%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU325+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 : n020.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 08:51:23 AM UTC 2026 % Result : Theorem 16.04s 16.25s % Output : Proof 16.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU325+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 % 0.18/0.34 % Computer : n020.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 16:57:11 EDT 2026 % 0.18/0.34 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 16.04/16.25 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 16.04/16.25 --- Run --no-e-matching --full-saturate-quant at 6... % 16.04/16.25 % SZS status Theorem % 16.04/16.25 % SZS output start Proof % 16.04/16.25 ( % 16.04/16.25 (declare-sort $$unsorted 0) % 16.04/16.25 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.empty_set $$unsorted) % 16.04/16.25 (declare-const tptp.is_a_cover_of_carrier (-> $$unsorted $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 16.04/16.25 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 16.04/16.25 (declare-const tptp.one_sorted_str (-> $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.cast_as_carrier_subset (-> $$unsorted $$unsorted)) % 16.04/16.25 (declare-const tptp.the_carrier (-> $$unsorted $$unsorted)) % 16.04/16.25 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 16.04/16.25 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.v3_membered (-> $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.natural (-> $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.empty_carrier (-> $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.v1_membered (-> $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.v1_xreal_0 (-> $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.v5_membered (-> $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.v2_membered (-> $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.v1_rat_1 (-> $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.empty (-> $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.v1_xcmplx_0 (-> $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.v1_int_1 (-> $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 16.04/16.25 (declare-const tptp.v4_membered (-> $$unsorted Bool)) % 16.04/16.25 (define @t1 () (@var "A" $$unsorted)) % 16.04/16.25 (define @t2 () (@var "B" $$unsorted)) % 16.04/16.25 (define @t3 () (tptp.in @t1 @t2)) % 16.04/16.25 (define @t4 () (@list @t1 @t2)) % 16.04/16.25 (define @t5 () (tptp.v1_xcmplx_0 @t2)) % 16.04/16.25 (define @t6 () (tptp.element @t2 @t1)) % 16.04/16.25 (define @t7 () (@list @t2)) % 16.04/16.25 (define @t8 () (tptp.v1_membered @t1)) % 16.04/16.25 (define @t9 () (@list @t1)) % 16.04/16.25 (define @t10 () (tptp.v1_xreal_0 @t2)) % 16.04/16.25 (define @t11 () (tptp.v2_membered @t1)) % 16.04/16.25 (define @t12 () (tptp.v1_rat_1 @t2)) % 16.04/16.25 (define @t13 () (tptp.v3_membered @t1)) % 16.04/16.25 (define @t14 () (tptp.v1_int_1 @t2)) % 16.04/16.25 (define @t15 () (tptp.v4_membered @t1)) % 16.04/16.25 (define @t16 () (tptp.v5_membered @t1)) % 16.04/16.25 (define @t17 () (tptp.empty @t1)) % 16.04/16.25 (define @t18 () (tptp.v1_membered @t2)) % 16.04/16.25 (define @t19 () (tptp.powerset @t1)) % 16.04/16.25 (define @t20 () (tptp.element @t2 @t19)) % 16.04/16.25 (define @t21 () (tptp.v2_membered @t2)) % 16.04/16.25 (define @t22 () (tptp.v3_membered @t2)) % 16.04/16.25 (define @t23 () (tptp.v4_membered @t2)) % 16.04/16.25 (define @t24 () (tptp.the_carrier @t1)) % 16.04/16.25 (define @t25 () (tptp.cast_as_carrier_subset @t1)) % 16.04/16.25 (define @t26 () (tptp.one_sorted_str @t1)) % 16.04/16.25 (define @t27 () (@var "D" $$unsorted)) % 16.04/16.25 (define @t28 () (tptp.in @t27 @t1)) % 16.04/16.25 (define @t29 () (@var "C" $$unsorted)) % 16.04/16.25 (define @t30 () (tptp.in @t29 @t27)) % 16.04/16.25 (define @t31 () (and @t30 @t28)) % 16.04/16.25 (define @t32 () (@list @t27)) % 16.04/16.25 (define @t33 () (exists @t32 @t31)) % 16.04/16.25 (define @t34 () (tptp.in @t29 @t2)) % 16.04/16.25 (define @t35 () (= @t34 @t33)) % 16.04/16.25 (define @t36 () (@list @t29)) % 16.04/16.25 (define @t37 () (forall @t36 @t35)) % 16.04/16.25 (define @t38 () (= @t2 (tptp.union @t1))) % 16.04/16.25 (define @t39 () (= @t38 @t37)) % 16.04/16.25 (define @t40 () (forall @t4 @t39)) % 16.04/16.25 (define @t41 () (tptp.is_a_cover_of_carrier @t1 @t2)) % 16.04/16.26 (define @t42 () (= @t41 (= @t25 (tptp.union_of_subsets @t24 @t2)))) % 16.04/16.26 (define @t43 () (tptp.powerset @t24)) % 16.04/16.26 (define @t44 () (tptp.powerset @t43)) % 16.04/16.26 (define @t45 () (tptp.element @t2 @t44)) % 16.04/16.26 (define @t46 () (forall @t7 (=> @t45 @t42))) % 16.04/16.26 (define @t47 () (=> @t26 @t46)) % 16.04/16.26 (define @t48 () (forall @t9 @t47)) % 16.04/16.26 (define @t49 () (tptp.union_of_subsets @t1 @t2)) % 16.04/16.26 (define @t50 () (tptp.element @t2 (tptp.powerset @t19))) % 16.04/16.26 (define @t51 () (tptp.empty_carrier @t1)) % 16.04/16.26 (define @t52 () (not @t51)) % 16.04/16.26 (define @t53 () (and @t52 @t26)) % 16.04/16.26 (define @t54 () (not (tptp.empty @t25))) % 16.04/16.26 (define @t55 () (forall @t9 (=> @t53 @t54))) % 16.04/16.26 (define @t56 () (tptp.empty tptp.empty_set)) % 16.04/16.26 (define @t57 () (not @t17)) % 16.04/16.26 (define @t58 () (tptp.empty @t2)) % 16.04/16.26 (define @t59 () (not @t58)) % 16.04/16.26 (define @t60 () (= @t49 (tptp.union @t2))) % 16.04/16.26 (define @t61 () (forall @t4 (=> @t50 @t60))) % 16.04/16.26 (define @t62 () (tptp.subset @t1 @t1)) % 16.04/16.26 (define @t63 () (forall @t4 @t62)) % 16.04/16.26 (define @t64 () (tptp.element @t1 @t2)) % 16.04/16.26 (define @t65 () (tptp.element @t2 (tptp.powerset @t29))) % 16.04/16.26 (define @t66 () (@list @t1 @t2 @t29)) % 16.04/16.26 (define @t67 () (tptp.empty @t29)) % 16.04/16.26 (define @t68 () (forall @t66 (not (and @t3 @t65 @t67)))) % 16.04/16.26 (define @t69 () (= @t2 tptp.empty_set)) % 16.04/16.26 (define @t70 () (not (and @t41 @t69))) % 16.04/16.26 (define @t71 () (forall @t7 (=> @t45 @t70))) % 16.04/16.26 (define @t72 () (=> @t53 @t71)) % 16.04/16.26 (define @t73 () (forall @t9 @t72)) % 16.04/16.26 (define @t74 () (not @t73)) % 16.04/16.26 (define @t75 () (not @t67)) % 16.04/16.26 (define @t76 () (not @t65)) % 16.04/16.26 (define @t77 () (not @t3)) % 16.04/16.26 (define @t78 () (or @t77 @t76 @t75)) % 16.04/16.26 (define @t79 () (forall @t32 (not @t31))) % 16.04/16.26 (define @t80 () (not @t79)) % 16.04/16.26 (define @t81 () (@list tptp.empty_set tptp.empty_set)) % 16.04/16.26 (define @t82 () (not (tptp.is_a_cover_of_carrier @t1 tptp.empty_set))) % 16.04/16.26 (define @t83 () (not (tptp.element tptp.empty_set @t44))) % 16.04/16.26 (define @t84 () (not @t26)) % 16.04/16.26 (define @t85 () (or @t51 @t84 @t83 @t82)) % 16.04/16.26 (define @t86 () (@quantifiers_skolemize (forall @t9 @t85) 0)) % 16.04/16.26 (define @t87 () (tptp.the_carrier @t86)) % 16.04/16.26 (define @t88 () (tptp.union_of_subsets @t87 tptp.empty_set)) % 16.04/16.26 (define @t89 () (tptp.union tptp.empty_set)) % 16.04/16.26 (define @t90 () (tptp.element tptp.empty_set (tptp.powerset (tptp.powerset @t87)))) % 16.04/16.26 (define @t91 () (not @t90)) % 16.04/16.26 (define @t92 () (or @t91 (= @t88 @t89))) % 16.04/16.26 (define @t93 () (forall @t4 (or (not @t50) @t60))) % 16.04/16.26 (define @t94 () (= @t89 @t88)) % 16.04/16.26 (define @t95 () (or @t91 @t94)) % 16.04/16.26 (define @t96 () (or @t83 @t82)) % 16.04/16.26 (define @t97 () (or @t51 @t84)) % 16.04/16.26 (define @t98 () (not @t53)) % 16.04/16.26 (define @t99 () (not (= tptp.empty_set tptp.empty_set))) % 16.04/16.26 (define @t100 () (or @t83 @t82 @t99)) % 16.04/16.26 (define @t101 () (not @t69)) % 16.04/16.26 (define @t102 () (not @t41)) % 16.04/16.26 (define @t103 () (not @t45)) % 16.04/16.26 (define @t104 () (or @t101 @t103 @t102 @t101)) % 16.04/16.26 (define @t105 () (or @t103 @t102 @t101)) % 16.04/16.26 (define @t106 () (tptp.is_a_cover_of_carrier @t86 tptp.empty_set)) % 16.04/16.26 (define @t107 () (not @t106)) % 16.04/16.26 (define @t108 () (tptp.one_sorted_str @t86)) % 16.04/16.26 (define @t109 () (not @t108)) % 16.04/16.26 (define @t110 () (tptp.empty_carrier @t86)) % 16.04/16.26 (define @t111 () (or @t110 @t109 @t91 @t107)) % 16.04/16.26 (define @t112 () (@list true)) % 16.04/16.26 (define @t113 () (@list @t111)) % 16.04/16.26 (define @t114 () (@list false false)) % 16.04/16.26 (define @t115 () (@var "BOUND_VARIABLE_7914" $$unsorted)) % 16.04/16.26 (define @t116 () (= (tptp.is_a_cover_of_carrier @t1 @t115) (= @t25 (tptp.union_of_subsets @t24 @t115)))) % 16.04/16.26 (define @t117 () (not (tptp.element @t115 @t44))) % 16.04/16.26 (define @t118 () (or @t117 @t116)) % 16.04/16.26 (define @t119 () (or @t84 @t118)) % 16.04/16.26 (define @t120 () (forall (@list @t1 @t115) @t119)) % 16.04/16.26 (define @t121 () (@list @t115)) % 16.04/16.26 (define @t122 () (forall @t121 @t119)) % 16.04/16.26 (define @t123 () (forall @t121 @t118)) % 16.04/16.26 (define @t124 () (or @t84 @t123)) % 16.04/16.26 (define @t125 () (forall @t7 (or @t103 @t42))) % 16.04/16.26 (define @t126 () (tptp.cast_as_carrier_subset @t86)) % 16.04/16.26 (define @t127 () (= @t126 @t88)) % 16.04/16.26 (define @t128 () (= @t106 @t127)) % 16.04/16.26 (define @t129 () (or @t109 @t91 @t128)) % 16.04/16.26 (define @t130 () (@list false false false)) % 16.04/16.26 (define @t131 () (tptp.empty @t126)) % 16.04/16.26 (define @t132 () (not @t131)) % 16.04/16.26 (define @t133 () (or @t110 @t109 @t132)) % 16.04/16.26 (define @t134 () (not @t94)) % 16.04/16.26 (define @t135 () (not @t127)) % 16.04/16.26 (define @t136 () (= tptp.empty_set @t89)) % 16.04/16.26 (define @t137 () (not @t136)) % 16.04/16.26 (define @t138 () (not @t56)) % 16.04/16.26 (define @t139 () (and @t56 @t136 @t94 @t127 @t132)) % 16.04/16.26 (define @t140 () (not (tptp.in @t27 tptp.empty_set))) % 16.04/16.26 (define @t141 () (forall @t36 (= (tptp.in @t29 tptp.empty_set) (not (forall @t32 (or (not @t30) @t140)))))) % 16.04/16.26 (define @t142 () (= @t136 @t141)) % 16.04/16.26 (define @t143 () (not @t141)) % 16.04/16.26 (define @t144 () (@list true false)) % 16.04/16.26 (define @t145 () (@quantifiers_skolemize @t141 0)) % 16.04/16.26 (define @t146 () (forall @t32 (or (not (tptp.in @t145 @t27)) @t140))) % 16.04/16.26 (define @t147 () (not @t146)) % 16.04/16.26 (define @t148 () (tptp.in @t145 tptp.empty_set)) % 16.04/16.26 (define @t149 () (= @t148 @t147)) % 16.04/16.26 (define @t150 () (not @t149)) % 16.04/16.26 (define @t151 () (tptp.subset tptp.empty_set tptp.empty_set)) % 16.04/16.26 (define @t152 () (tptp.element tptp.empty_set (tptp.powerset tptp.empty_set))) % 16.04/16.26 (define @t153 () (= @t152 @t151)) % 16.04/16.26 (define @t154 () (not @t152)) % 16.04/16.26 (define @t155 () (not @t148)) % 16.04/16.26 (define @t156 () (or @t155 @t154 @t138)) % 16.04/16.26 (define @t157 () (@quantifiers_skolemize @t146 0)) % 16.04/16.26 (define @t158 () (tptp.in @t157 tptp.empty_set)) % 16.04/16.26 (define @t159 () (not @t158)) % 16.04/16.26 (define @t160 () (or (not (tptp.in @t145 @t157)) @t159)) % 16.04/16.26 (define @t161 () (not @t160)) % 16.04/16.26 (define @t162 () (or @t159 @t154 @t138)) % 16.04/16.26 (define @t163 () (not @t162)) % 16.04/16.26 (define @t164 () (forall @t66 @t78)) % 16.04/16.26 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 16.04/16.26 (assume @p2 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 16.04/16.26 (assume @p3 (forall @t9 (=> @t11 (forall @t7 (=> @t6 (and @t5 @t10)))))) % 16.04/16.26 (assume @p4 (forall @t9 (=> @t13 (forall @t7 (=> @t6 (and @t5 @t10 @t12)))))) % 16.04/16.26 (assume @p5 (forall @t9 (=> @t15 (forall @t7 (=> @t6 (and @t5 @t10 @t14 @t12)))))) % 16.04/16.26 (assume @p6 (forall @t9 (=> @t16 (forall @t7 (=> @t6 (and @t5 (tptp.natural @t2) @t10 @t14 @t12)))))) % 16.04/16.26 (assume @p7 (forall @t9 (=> @t17 (and @t8 @t11 @t13 @t15 @t16)))) % 16.04/16.26 (assume @p8 (forall @t9 (=> @t8 (forall @t7 (=> @t20 @t18))))) % 16.04/16.26 (assume @p9 (forall @t9 (=> @t11 (forall @t7 (=> @t20 (and @t18 @t21)))))) % 16.04/16.26 (assume @p10 (forall @t9 (=> @t13 (forall @t7 (=> @t20 (and @t18 @t21 @t22)))))) % 16.04/16.26 (assume @p11 (forall @t9 (=> @t15 (forall @t7 (=> @t20 (and @t18 @t21 @t22 @t23)))))) % 16.04/16.26 (assume @p12 (forall @t9 (=> @t16 @t15))) % 16.04/16.26 (assume @p13 (forall @t9 (=> @t16 (forall @t7 (=> @t20 (and @t18 @t21 @t22 @t23 (tptp.v5_membered @t2))))))) % 16.04/16.26 (assume @p14 (forall @t9 (=> @t15 @t13))) % 16.04/16.26 (assume @p15 (forall @t9 (=> @t13 @t11))) % 16.04/16.26 (assume @p16 (forall @t9 (=> @t11 @t8))) % 16.04/16.26 (assume @p17 (forall @t9 (=> @t26 (= @t25 @t24)))) % 16.04/16.26 (assume @p18 @t40) % 16.04/16.26 (assume @p19 @t48) % 16.04/16.26 (assume @p20 true) % 16.04/16.26 (assume @p21 (forall @t9 (=> @t26 (tptp.element @t25 @t43)))) % 16.04/16.26 (assume @p22 (forall @t4 (=> @t50 (tptp.element @t49 @t19)))) % 16.04/16.26 (assume @p23 (exists @t9 @t26)) % 16.04/16.26 (assume @p24 (forall @t9 (exists @t7 @t6))) % 16.04/16.26 (assume @p25 (forall @t9 (=> @t53 (not (tptp.empty @t24))))) % 16.04/16.26 (assume @p26 (forall @t9 (not (tptp.empty @t19)))) % 16.04/16.26 (assume @p27 @t55) % 16.04/16.26 (assume @p28 (and @t56 (tptp.v1_membered tptp.empty_set) (tptp.v2_membered tptp.empty_set) (tptp.v3_membered tptp.empty_set) (tptp.v4_membered tptp.empty_set) (tptp.v5_membered tptp.empty_set))) % 16.04/16.26 (assume @p29 (exists @t9 (and @t57 @t8 @t11 @t13 @t15 @t16))) % 16.04/16.26 (assume @p30 (forall @t9 (=> @t57 (exists @t7 (and @t20 @t59))))) % 16.04/16.26 (assume @p31 (forall @t9 (exists @t7 (and @t20 @t58)))) % 16.04/16.26 (assume @p32 (exists @t9 (and @t26 @t52))) % 16.04/16.26 (assume @p33 (forall @t9 (=> @t53 (exists @t7 (and (tptp.element @t2 @t43) @t59))))) % 16.04/16.26 (assume @p34 @t61) % 16.04/16.26 (assume @p35 @t63) % 16.04/16.26 (assume @p36 (forall @t4 (=> @t3 @t64))) % 16.04/16.26 (assume @p37 (forall @t4 (=> @t64 (or @t58 @t3)))) % 16.04/16.26 (assume @p38 (forall @t4 (= (tptp.element @t1 (tptp.powerset @t2)) (tptp.subset @t1 @t2)))) % 16.04/16.26 (assume @p39 (forall @t66 (=> (and @t3 @t65) (tptp.element @t1 @t29)))) % 16.04/16.26 (assume @p40 @t68) % 16.04/16.26 (assume @p41 @t74) % 16.04/16.26 (assume @p42 (forall @t9 (=> @t17 (= @t1 tptp.empty_set)))) % 16.04/16.26 (assume @p43 (forall @t4 (not (and @t3 @t58)))) % 16.04/16.26 (assume @p44 (forall @t4 (not (and @t17 (not (= @t1 @t2)) @t58)))) % 16.04/16.26 (step @p45 :rule aci_norm :args ((= (or @t77 (or @t76 @t75)) @t78))) % 16.04/16.26 (step @p46 :rule bool-and-de-morgan :args (@t65 @t67 true)) % 16.04/16.26 (step @p47 :rule refl :args (@t77)) % 16.04/16.26 (step @p48 :rule nary_cong :premises (@p47 @p46) :args ((or @t77 (not (and @t65 @t67))))) % 16.04/16.26 (step @p49 :rule bool-and-de-morgan :args (@t3 @t65 (and @t67))) % 16.04/16.26 (step @p50 :rule trans :premises (@p49 @p48)) % 16.04/16.26 (step @p51 :rule trans :premises (@p50 @p45)) % 16.04/16.26 (step @p52 :rule cong :premises (@p51) :args (@t68)) % 16.04/16.26 (step @p53 :rule eq_resolve :premises (@p40 @p52)) % 16.04/16.26 (step @p54 :rule bool-and-de-morgan :args (@t30 @t28 true)) % 16.04/16.26 (step @p55 :rule cong :premises (@p54) :args (@t79)) % 16.04/16.26 (step @p56 :rule cong :premises (@p55) :args (@t80)) % 16.04/16.26 (step @p57 :rule exists-elim :args ((= @t33 @t80))) % 16.04/16.26 (step @p58 :rule trans :premises (@p57 @p56)) % 16.04/16.26 (step @p59 :rule refl :args (@t34)) % 16.04/16.26 (step @p60 :rule cong :premises (@p59 @p58) :args (@t35)) % 16.04/16.26 (step @p61 :rule cong :premises (@p60) :args (@t37)) % 16.04/16.26 (step @p62 :rule refl :args (@t38)) % 16.04/16.26 (step @p63 :rule cong :premises (@p62 @p61) :args (@t39)) % 16.04/16.26 (step @p64 :rule cong :premises (@p63) :args (@t40)) % 16.04/16.26 (step @p65 :rule eq_resolve :premises (@p18 @p64)) % 16.04/16.26 (step @p66 :rule instantiate :premises (@p65) :args (@t81)) % 16.04/16.26 (step @p67 :rule bool-impl-elim :args (@t50 @t60)) % 16.04/16.26 (step @p68 :rule cong :premises (@p67) :args (@t61)) % 16.04/16.26 (step @p69 :rule eq_resolve :premises (@p34 @p68)) % 16.04/16.26 (step @p70 :rule eq-symm :args (@t88 @t89)) % 16.04/16.26 (step @p71 :rule refl :args (@t91)) % 16.04/16.26 (step @p72 :rule nary_cong :premises (@p71 @p70) :args (@t92)) % 16.04/16.26 (step @p73 :rule refl :args (@t93)) % 16.04/16.26 (step @p74 :rule cong :premises (@p73 @p72) :args ((=> @t93 @t92))) % 16.04/16.26 (assume-push @p286 @t93) % 16.04/16.26 (step @p76 :rule instantiate :premises (@p69) :args ((@list @t87 tptp.empty_set))) % 16.04/16.26 (step-pop @p287 :rule scope :premises (@p76)) % 16.04/16.26 (step @p77 :rule process_scope :premises (@p287) :args (@t92)) % 16.04/16.26 (step @p79 :rule eq_resolve :premises (@p77 @p74)) % 16.04/16.26 (step @p80 :rule implies_elim :premises (@p79)) % 16.04/16.26 (step @p81 :rule chain_m_resolution :premises (@p80 @p69) :args (@t95 (@list false) (@list @t93))) % 16.04/16.26 (step @p82 :rule aci_norm :args ((= (or @t97 @t96) @t85))) % 16.04/16.26 (step @p83 :rule refl :args (@t96)) % 16.04/16.26 (step @p84 :rule refl :args (@t84)) % 16.04/16.26 (step @p85 :rule bool-double-not-elim :args (@t51)) % 16.04/16.26 (step @p86 :rule nary_cong :premises (@p85 @p84) :args ((or (not @t52) @t84))) % 16.04/16.26 (step @p87 :rule bool-and-de-morgan :args (@t52 @t26 true)) % 16.04/16.26 (step @p88 :rule trans :premises (@p87 @p86)) % 16.04/16.26 (step @p89 :rule nary_cong :premises (@p88 @p83) :args ((or @t98 @t96))) % 16.04/16.26 (step @p90 :rule trans :premises (@p89 @p82)) % 16.04/16.26 (step @p91 :rule bool-impl-elim :args (@t53 @t96)) % 16.04/16.26 (step @p92 :rule trans :premises (@p91 @p90)) % 16.04/16.26 (step @p93 :rule cong :premises (@p92) :args ((forall @t9 (=> @t53 @t96)))) % 16.04/16.26 (step @p94 :rule aci_norm :args ((= (or @t83 @t82 false) @t96))) % 16.04/16.26 (step @p95 :rule evaluate :args ((not true))) % 16.04/16.26 (step @p96 :rule eq-refl :args (tptp.empty_set)) % 16.04/16.26 (step @p97 :rule cong :premises (@p96) :args (@t99)) % 16.04/16.26 (step @p98 :rule trans :premises (@p97 @p95)) % 16.04/16.26 (step @p99 :rule refl :args (@t82)) % 16.04/16.26 (step @p100 :rule refl :args (@t83)) % 16.04/16.26 (step @p101 :rule nary_cong :premises (@p100 @p99 @p98) :args (@t100)) % 16.04/16.26 (step @p102 :rule trans :premises (@p101 @p94)) % 16.04/16.26 (step @p103 :rule quant-var-elim-eq :args ((= (forall @t7 @t104) @t100))) % 16.04/16.26 (step @p104 :rule aci_norm :args ((= @t105 @t104))) % 16.04/16.26 (step @p105 :rule cong :premises (@p104) :args ((forall @t7 @t105))) % 16.04/16.26 (step @p106 :rule trans :premises (@p105 @p103)) % 16.04/16.26 (step @p107 :rule trans :premises (@p106 @p102)) % 16.04/16.26 (step @p108 :rule aci_norm :args ((= (or @t103 (or @t102 @t101)) @t105))) % 16.04/16.26 (step @p109 :rule bool-and-de-morgan :args (@t41 @t69 true)) % 16.04/16.26 (step @p110 :rule refl :args (@t103)) % 16.04/16.26 (step @p111 :rule nary_cong :premises (@p110 @p109) :args ((or @t103 @t70))) % 16.04/16.26 (step @p112 :rule trans :premises (@p111 @p108)) % 16.04/16.26 (step @p113 :rule bool-impl-elim :args (@t45 @t70)) % 16.04/16.26 (step @p114 :rule trans :premises (@p113 @p112)) % 16.04/16.26 (step @p115 :rule cong :premises (@p114) :args (@t71)) % 16.04/16.26 (step @p116 :rule trans :premises (@p115 @p107)) % 16.04/16.26 (step @p117 :rule refl :args (@t53)) % 16.04/16.26 (step @p118 :rule cong :premises (@p117 @p116) :args (@t72)) % 16.04/16.26 (step @p119 :rule cong :premises (@p118) :args (@t73)) % 16.04/16.26 (step @p120 :rule trans :premises (@p119 @p93)) % 16.04/16.26 (step @p121 :rule cong :premises (@p120) :args (@t74)) % 16.04/16.26 (step @p122 :rule eq_resolve :premises (@p41 @p121)) % 16.04/16.26 (step @p123 :rule skolemize :premises (@p122)) % 16.04/16.26 (step @p124 :rule bool-double-not-elim :args (@t90)) % 16.04/16.26 (step @p125 :rule refl :args (@t111)) % 16.04/16.26 (step @p126 :rule nary_cong :premises (@p125 @p124) :args ((or @t111 (not @t91)))) % 16.04/16.26 (step @p127 :rule cnf_or_neg :args (@t111 2)) % 16.04/16.26 (step @p128 :rule eq_resolve :premises (@p127 @p126)) % 16.04/16.26 (step @p129 :rule reordering :premises (@p128) :args ((or @t90 @t111))) % 16.04/16.26 (step @p130 :rule chain_m_resolution :premises (@p129 @p123) :args (@t90 @t112 @t113)) % 16.04/16.26 (step @p131 :rule cnf_or_pos :args (@t95)) % 16.04/16.26 (step @p132 :rule reordering :premises (@p131) :args ((or @t91 @t94 (not @t95)))) % 16.04/16.26 (step @p133 :rule chain_m_resolution :premises (@p132 @p130 @p81) :args (@t94 @t114 (@list @t90 @t95))) % 16.04/16.26 (step @p134 :rule aci_norm :args ((= @t119 (or @t84 @t117 @t116)))) % 16.04/16.26 (step @p135 :rule cong :premises (@p134) :args (@t120)) % 16.04/16.26 (step @p136 :rule quant-merge-prenex :args ((= (forall @t9 @t122) @t120))) % 16.04/16.26 (step @p137 :rule alpha_equiv :args (@t123 (@list @t115) (@list @t2))) % 16.04/16.26 (step @p138 :rule nary_cong :premises (@p84 @p137) :args (@t124)) % 16.04/16.26 (step @p139 :rule quant-miniscope-or :args ((= @t122 @t124))) % 16.04/16.26 (step @p140 :rule trans :premises (@p139 @p138)) % 16.04/16.26 (step @p141 :rule symm :premises (@p140)) % 16.04/16.26 (step @p142 :rule cong :premises (@p141) :args ((forall @t9 (or @t84 @t125)))) % 16.04/16.26 (step @p143 :rule trans :premises (@p142 @p136)) % 16.04/16.26 (step @p144 :rule trans :premises (@p143 @p135)) % 16.04/16.26 (step @p145 :rule bool-impl-elim :args (@t26 @t125)) % 16.04/16.26 (step @p146 :rule cong :premises (@p145) :args ((forall @t9 (=> @t26 @t125)))) % 16.04/16.26 (step @p147 :rule trans :premises (@p146 @p144)) % 16.04/16.26 (step @p148 :rule bool-impl-elim :args (@t45 @t42)) % 16.04/16.26 (step @p149 :rule cong :premises (@p148) :args (@t46)) % 16.04/16.26 (step @p150 :rule refl :args (@t26)) % 16.04/16.26 (step @p151 :rule cong :premises (@p150 @p149) :args (@t47)) % 16.04/16.26 (step @p152 :rule cong :premises (@p151) :args (@t48)) % 16.04/16.26 (step @p153 :rule trans :premises (@p152 @p147)) % 16.04/16.26 (step @p154 :rule eq_resolve :premises (@p19 @p153)) % 16.04/16.26 (step @p155 :rule instantiate :premises (@p154) :args ((@list @t86 tptp.empty_set))) % 16.04/16.26 (step @p156 :rule bool-double-not-elim :args (@t108)) % 16.04/16.26 (step @p157 :rule nary_cong :premises (@p125 @p156) :args ((or @t111 (not @t109)))) % 16.04/16.26 (step @p158 :rule cnf_or_neg :args (@t111 1)) % 16.04/16.26 (step @p159 :rule eq_resolve :premises (@p158 @p157)) % 16.04/16.26 (step @p160 :rule reordering :premises (@p159) :args ((or @t108 @t111))) % 16.04/16.26 (step @p161 :rule chain_m_resolution :premises (@p160 @p123) :args (@t108 @t112 @t113)) % 16.04/16.26 (step @p162 :rule cnf_or_pos :args (@t129)) % 16.04/16.26 (step @p163 :rule reordering :premises (@p162) :args ((or @t109 @t91 @t128 (not @t129)))) % 16.04/16.26 (step @p164 :rule chain_m_resolution :premises (@p163 @p161 @p130 @p155) :args (@t128 @t130 (@list @t108 @t90 @t129))) % 16.04/16.26 (step @p165 :rule bool-double-not-elim :args (@t106)) % 16.04/16.26 (step @p166 :rule nary_cong :premises (@p125 @p165) :args ((or @t111 (not @t107)))) % 16.04/16.26 (step @p167 :rule cnf_or_neg :args (@t111 3)) % 16.04/16.26 (step @p168 :rule eq_resolve :premises (@p167 @p166)) % 16.04/16.26 (step @p169 :rule reordering :premises (@p168) :args ((or @t106 @t111))) % 16.04/16.26 (step @p170 :rule chain_m_resolution :premises (@p169 @p123) :args (@t106 @t112 @t113)) % 16.04/16.26 (step @p171 :rule cnf_equiv_pos1 :args (@t128)) % 16.04/16.26 (step @p172 :rule reordering :premises (@p171) :args ((or @t107 @t127 (not @t128)))) % 16.04/16.26 (step @p173 :rule chain_m_resolution :premises (@p172 @p170 @p164) :args (@t127 @t114 (@list @t106 @t128))) % 16.04/16.26 (step @p174 :rule aci_norm :args ((= (or @t97 @t54) (or @t51 @t84 @t54)))) % 16.04/16.26 (step @p175 :rule refl :args (@t54)) % 16.04/16.26 (step @p176 :rule nary_cong :premises (@p88 @p175) :args ((or @t98 @t54))) % 16.04/16.26 (step @p177 :rule trans :premises (@p176 @p174)) % 16.04/16.26 (step @p178 :rule bool-impl-elim :args (@t53 @t54)) % 16.04/16.26 (step @p179 :rule trans :premises (@p178 @p177)) % 16.04/16.26 (step @p180 :rule cong :premises (@p179) :args (@t55)) % 16.04/16.26 (step @p181 :rule eq_resolve :premises (@p27 @p180)) % 16.04/16.26 (step @p182 :rule instantiate :premises (@p181) :args ((@list @t86))) % 16.04/16.26 (step @p183 :rule cnf_or_neg :args (@t111 0)) % 16.04/16.26 (step @p184 :rule chain_m_resolution :premises (@p183 @p123) :args ((not @t110) @t112 @t113)) % 16.04/16.26 (step @p185 :rule cnf_or_pos :args (@t133)) % 16.04/16.26 (step @p186 :rule reordering :premises (@p185) :args ((or @t110 @t109 @t132 (not @t133)))) % 16.04/16.26 (step @p187 :rule chain_m_resolution :premises (@p186 @p184 @p161 @p182) :args (@t132 (@list true false false) (@list @t110 @t108 @t133))) % 16.04/16.26 (step @p188 :rule and_elim :premises (@p28) :args (0)) % 16.04/16.26 (step @p189 :rule refl :args (@t134)) % 16.04/16.26 (step @p190 :rule refl :args (@t135)) % 16.04/16.26 (step @p191 :rule bool-double-not-elim :args (@t131)) % 16.04/16.26 (step @p192 :rule refl :args (@t137)) % 16.04/16.26 (step @p193 :rule refl :args (@t138)) % 16.04/16.26 (step @p194 :rule nary_cong :premises (@p193 @p192 @p191 @p190 @p189) :args ((or @t138 @t137 (not @t132) @t135 @t134))) % 16.04/16.26 (assume-push @p288 @t56) % 16.04/16.26 (assume-push @p289 @t136) % 16.04/16.26 (assume-push @p290 @t94) % 16.04/16.26 (assume-push @p291 @t127) % 16.04/16.26 (assume-push @p292 @t132) % 16.04/16.26 (step @p200 :rule evaluate :args ((= false true))) % 16.04/16.26 (step @p201 :rule true_intro :premises (@p188)) % 16.04/16.26 (step @p202 :rule symm :premises (@p289)) % 16.04/16.26 (step @p203 :rule symm :premises (@p133)) % 16.04/16.26 (step @p204 :rule trans :premises (@p173 @p203 @p202)) % 16.04/16.26 (step @p205 :rule cong :premises (@p204) :args (@t131)) % 16.04/16.26 (step @p206 :rule false_intro :premises (@p187)) % 16.04/16.26 (step @p207 :rule symm :premises (@p206)) % 16.04/16.26 (step @p208 :rule trans :premises (@p207 @p205 @p201)) % 16.04/16.26 (step @p209 false :rule eq_resolve :premises (@p208 @p200)) % 16.04/16.26 (step-pop @p293 :rule scope :premises (@p209)) % 16.04/16.26 (step-pop @p294 :rule scope :premises (@p293)) % 16.04/16.26 (step-pop @p295 :rule scope :premises (@p294)) % 16.04/16.26 (step-pop @p296 :rule scope :premises (@p295)) % 16.04/16.26 (step-pop @p297 :rule scope :premises (@p296)) % 16.04/16.26 (step @p210 :rule process_scope :premises (@p297) :args (false)) % 16.04/16.26 (assume-push @p298 @t56) % 16.04/16.26 (assume-push @p299 @t136) % 16.04/16.26 (assume-push @p300 @t132) % 16.04/16.26 (assume-push @p301 @t127) % 16.04/16.26 (assume-push @p302 @t94) % 16.04/16.26 (step @p221 :rule and_intro :premises (@p188 @p299 @p133 @p173 @p187)) % 16.04/16.26 (step-pop @p303 :rule scope :premises (@p221)) % 16.04/16.26 (step-pop @p304 :rule scope :premises (@p303)) % 16.04/16.26 (step-pop @p305 :rule scope :premises (@p304)) % 16.04/16.26 (step-pop @p306 :rule scope :premises (@p305)) % 16.04/16.26 (step-pop @p307 :rule scope :premises (@p306)) % 16.04/16.26 (step @p222 :rule process_scope :premises (@p307) :args (@t139)) % 16.04/16.26 (step @p228 :rule implies_elim :premises (@p222)) % 16.04/16.26 (step @p229 :rule resolution :premises (@p228 @p210) :args (true @t139)) % 16.04/16.26 (step @p230 :rule not_and :premises (@p229)) % 16.04/16.26 (step @p231 :rule eq_resolve :premises (@p230 @p194)) % 16.04/16.26 (step @p232 :rule chain_m_resolution :premises (@p231 @p188 @p187 @p173 @p133) :args (@t137 (@list false true false false) (@list @t56 @t131 @t127 @t94))) % 16.04/16.26 (step @p233 :rule cnf_equiv_pos2 :args (@t142)) % 16.04/16.26 (step @p234 :rule reordering :premises (@p233) :args ((or @t136 @t143 (not @t142)))) % 16.04/16.26 (step @p235 :rule chain_m_resolution :premises (@p234 @p232 @p66) :args (@t143 @t144 (@list @t136 @t142))) % 16.04/16.26 (step @p236 :rule refl :args (@t150)) % 16.04/16.26 (step @p237 :rule bool-double-not-elim :args (@t141)) % 16.04/16.26 (step @p238 :rule nary_cong :premises (@p237 @p236) :args ((or (not @t143) @t150))) % 16.04/16.26 (assume-push @p308 @t143) % 16.04/16.26 (step @p240 :rule skolemize :premises (@p308)) % 16.04/16.26 (step-pop @p309 :rule scope :premises (@p240)) % 16.04/16.26 (step @p241 :rule process_scope :premises (@p309) :args (@t150)) % 16.04/16.26 (step @p243 :rule implies_elim :premises (@p241)) % 16.04/16.26 (step @p244 :rule eq_resolve :premises (@p243 @p238)) % 16.04/16.26 (step @p245 :rule chain_m_resolution :premises (@p244 @p235) :args (@t150 @t112 (@list @t141))) % 16.04/16.26 (step @p246 :rule instantiate :premises (@p53) :args ((@list @t145 tptp.empty_set tptp.empty_set))) % 16.04/16.26 (step @p247 :rule instantiate :premises (@p38) :args (@t81)) % 16.04/16.26 (step @p248 :rule quant-unused-vars :args ((= @t63 (forall @t9 @t62)))) % 16.04/16.26 (step @p249 :rule eq_resolve :premises (@p35 @p248)) % 16.04/16.26 (step @p250 :rule instantiate :premises (@p249) :args ((@list tptp.empty_set))) % 16.04/16.26 (step @p251 :rule cnf_equiv_pos2 :args (@t153)) % 16.04/16.26 (step @p252 :rule reordering :premises (@p251) :args ((or @t152 (not @t151) (not @t153)))) % 16.04/16.26 (step @p253 :rule chain_m_resolution :premises (@p252 @p250 @p247) :args (@t152 @t114 (@list @t151 @t153))) % 16.04/16.26 (step @p254 :rule cnf_or_pos :args (@t156)) % 16.04/16.26 (step @p255 :rule reordering :premises (@p254) :args ((or @t138 @t154 @t155 (not @t156)))) % 16.04/16.26 (step @p256 :rule chain_m_resolution :premises (@p255 @p188 @p253 @p246) :args (@t155 @t130 (@list @t56 @t152 @t156))) % 16.04/16.26 (step @p257 :rule cnf_equiv_neg1 :args (@t149)) % 16.04/16.26 (step @p258 :rule reordering :premises (@p257) :args ((or @t148 @t147 @t149))) % 16.04/16.26 (step @p259 :rule chain_m_resolution :premises (@p258 @p256 @p245) :args (@t147 (@list true true) (@list @t148 @t149))) % 16.04/16.26 (step @p260 :rule refl :args (@t161)) % 16.04/16.26 (step @p261 :rule bool-double-not-elim :args (@t146)) % 16.04/16.26 (step @p262 :rule nary_cong :premises (@p261 @p260) :args ((or (not @t147) @t161))) % 16.04/16.26 (assume-push @p310 @t147) % 16.04/16.26 (step @p264 :rule skolemize :premises (@p310)) % 16.04/16.26 (step-pop @p311 :rule scope :premises (@p264)) % 16.04/16.26 (step @p265 :rule process_scope :premises (@p311) :args (@t161)) % 16.04/16.26 (step @p267 :rule implies_elim :premises (@p265)) % 16.04/16.26 (step @p268 :rule eq_resolve :premises (@p267 @p262)) % 16.04/16.26 (step @p269 :rule chain_m_resolution :premises (@p268 @p259) :args (@t161 @t112 (@list @t146))) % 16.04/16.26 (step @p270 :rule bool-double-not-elim :args (@t158)) % 16.04/16.26 (step @p271 :rule refl :args (@t160)) % 16.04/16.26 (step @p272 :rule nary_cong :premises (@p271 @p270) :args ((or @t160 (not @t159)))) % 16.04/16.26 (step @p273 :rule cnf_or_neg :args (@t160 1)) % 16.04/16.26 (step @p274 :rule eq_resolve :premises (@p273 @p272)) % 16.04/16.26 (step @p275 :rule reordering :premises (@p274) :args ((or @t158 @t160))) % 16.04/16.26 (step @p276 :rule chain_m_resolution :premises (@p275 @p269) :args (@t158 @t112 (@list @t160))) % 16.04/16.26 (step @p277 :rule cnf_or_pos :args (@t162)) % 16.04/16.26 (step @p278 :rule reordering :premises (@p277) :args ((or @t138 @t154 @t159 @t163))) % 16.04/16.26 (step @p279 :rule chain_m_resolution :premises (@p278 @p188 @p253 @p276) :args (@t163 @t130 (@list @t56 @t152 @t158))) % 16.04/16.26 (assume-push @p312 @t164) % 16.04/16.26 (step @p281 :rule instantiate :premises (@p53) :args ((@list @t157 tptp.empty_set tptp.empty_set))) % 16.04/16.26 (step-pop @p313 :rule scope :premises (@p281)) % 16.04/16.26 (step @p282 :rule process_scope :premises (@p313) :args (@t162)) % 16.04/16.26 (step @p284 :rule implies_elim :premises (@p282)) % 16.04/16.26 (step @p285 false :rule chain_m_resolution :premises (@p284 @p279 @p53) :args (false @t144 (@list @t162 @t164))) % 16.04/16.26 ) % 16.04/16.26 % SZS output end Proof % 16.04/16.26 % cvc5 exiting %------------------------------------------------------------------------------