%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU298+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 : n014.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 08:51:17 AM UTC 2026 % Result : Theorem 0.40s 0.60s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU298+1 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n014.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 16:54:43 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.60 % SZS status Theorem % 0.40/0.60 % SZS output start Proof % 0.40/0.60 ( % 0.40/0.60 (declare-sort $$unsorted 0) % 0.40/0.60 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.natural (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.finite (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.function (-> $$unsorted Bool)) % 0.40/0.60 (define @t1 () (@var "A" $$unsorted)) % 0.40/0.60 (define @t2 () (tptp.singleton @t1)) % 0.40/0.60 (define @t3 () (@var "E" $$unsorted)) % 0.40/0.60 (define @t4 () (@var "D" $$unsorted)) % 0.40/0.60 (define @t5 () (= @t4 (tptp.set_difference @t3 @t2))) % 0.40/0.60 (define @t6 () (@var "B" $$unsorted)) % 0.40/0.60 (define @t7 () (tptp.in @t3 @t6)) % 0.40/0.60 (define @t8 () (and @t7 @t5)) % 0.40/0.60 (define @t9 () (@list @t3)) % 0.40/0.60 (define @t10 () (exists @t9 @t8)) % 0.40/0.60 (define @t11 () (tptp.powerset @t1)) % 0.40/0.60 (define @t12 () (tptp.in @t4 @t11)) % 0.40/0.60 (define @t13 () (and @t12 @t10)) % 0.40/0.60 (define @t14 () (@var "C" $$unsorted)) % 0.40/0.60 (define @t15 () (tptp.in @t4 @t14)) % 0.40/0.60 (define @t16 () (= @t15 @t13)) % 0.40/0.60 (define @t17 () (@list @t4)) % 0.40/0.60 (define @t18 () (forall @t17 @t16)) % 0.40/0.60 (define @t19 () (@list @t14)) % 0.40/0.60 (define @t20 () (exists @t19 @t18)) % 0.40/0.60 (define @t21 () (tptp.succ @t1)) % 0.40/0.60 (define @t22 () (tptp.element @t6 (tptp.powerset (tptp.powerset @t21)))) % 0.40/0.60 (define @t23 () (tptp.ordinal @t1)) % 0.40/0.60 (define @t24 () (and @t23 @t22)) % 0.40/0.60 (define @t25 () (=> @t24 @t20)) % 0.40/0.60 (define @t26 () (@list @t1 @t6)) % 0.40/0.60 (define @t27 () (forall @t26 @t25)) % 0.40/0.60 (define @t28 () (not @t27)) % 0.40/0.60 (define @t29 () (tptp.finite @t6)) % 0.40/0.60 (define @t30 () (tptp.ordinal @t6)) % 0.40/0.60 (define @t31 () (tptp.epsilon_connected @t6)) % 0.40/0.60 (define @t32 () (tptp.epsilon_transitive @t6)) % 0.40/0.60 (define @t33 () (tptp.relation @t6)) % 0.40/0.60 (define @t34 () (tptp.empty @t6)) % 0.40/0.60 (define @t35 () (tptp.element @t6 @t11)) % 0.40/0.60 (define @t36 () (@list @t6)) % 0.40/0.60 (define @t37 () (@list @t1)) % 0.40/0.60 (define @t38 () (tptp.one_to_one @t1)) % 0.40/0.60 (define @t39 () (tptp.function @t1)) % 0.40/0.60 (define @t40 () (tptp.relation @t1)) % 0.40/0.60 (define @t41 () (and @t40 @t39 @t38)) % 0.40/0.60 (define @t42 () (tptp.epsilon_connected @t1)) % 0.40/0.60 (define @t43 () (tptp.epsilon_transitive @t1)) % 0.40/0.60 (define @t44 () (tptp.empty @t1)) % 0.40/0.60 (define @t45 () (and @t40 @t44 @t39)) % 0.40/0.60 (define @t46 () (tptp.set_difference @t1 @t6)) % 0.40/0.60 (define @t47 () (not @t44)) % 0.40/0.60 (define @t48 () (tptp.natural @t1)) % 0.40/0.60 (define @t49 () (tptp.ordinal @t21)) % 0.40/0.60 (define @t50 () (tptp.epsilon_connected @t21)) % 0.40/0.60 (define @t51 () (tptp.epsilon_transitive @t21)) % 0.40/0.60 (define @t52 () (not (tptp.empty @t21))) % 0.40/0.60 (define @t53 () (tptp.finite @t1)) % 0.40/0.60 (define @t54 () (not @t34)) % 0.40/0.60 (define @t55 () (and @t43 @t42)) % 0.40/0.60 (define @t56 () (and @t43 @t42 @t23)) % 0.40/0.60 (define @t57 () (not (tptp.empty @t2))) % 0.40/0.60 (define @t58 () (@var "H" $$unsorted)) % 0.40/0.60 (define @t59 () (= @t4 (tptp.set_difference @t58 @t2))) % 0.40/0.60 (define @t60 () (tptp.in @t58 @t6)) % 0.40/0.60 (define @t61 () (and @t60 @t59)) % 0.40/0.60 (define @t62 () (@list @t58)) % 0.40/0.60 (define @t63 () (exists @t62 @t61)) % 0.40/0.60 (define @t64 () (= @t3 @t4)) % 0.40/0.60 (define @t65 () (tptp.in @t3 @t11)) % 0.40/0.60 (define @t66 () (and @t65 @t64 @t63)) % 0.40/0.60 (define @t67 () (exists @t9 @t66)) % 0.40/0.60 (define @t68 () (= @t15 @t67)) % 0.40/0.60 (define @t69 () (forall @t17 @t68)) % 0.40/0.60 (define @t70 () (exists @t19 @t69)) % 0.40/0.60 (define @t71 () (= @t4 @t3)) % 0.40/0.60 (define @t72 () (@var "G" $$unsorted)) % 0.40/0.60 (define @t73 () (= @t3 (tptp.set_difference @t72 @t2))) % 0.40/0.60 (define @t74 () (tptp.in @t72 @t6)) % 0.40/0.60 (define @t75 () (and @t74 @t73)) % 0.40/0.60 (define @t76 () (@list @t72)) % 0.40/0.60 (define @t77 () (exists @t76 @t75)) % 0.40/0.60 (define @t78 () (= @t14 @t3)) % 0.40/0.60 (define @t79 () (@var "F" $$unsorted)) % 0.40/0.60 (define @t80 () (= @t4 (tptp.set_difference @t79 @t2))) % 0.40/0.60 (define @t81 () (tptp.in @t79 @t6)) % 0.40/0.60 (define @t82 () (and @t81 @t80)) % 0.40/0.60 (define @t83 () (@list @t79)) % 0.40/0.60 (define @t84 () (exists @t83 @t82)) % 0.40/0.60 (define @t85 () (= @t14 @t4)) % 0.40/0.60 (define @t86 () (and @t85 @t84 @t78 @t77)) % 0.40/0.60 (define @t87 () (=> @t86 @t71)) % 0.40/0.60 (define @t88 () (@list @t14 @t4 @t3)) % 0.40/0.60 (define @t89 () (forall @t88 @t87)) % 0.40/0.60 (define @t90 () (=> @t89 @t70)) % 0.40/0.60 (define @t91 () (=> @t24 @t90)) % 0.40/0.60 (define @t92 () (forall @t26 @t91)) % 0.40/0.60 (define @t93 () (forall @t17 (= @t15 (and @t12 (not (forall @t9 (or (not @t7) (not @t5)))))))) % 0.40/0.60 (define @t94 () (not (forall @t19 (not @t93)))) % 0.40/0.60 (define @t95 () (not @t22)) % 0.40/0.60 (define @t96 () (not @t23)) % 0.40/0.60 (define @t97 () (or @t96 @t95 @t94)) % 0.40/0.60 (define @t98 () (or @t96 @t95)) % 0.40/0.60 (define @t99 () (not @t24)) % 0.40/0.60 (define @t100 () (forall @t9 (not @t8))) % 0.40/0.60 (define @t101 () (not @t100)) % 0.40/0.60 (define @t102 () (forall @t62 (or (not @t60) (not @t59)))) % 0.40/0.60 (define @t103 () (not @t102)) % 0.40/0.60 (define @t104 () (and @t12 @t103)) % 0.40/0.60 (define @t105 () (and @t103 @t12)) % 0.40/0.60 (define @t106 () (= @t15 @t105)) % 0.40/0.60 (define @t107 () (forall @t17 @t106)) % 0.40/0.60 (define @t108 () (not @t107)) % 0.40/0.60 (define @t109 () (forall @t19 @t108)) % 0.40/0.60 (define @t110 () (not @t109)) % 0.40/0.60 (define @t111 () (or @t96 @t95 @t110)) % 0.40/0.60 (define @t112 () (forall @t26 @t111)) % 0.40/0.60 (define @t113 () (forall @t26 (or @t96 @t95 (not (forall @t19 (not (forall @t17 (= @t15 @t104)))))))) % 0.40/0.60 (define @t114 () (@var "BOUND_VARIABLE_8217" $$unsorted)) % 0.40/0.60 (define @t115 () (@var "BOUND_VARIABLE_8220" $$unsorted)) % 