%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU098+1 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n018.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 08:50:34 AM UTC 2026 % Result : Theorem 0.35s 0.87s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU098+1 : TPTP v9.2.1. Released v3.2.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n018.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 16:29:35 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.35/0.87 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.35/0.87 % SZS status Theorem % 0.35/0.87 % SZS output start Proof % 0.35/0.87 ( % 0.35/0.87 (declare-sort $$unsorted 0) % 0.35/0.87 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.ordinal_yielding (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.being_limit_ordinal (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.35/0.87 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.87 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.function (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.function_image (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.87 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 0.35/0.87 (declare-const tptp.finite (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.empty_set $$unsorted) % 0.35/0.87 (declare-const tptp.natural (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.positive_rationals $$unsorted) % 0.35/0.87 (declare-const tptp.relation_of2 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.quasi_total (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.function_yielding (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.transfinite_sequence (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.first_projection_as_func_of (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.87 (declare-const tptp.relation_of2_as_subset (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.relation_image (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.87 (declare-const tptp.first_projection (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.87 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 0.35/0.87 (declare-const tptp.with_non_empty_elements (-> $$unsorted Bool)) % 0.35/0.87 (declare-const tptp.relation_non_empty (-> $$unsorted Bool)) % 0.35/0.87 (define @t1 () (@var "A" $$unsorted)) % 0.35/0.87 (define @t2 () (@var "B" $$unsorted)) % 0.35/0.87 (define @t3 () (tptp.in @t1 @t2)) % 0.35/0.87 (define @t4 () (@list @t1 @t2)) % 0.35/0.87 (define @t5 () (tptp.ordinal @t2)) % 0.35/0.87 (define @t6 () (tptp.epsilon_connected @t2)) % 0.35/0.87 (define @t7 () (tptp.epsilon_transitive @t2)) % 0.35/0.87 (define @t8 () (tptp.element @t2 @t1)) % 0.35/0.87 (define @t9 () (@list @t2)) % 0.35/0.87 (define @t10 () (tptp.ordinal @t1)) % 0.35/0.87 (define @t11 () (@list @t1)) % 0.35/0.87 (define @t12 () (tptp.finite @t1)) % 0.35/0.87 (define @t13 () (tptp.empty @t1)) % 0.35/0.87 (define @t14 () (tptp.function @t1)) % 0.35/0.87 (define @t15 () (tptp.epsilon_connected @t1)) % 0.35/0.87 (define @t16 () (tptp.epsilon_transitive @t1)) % 0.35/0.87 (define @t17 () (and @t16 @t15)) % 0.35/0.87 (define @t18 () (tptp.relation @t1)) % 0.35/0.87 (define @t19 () (@var "C" $$unsorted)) % 0.35/0.87 (define @t20 () (tptp.cartesian_product2 @t1 @t2)) % 0.35/0.87 (define @t21 () (tptp.element @t19 (tptp.powerset @t20))) % 0.35/0.87 (define @t22 () (@list @t1 @t2 @t19)) % 0.35/0.87 (define @t23 () (tptp.natural @t1)) % 0.35/0.87 (define @t24 () (and @t16 @t15 @t10 @t23)) % 0.35/0.87 (define @t25 () (tptp.finite @t2)) % 0.35/0.87 (define @t26 () (tptp.powerset @t1)) % 0.35/0.87 (define @t27 () (tptp.element @t2 @t26)) % 0.35/0.87 (define @t28 () (tptp.one_to_one @t1)) % 0.35/0.87 (define @t29 () (and @t18 @t14 @t28)) % 0.35/0.87 (define @t30 () (and @t18 @t13 @t14)) % 0.35/0.87 (define @t31 () (and @t16 @t15 @t10)) % 0.35/0.87 (define @t32 () (tptp.element @t1 tptp.positive_rationals)) % 0.35/0.87 (define @t33 () (tptp.powerset @t2)) % 0.35/0.87 (define @t34 () (@var "D" $$unsorted)) % 0.35/0.87 (define @t35 () (tptp.function_image @t1 @t2 @t19 @t34)) % 0.35/0.87 (define @t36 () (tptp.relation_of2 @t19 @t1 @t2)) % 0.35/0.87 (define @t37 () (tptp.quasi_total @t19 @t1 @t2)) % 0.35/0.87 (define @t38 () (tptp.function @t19)) % 0.35/0.87 (define @t39 () (and @t38 @t37 @t36)) % 0.35/0.87 (define @t40 () (@list @t1 @t2 @t19 @t34)) % 0.35/0.87 (define @t41 () (tptp.first_projection @t1 @t2)) % 0.35/0.87 (define @t42 () (tptp.function @t41)) % 0.35/0.87 (define @t43 () (tptp.relation @t41)) % 0.35/0.87 (define @t44 () (forall @t4 (and @t43 @t42))) % 0.35/0.87 (define @t45 () (tptp.first_projection_as_func_of @t1 @t2)) % 0.35/0.87 (define @t46 () (tptp.relation_of2_as_subset @t45 @t20 @t1)) % 0.35/0.87 (define @t47 () (tptp.quasi_total @t45 @t20 @t1)) % 0.35/0.87 (define @t48 () (tptp.function @t45)) % 0.35/0.87 (define @t49 () (forall @t4 (and @t48 @t47 @t46))) % 0.35/0.87 (define @t50 () (tptp.relation_of2_as_subset @t19 @t1 @t2)) % 0.35/0.87 (define @t51 () (@list @t19)) % 0.35/0.87 (define @t52 () (tptp.relation_empty_yielding tptp.empty_set)) % 0.35/0.87 (define @t53 () (tptp.relation tptp.empty_set)) % 0.35/0.87 (define @t54 () (tptp.empty tptp.empty_set)) % 0.35/0.87 (define @t55 () (tptp.finite (tptp.relation_image @t1 @t2))) % 0.35/0.87 (define @t56 () (and @t18 @t14 @t25)) % 0.35/0.87 (define @t57 () (forall @t4 (=> @t56 @t55))) % 0.35/0.87 (define @t58 () (tptp.finite @t20)) % 0.35/0.87 (define @t59 () (and @t12 @t25)) % 0.35/0.87 (define @t60 () (forall @t4 (=> @t59 @t58))) % 0.35/0.87 (define @t61 () (tptp.empty @t2)) % 0.35/0.87 (define @t62 () (not @t61)) % 0.35/0.87 (define @t63 () (not @t13)) % 0.35/0.87 (define @t64 () (tptp.relation_dom @t1)) % 0.35/0.87 (define @t65 () (tptp.transfinite_sequence @t1)) % 0.35/0.87 (define @t66 () (and @t18 @t14 @t65)) % 0.35/0.87 (define @t67 () (tptp.empty @t64)) % 0.35/0.87 (define @t68 () (and @t63 @t18)) % 0.35/0.87 (define @t69 () (tptp.relation_rng @t1)) % 0.35/0.87 (define @t70 () (and @t18 (tptp.relation_non_empty @t1) @t14)) % 0.35/0.87 (define @t71 () (tptp.empty @t69)) % 0.35/0.87 (define @t72 () (and @t18 @t14)) % 0.35/0.87 (define @t73 () (tptp.function @t2)) % 0.35/0.87 (define @t74 () (tptp.relation @t2)) % 0.35/0.87 (define @t75 () (tptp.relation_empty_yielding @t1)) % 0.35/0.87 (define @t76 () (= @t35 (tptp.relation_image @t19 @t34))) % 0.35/0.87 (define @t77 () (forall @t40 (=> @t39 @t76))) % 0.35/0.87 (define @t78 () (forall @t4 (= @t45 @t41))) % 0.35/0.87 (define @t79 () (forall @t22 (= @t50 @t36))) % 0.35/0.87 (define @t80 () (tptp.cartesian_product2 @t64 @t69)) % 0.35/0.87 (define @t81 () (tptp.function_image @t80 @t64 (tptp.first_projection_as_func_of @t64 @t69) @t1)) % 0.35/0.87 (define @t82 () (=> @t72 (= @t81 @t64))) % 0.35/0.87 (define @t83 () (forall @t11 @t82)) % 0.35/0.87 (define @t84 () (tptp.subset @t1 @t2)) % 0.35/0.87 (define @t85 () (and @t84 @t25)) % 0.35/0.87 (define @t86 () (forall @t4 (=> @t85 @t12))) % 0.35/0.87 (define @t87 () (tptp.element @t1 @t2)) % 0.35/0.87 (define @t88 () (tptp.subset @t1 @t80)) % 0.35/0.87 (define @t89 () (forall @t11 (=> @t18 @t88))) % 0.35/0.87 (define @t90 () (tptp.finite @t69)) % 0.35/0.87 (define @t91 () (tptp.finite @t64)) % 0.35/0.87 (define @t92 () (=> @t91 @t90)) % 0.35/0.87 (define @t93 () (forall @t11 (=> @t72 @t92))) % 0.35/0.87 (define @t94 () (=> @t72 (= @t91 @t12))) % 0.35/0.87 (define @t95 () (forall @t11 @t94)) % 0.35/0.87 (define @t96 () (not @t95)) % 0.35/0.87 (define @t97 () (tptp.element @t2 (tptp.powerset @t19))) % 0.35/0.87 (define @t98 () (forall @t4 @t46)) % 0.35/0.87 (define @t99 () (@list @t1 @t2)) % 0.35/0.87 (define @t100 () (forall @t4 @t47)) % 0.35/0.87 (define @t101 () (forall @t4 @t48)) % 0.35/0.87 (define @t102 () (and @t101 @t100 @t98)) % 0.35/0.87 (define @t103 () (= @t12 @t91)) % 0.35/0.87 (define @t104 () (not @t14)) % 0.35/0.87 (define @t105 () (not @t18)) % 0.35/0.87 (define @t106 () (or @t105 @t104 @t103)) % 0.35/0.87 (define @t107 () (@quantifiers_skolemize (forall @t11 @t106) 0)) % 0.35/0.87 (define @t108 () (tptp.relation_rng @t107)) % 0.35/0.87 (define @t109 () (tptp.relation_dom @t107)) % 0.35/0.87 (define @t110 () (@list @t109 @t108)) % 0.35/0.87 (define @t111 () (or @t105 @t104)) % 0.35/0.87 (define @t112 () (not @t72)) % 0.35/0.87 (define @t113 () (tptp.finite @t109)) % 0.35/0.87 (define @t114 () (tptp.finite @t107)) % 0.35/0.87 (define @t115 () (= @t114 @t113)) % 0.35/0.87 (define @t116 () (tptp.function @t107)) % 0.35/0.87 (define @t117 () (not @t116)) % 0.35/0.87 (define @t118 () (tptp.relation @t107)) % 0.35/0.87 (define @t119 () (not @t118)) % 0.35/0.87 (define @t120 () (or @t119 @t117 @t115)) % 0.35/0.87 (define @t121 () (@list true)) % 0.35/0.87 (define @t122 () (@list @t120)) % 0.35/0.87 (define @t123 () (@list @t107)) % 0.35/0.87 (define @t124 () (tptp.cartesian_product2 @t109 @t108)) % 0.35/0.87 (define @t125 () (tptp.subset @t107 @t124)) % 0.35/0.87 (define @t126 () (or @t119 @t125)) % 0.35/0.87 (define @t127 () (@list false false)) % 0.35/0.87 (define @t128 () (not @t25)) % 0.35/0.87 (define @t129 () (not @t84)) % 0.35/0.87 (define @t130 () (tptp.finite @t124)) % 0.35/0.87 (define @t131 () (not @t130)) % 0.35/0.87 (define @t132 () (not @t125)) % 0.35/0.87 (define @t133 () (or @t132 @t131 @t114)) % 0.35/0.87 (define @t134 () (not @t91)) % 0.35/0.87 (define @t135 () (tptp.finite @t108)) % 0.35/0.87 (define @t136 () (not @t113)) % 0.35/0.87 (define @t137 () (or @t119 @t117 @t136 @t135)) % 0.35/0.87 (define @t138 () (not @t12)) % 0.35/0.87 (define @t139 () (not @t135)) % 0.35/0.87 (define @t140 () (or @t136 @t139 @t130)) % 0.35/0.87 (define @t141 () (or @t105 @t104 @t128)) % 0.35/0.87 (define @t142 () (tptp.first_projection_as_func_of @t109 @t108)) % 0.35/0.87 (define @t143 () (forall @t4 @t42)) % 0.35/0.87 (define @t144 () (forall @t4 @t43)) % 0.35/0.87 (define @t145 () (and @t144 @t143)) % 0.35/0.87 (define @t146 () (tptp.first_projection @t109 @t108)) % 0.35/0.87 (define @t147 () (forall @t4 (= @t41 @t45))) % 0.35/0.87 (define @t148 () (= @t146 @t142)) % 0.35/0.87 (define @t149 () (tptp.relation @t142)) % 0.35/0.87 (define @t150 () (= @t64 @t81)) % 0.35/0.87 (define @t151 () (tptp.function_image @t124 @t109 @t142 @t107)) % 0.35/0.87 (define @t152 () (= @t109 @t151)) % 0.35/0.87 (define @t153 () (or @t119 @t117 @t152)) % 0.35/0.87 (define @t154 () (not @t36)) % 0.35/0.87 (define @t155 () (not @t37)) % 0.35/0.87 (define @t156 () (not @t38)) % 0.35/0.87 (define @t157 () (or @t156 @t155 @t154)) % 0.35/0.87 (define @t158 () (tptp.relation_of2_as_subset @t142 @t124 @t109)) % 0.35/0.87 (define @t159 () (tptp.relation_of2 @t142 @t124 @t109)) % 0.35/0.87 (define @t160 () (= @t159 @t158)) % 0.35/0.87 (define @t161 () (tptp.relation_image @t142 @t107)) % 0.35/0.87 (define @t162 () (= @t151 @t161)) % 0.35/0.87 (define @t163 () (not @t159)) % 0.35/0.87 (define @t164 () (tptp.quasi_total @t142 @t124 @t109)) % 0.35/0.87 (define @t165 () (not @t164)) % 0.35/0.87 (define @t166 () (tptp.function @t142)) % 0.35/0.87 (define @t167 () (not @t166)) % 0.35/0.87 (define @t168 () (or @t167 @t165 @t163 @t162)) % 0.35/0.87 (define @t169 () (tptp.finite @t161)) % 0.35/0.87 (define @t170 () (not @t114)) % 0.35/0.87 (define @t171 () (not @t149)) % 0.35/0.87 (define @t172 () (or @t171 @t167 @t170 @t169)) % 0.35/0.87 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 0.35/0.87 (assume @p2 (forall @t11 (=> @t10 (forall @t9 (=> @t8 (and @t7 @t6 @t5)))))) % 0.35/0.87 (assume @p3 (forall @t11 (=> @t13 @t12))) % 0.35/0.87 (assume @p4 (forall @t11 (=> @t13 @t14))) % 0.35/0.87 (assume @p5 (forall @t11 (=> @t10 @t17))) % 0.35/0.87 (assume @p6 (forall @t11 (=> @t13 @t18))) % 0.35/0.87 (assume @p7 (forall @t22 (=> @t21 (tptp.relation @t19)))) % 0.35/0.87 (assume @p8 (forall @t11 (=> (and @t13 @t10) @t24))) % 0.35/0.87 (assume @p9 (forall @t11 (=> @t12 (forall @t9 (=> @t27 @t25))))) % 0.35/0.87 (assume @p10 (forall @t11 (=> @t30 @t29))) % 0.35/0.87 (assume @p11 (forall @t11 (=> @t17 @t10))) % 0.35/0.87 (assume @p12 (forall @t11 (=> @t13 @t31))) % 0.35/0.87 (assume @p13 (forall @t11 (=> @t32 (=> @t10 @t24)))) % 0.35/0.87 (assume @p14 (forall @t40 (=> @t39 (tptp.element @t35 @t33)))) % 0.35/0.87 (assume @p15 @t44) % 0.35/0.87 (assume @p16 @t49) % 0.35/0.87 (assume @p17 (forall @t22 (=> @t50 @t21))) % 0.35/0.87 (assume @p18 (forall @t4 (exists @t51 @t36))) % 0.35/0.87 (assume @p19 (forall @t11 (exists @t9 @t8))) % 0.35/0.87 (assume @p20 (forall @t4 (exists @t51 @t50))) % 0.35/0.87 (assume @p21 (and @t54 @t53 @t52)) % 0.35/0.87 (assume @p22 @t57) % 0.35/0.87 (assume @p23 @t60) % 0.35/0.87 (assume @p24 (forall @t11 (not (tptp.empty @t26)))) % 0.35/0.87 (assume @p25 @t54) % 0.35/0.87 (assume @p26 (and @t53 @t52 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) @t54 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set))) % 0.35/0.87 (assume @p27 (and @t54 @t53)) % 0.35/0.87 (assume @p28 (forall @t4 (=> (and @t63 @t62) (not (tptp.empty @t20))))) % 0.35/0.87 (assume @p29 (forall @t11 (=> @t66 (and (tptp.epsilon_transitive @t64) (tptp.epsilon_connected @t64) (tptp.ordinal @t64))))) % 0.35/0.87 (assume @p30 (forall @t11 (=> @t68 (not @t67)))) % 0.35/0.87 (assume @p31 (forall @t11 (=> @t70 (tptp.with_non_empty_elements @t69)))) % 0.35/0.87 (assume @p32 (forall @t11 (=> @t68 (not @t71)))) % 0.35/0.87 (assume @p33 (forall @t11 (=> @t13 (and @t67 (tptp.relation @t64))))) % 0.35/0.87 (assume @p34 (not (tptp.empty tptp.positive_rationals))) % 0.35/0.87 (assume @p35 (forall @t11 (=> @t13 (and @t71 (tptp.relation @t69))))) % 0.35/0.87 (assume @p36 (exists @t11 (and @t63 @t16 @t15 @t10 @t23))) % 0.35/0.87 (assume @p37 (exists @t11 (and @t63 @t12))) % 0.35/0.87 (assume @p38 (exists @t11 (and @t18 @t14 (tptp.function_yielding @t1)))) % 0.35/0.87 (assume @p39 (exists @t11 @t72)) % 0.35/0.87 (assume @p40 (exists @t11 @t31)) % 0.35/0.87 (assume @p41 (exists @t11 (and @t16 @t15 @t10 (tptp.being_limit_ordinal @t1)))) % 0.35/0.87 (assume @p42 (exists @t11 (and @t13 @t18))) % 0.35/0.87 (assume @p43 (forall @t11 (=> @t63 (exists @t9 (and @t27 @t62))))) % 0.35/0.87 (assume @p44 (exists @t11 @t13)) % 0.35/0.87 (assume @p45 (exists @t11 (and @t32 @t63 @t16 @t15 @t10))) % 0.35/0.87 (assume @p46 (forall @t11 (exists @t9 (and @t27 @t61 @t74 @t73 (tptp.one_to_one @t2) @t7 @t6 @t5 (tptp.natural @t2) @t25)))) % 0.35/0.87 (assume @p47 (exists @t11 @t30)) % 0.35/0.87 (assume @p48 (exists @t11 (and @t18 @t14 @t28 @t13 @t16 @t15 @t10))) % 0.35/0.87 (assume @p49 (exists @t11 (and @t18 @t14 @t65 (tptp.ordinal_yielding @t1)))) % 0.35/0.87 (assume @p50 (exists @t11 @t68)) % 0.35/0.87 (assume @p51 (forall @t11 (exists @t9 (and @t27 @t61)))) % 0.35/0.87 (assume @p52 (exists @t11 @t63)) % 0.35/0.87 (assume @p53 (exists @t11 (and @t32 @t13 @t16 @t15 @t10 @t23))) % 0.35/0.87 (assume @p54 (forall @t11 (=> @t63 (exists @t9 (and @t27 @t62 @t25))))) % 0.35/0.87 (assume @p55 (exists @t11 @t29)) % 0.35/0.87 (assume @p56 (exists @t11 (and @t63 @t16 @t15 @t10))) % 0.35/0.87 (assume @p57 (exists @t11 (and @t18 @t75))) % 0.35/0.87 (assume @p58 (exists @t11 (and @t18 @t75 @t14))) % 0.35/0.87 (assume @p59 (exists @t11 @t66)) % 0.35/0.87 (assume @p60 (exists @t11 @t70)) % 0.35/0.87 (assume @p61 @t77) % 0.35/0.87 (assume @p62 @t78) % 0.35/0.87 (assume @p63 @t79) % 0.35/0.87 (assume @p64 (forall @t4 (tptp.subset @t1 @t1))) % 0.35/0.87 (assume @p65 @t83) % 0.35/0.87 (assume @p66 @t86) % 0.35/0.87 (assume @p67 (forall @t4 (=> (and @t74 @t73) (=> @t12 (tptp.finite (tptp.relation_image @t2 @t1)))))) % 0.35/0.87 (assume @p68 (forall @t4 (=> @t3 @t87))) % 0.35/0.87 (assume @p69 @t89) % 0.35/0.87 (assume @p70 @t93) % 0.35/0.87 (assume @p71 @t96) % 0.35/0.87 (assume @p72 (forall @t4 (=> @t87 (or @t61 @t3)))) % 0.35/0.87 (assume @p73 (forall @t4 (= (tptp.element @t1 @t33) @t84))) % 0.35/0.87 (assume @p74 (forall @t22 (=> (and @t3 @t97) (tptp.element @t1 @t19)))) % 0.35/0.87 (assume @p75 (forall @t22 (not (and @t3 @t97 (tptp.empty @t19))))) % 0.35/0.87 (assume @p76 (forall @t11 (=> @t13 (= @t1 tptp.empty_set)))) % 0.35/0.87 (assume @p77 (forall @t4 (not (and @t3 @t61)))) % 0.35/0.87 (assume @p78 (forall @t4 (not (and @t13 (not (= @t1 @t2)) @t61)))) % 0.35/0.87 (assume @p79 true) % 0.35/0.87 (step @p80 :rule alpha_equiv :args (@t98 @t99 (@list (@var "BOUND_VARIABLE_7872" $$unsorted) (@var "BOUND_VARIABLE_7874" $$unsorted)))) % 0.35/0.87 (step @p81 :rule alpha_equiv :args (@t100 @t99 (@list (@var "BOUND_VARIABLE_7863" $$unsorted) (@var "BOUND_VARIABLE_7865" $$unsorted)))) % 0.35/0.87 (step @p82 :rule alpha_equiv :args (@t101 @t99 (@list (@var "BOUND_VARIABLE_7855" $$unsorted) (@var "BOUND_VARIABLE_7857" $$unsorted)))) % 0.35/0.87 (step @p83 :rule nary_cong :premises (@p82 @p81 @p80) :args (@t102)) % 0.35/0.87 (step @p84 :rule quant-miniscope-and :args ((= @t49 @t102))) % 0.35/0.87 (step @p85 :rule trans :premises (@p84 @p83)) % 0.35/0.87 (step @p86 :rule eq_resolve :premises (@p16 @p85)) % 0.35/0.87 (step @p87 :rule and_elim :premises (@p86) :args (0)) % 0.35/0.87 (step @p88 :rule instantiate :premises (@p87) :args (@t110)) % 0.35/0.87 (step @p89 :rule aci_norm :args ((= (or @t111 @t103) @t106))) % 0.35/0.87 (step @p90 :rule refl :args (@t103)) % 0.35/0.87 (step @p91 :rule bool-and-de-morgan :args (@t18 @t14 true)) % 0.35/0.87 (step @p92 :rule nary_cong :premises (@p91 @p90) :args ((or @t112 @t103))) % 0.35/0.87 (step @p93 :rule trans :premises (@p92 @p89)) % 0.35/0.87 (step @p94 :rule bool-impl-elim :args (@t72 @t103)) % 0.35/0.87 (step @p95 :rule trans :premises (@p94 @p93)) % 0.35/0.87 (step @p96 :rule cong :premises (@p95) :args ((forall @t11 (=> @t72 @t103)))) % 0.35/0.87 (step @p97 :rule eq-symm :args (@t91 @t12)) % 0.35/0.87 (step @p98 :rule refl :args (@t72)) % 0.35/0.87 (step @p99 :rule cong :premises (@p98 @p97) :args (@t94)) % 0.35/0.87 (step @p100 :rule cong :premises (@p99) :args (@t95)) % 0.35/0.87 (step @p101 :rule trans :premises (@p100 @p96)) % 0.35/0.87 (step @p102 :rule cong :premises (@p101) :args (@t96)) % 0.35/0.87 (step @p103 :rule eq_resolve :premises (@p71 @p102)) % 0.35/0.87 (step @p104 :rule skolemize :premises (@p103)) % 0.35/0.87 (step @p105 :rule cnf_or_neg :args (@t120 2)) % 0.35/0.87 (step @p106 :rule chain_m_resolution :premises (@p105 @p104) :args ((not @t115) @t121 @t122)) % 0.35/0.87 (step @p107 :rule cnf_equiv_neg1 :args (@t115)) % 0.35/0.87 (step @p108 :rule reordering :premises (@p107) :args ((or @t114 @t113 @t115))) % 0.35/0.87 (step @p109 :rule bool-impl-elim :args (@t18 @t88)) % 0.35/0.87 (step @p110 :rule cong :premises (@p109) :args (@t89)) % 0.35/0.87 (step @p111 :rule eq_resolve :premises (@p69 @p110)) % 0.35/0.87 (step @p112 :rule instantiate :premises (@p111) :args (@t123)) % 0.35/0.87 (step @p113 :rule bool-double-not-elim :args (@t118)) % 0.35/0.87 (step @p114 :rule refl :args (@t120)) % 0.35/0.87 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((or @t120 (not @t119)))) % 0.35/0.87 (step @p116 :rule cnf_or_neg :args (@t120 0)) % 0.35/0.87 (step @p117 :rule eq_resolve :premises (@p116 @p115)) % 0.35/0.87 (step @p118 :rule reordering :premises (@p117) :args ((or @t118 @t120))) % 0.35/0.87 (step @p119 :rule chain_m_resolution :premises (@p118 @p104) :args (@t118 @t121 @t122)) % 0.35/0.87 (step @p120 :rule cnf_or_pos :args (@t126)) % 0.35/0.87 (step @p121 :rule reordering :premises (@p120) :args ((or @t119 @t125 (not @t126)))) % 0.35/0.87 (step @p122 :rule chain_m_resolution :premises (@p121 @p119 @p112) :args (@t125 @t127 (@list @t118 @t126))) % 0.35/0.87 (step @p123 :rule aci_norm :args ((= (or (or @t129 @t128) @t12) (or @t129 @t128 @t12)))) % 0.35/0.87 (step @p124 :rule refl :args (@t12)) % 0.35/0.87 (step @p125 :rule bool-and-de-morgan :args (@t84 @t25 true)) % 0.35/0.87 (step @p126 :rule nary_cong :premises (@p125 @p124) :args ((or (not @t85) @t12))) % 0.35/0.87 (step @p127 :rule trans :premises (@p126 @p123)) % 0.35/0.87 (step @p128 :rule bool-impl-elim :args (@t85 @t12)) % 0.35/0.87 (step @p129 :rule trans :premises (@p128 @p127)) % 0.35/0.87 (step @p130 :rule cong :premises (@p129) :args (@t86)) % 0.35/0.87 (step @p131 :rule eq_resolve :premises (@p66 @p130)) % 0.35/0.87 (step @p132 :rule instantiate :premises (@p131) :args ((@list @t107 @t124))) % 0.35/0.87 (step @p133 :rule cnf_or_pos :args (@t133)) % 0.35/0.87 (step @p134 :rule reordering :premises (@p133) :args ((or @t114 @t132 @t131 (not @t133)))) % 0.35/0.87 (step @p135 :rule bool-double-not-elim :args (@t116)) % 0.35/0.87 (step @p136 :rule nary_cong :premises (@p114 @p135) :args ((or @t120 (not @t117)))) % 0.35/0.87 (step @p137 :rule cnf_or_neg :args (@t120 1)) % 0.35/0.87 (step @p138 :rule eq_resolve :premises (@p137 @p136)) % 0.35/0.87 (step @p139 :rule reordering :premises (@p138) :args ((or @t116 @t120))) % 0.35/0.87 (step @p140 :rule chain_m_resolution :premises (@p139 @p104) :args (@t116 @t121 @t122)) % 0.35/0.87 (step @p141 :rule aci_norm :args ((= (or @t111 (or @t134 @t90)) (or @t105 @t104 @t134 @t90)))) % 0.35/0.87 (step @p142 :rule bool-impl-elim :args (@t91 @t90)) % 0.35/0.87 (step @p143 :rule nary_cong :premises (@p91 @p142) :args ((or @t112 @t92))) % 0.35/0.87 (step @p144 :rule trans :premises (@p143 @p141)) % 0.35/0.87 (step @p145 :rule bool-impl-elim :args (@t72 @t92)) % 0.35/0.87 (step @p146 :rule trans :premises (@p145 @p144)) % 0.35/0.87 (step @p147 :rule cong :premises (@p146) :args (@t93)) % 0.35/0.87 (step @p148 :rule eq_resolve :premises (@p70 @p147)) % 0.35/0.87 (step @p149 :rule instantiate :premises (@p148) :args (@t123)) % 0.35/0.87 (step @p150 :rule cnf_or_pos :args (@t137)) % 0.35/0.87 (step @p151 :rule reordering :premises (@p150) :args ((or @t119 @t117 @t136 @t135 (not @t137)))) % 0.35/0.87 (step @p152 :rule aci_norm :args ((= (or (or @t138 @t128) @t58) (or @t138 @t128 @t58)))) % 0.35/0.87 (step @p153 :rule refl :args (@t58)) % 0.35/0.87 (step @p154 :rule bool-and-de-morgan :args (@t12 @t25 true)) % 0.35/0.87 (step @p155 :rule nary_cong :premises (@p154 @p153) :args ((or (not @t59) @t58))) % 0.35/0.87 (step @p156 :rule trans :premises (@p155 @p152)) % 0.35/0.87 (step @p157 :rule bool-impl-elim :args (@t59 @t58)) % 0.35/0.87 (step @p158 :rule trans :premises (@p157 @p156)) % 0.35/0.87 (step @p159 :rule cong :premises (@p158) :args (@t60)) % 0.35/0.87 (step @p160 :rule eq_resolve :premises (@p23 @p159)) % 0.35/0.87 (step @p161 :rule instantiate :premises (@p160) :args (@t110)) % 0.35/0.87 (step @p162 :rule cnf_or_pos :args (@t140)) % 0.35/0.87 (step @p163 :rule reordering :premises (@p162) :args ((or @t136 @t139 @t130 (not @t140)))) % 0.35/0.87 (step @p164 :rule chain_m_resolution :premises (@p163 @p161 @p151 @p149 @p140 @p119 @p134 @p132 @p122 @p108 @p106) :args (@t114 (@list false false false false false true false false false true) (@list @t140 @t135 @t137 @t116 @t118 @t130 @t133 @t125 @t113 @t115))) % 0.35/0.87 (step @p165 :rule aci_norm :args ((= (or @t141 @t55) (or @t105 @t104 @t128 @t55)))) % 0.35/0.87 (step @p166 :rule refl :args (@t55)) % 0.35/0.87 (step @p167 :rule aci_norm :args ((= (or @t105 (or @t104 @t128)) @t141))) % 0.35/0.87 (step @p168 :rule bool-and-de-morgan :args (@t14 @t25 true)) % 0.35/0.87 (step @p169 :rule refl :args (@t105)) % 0.35/0.87 (step @p170 :rule nary_cong :premises (@p169 @p168) :args ((or @t105 (not (and @t14 @t25))))) % 0.35/0.87 (step @p171 :rule bool-and-de-morgan :args (@t18 @t14 (and @t25))) % 0.35/0.87 (step @p172 :rule trans :premises (@p171 @p170)) % 0.35/0.87 (step @p173 :rule trans :premises (@p172 @p167)) % 0.35/0.87 (step @p174 :rule nary_cong :premises (@p173 @p166) :args ((or (not @t56) @t55))) % 0.35/0.87 (step @p175 :rule trans :premises (@p174 @p165)) % 0.35/0.87 (step @p176 :rule bool-impl-elim :args (@t56 @t55)) % 0.35/0.87 (step @p177 :rule trans :premises (@p176 @p175)) % 0.35/0.87 (step @p178 :rule cong :premises (@p177) :args (@t57)) % 0.35/0.87 (step @p179 :rule eq_resolve :premises (@p22 @p178)) % 0.35/0.87 (step @p180 :rule instantiate :premises (@p179) :args ((@list @t142 @t107))) % 0.35/0.87 (step @p181 :rule alpha_equiv :args (@t143 @t99 (@list (@var "BOUND_VARIABLE_7845" $$unsorted) (@var "BOUND_VARIABLE_7847" $$unsorted)))) % 0.35/0.87 (step @p182 :rule alpha_equiv :args (@t144 @t99 (@list (@var "BOUND_VARIABLE_7837" $$unsorted) (@var "BOUND_VARIABLE_7839" $$unsorted)))) % 0.35/0.87 (step @p183 :rule nary_cong :premises (@p182 @p181) :args (@t145)) % 0.35/0.87 (step @p184 :rule quant-miniscope-and :args ((= @t44 @t145))) % 0.35/0.87 (step @p185 :rule trans :premises (@p184 @p183)) % 0.35/0.87 (step @p186 :rule eq_resolve :premises (@p15 @p185)) % 0.35/0.87 (step @p187 :rule and_elim :premises (@p186) :args (0)) % 0.35/0.87 (step @p188 :rule instantiate :premises (@p187) :args (@t110)) % 0.35/0.87 (step @p189 :rule true_intro :premises (@p188)) % 0.35/0.87 (step @p190 :rule eq-symm :args (@t45 @t41)) % 0.35/0.87 (step @p191 :rule cong :premises (@p190) :args (@t78)) % 0.35/0.87 (step @p192 :rule eq_resolve :premises (@p62 @p191)) % 0.35/0.87 (step @p193 :rule eq-symm :args (@t146 @t142)) % 0.35/0.87 (step @p194 :rule refl :args (@t147)) % 0.35/0.87 (step @p195 :rule cong :premises (@p194 @p193) :args ((=> @t147 @t148))) % 0.35/0.87 (assume-push @p264 @t147) % 0.35/0.87 (step @p197 :rule instantiate :premises (@p192) :args (@t110)) % 0.35/0.87 (step-pop @p265 :rule scope :premises (@p197)) % 0.35/0.87 (step @p198 :rule process_scope :premises (@p265) :args (@t148)) % 0.35/0.87 (step @p200 :rule eq_resolve :premises (@p198 @p195)) % 0.35/0.87 (step @p201 :rule implies_elim :premises (@p200)) % 0.35/0.87 (step @p202 :rule chain_m_resolution :premises (@p201 @p192) :args ((= @t142 @t146) (@list false) (@list @t147))) % 0.35/0.87 (step @p203 :rule cong :premises (@p202) :args (@t149)) % 0.35/0.87 (step @p204 :rule trans :premises (@p203 @p189)) % 0.35/0.87 (step @p205 :rule true_elim :premises (@p204)) % 0.35/0.87 (step @p206 :rule cnf_equiv_neg2 :args (@t115)) % 0.35/0.87 (step @p207 :rule chain_m_resolution :premises (@p206 @p106 @p164) :args (@t136 (@list true false) (@list @t115 @t114))) % 0.35/0.87 (step @p208 :rule false_intro :premises (@p207)) % 0.35/0.87 (step @p209 :rule aci_norm :args ((= (or @t111 @t150) (or @t105 @t104 @t150)))) % 0.35/0.87 (step @p210 :rule refl :args (@t150)) % 0.35/0.87 (step @p211 :rule nary_cong :premises (@p91 @p210) :args ((or @t112 @t150))) % 0.35/0.87 (step @p212 :rule trans :premises (@p211 @p209)) % 0.35/0.87 (step @p213 :rule bool-impl-elim :args (@t72 @t150)) % 0.35/0.87 (step @p214 :rule trans :premises (@p213 @p212)) % 0.35/0.87 (step @p215 :rule cong :premises (@p214) :args ((forall @t11 (=> @t72 @t150)))) % 0.35/0.87 (step @p216 :rule eq-symm :args (@t81 @t64)) % 0.35/0.87 (step @p217 :rule cong :premises (@p98 @p216) :args (@t82)) % 0.35/0.87 (step @p218 :rule cong :premises (@p217) :args (@t83)) % 0.35/0.87 (step @p219 :rule trans :premises (@p218 @p215)) % 0.35/0.87 (step @p220 :rule eq_resolve :premises (@p65 @p219)) % 0.35/0.87 (step @p221 :rule instantiate :premises (@p220) :args (@t123)) % 0.35/0.87 (step @p222 :rule cnf_or_pos :args (@t153)) % 0.35/0.87 (step @p223 :rule reordering :premises (@p222) :args ((or @t119 @t117 @t152 (not @t153)))) % 0.35/0.87 (step @p224 :rule chain_m_resolution :premises (@p223 @p119 @p140 @p221) :args (@t152 (@list false false false) (@list @t118 @t116 @t153))) % 0.35/0.87 (step @p225 :rule symm :premises (@p224)) % 0.35/0.87 (step @p226 :rule aci_norm :args ((= (or @t157 @t76) (or @t156 @t155 @t154 @t76)))) % 0.35/0.87 (step @p227 :rule refl :args (@t76)) % 0.35/0.87 (step @p228 :rule aci_norm :args ((= (or @t156 (or @t155 @t154)) @t157))) % 0.35/0.87 (step @p229 :rule bool-and-de-morgan :args (@t37 @t36 true)) % 0.35/0.87 (step @p230 :rule refl :args (@t156)) % 0.35/0.87 (step @p231 :rule nary_cong :premises (@p230 @p229) :args ((or @t156 (not (and @t37 @t36))))) % 0.35/0.87 (step @p232 :rule bool-and-de-morgan :args (@t38 @t37 (and @t36))) % 0.35/0.87 (step @p233 :rule trans :premises (@p232 @p231)) % 0.35/0.87 (step @p234 :rule trans :premises (@p233 @p228)) % 0.35/0.87 (step @p235 :rule nary_cong :premises (@p234 @p227) :args ((or (not @t39) @t76))) % 0.35/0.87 (step @p236 :rule trans :premises (@p235 @p226)) % 0.35/0.87 (step @p237 :rule bool-impl-elim :args (@t39 @t76)) % 0.35/0.87 (step @p238 :rule trans :premises (@p237 @p236)) % 0.35/0.87 (step @p239 :rule cong :premises (@p238) :args (@t77)) % 0.35/0.87 (step @p240 :rule eq_resolve :premises (@p61 @p239)) % 0.35/0.87 (step @p241 :rule instantiate :premises (@p240) :args ((@list @t124 @t109 @t142 @t107))) % 0.35/0.87 (step @p242 :rule eq-symm :args (@t50 @t36)) % 0.35/0.87 (step @p243 :rule cong :premises (@p242) :args (@t79)) % 0.35/0.87 (step @p244 :rule eq_resolve :premises (@p63 @p243)) % 0.35/0.87 (step @p245 :rule instantiate :premises (@p244) :args ((@list @t124 @t109 @t142))) % 0.35/0.87 (step @p246 :rule and_elim :premises (@p86) :args (2)) % 0.35/0.87 (step @p247 :rule instantiate :premises (@p246) :args (@t110)) % 0.35/0.87 (step @p248 :rule cnf_equiv_pos2 :args (@t160)) % 0.35/0.87 (step @p249 :rule reordering :premises (@p248) :args ((or @t159 (not @t158) (not @t160)))) % 0.35/0.87 (step @p250 :rule chain_m_resolution :premises (@p249 @p247 @p245) :args (@t159 @t127 (@list @t158 @t160))) % 0.35/0.87 (step @p251 :rule and_elim :premises (@p86) :args (1)) % 0.35/0.87 (step @p252 :rule instantiate :premises (@p251) :args (@t110)) % 0.35/0.87 (step @p253 :rule cnf_or_pos :args (@t168)) % 0.35/0.87 (step @p254 :rule reordering :premises (@p253) :args ((or @t167 @t165 @t163 @t162 (not @t168)))) % 0.35/0.87 (step @p255 :rule chain_m_resolution :premises (@p254 @p88 @p252 @p250 @p241) :args (@t162 (@list false false false false) (@list @t166 @t164 @t159 @t168))) % 0.35/0.88 (step @p256 :rule symm :premises (@p255)) % 0.35/0.88 (step @p257 :rule trans :premises (@p256 @p225)) % 0.35/0.88 (step @p258 :rule cong :premises (@p257) :args (@t169)) % 0.35/0.88 (step @p259 :rule trans :premises (@p258 @p208)) % 0.35/0.88 (step @p260 :rule false_elim :premises (@p259)) % 0.35/0.88 (step @p261 :rule cnf_or_pos :args (@t172)) % 0.35/0.88 (step @p262 :rule reordering :premises (@p261) :args ((or @t170 @t167 @t171 @t169 (not @t172)))) % 0.35/0.88 (step @p263 false :rule chain_m_resolution :premises (@p262 @p260 @p205 @p180 @p164 @p88) :args (false (@list true false false false false) (@list @t169 @t149 @t172 @t114 @t166))) % 0.35/0.88 ) % 0.35/0.88 % SZS output end Proof % 0.35/0.88 % cvc5 exiting %------------------------------------------------------------------------------