%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : MGT034+2 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:04:47 AM UTC 2026 % Result : Theorem 0.30s 0.63s % Output : Proof 0.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT034+2 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.13/0.38 % Computer : n008.cluster.edu % 0.13/0.38 % Model : x86_64 x86_64 % 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.38 % Memory : 8046.5625MB % 0.13/0.38 % OS : Linux 6.8.0-71-generic % 0.13/0.38 % CPULimit : 300 % 0.13/0.38 % WCLimit : 300 % 0.13/0.38 % DateTime : Mon Sep 7 12:32:53 UTC 2026 % 0.13/0.38 % CPUTime : % 0.13/0.46 %----Proving TF0_NAR, FOF, or CNF % 0.30/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.30/0.63 % SZS status Theorem % 0.30/0.63 % SZS output start Proof % 0.30/0.63 ( % 0.30/0.63 (declare-sort $$unsorted 0) % 0.30/0.63 (declare-const tptp.cardinality_at_time (-> $$unsorted $$unsorted $$unsorted)) % 0.30/0.63 (declare-const tptp.start_time (-> $$unsorted $$unsorted)) % 0.30/0.63 (declare-const tptp.selection_favors (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.30/0.63 (declare-const tptp.founding_rate (-> $$unsorted $$unsorted $$unsorted)) % 0.30/0.63 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.30/0.63 (declare-const tptp.zero $$unsorted) % 0.30/0.63 (declare-const tptp.critical_point (-> $$unsorted $$unsorted)) % 0.30/0.63 (declare-const tptp.growth_rate (-> $$unsorted $$unsorted $$unsorted)) % 0.30/0.63 (declare-const tptp.appear (-> $$unsorted $$unsorted $$unsorted)) % 0.30/0.63 (declare-const tptp.greater (-> $$unsorted $$unsorted Bool)) % 0.30/0.63 (declare-const tptp.efficient_producers $$unsorted) % 0.30/0.63 (declare-const tptp.subpopulations (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.30/0.63 (declare-const tptp.environment (-> $$unsorted Bool)) % 0.30/0.63 (declare-const tptp.disbanding_rate (-> $$unsorted $$unsorted $$unsorted)) % 0.30/0.63 (declare-const tptp.first_movers $$unsorted) % 0.30/0.63 (declare-const tptp.decreases (-> $$unsorted Bool)) % 0.30/0.63 (declare-const tptp.greater_or_equal (-> $$unsorted $$unsorted Bool)) % 0.30/0.63 (declare-const tptp.in_environment (-> $$unsorted $$unsorted Bool)) % 0.30/0.63 (define @t1 () (@var "T" $$unsorted)) % 0.30/0.63 (define @t2 () (@var "S1" $$unsorted)) % 0.30/0.63 (define @t3 () (@var "S2" $$unsorted)) % 0.30/0.63 (define @t4 () (tptp.selection_favors @t3 @t2 @t1)) % 0.30/0.63 (define @t5 () (tptp.greater (tptp.growth_rate @t3 @t1) (tptp.growth_rate @t2 @t1))) % 0.30/0.63 (define @t6 () (@var "E" $$unsorted)) % 0.30/0.63 (define @t7 () (tptp.subpopulations @t2 @t3 @t6 @t1)) % 0.30/0.63 (define @t8 () (tptp.environment @t6)) % 0.30/0.63 (define @t9 () (and @t8 @t7 @t5)) % 0.30/0.63 (define @t10 () (forall (@list @t6 @t2 @t3 @t1) (=> @t9 @t4))) % 0.30/0.63 (define @t11 () (tptp.decreases (tptp.difference (tptp.disbanding_rate tptp.first_movers @t1) (tptp.disbanding_rate tptp.efficient_producers @t1)))) % 0.30/0.63 (define @t12 () (not @t11)) % 0.30/0.63 (define @t13 () (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t6 @t1)) % 0.30/0.63 (define @t14 () (and @t8 @t13)) % 0.30/0.63 (define @t15 () (@list @t6 @t1)) % 0.30/0.63 (define @t16 () (forall @t15 (=> @t14 @t12))) % 0.30/0.63 (define @t17 () (tptp.critical_point @t6)) % 0.30/0.63 (define @t18 () (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t6 @t17)) % 0.30/0.63 (define @t19 () (tptp.in_environment @t6 @t17)) % 0.30/0.63 (define @t20 () (and @t8 @t19)) % 0.30/0.63 (define @t21 () (@list @t6)) % 0.30/0.63 (define @t22 () (forall @t21 (=> @t20 @t18))) % 0.30/0.63 (define @t23 () (tptp.appear tptp.efficient_producers @t6)) % 0.30/0.63 (define @t24 () (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t6 @t23)) % 0.30/0.63 (define @t25 () (tptp.in_environment @t6 @t23)) % 0.30/0.63 (define @t26 () (and @t8 @t25)) % 0.30/0.63 (define @t27 () (forall @t21 (=> @t26 @t24))) % 0.30/0.63 (define @t28 () (tptp.growth_rate tptp.efficient_producers @t1)) % 0.30/0.63 (define @t29 () (tptp.growth_rate tptp.first_movers @t1)) % 0.30/0.63 (define @t30 () (tptp.difference @t29 @t28)) % 0.30/0.63 (define @t31 () (tptp.decreases @t30)) % 0.30/0.63 (define @t32 () (tptp.decreases (tptp.difference (tptp.founding_rate tptp.first_movers @t1) (tptp.founding_rate tptp.efficient_producers @t1)))) % 0.30/0.63 (define @t33 () (and @t32 @t12)) % 0.30/0.63 (define @t34 () (@list @t1)) % 0.30/0.63 (define @t35 () (forall @t34 (=> @t33 @t31))) % 0.30/0.63 (define @t36 () (tptp.greater @t30 tptp.zero)) % 0.30/0.63 (define @t37 () (=> @t31 @t36)) % 0.30/0.63 (define @t38 () (@var "To" $$unsorted)) % 0.30/0.63 (define @t39 () (tptp.greater @t38 @t1)) % 0.30/0.63 (define @t40 () (tptp.greater_or_equal @t1 @t23)) % 0.30/0.63 (define @t41 () (tptp.greater_or_equal (tptp.difference (tptp.growth_rate tptp.first_movers @t38) (tptp.growth_rate tptp.efficient_producers @t38)) tptp.zero)) % 0.30/0.63 (define @t42 () (tptp.in_environment @t6 @t38)) % 0.30/0.63 (define @t43 () (and @t8 @t42 @t41 @t40 @t39)) % 0.30/0.63 (define @t44 () (forall (@list @t6 @t1 @t38) (=> @t43 @t37))) % 0.30/0.63 (define @t45 () (tptp.greater @t28 @t29)) % 0.30/0.63 (define @t46 () (tptp.greater tptp.zero @t30)) % 0.30/0.63 (define @t47 () (forall @t34 (= @t46 @t45))) % 0.30/0.63 (define @t48 () (tptp.in_environment @t6 @t1)) % 0.30/0.63 (define @t49 () (@var "T1" $$unsorted)) % 0.30/0.63 (define @t50 () (tptp.greater_or_equal @t1 @t49)) % 0.30/0.63 (define @t51 () (@var "T2" $$unsorted)) % 0.30/0.63 (define @t52 () (tptp.greater_or_equal @t51 @t1)) % 0.30/0.63 (define @t53 () (tptp.in_environment @t6 @t51)) % 0.30/0.63 (define @t54 () (tptp.in_environment @t6 @t49)) % 0.30/0.63 (define @t55 () (and @t8 @t54 @t53 @t52 @t50)) % 0.30/0.63 (define @t56 () (@list @t6 @t49 @t51 @t1)) % 0.30/0.63 (define @t57 () (forall @t56 (=> @t55 @t48))) % 0.30/0.63 (define @t58 () (tptp.start_time @t6)) % 0.30/0.63 (define @t59 () (tptp.greater @t17 @t1)) % 0.30/0.63 (define @t60 () (and @t8 @t19 @t40 @t59)) % 0.30/0.63 (define @t61 () (forall @t15 (=> @t60 @t48))) % 0.30/0.63 (define @t62 () (tptp.subpopulations tptp.efficient_producers tptp.first_movers @t6 @t1)) % 0.30/0.63 (define @t63 () (forall @t15 (=> @t14 @t62))) % 0.30/0.63 (define @t64 () (forall @t15 (=> @t14 @t40))) % 0.30/0.63 (define @t65 () (@var "Y" $$unsorted)) % 0.30/0.63 (define @t66 () (@var "X" $$unsorted)) % 0.30/0.63 (define @t67 () (forall (@list @t66 @t65) (= (tptp.greater_or_equal @t66 @t65) (or (tptp.greater @t66 @t65) (= @t66 @t65))))) % 0.30/0.63 (define @t68 () (tptp.greater_or_equal @t30 tptp.zero)) % 0.30/0.63 (define @t69 () (not @t46)) % 0.30/0.63 (define @t70 () (and @t8 @t13 @t69)) % 0.30/0.63 (define @t71 () (forall @t15 (=> @t70 @t68))) % 0.30/0.63 (define @t72 () (@var "Tc" $$unsorted)) % 0.30/0.63 (define @t73 () (tptp.greater @t1 @t72)) % 0.30/0.63 (define @t74 () (and @t13 @t73)) % 0.30/0.63 (define @t75 () (forall @t34 (=> @t74 @t45))) % 0.30/0.63 (define @t76 () (not (tptp.greater (tptp.growth_rate tptp.efficient_producers @t72) (tptp.growth_rate tptp.first_movers @t72)))) % 0.30/0.63 (define @t77 () (and @t76 @t75)) % 0.30/0.63 (define @t78 () (= @t72 @t17)) % 0.30/0.63 (define @t79 () (and @t8 @t78)) % 0.30/0.63 (define @t80 () (=> @t79 @t77)) % 0.30/0.63 (define @t81 () (@list @t6 @t72)) % 0.30/0.63 (define @t82 () (forall @t81 @t80)) % 0.30/0.63 (define @t83 () (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t6 @t51)) % 0.30/0.63 (define @t84 () (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t6 @t49)) % 0.30/0.63 (define @t85 () (and @t8 @t84 @t83 @t50 @t52)) % 0.30/0.63 (define @t86 () (forall @t56 (=> @t85 @t13))) % 0.30/0.63 (define @t87 () (forall @t15 (=> @t14 @t32))) % 0.30/0.63 (define @t88 () (tptp.selection_favors tptp.first_movers tptp.efficient_producers @t1)) % 0.30/0.63 (define @t89 () (forall @t15 (=> @t60 @t88))) % 0.30/0.63 (define @t90 () (not @t89)) % 0.30/0.63 (define @t91 () (not @t59)) % 0.30/0.63 (define @t92 () (not @t40)) % 0.30/0.63 (define @t93 () (not @t19)) % 0.30/0.63 (define @t94 () (not @t8)) % 0.30/0.63 (define @t95 () (or @t94 @t93 @t92 @t91 @t88)) % 0.30/0.63 (define @t96 () (or @t94 @t93 @t92 @t91)) % 0.30/0.63 (define @t97 () (not @t60)) % 0.30/0.63 (define @t98 () (forall @t15 @t95)) % 0.30/0.63 (define @t99 () (@quantifiers_skolemize @t98 0)) % 0.30/0.63 (define @t100 () (tptp.environment @t99)) % 0.30/0.63 (define @t101 () (@quantifiers_skolemize @t98 1)) % 0.30/0.63 (define @t102 () (tptp.selection_favors tptp.first_movers tptp.efficient_producers @t101)) % 0.30/0.63 (define @t103 () (tptp.critical_point @t99)) % 0.30/0.63 (define @t104 () (tptp.greater @t103 @t101)) % 0.30/0.63 (define @t105 () (not @t104)) % 0.30/0.63 (define @t106 () (tptp.appear tptp.efficient_producers @t99)) % 0.30/0.63 (define @t107 () (tptp.greater_or_equal @t101 @t106)) % 0.30/0.63 (define @t108 () (not @t107)) % 0.30/0.63 (define @t109 () (tptp.in_environment @t99 @t103)) % 0.30/0.63 (define @t110 () (not @t109)) % 0.30/0.63 (define @t111 () (not @t100)) % 0.30/0.63 (define @t112 () (or @t111 @t110 @t108 @t105 @t102)) % 0.30/0.63 (define @t113 () (@list true)) % 0.30/0.63 (define @t114 () (@list @t112)) % 0.30/0.63 (define @t115 () (not @t31)) % 0.30/0.63 (define @t116 () (not @t39)) % 0.30/0.63 (define @t117 () (not @t41)) % 0.30/0.63 (define @t118 () (not @t42)) % 0.30/0.63 (define @t119 () (or @t94 @t118 @t117 @t92 @t116)) % 0.30/0.63 (define @t120 () (not @t13)) % 0.30/0.63 (define @t121 () (not @t69)) % 0.30/0.63 (define @t122 () (or @t94 @t120 @t121)) % 0.30/0.63 (define @t123 () (@list @t99 @t103)) % 0.30/0.63 (define @t124 () (tptp.growth_rate tptp.efficient_producers @t103)) % 0.30/0.63 (define @t125 () (tptp.growth_rate