%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU272+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n019.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 08:51:12 AM UTC 2026 % Result : Theorem 0.40s 0.57s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU272+1 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n019.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 16:50:04 EDT 2026 % 0.16/0.34 % CPUTime : % 0.32/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.57 % SZS status Theorem % 0.40/0.57 % SZS output start Proof % 0.40/0.57 ( % 0.40/0.57 (declare-sort $$unsorted 0) % 0.40/0.57 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 0.40/0.57 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 0.40/0.57 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.40/0.57 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 0.40/0.57 (declare-const tptp.function (-> $$unsorted Bool)) % 0.40/0.57 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 0.40/0.57 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.40/0.57 (define @t1 () (@var "A" $$unsorted)) % 0.40/0.57 (define @t2 () (@var "E" $$unsorted)) % 0.40/0.57 (define @t3 () (tptp.in @t2 @t1)) % 0.40/0.57 (define @t4 () (@var "D" $$unsorted)) % 0.40/0.57 (define @t5 () (= @t4 @t2)) % 0.40/0.57 (define @t6 () (tptp.ordinal @t2)) % 0.40/0.57 (define @t7 () (and @t6 @t5 @t3)) % 0.40/0.57 (define @t8 () (@list @t2)) % 0.40/0.57 (define @t9 () (exists @t8 @t7)) % 0.40/0.57 (define @t10 () (@var "B" $$unsorted)) % 0.40/0.57 (define @t11 () (tptp.succ @t10)) % 0.40/0.57 (define @t12 () (tptp.in @t4 @t11)) % 0.40/0.57 (define @t13 () (and @t12 @t9)) % 0.40/0.57 (define @t14 () (@var "C" $$unsorted)) % 0.40/0.57 (define @t15 () (tptp.in @t4 @t14)) % 0.40/0.57 (define @t16 () (= @t15 @t13)) % 0.40/0.57 (define @t17 () (@list @t4)) % 0.40/0.57 (define @t18 () (forall @t17 @t16)) % 0.40/0.57 (define @t19 () (@list @t14)) % 0.40/0.57 (define @t20 () (exists @t19 @t18)) % 0.40/0.57 (define @t21 () (tptp.ordinal @t10)) % 0.40/0.57 (define @t22 () (=> @t21 @t20)) % 0.40/0.57 (define @t23 () (@list @t1 @t10)) % 0.40/0.57 (define @t24 () (forall @t23 @t22)) % 0.40/0.57 (define @t25 () (not @t24)) % 0.40/0.57 (define @t26 () (tptp.empty @t1)) % 0.40/0.57 (define @t27 () (@list @t1)) % 0.40/0.57 (define @t28 () (tptp.ordinal @t1)) % 0.40/0.57 (define @t29 () (tptp.epsilon_connected @t1)) % 0.40/0.57 (define @t30 () (tptp.epsilon_transitive @t1)) % 0.40/0.57 (define @t31 () (and @t30 @t29)) % 0.40/0.57 (define @t32 () (and @t30 @t29 @t28)) % 0.40/0.57 (define @t33 () (not @t26)) % 0.40/0.57 (define @t34 () (tptp.succ @t1)) % 0.40/0.57 (define @t35 () (not (tptp.empty @t34))) % 0.40/0.57 (define @t36 () (@var "H" $$unsorted)) % 0.40/0.57 (define @t37 () (tptp.in @t36 @t1)) % 0.40/0.57 (define @t38 () (= @t4 @t36)) % 0.40/0.57 (define @t39 () (tptp.ordinal @t36)) % 0.40/0.57 (define @t40 () (and @t39 @t38 @t37)) % 0.40/0.57 (define @t41 () (@list @t36)) % 0.40/0.57 (define @t42 () (exists @t41 @t40)) % 0.40/0.57 (define @t43 () (= @t2 @t4)) % 0.40/0.57 (define @t44 () (tptp.in @t2 @t11)) % 0.40/0.57 (define @t45 () (and @t44 @t43 @t42)) % 0.40/0.57 (define @t46 () (exists @t8 @t45)) % 0.40/0.57 (define @t47 () (= @t15 @t46)) % 0.40/0.57 (define @t48 () (forall @t17 @t47)) % 0.40/0.57 (define @t49 () (exists @t19 @t48)) % 0.40/0.57 (define @t50 () (@var "G" $$unsorted)) % 0.40/0.57 (define @t51 () (tptp.in @t50 @t1)) % 0.40/0.57 (define @t52 () (= @t2 @t50)) % 0.40/0.57 (define @t53 () (tptp.ordinal @t50)) % 0.40/0.57 (define @t54 () (and @t53 @t52 @t51)) % 0.40/0.57 (define @t55 () (@list @t50)) % 0.40/0.57 (define @t56 () (exists @t55 @t54)) % 0.40/0.57 (define @t57 () (= @t14 @t2)) % 0.40/0.57 (define @t58 () (@var "F" $$unsorted)) % 0.40/0.57 (define @t59 () (tptp.in @t58 @t1)) % 0.40/0.57 (define @t60 () (= @t4 @t58)) % 0.40/0.57 (define @t61 () (tptp.ordinal @t58)) % 0.40/0.57 (define @t62 () (and @t61 @t60 @t59)) % 0.40/0.57 (define @t63 () (@list @t58)) % 0.40/0.57 (define @t64 () (exists @t63 @t62)) % 0.40/0.57 (define @t65 () (= @t14 @t4)) % 0.40/0.57 (define @t66 () (and @t65 @t64 @t57 @t56)) % 0.40/0.57 (define @t67 () (=> @t66 @t5)) % 0.40/0.57 (define @t68 () (@list @t14 @t4 @t2)) % 0.40/0.57 (define @t69 () (forall @t68 @t67)) % 0.40/0.57 (define @t70 () (=> @t69 @t49)) % 0.40/0.57 (define @t71 () (=> @t21 @t70)) % 0.40/0.57 (define @t72 () (forall @t23 @t71)) % 0.40/0.57 (define @t73 () (tptp.in @t4 @t1)) % 0.40/0.57 (define @t74 () (tptp.ordinal @t4)) % 0.40/0.57 (define @t75 () (and @t12 @t74 @t73)) % 0.40/0.57 (define @t76 () (forall @t17 (= @t15 @t75))) % 0.40/0.57 (define @t77 () (not (forall @t19 (not @t76)))) % 0.40/0.57 (define @t78 () (not @t73)) % 0.40/0.57 (define @t79 () (not @t78)) % 0.40/0.57 (define @t80 () (not @t74)) % 0.40/0.57 (define @t81 () (not @t80)) % 0.40/0.57 (define @t82 () (or @t80 @t78)) % 0.40/0.57 (define @t83 () (not @t82)) % 0.40/0.57 (define @t84 () (and @t12 @t83)) % 0.40/0.57 (define @t85 () (= @t15 @t84)) % 0.40/0.57 (define @t86 () (not (= @t4 @t4))) % 0.40/0.57 (define @t87 () (or @t80 @t86 @t78)) % 0.40/0.57 (define @t88 () (not @t3)) % 0.40/0.57 (define @t89 () (not @t5)) % 0.40/0.57 (define @t90 () (not @t6)) % 0.40/0.57 (define @t91 () (not @t43)) % 0.40/0.57 (define @t92 () (or @t89 @t90 @t89 @t88)) % 0.40/0.57 (define @t93 () (or @t90 @t89 @t88)) % 0.40/0.57 (define @t94 () (forall @t8 (not @t7))) % 0.40/0.57 (define @t95 () (not @t94)) % 0.40/0.57 (define @t96 () (and @t74 @t73 @t12)) % 0.40/0.57 (define @t97 () (= @t15 @t96)) % 0.40/0.57 (define @t98 () (forall @t17 @t97)) % 0.40/0.57 (define @t99 () (not @t98)) % 0.40/0.57 (define @t100 () (forall @t19 @t99)) % 0.40/0.57 (define @t101 () (not @t100)) % 0.40/0.57 (define @t102 () (not @t21)) % 0.40/0.57 (define @t103 () (or @t102 @t101)) % 0.40/0.57 (define @t104 () (forall @t23 @t103)) % 0.40/0.57 (define @t105 () (forall @t23 (or @t102 @t77))) % 0.40/0.57 (define @t106 () (@list true)) % 0.40/0.57 (define @t107 () (not @t12)) % 0.40/0.57 (define @t108 () (not @t107)) % 0.40/0.57 (define @t109 () (and @t81 @t79 @t108)) % 0.40/0.57 (define @t110 () (= @t15 (not (or @t80 @t78 @t107)))) % 0.40/0.57 (define @t111 () (or @t107 @t86)) % 0.40/0.57 (define @t112 () (not @t44)) % 0.40/0.57 (define @t113 () (or @t89 @t112 @t89)) % 0.40/0.57 (define @t114 () (or @t112 @t89)) % 0.40/0.57 (define @t115 () (forall @t8 @t114)) % 0.40/0.57 (define @t116 () (or @t80 @t78 @t115)) % 0.40/0.57 (define @t117 () (or @t80 @t78 @t114)) % 0.40/0.57 (define @t118 () (or @t112 @t89 @t80 @t78)) % 0.40/0.57 (define @t119 () (not @t83)) % 0.40/0.57 (define @t120 () (or @t112 @t89 @t119)) % 0.40/0.57 (define @t121 () (and @t44 @t5 @t83)) % 0.40/0.57 (define @t122 () (forall @t8 (not @t121))) % 0.40/0.57 (define @t123 () (not @t122)) % 0.40/0.57 (define @t124 () (not @t37)) % 0.40/0.57 (define @t125 () (not @t38)) % 0.40/0.57 (define @t126 () (not @t39)) % 0.40/0.57 (define @t127 () (or @t125 @t126 @t125 @t124)) % 0.40/0.57 (define @t128 () (or @t126 @t125 @t124)) % 0.40/0.57 (define @t129 () (forall @t41 (not @t40))) % 0.40/0.57 (define @t130 () (not @t129)) % 0.40/0.57 (define @t131 () (@list @t4 @t2)) % 0.40/0.57 (define @t132 () (or @t80 @t78 @t89 @t90 @t88 @t5)) % 0.40/0.57 (define @t133 () (or @t86 @t80 @t78 @t89 @t90 @t88 @t5)) % 0.40/0.57 (define @t134 () (not @t57)) % 0.40/0.57 (define @t135 () (not @t65)) % 0.40/0.57 (define @t136 () (or @t135 @t135 @t80 @t78 @t134 @t90 @t88 @t5)) % 0.40/0.57 (define @t137 () (or @t135 @t80 @t78 @t134 @t90 @t88 @t5)) % 0.40/0.57 (define @t138 () (forall @t19 @t137)) % 0.40/0.57 (define @t139 () (forall @t131 @t138)) % 0.40/0.57 (define @t140 () (forall (@list @t4 @t2 @t14) @t137)) % 0.40/0.57 (define @t141 () (or @t135 @t80 @t78 @t134 @t90 @t88)) % 0.40/0.57 (define @t142 () (or @t90 @t88)) % 0.40/0.57 (define @t143 () (not @t142)) % 0.40/0.57 (define @t144 () (not @t143)) % 0.40/0.57 (define @t145 () (or @t135 @t119 @t134 @t144)) % 0.40/0.57 (define @t146 () (and @t65 @t83 @t57 @t143)) % 0.40/0.57 (define @t147 () (not (= @t2 @t2))) % 0.40/0.57 (define @t148 () (or @t90 @t147 @t88)) % 0.40/0.57 (define @t149 () (not @t51)) % 0.40/0.57 (define @t150 () (not @t52)) % 0.40/0.57 (define @t151 () (not @t53)) % 0.40/0.57 (define @t152 () (or @t150 @t151 @t150 @t149)) % 0.40/0.57 (define @t153 () (or @t151 @t150 @t149)) % 0.40/0.57 (define @t154 () (forall @t55 (not @t54))) % 0.40/0.57 (define @t155 () (not @t154)) % 0.40/0.57 (define @t156 () (not @t59)) % 0.40/0.57 (define @t157 () (not @t60)) % 0.40/0.57 (define @t158 () (not @t61)) % 0.40/0.57 (define @t159 () (or @t157 @t158 @t157 @t156)) % 0.40/0.57 (define @t160 () (or @t158 @t157 @t156)) % 0.40/0.57 (define @t161 () (forall @t63 (not @t62))) % 0.40/0.57 (define @t162 () (not @t161)) % 0.40/0.57 (assume @p1 @t25) % 0.40/0.57 (assume @p2 (forall @t27 (=> @t26 (tptp.function @t1)))) % 0.40/0.57 (assume @p3 (forall @t27 (=> @t31 @t28))) % 0.40/0.57 (assume @p4 (exists @t27 @t32)) % 0.40/0.57 (assume @p5 (forall @t27 (=> @t26 @t32))) % 0.40/0.57 (assume @p6 (exists @t27 (and @t33 @t30 @t29 @t28))) % 0.40/0.57 (assume @p7 (exists @t27 @t26)) % 0.40/0.57 (assume @p8 (exists @t27 @t33)) % 0.40/0.57 (assume @p9 (forall @t23 (=> (tptp.in @t1 @t10) (not (tptp.in @t10 @t1))))) % 0.40/0.57 (assume @p10 true) % 0.40/0.57 (assume @p11 (forall @t27 @t35)) % 0.40/0.57 (assume @p12 (forall @t27 (=> @t28 @t31))) % 0.40/0.57 (assume @p13 (forall @t27 (=> @t28 (and @t35 (tptp.epsilon_transitive @t34) (tptp.epsilon_connected @t34) (tptp.ordinal @t34))))) % 0.40/0.57 (assume @p14 @t72) % 0.40/0.57 (step @p15 :rule bool-impl-elim :args (@t21 @t77)) % 0.40/0.57 (step @p16 :rule cong :premises (@p15) :args ((forall @t23 (=> @t21 @t77)))) % 0.40/0.57 (step @p17 :rule exists-elim :args ((= (exists @t19 @t76) @t77))) % 0.40/0.57 (step @p18 :rule aci_norm :args ((= (and @t12 (and @t74 @t73)) @t75))) % 0.40/0.57 (step @p19 :rule bool-double-not-elim :args (@t73)) % 0.40/0.57 (step @p20 :rule bool-double-not-elim :args (@t74)) % 0.40/0.57 (step @p21 :rule nary_cong :premises (@p20 @p19) :args ((and @t81 @t79))) % 0.40/0.57 (step @p22 :rule bool-or-de-morgan :args (@t80 @t78 false)) % 0.40/0.57 (step @p23 :rule trans :premises (@p22 @p21)) % 0.40/0.57 (step @p24 :rule refl :args (@t12)) % 0.40/0.57 (step @p25 :rule nary_cong :premises (@p24 @p23) :args (@t84)) % 0.40/0.57 (step @p26 :rule trans :premises (@p25 @p18)) % 0.40/0.57 (step @p27 :rule refl :args (@t15)) % 0.40/0.57 (step @p28 :rule cong :premises (@p27 @p26) :args (@t85)) % 0.40/0.57 (step @p29 :rule cong :premises (@p28) :args ((forall @t17 @t85))) % 0.40/0.57 (step @p30 :rule aci_norm :args ((= (or @t80 false @t78) @t82))) % 0.40/0.57 (step @p31 :rule refl :args (@t78)) % 0.40/0.57 (step @p32 :rule evaluate :args ((not true))) % 0.40/0.57 (step @p33 :rule eq-refl :args (@t4)) % 0.40/0.57 (step @p34 :rule cong :premises (@p33) :args (@t86)) % 0.40/0.57 (step @p35 :rule trans :premises (@p34 @p32)) % 0.40/0.57 (step @p36 :rule refl :args (@t80)) % 0.40/0.57 (step @p37 :rule nary_cong :premises (@p36 @p35 @p31) :args (@t87)) % 0.40/0.57 (step @p38 :rule trans :premises (@p37 @p30)) % 0.40/0.57 (step @p39 :rule quant-var-elim-eq :args ((= (forall @t8 (or @t91 @t90 @t89 @t88)) @t87))) % 0.40/0.57 (step @p40 :rule refl :args (@t88)) % 0.40/0.57 (step @p41 :rule refl :args (@t89)) % 0.40/0.57 (step @p42 :rule refl :args (@t90)) % 0.40/0.57 (step @p43 :rule eq-symm :args (@t4 @t2)) % 0.40/0.57 (step @p44 :rule cong :premises (@p43) :args (@t89)) % 0.40/0.57 (step @p45 :rule nary_cong :premises (@p44 @p42 @p41 @p40) :args (@t92)) % 0.40/0.57 (step @p46 :rule aci_norm :args ((= @t93 @t92))) % 0.40/0.57 (step @p47 :rule trans :premises (@p46 @p45)) % 0.40/0.57 (step @p48 :rule cong :premises (@p47) :args ((forall @t8 @t93))) % 0.40/0.57 (step @p49 :rule trans :premises (@p48 @p39)) % 0.40/0.57 (step @p50 :rule trans :premises (@p49 @p38)) % 0.40/0.57 (step @p51 :rule aci_norm :args ((= (or @t90 (or @t89 @t88)) @t93))) % 0.40/0.57 (step @p52 :rule bool-and-de-morgan :args (@t5 @t3 true)) % 0.40/0.57 (step @p53 :rule nary_cong :premises (@p42 @p52) :args ((or @t90 (not (and @t5 @t3))))) % 0.40/0.57 (step @p54 :rule bool-and-de-morgan :args (@t6 @t5 (and @t3))) % 0.40/0.57 (step @p55 :rule trans :premises (@p54 @p53)) % 0.40/0.57 (step @p56 :rule trans :premises (@p55 @p51)) % 0.40/0.57 (step @p57 :rule cong :premises (@p56) :args (@t94)) % 0.40/0.57 (step @p58 :rule trans :premises (@p57 @p50)) % 0.40/0.57 (step @p59 :rule cong :premises (@p58) :args (@t95)) % 0.40/0.57 (step @p60 :rule exists-elim :args ((= @t9 @t95))) % 0.40/0.57 (step @p61 :rule trans :premises (@p60 @p59)) % 0.40/0.57 (step @p62 :rule refl :args (@t12)) % 0.40/0.57 (step @p63 :rule nary_cong :premises (@p62 @p61) :args (@t13)) % 0.40/0.57 (step @p64 :rule refl :args (@t15)) % 0.40/0.57 (step @p65 :rule cong :premises (@p64 @p63) :args (@t16)) % 0.40/0.57 (step @p66 :rule cong :premises (@p65) :args (@t18)) % 0.40/0.57 (step @p67 :rule trans :premises (@p66 @p29)) % 0.40/0.57 (step @p68 :rule cong :premises (@p67) :args (@t20)) % 0.40/0.57 (step @p69 :rule trans :premises (@p68 @p17)) % 0.40/0.57 (step @p70 :rule refl :args (@t21)) % 0.40/0.57 (step @p71 :rule cong :premises (@p70 @p69) :args (@t22)) % 0.40/0.57 (step @p72 :rule cong :premises (@p71) :args (@t24)) % 0.40/0.57 (step @p73 :rule trans :premises (@p72 @p16)) % 0.40/0.57 (step @p74 :rule cong :premises (@p73) :args (@t25)) % 0.40/0.57 (step @p75 :rule eq_resolve :premises (@p1 @p74)) % 0.40/0.57 (step @p76 :rule aci_norm :args ((= @t96 @t75))) % 0.40/0.57 (step @p77 :rule cong :premises (@p27 @p76) :args (@t97)) % 0.40/0.57 (step @p78 :rule cong :premises (@p77) :args (@t98)) % 0.40/0.57 (step @p79 :rule cong :premises (@p78) :args (@t99)) % 0.40/0.57 (step @p80 :rule cong :premises (@p79) :args (@t100)) % 0.40/0.57 (step @p81 :rule cong :premises (@p80) :args (@t101)) % 0.40/0.57 (step @p82 :rule refl :args (@t102)) % 0.40/0.57 (step @p83 :rule nary_cong :premises (@p82 @p81) :args (@t103)) % 0.40/0.57 (step @p84 :rule cong :premises (@p83) :args (@t104)) % 0.40/0.57 (step @p85 :rule true_intro :premises (@p84)) % 0.40/0.57 (step @p86 :rule eq-symm :args (@t105 @t104)) % 0.40/0.57 (step @p87 :rule trans :premises (@p86 @p85)) % 0.40/0.57 (step @p88 :rule true_elim :premises (@p87)) % 0.40/0.57 (step @p89 :rule equiv_elim2 :premises (@p88)) % 0.40/0.57 (step @p90 :rule chain_m_resolution :premises (@p89 @p75) :args ((not @t104) @t106 (@list @t105))) % 0.40/0.57 (step @p91 :rule bool-impl-elim :args (@t21 @t101)) % 0.40/0.57 (step @p92 :rule cong :premises (@p91) :args ((forall @t23 (=> @t21 @t101)))) % 0.40/0.57 (step @p93 :rule bool-impl-true2 :args (@t101)) % 0.40/0.57 (step @p94 :rule exists-elim :args ((= (exists @t19 @t98) @t101))) % 0.40/0.57 (step @p95 :rule bool-double-not-elim :args (@t12)) % 0.40/0.57 (step @p96 :rule nary_cong :premises (@p20 @p19 @p95) :args (@t109)) % 0.40/0.57 (step @p97 :rule aci_norm :args ((= (and @t81 (and @t79 @t108)) @t109))) % 0.40/0.57 (step @p98 :rule trans :premises (@p97 @p96)) % 0.40/0.57 (step @p99 :rule bool-or-de-morgan :args (@t78 @t107 false)) % 0.40/0.57 (step @p100 :rule refl :args (@t81)) % 0.40/0.57 (step @p101 :rule nary_cong :premises (@p100 @p99) :args ((and @t81 (not (or @t78 @t107))))) % 0.40/0.57 (step @p102 :rule bool-or-de-morgan :args (@t80 @t78 (or @t107))) % 0.40/0.57 (step @p103 :rule trans :premises (@p102 @p101)) % 0.40/0.57 (step @p104 :rule trans :premises (@p103 @p98)) % 0.40/0.57 (step @p105 :rule cong :premises (@p27 @p104) :args (@t110)) % 0.40/0.57 (step @p106 :rule cong :premises (@p105) :args ((forall @t17 @t110))) % 0.40/0.57 (step @p107 :rule aci_norm :args ((= (or @t107 false) @t107))) % 0.40/0.57 (step @p108 :rule refl :args (@t107)) % 0.40/0.57 (step @p109 :rule nary_cong :premises (@p108 @p35) :args (@t111)) % 0.40/0.57 (step @p110 :rule trans :premises (@p109 @p107)) % 0.40/0.57 (step @p111 :rule quant-var-elim-eq :args ((= (forall @t8 (or @t91 @t112 @t89)) @t111))) % 0.40/0.57 (step @p112 :rule refl :args (@t112)) % 0.40/0.57 (step @p113 :rule nary_cong :premises (@p44 @p112 @p41) :args (@t113)) % 0.40/0.57 (step @p114 :rule aci_norm :args ((= @t114 @t113))) % 0.40/0.57 (step @p115 :rule trans :premises (@p114 @p113)) % 0.40/0.57 (step @p116 :rule cong :premises (@p115) :args (@t115)) % 0.40/0.57 (step @p117 :rule trans :premises (@p116 @p111)) % 0.40/0.57 (step @p118 :rule trans :premises (@p117 @p110)) % 0.40/0.57 (step @p119 :rule nary_cong :premises (@p36 @p31 @p118) :args (@t116)) % 0.40/0.57 (step @p120 :rule quant-miniscope-or :args ((= (forall @t8 @t117) @t116))) % 0.40/0.57 (step @p121 :rule aci_norm :args ((= @t118 @t117))) % 0.40/0.57 (step @p122 :rule cong :premises (@p121) :args ((forall @t8 @t118))) % 0.40/0.57 (step @p123 :rule trans :premises (@p122 @p120)) % 0.40/0.57 (step @p124 :rule trans :premises (@p123 @p119)) % 0.40/0.57 (step @p125 :rule aci_norm :args ((= (or @t112 @t89 @t82) @t118))) % 0.40/0.57 (step @p126 :rule bool-double-not-elim :args (@t82)) % 0.40/0.57 (step @p127 :rule nary_cong :premises (@p112 @p41 @p126) :args (@t120)) % 0.40/0.57 (step @p128 :rule aci_norm :args ((= (or @t112 (or @t89 @t119)) @t120))) % 0.40/0.57 (step @p129 :rule trans :premises (@p128 @p127)) % 0.40/0.57 (step @p130 :rule bool-and-de-morgan :args (@t5 @t83 true)) % 0.40/0.57 (step @p131 :rule nary_cong :premises (@p112 @p130) :args ((or @t112 (not (and @t5 @t83))))) % 0.40/0.57 (step @p132 :rule bool-and-de-morgan :args (@t44 @t5 (and @t83))) % 0.40/0.57 (step @p133 :rule trans :premises (@p132 @p131)) % 0.40/0.57 (step @p134 :rule trans :premises (@p133 @p129)) % 0.40/0.57 (step @p135 :rule trans :premises (@p134 @p125)) % 0.40/0.57 (step @p136 :rule cong :premises (@p135) :args (@t122)) % 0.40/0.57 (step @p137 :rule trans :premises (@p136 @p124)) % 0.40/0.57 (step @p138 :rule cong :premises (@p137) :args (@t123)) % 0.40/0.57 (step @p139 :rule exists-elim :args ((= (exists @t8 @t121) @t123))) % 0.40/0.57 (step @p140 :rule trans :premises (@p139 @p138)) % 0.40/0.57 (step @p141 :rule quant-var-elim-eq :args ((= (forall @t41 (or (not (= @t36 @t4)) @t126 @t125 @t124)) @t87))) % 0.40/0.57 (step @p142 :rule refl :args (@t124)) % 0.40/0.57 (step @p143 :rule refl :args (@t125)) % 0.40/0.57 (step @p144 :rule refl :args (@t126)) % 0.40/0.57 (step @p145 :rule eq-symm :args (@t4 @t36)) % 0.40/0.57 (step @p146 :rule cong :premises (@p145) :args (@t125)) % 0.40/0.57 (step @p147 :rule nary_cong :premises (@p146 @p144 @p143 @p142) :args (@t127)) % 0.40/0.57 (step @p148 :rule aci_norm :args ((= @t128 @t127))) % 0.40/0.57 (step @p149 :rule trans :premises (@p148 @p147)) % 0.40/0.57 (step @p150 :rule cong :premises (@p149) :args ((forall @t41 @t128))) % 0.40/0.57 (step @p151 :rule trans :premises (@p150 @p141)) % 0.40/0.57 (step @p152 :rule trans :premises (@p151 @p38)) % 0.40/0.57 (step @p153 :rule aci_norm :args ((= (or @t126 (or @t125 @t124)) @t128))) % 0.40/0.57 (step @p154 :rule bool-and-de-morgan :args (@t38 @t37 true)) % 0.40/0.57 (step @p155 :rule nary_cong :premises (@p144 @p154) :args ((or @t126 (not (and @t38 @t37))))) % 0.40/0.57 (step @p156 :rule bool-and-de-morgan :args (@t39 @t38 (and @t37))) % 0.40/0.57 (step @p157 :rule trans :premises (@p156 @p155)) % 0.40/0.57 (step @p158 :rule trans :premises (@p157 @p153)) % 0.40/0.57 (step @p159 :rule cong :premises (@p158) :args (@t129)) % 0.40/0.57 (step @p160 :rule trans :premises (@p159 @p152)) % 0.40/0.57 (step @p161 :rule cong :premises (@p160) :args (@t130)) % 0.40/0.57 (step @p162 :rule exists-elim :args ((= @t42 @t130))) % 0.40/0.57 (step @p163 :rule trans :premises (@p162 @p161)) % 0.40/0.57 (step @p164 :rule eq-symm :args (@t2 @t4)) % 0.40/0.57 (step @p165 :rule refl :args (@t44)) % 0.40/0.57 (step @p166 :rule nary_cong :premises (@p165 @p164 @p163) :args (@t45)) % 0.40/0.57 (step @p167 :rule cong :premises (@p166) :args (@t46)) % 0.40/0.57 (step @p168 :rule trans :premises (@p167 @p140)) % 0.40/0.57 (step @p169 :rule cong :premises (@p64 @p168) :args (@t47)) % 0.40/0.57 (step @p170 :rule cong :premises (@p169) :args (@t48)) % 0.40/0.57 (step @p171 :rule trans :premises (@p170 @p106)) % 0.40/0.57 (step @p172 :rule cong :premises (@p171) :args (@t49)) % 0.40/0.57 (step @p173 :rule trans :premises (@p172 @p94)) % 0.40/0.57 (step @p174 :rule quant-unused-vars :args ((= (forall @t131 true) true))) % 0.40/0.57 (step @p175 :rule bool-or-taut2 :args ((or @t80 @t78) @t5 (or @t90 @t88) false)) % 0.40/0.57 (step @p176 :rule cong :premises (@p175) :args ((forall @t131 @t132))) % 0.40/0.57 (step @p177 :rule trans :premises (@p176 @p174)) % 0.40/0.57 (step @p178 :rule aci_norm :args ((= (or false @t80 @t78 @t89 @t90 @t88 @t5) @t132))) % 0.40/0.57 (step @p179 :rule refl :args (@t5)) % 0.40/0.57 (step @p180 :rule refl :args (@t88)) % 0.40/0.57 (step @p181 :rule refl :args (@t90)) % 0.40/0.57 (step @p182 :rule refl :args (@t89)) % 0.40/0.57 (step @p183 :rule nary_cong :premises (@p35 @p36 @p31 @p182 @p181 @p180 @p179) :args (@t133)) % 0.40/0.57 (step @p184 :rule trans :premises (@p183 @p178)) % 0.40/0.57 (step @p185 :rule cong :premises (@p184) :args ((forall @t131 @t133))) % 0.40/0.57 (step @p186 :rule trans :premises (@p185 @p177)) % 0.40/0.57 (step @p187 :rule quant-var-elim-eq :args ((= (forall @t19 @t136) @t133))) % 0.40/0.57 (step @p188 :rule aci_norm :args ((= @t137 @t136))) % 0.40/0.57 (step @p189 :rule cong :premises (@p188) :args (@t138)) % 0.40/0.57 (step @p190 :rule trans :premises (@p189 @p187)) % 0.40/0.57 (step @p191 :rule cong :premises (@p190) :args (@t139)) % 0.40/0.57 (step @p192 :rule quant-merge-prenex :args ((= @t139 @t140))) % 0.40/0.57 (step @p193 :rule symm :premises (@p192)) % 0.40/0.57 (step @p194 :rule quant_var_reordering :args ((= (forall @t68 @t137) @t140))) % 0.40/0.57 (step @p195 :rule trans :premises (@p194 @p193 @p191)) % 0.40/0.57 (step @p196 :rule trans :premises (@p195 @p186)) % 0.40/0.57 (step @p197 :rule aci_norm :args ((= (or @t141 @t5) @t137))) % 0.40/0.57 (step @p198 :rule refl :args (@t5)) % 0.40/0.57 (step @p199 :rule aci_norm :args ((= (or @t135 @t82 @t134 @t142) @t141))) % 0.40/0.57 (step @p200 :rule bool-double-not-elim :args (@t142)) % 0.40/0.57 (step @p201 :rule refl :args (@t134)) % 0.40/0.57 (step @p202 :rule refl :args (@t135)) % 0.40/0.57 (step @p203 :rule nary_cong :premises (@p202 @p126 @p201 @p200) :args (@t145)) % 0.40/0.57 (step @p204 :rule aci_norm :args ((= (or @t135 (or @t119 (or @t134 @t144))) @t145))) % 0.40/0.57 (step @p205 :rule trans :premises (@p204 @p203)) % 0.40/0.57 (step @p206 :rule bool-and-de-morgan :args (@t57 @t143 true)) % 0.40/0.57 (step @p207 :rule refl :args (@t119)) % 0.40/0.57 (step @p208 :rule nary_cong :premises (@p207 @p206) :args ((or @t119 (not (and @t57 @t143))))) % 0.40/0.57 (step @p209 :rule bool-and-de-morgan :args (@t83 @t57 (and @t143))) % 0.40/0.57 (step @p210 :rule trans :premises (@p209 @p208)) % 0.40/0.57 (step @p211 :rule nary_cong :premises (@p202 @p210) :args ((or @t135 (not (and @t83 @t57 @t143))))) % 0.40/0.57 (step @p212 :rule bool-and-de-morgan :args (@t65 @t83 (and @t57 @t143))) % 0.40/0.57 (step @p213 :rule trans :premises (@p212 @p211)) % 0.40/0.57 (step @p214 :rule trans :premises (@p213 @p205)) % 0.40/0.57 (step @p215 :rule trans :premises (@p214 @p199)) % 0.40/0.57 (step @p216 :rule nary_cong :premises (@p215 @p198) :args ((or (not @t146) @t5))) % 0.40/0.57 (step @p217 :rule trans :premises (@p216 @p197)) % 0.40/0.57 (step @p218 :rule bool-impl-elim :args (@t146 @t5)) % 0.40/0.57 (step @p219 :rule trans :premises (@p218 @p217)) % 0.40/0.57 (step @p220 :rule cong :premises (@p219) :args ((forall @t68 (=> @t146 @t5)))) % 0.40/0.57 (step @p221 :rule trans :premises (@p220 @p196)) % 0.40/0.57 (step @p222 :rule aci_norm :args ((= (or @t90 false @t88) @t142))) % 0.40/0.57 (step @p223 :rule eq-refl :args (@t2)) % 0.40/0.57 (step @p224 :rule cong :premises (@p223) :args (@t147)) % 0.40/0.57 (step @p225 :rule trans :premises (@p224 @p32)) % 0.40/0.57 (step @p226 :rule nary_cong :premises (@p181 @p225 @p180) :args (@t148)) % 0.40/0.57 (step @p227 :rule trans :premises (@p226 @p222)) % 0.40/0.57 (step @p228 :rule quant-var-elim-eq :args ((= (forall @t55 (or (not (= @t50 @t2)) @t151 @t150 @t149)) @t148))) % 0.40/0.57 (step @p229 :rule refl :args (@t149)) % 0.40/0.57 (step @p230 :rule refl :args (@t150)) % 0.40/0.57 (step @p231 :rule refl :args (@t151)) % 0.40/0.57 (step @p232 :rule eq-symm :args (@t2 @t50)) % 0.40/0.57 (step @p233 :rule cong :premises (@p232) :args (@t150)) % 0.40/0.57 (step @p234 :rule nary_cong :premises (@p233 @p231 @p230 @p229) :args (@t152)) % 0.40/0.57 (step @p235 :rule aci_norm :args ((= @t153 @t152))) % 0.40/0.57 (step @p236 :rule trans :premises (@p235 @p234)) % 0.40/0.57 (step @p237 :rule cong :premises (@p236) :args ((forall @t55 @t153))) % 0.40/0.57 (step @p238 :rule trans :premises (@p237 @p228)) % 0.40/0.57 (step @p239 :rule trans :premises (@p238 @p227)) % 0.40/0.57 (step @p240 :rule aci_norm :args ((= (or @t151 (or @t150 @t149)) @t153))) % 0.40/0.57 (step @p241 :rule bool-and-de-morgan :args (@t52 @t51 true)) % 0.40/0.57 (step @p242 :rule nary_cong :premises (@p231 @p241) :args ((or @t151 (not (and @t52 @t51))))) % 0.40/0.57 (step @p243 :rule bool-and-de-morgan :args (@t53 @t52 (and @t51))) % 0.40/0.57 (step @p244 :rule trans :premises (@p243 @p242)) % 0.40/0.57 (step @p245 :rule trans :premises (@p244 @p240)) % 0.40/0.57 (step @p246 :rule cong :premises (@p245) :args (@t154)) % 0.40/0.57 (step @p247 :rule trans :premises (@p246 @p239)) % 0.40/0.57 (step @p248 :rule cong :premises (@p247) :args (@t155)) % 0.40/0.57 (step @p249 :rule exists-elim :args ((= @t56 @t155))) % 0.40/0.57 (step @p250 :rule trans :premises (@p249 @p248)) % 0.40/0.57 (step @p251 :rule refl :args (@t57)) % 0.40/0.57 (step @p252 :rule quant-var-elim-eq :args ((= (forall @t63 (or (not (= @t58 @t4)) @t158 @t157 @t156)) @t87))) % 0.40/0.58 (step @p253 :rule refl :args (@t156)) % 0.40/0.58 (step @p254 :rule refl :args (@t157)) % 0.40/0.58 (step @p255 :rule refl :args (@t158)) % 0.40/0.58 (step @p256 :rule eq-symm :args (@t4 @t58)) % 0.40/0.58 (step @p257 :rule cong :premises (@p256) :args (@t157)) % 0.40/0.58 (step @p258 :rule nary_cong :premises (@p257 @p255 @p254 @p253) :args (@t159)) % 0.40/0.58 (step @p259 :rule aci_norm :args ((= @t160 @t159))) % 0.40/0.58 (step @p260 :rule trans :premises (@p259 @p258)) % 0.40/0.58 (step @p261 :rule cong :premises (@p260) :args ((forall @t63 @t160))) % 0.40/0.58 (step @p262 :rule trans :premises (@p261 @p252)) % 0.40/0.58 (step @p263 :rule trans :premises (@p262 @p38)) % 0.40/0.58 (step @p264 :rule aci_norm :args ((= (or @t158 (or @t157 @t156)) @t160))) % 0.40/0.58 (step @p265 :rule bool-and-de-morgan :args (@t60 @t59 true)) % 0.40/0.58 (step @p266 :rule nary_cong :premises (@p255 @p265) :args ((or @t158 (not (and @t60 @t59))))) % 0.40/0.58 (step @p267 :rule bool-and-de-morgan :args (@t61 @t60 (and @t59))) % 0.40/0.58 (step @p268 :rule trans :premises (@p267 @p266)) % 0.40/0.58 (step @p269 :rule trans :premises (@p268 @p264)) % 0.40/0.58 (step @p270 :rule cong :premises (@p269) :args (@t161)) % 0.40/0.58 (step @p271 :rule trans :premises (@p270 @p263)) % 0.40/0.58 (step @p272 :rule cong :premises (@p271) :args (@t162)) % 0.40/0.58 (step @p273 :rule exists-elim :args ((= @t64 @t162))) % 0.40/0.58 (step @p274 :rule trans :premises (@p273 @p272)) % 0.40/0.58 (step @p275 :rule refl :args (@t65)) % 0.40/0.58 (step @p276 :rule nary_cong :premises (@p275 @p274 @p251 @p250) :args (@t66)) % 0.40/0.58 (step @p277 :rule cong :premises (@p276 @p179) :args (@t67)) % 0.40/0.58 (step @p278 :rule cong :premises (@p277) :args (@t69)) % 0.40/0.58 (step @p279 :rule trans :premises (@p278 @p221)) % 0.40/0.58 (step @p280 :rule cong :premises (@p279 @p173) :args (@t70)) % 0.40/0.58 (step @p281 :rule trans :premises (@p280 @p93)) % 0.40/0.58 (step @p282 :rule cong :premises (@p70 @p281) :args (@t71)) % 0.40/0.58 (step @p283 :rule cong :premises (@p282) :args (@t72)) % 0.40/0.58 (step @p284 :rule trans :premises (@p283 @p92)) % 0.40/0.58 (step @p285 :rule eq_resolve :premises (@p14 @p284)) % 0.40/0.58 (step @p286 false :rule chain_m_resolution :premises (@p285 @p90) :args (false @t106 (@list @t104))) % 0.40/0.58 ) % 0.40/0.58 % SZS output end Proof % 0.40/0.58 % cvc5 exiting %------------------------------------------------------------------------------