0.40/0.60 (define @t116 () (@var "BOUND_VARIABLE_8219" $$unsorted)) % 0.40/0.60 (define @t117 () (@var "BOUND_VARIABLE_8216" $$unsorted)) % 0.40/0.60 (define @t118 () (@var "BOUND_VARIABLE_8218" $$unsorted)) % 0.40/0.60 (define @t119 () (@list @t117 @t114 @t118 @t116 @t115)) % 0.40/0.60 (define @t120 () (forall @t26 @t97)) % 0.40/0.60 (define @t121 () (@list true)) % 0.40/0.60 (define @t122 () (not @t12)) % 0.40/0.60 (define @t123 () (= @t15 (not (or @t102 @t122)))) % 0.40/0.60 (define @t124 () (not (= @t4 @t4))) % 0.40/0.60 (define @t125 () (or @t122 @t124)) % 0.40/0.60 (define @t126 () (not @t71)) % 0.40/0.60 (define @t127 () (not @t65)) % 0.40/0.60 (define @t128 () (or @t126 @t127 @t126)) % 0.40/0.60 (define @t129 () (or @t127 @t126)) % 0.40/0.60 (define @t130 () (forall @t9 @t129)) % 0.40/0.60 (define @t131 () (or @t102 @t130)) % 0.40/0.60 (define @t132 () (or @t102 @t129)) % 0.40/0.60 (define @t133 () (or @t127 @t126 @t102)) % 0.40/0.60 (define @t134 () (not @t103)) % 0.40/0.60 (define @t135 () (or @t127 @t126 @t134)) % 0.40/0.60 (define @t136 () (and @t65 @t71 @t103)) % 0.40/0.60 (define @t137 () (forall @t9 (not @t136))) % 0.40/0.60 (define @t138 () (not @t137)) % 0.40/0.60 (define @t139 () (forall @t62 (not @t61))) % 0.40/0.60 (define @t140 () (not @t139)) % 0.40/0.60 (define @t141 () (@var "BOUND_VARIABLE_7912" $$unsorted)) % 0.40/0.60 (define @t142 () (@var "BOUND_VARIABLE_7904" $$unsorted)) % 0.40/0.60 (define @t143 () (@list @t4 @t3 @t142 @t141)) % 0.40/0.60 (define @t144 () (not (= @t3 (tptp.set_difference @t141 @t2)))) % 0.40/0.60 (define @t145 () (not (tptp.in @t141 @t6))) % 0.40/0.60 (define @t146 () (not (= @t4 (tptp.set_difference @t142 @t2)))) % 0.40/0.60 (define @t147 () (not (tptp.in @t142 @t6))) % 0.40/0.60 (define @t148 () (or @t126 @t71 @t147 @t146 @t145 @t144)) % 0.40/0.60 (define @t149 () (or @t124 @t126 @t71 @t147 @t146 @t145 @t144)) % 0.40/0.60 (define @t150 () (not @t78)) % 0.40/0.60 (define @t151 () (not @t85)) % 0.40/0.60 (define @t152 () (or @t151 @t151 @t150 @t71 @t147 @t146 @t145 @t144)) % 0.40/0.60 (define @t153 () (or @t151 @t150 @t71 @t147 @t146 @t145 @t144)) % 0.40/0.60 (define @t154 () (forall @t19 @t153)) % 0.40/0.60 (define @t155 () (forall @t143 @t154)) % 0.40/0.60 (define @t156 () (forall (@list @t4 @t3 @t142 @t141 @t14) @t153)) % 0.40/0.60 (define @t157 () (@list @t14 @t4 @t3 @t142 @t141)) % 0.40/0.60 (define @t158 () (or @t145 @t144)) % 0.40/0.60 (define @t159 () (or @t147 @t146)) % 0.40/0.60 (define @t160 () (or @t151 @t159 @t150 @t158 @t71)) % 0.40/0.60 (define @t161 () (forall @t157 @t160)) % 0.40/0.60 (define @t162 () (forall (@list @t142 @t141) @t160)) % 0.40/0.60 (define @t163 () (forall (@list @t141) @t158)) % 0.40/0.60 (define @t164 () (forall (@list @t142) @t159)) % 0.40/0.60 (define @t165 () (or @t151 @t164 @t150 @t163 @t71)) % 0.40/0.60 (define @t166 () (forall @t76 (or (not @t74) (not @t73)))) % 0.40/0.60 (define @t167 () (forall @t83 (or (not @t81) (not @t80)))) % 0.40/0.60 (define @t168 () (or @t151 @t167 @t150 @t166 @t71)) % 0.40/0.60 (define @t169 () (not @t166)) % 0.40/0.60 (define @t170 () (not @t169)) % 0.40/0.60 (define @t171 () (not @t167)) % 0.40/0.60 (define @t172 () (not @t171)) % 0.40/0.60 (define @t173 () (or @t151 @t172 @t150 @t170)) % 0.40/0.60 (define @t174 () (and @t85 @t171 @t78 @t169)) % 0.40/0.60 (define @t175 () (forall @t76 (not @t75))) % 0.40/0.60 (define @t176 () (not @t175)) % 0.40/0.60 (define @t177 () (forall @t83 (not @t82))) % 0.40/0.60 (define @t178 () (not @t177)) % 0.40/0.60 (assume @p1 @t28) % 0.40/0.60 (assume @p2 (forall @t37 (exists @t36 (and @t35 @t34 @t33 (tptp.function @t6) (tptp.one_to_one @t6) @t32 @t31 @t30 (tptp.natural @t6) @t29)))) % 0.40/0.60 (assume @p3 (exists @t37 @t41)) % 0.40/0.60 (assume @p4 (exists @t37 (and @t40 @t39 @t38 @t44 @t43 @t42 @t23))) % 0.40/0.60 (assume @p5 (exists @t37 (and @t40 @t39))) % 0.40/0.60 (assume @p6 (exists @t37 @t45)) % 0.40/0.60 (assume @p7 (forall @t37 (=> @t45 @t41))) % 0.40/0.60 (assume @p8 (exists @t37 (and @t44 @t40))) % 0.40/0.60 (assume @p9 (forall @t26 (=> (and @t40 @t33) (tptp.relation @t46)))) % 0.40/0.60 (assume @p10 (exists @t37 (and @t47 @t40))) % 0.40/0.60 (assume @p11 (exists @t37 (and @t47 @t43 @t42 @t23 @t48))) % 0.40/0.60 (assume @p12 (forall @t37 (=> (and @t23 @t48) (and @t52 @t51 @t50 @t49 (tptp.natural @t21))))) % 0.40/0.60 (assume @p13 (exists @t37 (and @t47 @t53))) % 0.40/0.60 (assume @p14 (forall @t37 (=> @t44 @t53))) % 0.40/0.60 (assume @p15 (forall @t37 (=> @t47 (exists @t36 (and @t35 @t54 @t29))))) % 0.40/0.60 (assume @p16 (forall @t37 (=> @t53 (forall @t36 (=> @t35 @t29))))) % 0.40/0.60 (assume @p17 (forall @t26 (=> @t53 (tptp.finite @t46)))) % 0.40/0.60 (assume @p18 (forall @t37 (=> @t44 @t39))) % 0.40/0.60 (assume @p19 (forall @t37 (=> @t44 @t40))) % 0.40/0.60 (assume @p20 (forall @t37 (=> (and @t44 @t23) (and @t43 @t42 @t23 @t48)))) % 0.40/0.60 (assume @p21 (forall @t37 (=> @t55 @t23))) % 0.40/0.60 (assume @p22 (exists @t37 @t56)) % 0.40/0.60 (assume @p23 (forall @t37 (=> @t44 @t56))) % 0.40/0.60 (assume @p24 (exists @t37 (and @t47 @t43 @t42 @t23))) % 0.40/0.60 (assume @p25 (forall @t37 (=> @t47 (exists @t36 (and @t35 @t54))))) % 0.40/0.60 (assume @p26 (forall @t37 (exists @t36 (and @t35 @t34)))) % 0.40/0.60 (assume @p27 (exists @t37 @t44)) % 0.40/0.60 (assume @p28 (exists @t37 @t47)) % 0.40/0.60 (assume @p29 (forall @t26 (=> (tptp.in @t1 @t6) (not (tptp.in @t6 @t1))))) % 0.40/0.60 (assume @p30 true) % 0.40/0.60 (assume @p31 (forall @t37 (and @t57 (tptp.finite @t2)))) % 0.40/0.60 (assume @p32 (forall @t37 (=> @t23 (forall @t36 (=> (tptp.element @t6 @t1) (and @t32 @t31 @t30)))))) % 0.40/0.60 (assume @p33 (forall @t37 @t52)) % 0.40/0.60 (assume @p34 (forall @t37 (=> @t23 @t55))) % 0.40/0.60 (assume @p35 (forall @t37 (=> @t23 (and @t52 @t51 @t50 @t49)))) % 0.40/0.60 (assume @p36 (forall @t37 (not (tptp.empty @t11)))) % 0.40/0.60 (assume @p37 (forall @t37 @t57)) % 0.40/0.60 (assume @p38 @t92) % 0.40/0.60 (step @p39 :rule aci_norm :args ((= (or @t98 @t94) @t97))) % 0.40/0.60 (step @p40 :rule refl :args (@t94)) % 0.40/0.60 (step @p41 :rule bool-and-de-morgan :args (@t23 @t22 true)) % 0.40/0.60 (step @p42 :rule nary_cong :premises (@p41 @p40) :args ((or @t99 @t94))) % 0.40/0.60 (step @p43 :rule trans :premises (@p42 @p39)) % 0.40/0.60 (step @p44 :rule bool-impl-elim :args (@t24 @t94)) % 0.40/0.60 (step @p45 :rule trans :premises (@p44 @p43)) % 0.40/0.60 (step @p46 :rule cong :premises (@p45) :args ((forall @t26 (=> @t24 @t94)))) % 0.40/0.60 (step @p47 :rule exists-elim :args ((= (exists @t19 @t93) @t94))) % 0.40/0.60 (step @p48 :rule bool-and-de-morgan :args (@t7 @t5 true)) % 0.40/0.60 (step @p49 :rule cong :premises (@p48) :args (@t100)) % 0.40/0.60 (step @p50 :rule cong :premises (@p49) :args (@t101)) % 0.40/0.60 (step @p51 :rule exists-elim :args ((= @t10 @t101))) % 0.40/0.60 (step @p52 :rule trans :premises (@p51 @p50)) % 0.40/0.60 (step @p53 :rule refl :args (@t12)) % 0.40/0.60 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t13)) % 0.40/0.60 (step @p55 :rule refl :args (@t15)) % 0.40/0.60 (step @p56 :rule cong :premises (@p55 @p54) :args (@t16)) % 0.40/0.60 (step @p57 :rule cong :premises (@p56) :args (@t18)) % 0.40/0.60 (step @p58 :rule cong :premises (@p57) :args (@t20)) % 0.40/0.60 (step @p59 :rule trans :premises (@p58 @p47)) % 0.40/0.60 (step @p60 :rule refl :args (@t24)) % 0.40/0.60 (step @p61 :rule cong :premises (@p60 @p59) :args (@t25)) % 0.40/0.60 (step @p62 :rule cong :premises (@p61) :args (@t27)) % 0.40/0.60 (step @p63 :rule trans :premises (@p62 @p46)) % 0.40/0.60 (step @p64 :rule cong :premises (@p63) :args (@t28)) % 0.40/0.60 (step @p65 :rule eq_resolve :premises (@p1 @p64)) % 0.40/0.60 (step @p66 :rule aci_norm :args ((= @t105 @t104))) % 0.40/0.60 (step @p67 :rule refl :args (@t15)) % 0.40/0.60 (step @p68 :rule cong :premises (@p67 @p66) :args (@t106)) % 0.40/0.60 (step @p69 :rule cong :premises (@p68) :args (@t107)) % 0.40/0.60 (step @p70 :rule cong :premises (@p69) :args (@t108)) % 0.40/0.60 (step @p71 :rule cong :premises (@p70) :args (@t109)) % 0.40/0.60 (step @p72 :rule cong :premises (@p71) :args (@t110)) % 0.40/0.60 (step @p73 :rule refl :args (@t95)) % 0.40/0.60 (step @p74 :rule refl :args (@t96)) % 0.40/0.60 (step @p75 :rule nary_cong :premises (@p74 @p73 @p72) :args (@t111)) % 0.40/0.60 (step @p76 :rule cong :premises (@p75) :args (@t112)) % 0.40/0.60 (step @p77 :rule symm :premises (@p76)) % 0.40/0.60 (step @p78 :rule true_intro :premises (@p77)) % 0.40/0.60 (step @p79 :rule eq-symm :args (@t112 @t113)) % 0.40/0.60 (step @p80 :rule trans :premises (@p79 @p78)) % 0.40/0.60 (step @p81 :rule cong :premises (@p77 @p76) :args ((= @t113 @t112))) % 0.40/0.60 (step @p82 :rule trans :premises (@p81 @p80)) % 0.40/0.60 (step @p83 :rule true_elim :premises (@p82)) % 0.40/0.60 (step @p84 :rule alpha_equiv :args ((forall (@list @t114 @t117) (or (not (tptp.ordinal @t114)) (not (tptp.element @t117 (tptp.powerset (tptp.powerset (tptp.succ @t114))))) (not (forall (@list @t118) (not (forall (@list @t116) (= (tptp.in @t116 @t118) (and (tptp.in @t116 (tptp.powerset @t114)) (not (forall (@list @t115) (or (not (tptp.in @t115 @t117)) (not (= @t116 (tptp.set_difference @t115 (tptp.singleton @t114))))))))))))))) @t119 (@list @t6 @t1 @t14 @t4 @t58))) % 0.40/0.60 (step @p85 :rule alpha_equiv :args (@t120 (@list @t6 @t1 @t14 @t4 @t3) @t119)) % 0.40/0.60 (step @p86 :rule trans :premises (@p85 @p84 @p83)) % 0.40/0.60 (step @p87 :rule equiv_elim2 :premises (@p86)) % 0.40/0.60 (step @p88 :rule chain_m_resolution :premises (@p87 @p65) :args ((not @t112) @t121 (@list @t120))) % 0.40/0.60 (step @p89 :rule aci_norm :args ((= (or @t98 @t110) @t111))) % 0.40/0.60 (step @p90 :rule refl :args (@t110)) % 0.40/0.60 (step @p91 :rule nary_cong :premises (@p41 @p90) :args ((or @t99 @t110))) % 