tptp.first_movers @t103)) % 0.30/0.63 (define @t126 () (tptp.difference @t125 @t124)) % 0.30/0.63 (define @t127 () (tptp.greater tptp.zero @t126)) % 0.30/0.63 (define @t128 () (tptp.greater @t124 @t125)) % 0.30/0.63 (define @t129 () (= @t127 @t128)) % 0.30/0.63 (define @t130 () (= @t128 @t127)) % 0.30/0.63 (define @t131 () (@list false)) % 0.30/0.63 (define @t132 () (@var "BOUND_VARIABLE_7674" $$unsorted)) % 0.30/0.63 (define @t133 () (tptp.greater (tptp.growth_rate tptp.efficient_producers @t132) (tptp.growth_rate tptp.first_movers @t132))) % 0.30/0.63 (define @t134 () (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t6 @t132))) % 0.30/0.63 (define @t135 () (and (not (tptp.greater (tptp.growth_rate tptp.efficient_producers @t17) (tptp.growth_rate tptp.first_movers @t17))) (or @t134 (not (tptp.greater @t132 @t17)) @t133))) % 0.30/0.63 (define @t136 () (not (= @t17 @t17))) % 0.30/0.63 (define @t137 () (or @t94 @t136 @t135)) % 0.30/0.63 (define @t138 () (@list @t6 @t132)) % 0.30/0.63 (define @t139 () (or @t134 (not (tptp.greater @t132 @t72)) @t133)) % 0.30/0.63 (define @t140 () (and @t76 @t139)) % 0.30/0.63 (define @t141 () (= @t17 @t72)) % 0.30/0.63 (define @t142 () (not @t141)) % 0.30/0.63 (define @t143 () (@list @t72)) % 0.30/0.63 (define @t144 () (or @t142 @t94 @t142 @t140)) % 0.30/0.63 (define @t145 () (or @t94 @t142 @t140)) % 0.30/0.63 (define @t146 () (forall @t143 @t145)) % 0.30/0.63 (define @t147 () (forall @t138 @t146)) % 0.30/0.63 (define @t148 () (forall (@list @t6 @t132 @t72) @t145)) % 0.30/0.63 (define @t149 () (forall (@list @t6 @t72 @t132) @t145)) % 0.30/0.63 (define @t150 () (@list @t132)) % 0.30/0.63 (define @t151 () (forall @t150 @t145)) % 0.30/0.63 (define @t152 () (forall @t150 @t139)) % 0.30/0.63 (define @t153 () (forall @t150 @t76)) % 0.30/0.63 (define @t154 () (and @t153 @t152)) % 0.30/0.63 (define @t155 () (forall @t150 @t140)) % 0.30/0.63 (define @t156 () (or @t94 @t142 @t155)) % 0.30/0.63 (define @t157 () (not @t73)) % 0.30/0.63 (define @t158 () (or @t120 @t157 @t45)) % 0.30/0.63 (define @t159 () (and @t76 (forall @t34 @t158))) % 0.30/0.63 (define @t160 () (or @t94 @t142 @t159)) % 0.30/0.63 (define @t161 () (and @t8 @t141)) % 0.30/0.63 (define @t162 () (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t99 @t103)) % 0.30/0.63 (define @t163 () (not @t162)) % 0.30/0.63 (define @t164 () (not @t128)) % 0.30/0.63 (define @t165 () (and @t164 (or @t163 (not (tptp.greater @t103 @t103)) @t128))) % 0.30/0.63 (define @t166 () (or @t111 @t165)) % 0.30/0.63 (define @t167 () (@list false false)) % 0.30/0.63 (define @t168 () (not @t127)) % 0.30/0.63 (define @t169 () (@list true false)) % 0.30/0.63 (define @t170 () (@list @t99)) % 0.30/0.63 (define @t171 () (or @t111 @t110 @t162)) % 0.30/0.63 (define @t172 () (@list false false false)) % 0.30/0.63 (define @t173 () (tptp.greater_or_equal @t126 tptp.zero)) % 0.30/0.63 (define @t174 () (or @t111 @t163 @t127 @t173)) % 0.30/0.63 (define @t175 () (not @t32)) % 0.30/0.63 (define @t176 () (@list @t101)) % 0.30/0.63 (define @t177 () (or @t94 @t120)) % 0.30/0.63 (define @t178 () (not @t14)) % 0.30/0.63 (define @t179 () (@list @t99 @t101)) % 0.30/0.63 (define @t180 () (not @t52)) % 0.30/0.63 (define @t181 () (not @t50)) % 0.30/0.63 (define @t182 () (not @t83)) % 0.30/0.63 (define @t183 () (not @t84)) % 0.30/0.63 (define @t184 () (or @t94 @t183 @t182 @t181 @t180)) % 0.30/0.63 (define @t185 () (or @t104 (= @t103 @t101))) % 0.30/0.63 (define @t186 () (tptp.greater_or_equal @t103 @t101)) % 0.30/0.63 (define @t187 () (= @t186 @t185)) % 0.30/0.63 (define @t188 () (or @t104 (= @t101 @t103))) % 0.30/0.63 (define @t189 () (= @t186 @t188)) % 0.30/0.63 (define @t190 () (@list @t67)) % 0.30/0.63 (define @t191 () (not @t25)) % 0.30/0.63 (define @t192 () (not @t53)) % 0.30/0.63 (define @t193 () (not @t54)) % 0.30/0.63 (define @t194 () (or @t94 @t193 @t192 @t180 @t181)) % 0.30/0.63 (define @t195 () (tptp.in_environment @t99 @t101)) % 0.30/0.63 (define @t196 () (or @t111 @t110 @t108 @t105 @t195)) % 0.30/0.63 (define @t197 () (tptp.in_environment @t99 @t106)) % 0.30/0.63 (define @t198 () (tptp.greater_or_equal @t106 @t103)) % 0.30/0.63 (define @t199 () (not @t198)) % 0.30/0.63 (define @t200 () (not @t195)) % 0.30/0.63 (define @t201 () (or @t111 @t110 @t200 @t108 @t199 @t197)) % 0.30/0.63 (define @t202 () (tptp.greater_or_equal @t106 @t106)) % 0.30/0.63 (define @t203 () (tptp.greater @t106 @t106)) % 0.30/0.63 (define @t204 () (or @t203 (= @t106 @t106))) % 0.30/0.63 (define @t205 () (= @t202 @t204)) % 0.30/0.63 (define @t206 () (tptp.greater @t103 @t106)) % 0.30/0.63 (define @t207 () (not @t206)) % 0.30/0.63 (define @t208 () (not @t202)) % 0.30/0.63 (define @t209 () (or @t111 @t110 @t208 @t207 @t197)) % 0.30/0.63 (define @t210 () (tptp.greater @t106 @t103)) % 0.30/0.63 (define @t211 () (or @t210 (= @t106 @t103))) % 0.23/0.63 (define @t212 () (= @t198 @t211)) % 0.23/0.63 (define @t213 () (= @t103 @t106)) % 0.23/0.63 (define @t214 () (or @t210 @t213)) % 0.23/0.63 (define @t215 () (= @t198 @t214)) % 0.23/0.63 (define @t216 () (tptp.greater_or_equal @t103 @t106)) % 0.23/0.63 (define @t217 () (or @t111 @t163 @t216)) % 0.23/0.63 (define @t218 () (or @t206 @t213)) % 0.23/0.63 (define @t219 () (= @t216 @t218)) % 0.23/0.63 (define @t220 () (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t99 @t106)) % 0.23/0.63 (define @t221 () (not @t197)) % 0.23/0.63 (define @t222 () (or @t111 @t221 @t220)) % 0.23/0.63 (define @t223 () (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t99 @t101)) % 0.23/0.63 (define @t224 () (not @t186)) % 0.23/0.63 (define @t225 () (not @t220)) % 0.23/0.63 (define @t226 () (or @t111 @t225 @t163 @t108 @t224 @t223)) % 0.23/0.63 (define @t227 () (tptp.decreases (tptp.difference (tptp.disbanding_rate tptp.first_movers @t101) (tptp.disbanding_rate tptp.efficient_producers @t101)))) % 0.23/0.63 (define @t228 () (not @t227)) % 0.23/0.63 (define @t229 () (not @t223)) % 0.23/0.63 (define @t230 () (or @t111 @t229 @t228)) % 0.23/0.63 (define @t231 () (tptp.decreases (tptp.difference (tptp.founding_rate tptp.first_movers @t101) (tptp.founding_rate tptp.efficient_producers @t101)))) % 0.23/0.63 (define @t232 () (or @t111 @t229 @t231)) % 0.23/0.63 (define @t233 () (tptp.growth_rate tptp.efficient_producers @t101)) % 0.23/0.63 (define @t234 () (tptp.growth_rate tptp.first_movers @t101)) % 0.23/0.63 (define @t235 () (tptp.difference @t234 @t233)) % 0.23/0.63 (define @t236 () (tptp.decreases @t235)) % 0.23/0.63 (define @t237 () (not @t231)) % 0.23/0.63 (define @t238 () (or @t237 @t227 @t236)) % 0.23/0.63 (define @t239 () (not @t5)) % 0.23/0.63 (define @t240 () (not @t7)) % 0.23/0.63 (define @t241 () (or @t94 @t240 @t239)) % 0.23/0.63 (define @t242 () (tptp.subpopulations tptp.efficient_producers tptp.first_movers @t99 @t101)) % 0.23/0.63 (define @t243 () (or @t111 @t229 @t242)) % 0.23/0.63 (define @t244 () (tptp.greater @t234 @t233)) % 0.23/0.63 (define @t245 () (not @t244)) % 0.23/0.63 (define @t246 () (not @t242)) % 0.23/0.63 (define @t247 () (or @t111 @t246 @t245 @t102)) % 0.23/0.63 (define @t248 () (tptp.greater @t235 tptp.zero)) % 0.23/0.63 (define @t249 () (= @t248 @t244)) % 0.23/0.63 (define @t250 () (not @t248)) % 0.23/0.63 (define @t251 () (not @t236)) % 0.23/0.63 (define @t252 () (not @t173)) % 0.23/0.63 (define @t253 () (or @t111 @t110 @t252 @t108 @t105 @t251 @t248)) % 0.23/0.63 (assume @p1 @t10) % 0.23/0.63 (assume @p2 @t16) % 0.23/0.63 (assume @p3 @t22) % 0.23/0.63 (assume @p4 @t27) % 0.23/0.63 (assume @p5 @t35) % 0.23/0.63 (assume @p6 @t44) % 0.23/0.63 (assume @p7 @t47) % 0.23/0.63 (assume @p8 (forall @t34 (= @t36 (tptp.greater @t29 @t28)))) % 0.23/0.63 (assume @p9 @t57) % 0.23/0.63 (assume @p10 (forall @t21 (=> @t8 (tptp.in_environment @t6 @t58)))) % 0.23/0.63 (assume @p11 (forall @t21 (=> @t8 (tptp.greater_or_equal (tptp.appear tptp.first_movers @t6) @t58)))) % 0.23/0.63 (assume @p12 @t61) % 0.23/0.63 (assume @p13 (forall @t15 (=> (and @t8 @t48 (tptp.greater (tptp.cardinality_at_time tptp.first_movers @t1) tptp.zero) (tptp.greater (tptp.cardinality_at_time tptp.efficient_producers @t1) tptp.zero)) @t13))) % 0.23/0.63 (assume @p14 @t63) % 0.23/0.63 (assume @p15 @t64) % 0.23/0.63 (assume @p16 @t67) % 0.23/0.63 (assume @p17 @t71) % 0.23/0.63 (assume @p18 @t82) % 0.23/0.63 (assume @p19 @t86) % 0.23/0.63 (assume @p20 @t87) % 0.23/0.63 (assume @p21 @t90) % 0.23/0.63 (assume @p22 true) % 0.23/0.63 (step @p23 :rule aci_norm :args ((= (or @t96 @t88) @t95))) % 0.23/0.63 (step @p24 :rule refl :args (@t88)) % 0.23/0.63 (step @p25 :rule aci_norm :args ((= (or @t94 (or @t93 (or @t92 @t91))) @t96))) % 0.23/0.63 (step @p26 :rule bool-and-de-morgan :args (@t40 @t59 true)) % 0.23/0.63 (step @p27 :rule refl :args (@t93)) % 0.23/0.63 (step @p28 :rule nary_cong :premises (@p27 @p26) :args ((or @t93 (not (and @t40 @t59))))) % 0.23/0.63 (step @p29 :rule bool-and-de-morgan :args (@t19 @t40 (and @t59))) % 0.23/0.63 (step @p30 :rule trans :premises (@p29 @p28)) % 0.23/0.63 (step @p31 :rule refl :args (@t94)) % 0.23/0.63 (step @p32 :rule nary_cong :premises (@p31 @p30) :args ((or @t94 (not (and @t19 @t40 @t59))))) % 0.23/0.63 (step @p33 :rule bool-and-de-morgan :args (@t8 @t19 (and @t40 @t59))) % 0.23/0.63 (step @p34 :rule trans :premises (@p33 @p32)) % 0.23/0.63 (step @p35 :rule trans :premises (@p34 @p25)) % 0.23/0.63 (step @p36 :rule nary_cong :premises (@p35 @p24) :args ((or @t97 @t88))) % 0.23/0.63 (step @p37 :rule trans :premises (@p36 @p23)) % 0.23/0.63 (step @p38 :rule bool-impl-elim :args (@t60 @t88)) % 0.23/0.63 (step @p39 :rule trans :premises (@p38 @p37)) % 0.23/0.63 (step @p40 :rule cong :premises (@p39) :args (@t89)) % 0.23/0.63 (step @p41 :rule cong :premises (@p40) :args (@t90)) % 0.23/0.63 (step @p42 :rule eq_resolve :premises (@p21 @p41)) % 