t2 @t49)) % 0.85/1.04 (define @t130 () (_ @t108 @t13 @t2 @t1)) % 0.85/1.04 (define @t131 () (_ @t110 @t13 @t2 @t1)) % 0.85/1.04 (define @t132 () (or @t131 @t130)) % 0.85/1.04 (define @t133 () (forall @t11 @t132)) % 0.85/1.04 (define @t134 () (not @t133)) % 0.85/1.04 (define @t135 () (_ @t108 @t3 @t13 @t1)) % 0.85/1.04 (define @t136 () (_ @t110 @t3 @t13 @t1)) % 0.85/1.04 (define @t137 () (or @t136 @t135)) % 0.85/1.04 (define @t138 () (forall @t11 @t137)) % 0.85/1.04 (define @t139 () (not @t138)) % 0.85/1.04 (define @t140 () (or @t139 @t134 @t129 @t128)) % 0.85/1.04 (define @t141 () (forall @t61 @t140)) % 0.85/1.04 (define @t142 () (not @t141)) % 0.85/1.04 (define @t143 () (_ @t108 @t3 @t3 @t1)) % 0.85/1.04 (define @t144 () (_ @t110 @t3 @t3 @t1)) % 0.85/1.04 (define @t145 () (or @t144 @t143)) % 0.85/1.04 (define @t146 () (forall @t29 @t145)) % 0.85/1.04 (define @t147 () (not @t146)) % 0.85/1.04 (define @t148 () (or @t147 @t142 @t111 @t109)) % 0.85/1.04 (assume @p1 @t41) % 0.85/1.04 (assume @p2 true) % 0.85/1.04 (step @p3 :rule bool-double-not-elim :args (@t70)) % 0.85/1.04 (step @p4 :rule aci_norm :args ((= @t72 @t68))) % 0.85/1.04 (step @p5 :rule cong :premises (@p4) :args (@t73)) % 0.85/1.04 (step @p6 :rule quant-merge-prenex :args ((= (forall @t39 @t75) @t73))) % 0.85/1.04 (step @p7 :rule refl :args (@t63)) % 0.85/1.04 (step @p8 :rule refl :args (@t67)) % 0.85/1.04 (step @p9 :rule alpha_equiv :args (@t76 (@list @t42) @t77)) % 0.85/1.04 (step @p10 :rule nary_cong :premises (@p9 @p8 @p7) :args (@t78)) % 0.85/1.04 (step @p11 :rule quant-miniscope-or :args ((= @t75 @t78))) % 0.85/1.04 (step @p12 :rule trans :premises (@p11 @p10)) % 0.85/1.04 (step @p13 :rule symm :premises (@p12)) % 0.85/1.04 (step @p14 :rule cong :premises (@p13) :args ((forall @t39 (or @t81 @t67 @t63)))) % 0.85/1.04 (step @p15 :rule trans :premises (@p14 @p6)) % 0.85/1.04 (step @p16 :rule trans :premises (@p15 @p5)) % 0.85/1.04 (step @p17 :rule bool-double-not-elim :args (@t81)) % 0.85/1.04 (step @p18 :rule nary_cong :premises (@p17 @p8 @p7) :args (@t84)) % 0.85/1.04 (step @p19 :rule aci_norm :args ((= (or @t83 (or @t67 @t63)) @t84))) % 0.85/1.04 (step @p20 :rule trans :premises (@p19 @p18)) % 0.85/1.04 (step @p21 :rule bool-and-de-morgan :args (@t66 @t62 true)) % 0.85/1.04 (step @p22 :rule refl :args (@t83)) % 0.85/1.04 (step @p23 :rule nary_cong :premises (@p22 @p21) :args ((or @t83 (not (and @t66 @t62))))) % 0.85/1.04 (step @p24 :rule bool-and-de-morgan :args (@t82 @t66 (and @t62))) % 0.85/1.04 (step @p25 :rule trans :premises (@p24 @p23)) % 0.85/1.04 (step @p26 :rule trans :premises (@p25 @p20)) % 0.85/1.04 (step @p27 :rule cong :premises (@p26) :args (@t86)) % 0.85/1.04 (step @p28 :rule trans :premises (@p27 @p16)) % 0.85/1.04 (step @p29 :rule cong :premises (@p28) :args (@t87)) % 0.85/1.04 (step @p30 :rule exists-elim :args ((= (exists @t39 @t85) @t87))) % 0.85/1.04 (step @p31 :rule trans :premises (@p30 @p29)) % 0.85/1.04 (step @p32 :rule aci_norm :args ((= @t89 @t60))) % 0.85/1.04 (step @p33 :rule cong :premises (@p32) :args (@t90)) % 0.85/1.04 (step @p34 :rule quant-merge-prenex :args ((= (forall @t24 @t92) @t90))) % 0.85/1.04 (step @p35 :rule alpha_equiv :args (@t93 (@list @t49) @t77)) % 0.85/1.04 (step @p36 :rule refl :args (@t55)) % 0.85/1.04 (step @p37 :rule refl :args (@t59)) % 0.85/1.04 (step @p38 :rule nary_cong :premises (@p37 @p36 @p35) :args (@t94)) % 0.85/1.04 (step @p39 :rule quant-miniscope-or :args ((= @t92 @t94))) % 0.85/1.04 (step @p40 :rule trans :premises (@p39 @p38)) % 0.85/1.04 (step @p41 :rule symm :premises (@p40)) % 0.85/1.04 (step @p42 :rule cong :premises (@p41) :args ((forall @t24 @t98))) % 0.85/1.04 (step @p43 :rule trans :premises (@p42 @p34)) % 0.85/1.04 (step @p44 :rule trans :premises (@p43 @p33)) % 0.85/1.04 (step @p45 :rule aci_norm :args ((= (or (or @t59 @t55) @t97) @t98))) % 0.85/1.04 (step @p46 :rule refl :args (@t97)) % 0.85/1.04 (step @p47 :rule bool-and-de-morgan :args (@t58 @t54 true)) % 0.85/1.04 (step @p48 :rule nary_cong :premises (@p47 @p46) :args ((or (not @t99) @t97))) % 0.85/1.04 (step @p49 :rule trans :premises (@p48 @p45)) % 0.85/1.04 (step @p50 :rule bool-impl-elim :args (@t99 @t97)) % 0.85/1.04 (step @p51 :rule trans :premises (@p50 @p49)) % 0.85/1.04 (step @p52 :rule cong :premises (@p51) :args ((forall @t24 (=> @t99 @t97)))) % 0.85/1.04 (step @p53 :rule trans :premises (@p52 @p44)) % 0.85/1.04 (step @p54 :rule refl :args (@t95)) % 0.85/1.04 (step @p55 :rule refl :args (@t6)) % 0.85/1.04 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t6 @t95))) % 0.85/1.04 (step @p57 :rule symm :premises (@p56)) % 0.85/1.04 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 0.85/1.04 (step @p59 :rule refl :args (@t96)) % 0.85/1.04 (step @p60 :rule refl :args (@t9)) % 0.85/1.04 (step @p61 :rule cong :premises (@p60 @p59) :args ((= @t9 @t96))) % 0.85/1.04 (step @p62 :rule symm :premises (@p61)) % 0.85/1.04 (step @p63 :rule eq_resolve :premises (@p60 @p62)) % 0.85/1.04 (step @p64 :rule nary_cong :premises (@p63 @p58) :args (@t10)) % 0.85/1.04 (step @p65 :rule cong :premises (@p64) :args (@t12)) % 0.85/1.04 (step @p66 :rule refl :args (@t52)) % 0.85/1.04 (step @p67 :rule refl :args (@t14)) % 0.85/1.04 (step @p68 :rule cong :premises (@p67 @p66) :args ((= @t14 @t52))) % 0.85/1.04 (step @p69 :rule symm :premises (@p68)) % 0.85/1.04 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 0.85/1.04 (step @p71 :rule refl :args (@t53)) % 0.85/1.04 (step @p72 :rule refl :args (@t15)) % 0.85/1.04 (step @p73 :rule cong :premises (@p72 @p71) :args ((= @t15 @t53))) % 0.85/1.04 (step @p74 :rule symm :premises (@p73)) % 0.85/1.04 (step @p75 :rule eq_resolve :premises (@p72 @p74)) % 0.85/1.04 (step @p76 :rule nary_cong :premises (@p75 @p70) :args (@t16)) % 0.85/1.04 (step @p77 :rule cong :premises (@p76) :args (@t17)) % 0.85/1.04 (step @p78 :rule refl :args (@t56)) % 0.85/1.04 (step @p79 :rule refl :args (@t18)) % 0.85/1.04 (step @p80 :rule cong :premises (@p79 @p78) :args ((= @t18 @t56))) % 0.85/1.04 (step @p81 :rule symm :premises (@p80)) % 0.85/1.04 (step @p82 :rule eq_resolve :premises (@p79 @p81)) % 0.85/1.04 (step @p83 :rule refl :args (@t57)) % 0.85/1.04 (step @p84 :rule refl :args (@t19)) % 0.85/1.04 (step @p85 :rule cong :premises (@p84 @p83) :args ((= @t19 @t57))) % 0.85/1.04 (step @p86 :rule symm :premises (@p85)) % 0.85/1.04 (step @p87 :rule eq_resolve :premises (@p84 @p86)) % 0.85/1.04 (step @p88 :rule nary_cong :premises (@p87 @p82) :args (@t20)) % 0.85/1.04 (step @p89 :rule cong :premises (@p88) :args (@t21)) % 0.85/1.04 (step @p90 :rule nary_cong :premises (@p89 @p77) :args (@t22)) % 0.85/1.04 (step @p91 :rule cong :premises (@p90 @p65) :args (@t23)) % 0.85/1.04 (step @p92 :rule cong :premises (@p91) :args (@t25)) % 0.85/1.04 (step @p93 :rule trans :premises (@p92 @p53)) % 0.85/1.04 (step @p94 :rule refl :args (@t64)) % 0.85/1.04 (step @p95 :rule refl :args (@t26)) % 0.85/1.04 (step @p96 :rule cong :premises (@p95 @p94) :args ((= @t26 @t64))) % 0.85/1.04 (step @p97 :rule symm :premises (@p96)) % 0.85/1.04 (step @p98 :rule eq_resolve :premises (@p95 @p97)) % 0.85/1.04 (step @p99 :rule refl :args (@t65)) % 0.85/1.04 (step @p100 :rule refl :args (@t27)) % 0.85/1.04 (step @p101 :rule cong :premises (@p100 @p99) :args ((= @t27 @t65))) % 0.85/1.04 (step @p102 :rule symm :premises (@p101)) % 0.85/1.04 (step @p103 :rule eq_resolve :premises (@p100 @p102)) % 0.85/1.04 (step @p104 :rule nary_cong :premises (@p103 @p98) :args (@t28)) % 0.85/1.04 (step @p105 :rule cong :premises (@p104) :args (@t30)) % 0.85/1.04 (step @p106 :rule refl :args ((_ @t4 @t46 @t44 @t1))) % 0.85/1.04 (step @p107 :rule refl :args (@t1)) % 0.85/1.04 (step @p108 :rule refl :args (@t44)) % 0.85/1.04 (step @p109 :rule refl :args (@t46)) % 0.85/1.04 (step @p110 :rule cong :premises (@p109 @p108 @p107) :args (@t79)) % 0.85/1.04 (step @p111 :rule trans :premises (@p110 @p106)) % 0.85/1.04 (step @p112 :rule refl :args (@t4)) % 0.85/1.04 (step @p113 :rule ho_cong :premises (@p112 @p109)) % 0.85/1.04 (step @p114 :rule ho_cong :premises (@p113 @p108)) % 0.85/1.04 (step @p115 :rule ho_cong :premises (@p114 @p107)) % 0.85/1.04 (step @p116 :rule cong :premises (@p115 @p111) :args ((= @t100 @t79))) % 0.85/1.04 (step @p117 :rule symm :premises (@p116)) % 0.85/1.04 (step @p118 :rule refl :args ((_ (_ (_ @t4 @t46) @t44) @t1))) % 0.85/1.04 (step @p119 :rule eq_resolve :premises (@p118 @p117)) % 0.85/1.04 (step @p120 :rule refl :args ((_ @t7 @t46 @t44 @t1))) % 0.85/1.04 (step @p121 :rule cong :premises (@p109 @p108 @p107) :args (@t80)) % 0.85/1.04 (step @p122 :rule trans :premises (@p121 @p120)) % 0.85/1.04 (step @p123 :rule refl :args (@t7)) % 0.85/1.04 (step @p124 :rule ho_cong :premises (@p123 @p109)) % 0.85/1.04 (step @p125 :rule ho_cong :premises (@p124 @p108)) % 0.85/1.04 (step @p126 :rule ho_cong :premises (@p125 @p107)) % 0.85/1.04 (step @p127 :rule cong :premises (@p126 @p122) :args ((= @t101 @t80))) % 0.85/1.04 (step @p128 :rule symm :premises (@p127)) % 0.85/1.04 (step @p129 :rule refl :args ((_ (_ (_ @t7 @t46) @t44) @t1))) % 0.85/1.04 (step @p130 :rule eq_resolve :premises (@p129 @p128)) % 0.85/1.04 (step @p131 :rule nary_cong :premises (@p130 @p119) :args (@t102)) % 0.85/1.04 (step @p132 :rule cong :premises (@p131) :args ((forall @t11 @t102))) % 0.85/1.04 (step @p133 :rule refl :args (@t1)) % 0.85/1.04 (step @p134 :rule symm :premises (@p108)) % 0.85/1.04 (step @p135 :rule alpha_equiv :args (@t33 @t103 (@list @t43))) % 0.85/1.04 (step @p136 :rule trans :premises (@p135 @p134)) % 0.85/1.04 (step @p137 :rule symm :premises (@p109)) % 0.85/1.04 (step @p138 :rule alpha_equiv :args (@t34 @t103 (@list @t45))) % 0.85/1.04 (step @p139 :rule trans :premises (@p138 @p137)) % 0.85/1.04 (step @p140 :rule refl :args (@t4)) % 0.85/1.04 (step @p141 :rule ho_cong :premises (@p140 @p139)) % 0.85/1.04 (step @p142 :rule ho_cong :premises (@p141 @p136)) % 0.85/1.04 (step @p143 :rule ho_cong :premises (@p142 @p133)) % 0.85/1.04 (step @p144 :rule refl :args (@t7)) % 0.85/1.04 (step @p145 :rule ho_cong :premises (@p144 @p139)) % 0.85/1.04 (step @p146 :rule ho_cong :premises (@p145 @p136)) % 0.85/1.04 (step @p147 :rule ho_cong :premises (@p146 @p133)) % 0.85/1.04 (step @p148 :rule nary_cong :premises (@p147 @p143) :args (@t35)) % 0.85/1.04 (step @p149 :rule cong :premises (@p148) :args (@t36)) % 0.85/1.04 (step @p150 :rule trans :premises (@p149 @p132)) % 0.85/1.04 (step @p151 :rule cong :premises (@p150) :args (@t37)) % 0.85/1.04 (step @p152 :rule nary_cong :premises (@p151 @p105 @p93) :args (@t38)) % 0.85/1.04 (step @p153 :rule cong :premises (@p152) :args (@t40)) % 0.85/1.04 (step @p154 :rule trans :premises (@p153 @p31)) % 0.85/1.04 (step @p155 :rule cong :premises (@p154) :args (@t41)) % 0.85/1.04 (step @p156 :rule trans :premises (@p155 @p3)) % 0.85/1.04 (step @p157 :rule eq_resolve :premises (@p1 @p156)) % 0.85/1.04 (step @p158 :rule bool-impl-false1 :args (@t70)) % 0.85/1.04 (step @p159 :rule evaluate :args ((or false false false false))) % 0.85/1.04 ; WARNING: add trust step for DISTINCT_VALUES % 0.85/1.04 ; trust DISTINCT_VALUES % 0.85/1.04 (step @p160 :rule trust :premises () :args ((not @t104))) % 0.85/1.04 (step @p161 :rule false_intro :premises (@p160)) % 0.85/1.04 (step @p162 :rule beta-reduce :args ((= @t109 @t104))) % 0.85/1.04 (step @p163 :rule trans :premises (@p162 @p161)) % 0.85/1.04 (step @p164 :rule beta-reduce :args ((= @t111 false))) % 0.85/1.04 (step @p165 :rule evaluate :args ((not true))) % 0.85/1.04 (step @p166 :rule quant-unused-vars :args ((= (forall @t112 true) true))) % 0.85/1.04 (step @p167 :rule bool-or-taut2 :args (false @t113 false false)) % 0.85/1.04 (step @p168 :rule cong :premises (@p167) :args ((forall @t112 @t115))) % 0.85/1.04 (step @p169 :rule trans :premises (@p168 @p166)) % 0.85/1.04 (step @p170 :rule aci_norm :args ((= (or false @t114 @t113) @t115))) % 0.85/1.04 (step @p171 :rule refl :args (@t113)) % 0.85/1.04 (step @p172 :rule refl :args (@t114)) % 0.85/1.04 (step @p173 :rule eq-refl :args (@t13)) % 0.85/1.04 (step @p174 :rule cong :premises (@p173) :args (@t116)) % 0.85/1.04 (step @p175 :rule trans :premises (@p174 @p165)) % 0.85/1.04 (step @p176 :rule nary_cong :premises (@p175 @p172 @p171) :args (@t117)) % 0.85/1.04 (step @p177 :rule trans :premises (@p176 @p170)) % 0.85/1.04 (step @p178 :rule cong :premises (@p177) :args ((forall @t112 @t117))) % 0.85/1.04 (step @p179 :rule trans :premises (@p178 @p169)) % 0.85/1.04 (step @p180 :rule quant-var-elim-eq :args ((= (forall @t122 @t121) @t117))) % 0.85/1.04 (step @p181 :rule aci_norm :args ((= @t123 @t121))) % 0.85/1.04 (step @p182 :rule cong :premises (@p181) :args (@t124)) % 0.85/1.04 (step @p183 :rule trans :premises (@p182 @p180)) % 0.85/1.04 (step @p184 :rule cong :premises (@p183) :args (@t125)) % 0.85/1.04 (step @p185 :rule quant-merge-prenex :args ((= @t125 @t126))) % 0.85/1.04 (step @p186 :rule symm :premises (@p185)) % 0.85/1.04 (step @p187 :rule quant_var_reordering :args ((= @t127 @t126))) % 0.85/1.04 (step @p188 :rule trans :premises (@p187 @p186 @p184)) % 0.85/1.04 (step @p189 :rule trans :premises (@p188 @p179)) % 0.85/1.04 (step @p190 :rule quant-unused-vars :args ((= (forall @t61 @t123) @t127))) % 0.85/1.04 (step @p191 :rule trans :premises (@p190 @p189)) % 0.85/1.04 (step @p192 :rule aci_norm :args ((= (or @t120 @t114 false @t118) @t123))) % 0.85/1.04 (step @p193 :rule beta-reduce :args ((= @t128 @t118))) % 0.85/1.04 (step @p194 :rule beta-reduce :args ((= @t129 false))) % 0.85/1.05 (step @p195 :rule quant-unused-vars :args ((= (forall @t11 @t113) @t113))) % 0.85/1.05 (step @p196 :rule aci_norm :args ((= (or false @t113) @t113))) % 0.85/1.05 (step @p197 :rule beta-reduce :args ((= @t130 @t113))) % 0.85/1.05 (step @p198 :rule beta-reduce :args ((= @t131 false))) % 0.85/1.05 (step @p199 :rule nary_cong :premises (@p198 @p197) :args (@t132)) % 0.85/1.05 (step @p200 :rule trans :premises (@p199 @p196)) % 0.85/1.05 (step @p201 :rule cong :premises (@p200) :args (@t133)) % 0.85/1.05 (step @p202 :rule trans :premises (@p201 @p195)) % 0.85/1.05 (step @p203 :rule cong :premises (@p202) :args (@t134)) % 0.85/1.05 (step @p204 :rule quant-unused-vars :args ((= (forall @t11 @t119) @t119))) % 0.85/1.05 (step @p205 :rule aci_norm :args ((= (or false @t119) @t119))) % 0.85/1.05 (step @p206 :rule beta-reduce :args ((= @t135 @t119))) % 0.85/1.05 (step @p207 :rule beta-reduce :args ((= @t136 false))) % 0.85/1.05 (step @p208 :rule nary_cong :premises (@p207 @p206) :args (@t137)) % 0.85/1.05 (step @p209 :rule trans :premises (@p208 @p205)) % 0.85/1.05 (step @p210 :rule cong :premises (@p209) :args (@t138)) % 0.85/1.05 (step @p211 :rule trans :premises (@p210 @p204)) % 0.85/1.05 (step @p212 :rule cong :premises (@p211) :args (@t139)) % 0.85/1.05 (step @p213 :rule nary_cong :premises (@p212 @p203 @p194 @p193) :args (@t140)) % 0.85/1.05 (step @p214 :rule trans :premises (@p213 @p192)) % 0.85/1.05 (step @p215 :rule cong :premises (@p214) :args (@t141)) % 0.85/1.05 (step @p216 :rule trans :premises (@p215 @p191)) % 0.85/1.05 (step @p217 :rule cong :premises (@p216) :args (@t142)) % 0.85/1.05 (step @p218 :rule trans :premises (@p217 @p165)) % 0.85/1.05 (step @p219 :rule quant-unused-vars :args ((= (forall @t29 true) true))) % 0.85/1.05 (step @p220 :rule evaluate :args ((or false true))) % 0.85/1.05 (step @p221 :rule eq-refl :args (@t3)) % 0.85/1.05 (step @p222 :rule beta-reduce :args ((= @t143 (= @t3 @t3)))) % 0.85/1.05 (step @p223 :rule trans :premises (@p222 @p221)) % 0.85/1.05 (step @p224 :rule beta-reduce :args ((= @t144 false))) % 0.85/1.05 (step @p225 :rule nary_cong :premises (@p224 @p223) :args (@t145)) % 0.85/1.05 (step @p226 :rule trans :premises (@p225 @p220)) % 0.85/1.05 (step @p227 :rule cong :premises (@p226) :args (@t146)) % 0.85/1.05 (step @p228 :rule trans :premises (@p227 @p219)) % 0.85/1.05 (step @p229 :rule cong :premises (@p228) :args (@t147)) % 0.85/1.05 (step @p230 :rule trans :premises (@p229 @p165)) % 0.85/1.05 (step @p231 :rule nary_cong :premises (@p230 @p218 @p164 @p163) :args (@t148)) % 0.85/1.05 (step @p232 :rule trans :premises (@p231 @p159)) % 0.85/1.05 (step @p233 :rule refl :args (@t70)) % 0.85/1.05 (step @p234 :rule cong :premises (@p233 @p232) :args ((=> @t70 @t148))) % 0.85/1.05 (step @p235 :rule trans :premises (@p234 @p158)) % 0.85/1.05 (assume-push @p242 @t70) % 0.85/1.05 (step @p237 :rule instantiate :premises (@p157) :args ((@list @t108 @t110 @t105))) % 0.85/1.05 (step-pop @p243 :rule scope :premises (@p237)) % 0.85/1.05 (step @p238 :rule process_scope :premises (@p243) :args (@t148)) % 0.85/1.05 (step @p240 :rule eq_resolve :premises (@p238 @p235)) % 0.85/1.05 (step @p241 false :rule chain_m_resolution :premises (@p240 @p157) :args (false (@list false) (@list @t70))) % 0.85/1.05 ) % 0.85/1.05 % SZS output end Proof % 0.85/1.05 % cvc5 exiting %------------------------------------------------------------------------------