0.40/0.60 (step @p92 :rule trans :premises (@p91 @p89)) % 0.40/0.60 (step @p93 :rule bool-impl-elim :args (@t24 @t110)) % 0.40/0.60 (step @p94 :rule trans :premises (@p93 @p92)) % 0.40/0.60 (step @p95 :rule cong :premises (@p94) :args ((forall @t26 (=> @t24 @t110)))) % 0.40/0.60 (step @p96 :rule bool-impl-true2 :args (@t110)) % 0.40/0.60 (step @p97 :rule exists-elim :args ((= (exists @t19 @t107) @t110))) % 0.40/0.60 (step @p98 :rule bool-double-not-elim :args (@t12)) % 0.40/0.60 (step @p99 :rule refl :args (@t103)) % 0.40/0.60 (step @p100 :rule nary_cong :premises (@p99 @p98) :args ((and @t103 (not @t122)))) % 0.40/0.60 (step @p101 :rule bool-or-de-morgan :args (@t102 @t122 false)) % 0.40/0.60 (step @p102 :rule trans :premises (@p101 @p100)) % 0.40/0.60 (step @p103 :rule cong :premises (@p67 @p102) :args (@t123)) % 0.40/0.60 (step @p104 :rule cong :premises (@p103) :args ((forall @t17 @t123))) % 0.40/0.60 (step @p105 :rule aci_norm :args ((= (or @t122 false) @t122))) % 0.40/0.60 (step @p106 :rule evaluate :args ((not true))) % 0.40/0.60 (step @p107 :rule eq-refl :args (@t4)) % 0.40/0.60 (step @p108 :rule cong :premises (@p107) :args (@t124)) % 0.40/0.60 (step @p109 :rule trans :premises (@p108 @p106)) % 0.40/0.60 (step @p110 :rule refl :args (@t122)) % 0.40/0.60 (step @p111 :rule nary_cong :premises (@p110 @p109) :args (@t125)) % 0.40/0.60 (step @p112 :rule trans :premises (@p111 @p105)) % 0.40/0.60 (step @p113 :rule quant-var-elim-eq :args ((= (forall @t9 (or (not @t64) @t127 @t126)) @t125))) % 0.40/0.60 (step @p114 :rule refl :args (@t126)) % 0.40/0.60 (step @p115 :rule refl :args (@t127)) % 0.40/0.60 (step @p116 :rule eq-symm :args (@t4 @t3)) % 0.40/0.60 (step @p117 :rule cong :premises (@p116) :args (@t126)) % 0.40/0.60 (step @p118 :rule nary_cong :premises (@p117 @p115 @p114) :args (@t128)) % 0.40/0.60 (step @p119 :rule aci_norm :args ((= @t129 @t128))) % 0.40/0.60 (step @p120 :rule trans :premises (@p119 @p118)) % 0.40/0.60 (step @p121 :rule cong :premises (@p120) :args (@t130)) % 0.40/0.60 (step @p122 :rule trans :premises (@p121 @p113)) % 0.40/0.60 (step @p123 :rule trans :premises (@p122 @p112)) % 0.40/0.60 (step @p124 :rule refl :args (@t102)) % 0.40/0.60 (step @p125 :rule nary_cong :premises (@p124 @p123) :args (@t131)) % 0.40/0.60 (step @p126 :rule quant-miniscope-or :args ((= (forall @t9 @t132) @t131))) % 0.40/0.60 (step @p127 :rule aci_norm :args ((= @t133 @t132))) % 0.40/0.60 (step @p128 :rule cong :premises (@p127) :args ((forall @t9 @t133))) % 0.40/0.60 (step @p129 :rule trans :premises (@p128 @p126)) % 0.40/0.60 (step @p130 :rule trans :premises (@p129 @p125)) % 0.40/0.60 (step @p131 :rule bool-double-not-elim :args (@t102)) % 0.40/0.60 (step @p132 :rule nary_cong :premises (@p115 @p114 @p131) :args (@t135)) % 0.40/0.60 (step @p133 :rule aci_norm :args ((= (or @t127 (or @t126 @t134)) @t135))) % 0.40/0.60 (step @p134 :rule trans :premises (@p133 @p132)) % 0.40/0.60 (step @p135 :rule bool-and-de-morgan :args (@t71 @t103 true)) % 0.40/0.60 (step @p136 :rule nary_cong :premises (@p115 @p135) :args ((or @t127 (not (and @t71 @t103))))) % 0.40/0.60 (step @p137 :rule bool-and-de-morgan :args (@t65 @t71 (and @t103))) % 0.40/0.60 (step @p138 :rule trans :premises (@p137 @p136)) % 0.40/0.60 (step @p139 :rule trans :premises (@p138 @p134)) % 0.40/0.60 (step @p140 :rule cong :premises (@p139) :args (@t137)) % 0.40/0.60 (step @p141 :rule trans :premises (@p140 @p130)) % 0.40/0.60 (step @p142 :rule cong :premises (@p141) :args (@t138)) % 0.40/0.60 (step 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:rule cong :premises (@p157) :args (@t70)) % 0.40/0.60 (step @p159 :rule trans :premises (@p158 @p97)) % 0.40/0.60 (step @p160 :rule quant-unused-vars :args ((= (forall @t143 true) true))) % 0.40/0.60 (step @p161 :rule bool-or-taut2 :args (false @t71 false (or @t147 @t146 @t145 @t144))) % 0.40/0.60 (step @p162 :rule cong :premises (@p161) :args ((forall @t143 @t148))) % 0.40/0.60 (step @p163 :rule trans :premises (@p162 @p160)) % 0.40/0.60 (step @p164 :rule aci_norm :args ((= (or false @t126 @t71 @t147 @t146 @t145 @t144) @t148))) % 0.40/0.60 (step @p165 :rule refl :args (@t144)) % 0.40/0.60 (step @p166 :rule refl :args (@t145)) % 0.40/0.60 (step @p167 :rule refl :args (@t146)) % 0.40/0.60 (step @p168 :rule refl :args (@t147)) % 0.40/0.60 (step @p169 :rule refl :args (@t71)) % 0.40/0.60 (step @p170 :rule refl :args (@t126)) % 0.40/0.60 (step @p171 :rule nary_cong :premises (@p109 @p170 @p169 @p168 @p167 @p166 @p165) :args (@t149)) % 0.40/0.60 (step @p172 :rule trans :premises (@p171 @p164)) % 0.40/0.60 (step @p173 :rule cong :premises (@p172) :args ((forall @t143 @t149))) % 0.40/0.60 (step @p174 :rule trans :premises (@p173 @p163)) % 0.40/0.60 (step @p175 :rule quant-var-elim-eq :args ((= (forall @t19 @t152) @t149))) % 0.40/0.60 (step @p176 :rule aci_norm :args ((= @t153 @t152))) % 0.40/0.60 (step @p177 :rule cong :premises (@p176) :args (@t154)) % 0.40/0.60 (step @p178 :rule trans :premises (@p177 @p175)) % 0.40/0.60 (step @p179 :rule cong :premises (@p178) :args (@t155)) % 0.40/0.60 (step @p180 :rule quant-merge-prenex :args ((= @t155 @t156))) % 0.40/0.60 (step @p181 :rule symm :premises (@p180)) % 0.40/0.60 (step @p182 :rule quant_var_reordering :args ((= (forall @t157 @t153) @t156))) % 0.40/0.60 (step @p183 :rule trans :premises (@p182 @p181 @p179)) % 0.40/0.60 (step @p184 :rule trans :premises (@p183 @p174)) % 0.40/0.60 (step @p185 :rule aci_norm :args ((= @t160 @t153))) % 0.40/0.60 (step @p186 :rule cong :premises (@p185) :args (@t161)) % 0.40/0.60 (step @p187 :rule trans :premises (@p186 @p184)) % 0.40/0.60 (step @p188 :rule quant-merge-prenex :args ((= (forall @t88 @t162) @t161))) % 0.40/0.60 (step @p189 :rule refl :args (@t71)) % 0.40/0.60 (step @p190 :rule alpha_equiv :args (@t163 (@list @t141) (@list @t72))) % 0.40/0.60 (step @p191 :rule refl :args (@t150)) % 0.40/0.60 (step @p192 :rule alpha_equiv :args (@t164 (@list @t142) (@list @t79))) % 0.40/0.60 (step @p193 :rule refl :args (@t151)) % 0.40/0.60 (step @p194 :rule nary_cong :premises (@p193 @p192 @p191 @p190 @p189) :args (@t165)) % 0.40/0.60 (step @p195 :rule quant-miniscope-or :args ((= @t162 @t165))) % 0.40/0.60 (step @p196 :rule trans :premises (@p195 @p194)) % 0.40/0.60 (step @p197 :rule symm :premises (@p196)) % 0.40/0.60 (step @p198 :rule cong :premises (@p197) :args ((forall @t88 @t168))) % 0.40/0.60 (step @p199 :rule trans :premises (@p198 @p188)) % 0.40/0.60 (step @p200 :rule trans :premises (@p199 @p187)) % 0.40/0.60 (step @p201 :rule aci_norm :args ((= (or (or @t151 @t167 @t150 @t166) @t71) @t168))) % 0.40/0.60 (step @p202 :rule bool-double-not-elim :args (@t166)) % 0.40/0.60 (step @p203 :rule bool-double-not-elim :args (@t167)) % 0.40/0.60 (step @p204 :rule nary_cong :premises (@p193 @p203 @p191 @p202) :args (@t173)) % 0.40/0.60 (step @p205 :rule aci_norm :args ((= (or @t151 (or @t172 (or @t150 @t170))) @t173))) % 0.40/0.60 (step @p206 :rule trans :premises (@p205 @p204)) % 0.40/0.60 (step @p207 :rule bool-and-de-morgan :args (@t78 @t169 true)) % 0.40/0.60 (step @p208 :rule refl :args (@t172)) % 0.40/0.60 (step @p209 :rule nary_cong :premises (@p208 @p207) :args ((or @t172 (not (and @t78 @t169))))) % 0.40/0.60 (step @p210 :rule bool-and-de-morgan :args (@t171 @t78 (and @t169))) % 0.40/0.60 (step @p211 :rule trans :premises (@p210 @p209)) % 0.40/0.60 (step @p212 :rule nary_cong :premises (@p193 @p211) :args ((or @t151 (not (and @t171 @t78 @t169))))) % 0.40/0.60 (step @p213 :rule bool-and-de-morgan :args (@t85 @t171 (and @t78 @t169))) % 0.40/0.60 (step @p214 :rule trans :premises (@p213 @p212)) % 0.40/0.60 (step @p215 :rule trans :premises (@p214 @p206)) % 0.40/0.61 (step @p216 :rule nary_cong :premises (@p215 @p189) :args ((or (not @t174) @t71))) % 0.40/0.61 (step @p217 :rule trans :premises (@p216 @p201)) % 0.40/0.61 (step @p218 :rule bool-impl-elim :args (@t174 @t71)) % 0.40/0.61 (step @p219 :rule trans :premises (@p218 @p217)) % 0.40/0.61 (step @p220 :rule cong :premises (@p219) :args ((forall @t88 (=> @t174 @t71)))) % 0.40/0.61 (step @p221 :rule trans :premises (@p220 @p200)) % 0.40/0.61 (step @p222 :rule bool-and-de-morgan :args (@t74 @t73 true)) % 0.40/0.61 (step @p223 :rule cong :premises (@p222) :args (@t175)) % 0.40/0.61 (step @p224 :rule cong :premises (@p223) :args (@t176)) % 0.40/0.61 (step @p225 :rule exists-elim :args ((= @t77 @t176))) % 0.40/0.61 (step @p226 :rule trans :premises (@p225 @p224)) % 0.40/0.61 (step @p227 :rule refl :args (@t78)) % 0.40/0.61 (step @p228 :rule bool-and-de-morgan :args (@t81 @t80 true)) % 0.40/0.61 (step @p229 :rule cong :premises (@p228) :args (@t177)) % 0.40/0.61 (step @p230 :rule cong :premises (@p229) :args (@t178)) % 0.40/0.61 (step @p231 :rule exists-elim :args ((= @t84 @t178))) % 0.40/0.61 (step @p232 :rule trans :premises (@p231 @p230)) % 0.40/0.61 (step @p233 :rule refl :args (@t85)) % 0.40/0.61 (step @p234 :rule nary_cong :premises (@p233 @p232 @p227 @p226) :args (@t86)) % 0.40/0.61 (step @p235 :rule cong :premises (@p234 @p169) :args (@t87)) % 0.40/0.61 (step @p236 :rule cong :premises (@p235) :args (@t89)) % 0.40/0.61 (step @p237 :rule trans :premises (@p236 @p221)) % 0.40/0.61 (step @p238 :rule cong :premises (@p237 @p159) :args (@t90)) % 0.40/0.61 (step @p239 :rule trans :premises (@p238 @p96)) % 0.40/0.61 (step @p240 :rule cong :premises (@p60 @p239) :args (@t91)) % 0.40/0.61 (step @p241 :rule cong :premises (@p240) :args (@t92)) % 0.40/0.61 (step @p242 :rule trans :premises (@p241 @p95)) % 0.40/0.61 (step @p243 :rule eq_resolve :premises (@p38 @p242)) % 0.40/0.61 (step @p244 false :rule chain_m_resolution :premises (@p243 @p88) :args (false @t121 (@list @t112))) % 0.40/0.61 ) % 0.40/0.61 % SZS output end Proof % 0.40/0.61 % cvc5 exiting %------------------------------------------------------------------------------