0.23/0.63 (step @p43 :rule skolemize :premises (@p42)) % 0.23/0.63 (step @p44 :rule bool-double-not-elim :args (@t100)) % 0.23/0.63 (step @p45 :rule refl :args (@t112)) % 0.23/0.63 (step @p46 :rule nary_cong :premises (@p45 @p44) :args ((or @t112 (not @t111)))) % 0.23/0.63 (step @p47 :rule cnf_or_neg :args (@t112 0)) % 0.23/0.63 (step @p48 :rule eq_resolve :premises (@p47 @p46)) % 0.23/0.63 (step @p49 :rule reordering :premises (@p48) :args ((or @t100 @t112))) % 0.23/0.63 (step @p50 :rule chain_m_resolution :premises (@p49 @p43) :args (@t100 @t113 @t114)) % 0.23/0.63 (step @p51 :rule bool-double-not-elim :args (@t109)) % 0.23/0.63 (step @p52 :rule nary_cong :premises (@p45 @p51) :args ((or @t112 (not @t110)))) % 0.23/0.63 (step @p53 :rule cnf_or_neg :args (@t112 1)) % 0.23/0.63 (step @p54 :rule eq_resolve :premises (@p53 @p52)) % 0.23/0.63 (step @p55 :rule reordering :premises (@p54) :args ((or @t109 @t112))) % 0.23/0.63 (step @p56 :rule chain_m_resolution :premises (@p55 @p43) :args (@t109 @t113 @t114)) % 0.23/0.63 (step @p57 :rule bool-double-not-elim :args (@t107)) % 0.23/0.63 (step @p58 :rule nary_cong :premises (@p45 @p57) :args ((or @t112 (not @t108)))) % 0.23/0.63 (step @p59 :rule cnf_or_neg :args (@t112 2)) % 0.23/0.63 (step @p60 :rule eq_resolve :premises (@p59 @p58)) % 0.23/0.63 (step @p61 :rule reordering :premises (@p60) :args ((or @t107 @t112))) % 0.23/0.63 (step @p62 :rule chain_m_resolution :premises (@p61 @p43) :args (@t107 @t113 @t114)) % 0.23/0.63 (step @p63 :rule bool-double-not-elim :args (@t104)) % 0.23/0.63 (step @p64 :rule nary_cong :premises (@p45 @p63) :args ((or @t112 (not @t105)))) % 0.23/0.63 (step @p65 :rule cnf_or_neg :args (@t112 3)) % 0.23/0.63 (step @p66 :rule eq_resolve :premises (@p65 @p64)) % 0.23/0.63 (step @p67 :rule reordering :premises (@p66) :args ((or @t104 @t112))) % 0.23/0.63 (step @p68 :rule chain_m_resolution :premises (@p67 @p43) :args (@t104 @t113 @t114)) % 0.23/0.63 (step @p69 :rule aci_norm :args ((= (or @t119 (or @t115 @t36)) (or @t94 @t118 @t117 @t92 @t116 @t115 @t36)))) % 0.23/0.63 (step @p70 :rule bool-impl-elim :args (@t31 @t36)) % 0.23/0.63 (step @p71 :rule aci_norm :args ((= (or @t94 (or @t118 (or @t117 (or @t92 @t116)))) @t119))) % 0.23/0.63 (step @p72 :rule bool-and-de-morgan :args (@t40 @t39 true)) % 0.23/0.63 (step @p73 :rule refl :args (@t117)) % 0.23/0.63 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or @t117 (not (and @t40 @t39))))) % 0.23/0.63 (step @p75 :rule bool-and-de-morgan :args (@t41 @t40 (and @t39))) % 0.23/0.63 (step @p76 :rule trans :premises (@p75 @p74)) % 0.23/0.63 (step @p77 :rule refl :args (@t118)) % 0.23/0.63 (step @p78 :rule nary_cong :premises (@p77 @p76) :args ((or @t118 (not (and @t41 @t40 @t39))))) % 0.23/0.63 (step @p79 :rule bool-and-de-morgan :args (@t42 @t41 (and @t40 @t39))) % 0.23/0.63 (step @p80 :rule trans :premises (@p79 @p78)) % 0.23/0.63 (step @p81 :rule nary_cong :premises (@p31 @p80) :args ((or @t94 (not (and @t42 @t41 @t40 @t39))))) % 0.23/0.63 (step @p82 :rule bool-and-de-morgan :args (@t8 @t42 (and @t41 @t40 @t39))) % 0.23/0.63 (step @p83 :rule trans :premises (@p82 @p81)) % 0.23/0.63 (step @p84 :rule trans :premises (@p83 @p71)) % 0.23/0.63 (step @p85 :rule nary_cong :premises (@p84 @p70) :args ((or (not @t43) @t37))) % 0.23/0.63 (step @p86 :rule trans :premises (@p85 @p69)) % 0.23/0.63 (step @p87 :rule bool-impl-elim :args (@t43 @t37)) % 0.23/0.63 (step @p88 :rule trans :premises (@p87 @p86)) % 0.23/0.63 (step @p89 :rule cong :premises (@p88) :args (@t44)) % 0.23/0.63 (step @p90 :rule eq_resolve :premises (@p6 @p89)) % 0.23/0.63 (step @p91 :rule instantiate :premises (@p90) :args ((@list @t99 @t101 @t103))) % 0.23/0.63 (step @p92 :rule aci_norm :args ((= (or (or @t94 @t120 @t46) @t68) (or @t94 @t120 @t46 @t68)))) % 0.23/0.63 (step @p93 :rule refl :args (@t68)) % 0.23/0.63 (step @p94 :rule bool-double-not-elim :args (@t46)) % 0.23/0.63 (step @p95 :rule refl :args (@t120)) % 0.23/0.63 (step @p96 :rule nary_cong :premises (@p31 @p95 @p94) :args (@t122)) % 0.23/0.63 (step @p97 :rule aci_norm :args ((= (or @t94 (or @t120 @t121)) @t122))) % 0.23/0.63 (step @p98 :rule trans :premises (@p97 @p96)) % 0.23/0.63 (step @p99 :rule bool-and-de-morgan :args (@t13 @t69 true)) % 0.23/0.63 (step @p100 :rule nary_cong :premises (@p31 @p99) :args ((or @t94 (not (and @t13 @t69))))) % 0.23/0.63 (step @p101 :rule bool-and-de-morgan :args (@t8 @t13 (and @t69))) % 0.23/0.63 (step @p102 :rule trans :premises (@p101 @p100)) % 0.23/0.63 (step @p103 :rule trans :premises (@p102 @p98)) % 0.23/0.63 (step @p104 :rule nary_cong :premises (@p103 @p93) :args ((or (not @t70) @t68))) % 0.23/0.63 (step @p105 :rule trans :premises (@p104 @p92)) % 0.23/0.63 (step @p106 :rule bool-impl-elim :args (@t70 @t68)) % 0.23/0.63 (step @p107 :rule trans :premises (@p106 @p105)) % 0.23/0.63 (step @p108 :rule cong :premises (@p107) :args (@t71)) % 0.23/0.63 (step @p109 :rule eq_resolve :premises (@p17 @p108)) % 0.23/0.63 (step @p110 :rule instantiate :premises (@p109) :args (@t123)) % 0.23/0.63 (step @p111 :rule eq-symm :args (@t127 @t128)) % 0.23/0.63 (step @p112 :rule refl :args (@t47)) % 0.23/0.63 (step @p113 :rule cong :premises (@p112 @p111) :args ((=> @t47 @t129))) % 0.23/0.63 (assume-push @p443 @t47) % 0.23/0.63 (step @p115 :rule instantiate :premises (@p7) :args ((@list @t103))) % 0.23/0.63 (step-pop @p444 :rule scope :premises (@p115)) % 0.23/0.63 (step @p116 :rule process_scope :premises (@p444) :args (@t129)) % 0.23/0.63 (step @p118 :rule eq_resolve :premises (@p116 @p113)) % 0.23/0.63 (step @p119 :rule implies_elim :premises (@p118)) % 0.23/0.63 (step @p120 :rule chain_m_resolution :premises (@p119 @p7) :args (@t130 @t131 (@list @t47))) % 0.23/0.63 (step @p121 :rule aci_norm :args ((= (or @t94 false @t135) (or @t94 @t135)))) % 0.23/0.63 (step @p122 :rule refl :args (@t135)) % 0.23/0.63 (step @p123 :rule evaluate :args ((not true))) % 0.23/0.63 (step @p124 :rule eq-refl :args (@t17)) % 0.23/0.63 (step @p125 :rule cong :premises (@p124) :args (@t136)) % 0.23/0.63 (step @p126 :rule trans :premises (@p125 @p123)) % 0.23/0.63 (step @p127 :rule refl :args (@t94)) % 0.23/0.63 (step @p128 :rule nary_cong :premises (@p127 @p126 @p122) :args (@t137)) % 0.23/0.63 (step @p129 :rule trans :premises (@p128 @p121)) % 0.23/0.63 (step @p130 :rule cong :premises (@p129) :args ((forall @t138 @t137))) % 0.23/0.63 (step @p131 :rule quant-var-elim-eq :args ((= (forall @t143 (or (not @t78) @t94 @t142 @t140)) @t137))) % 0.23/0.63 (step @p132 :rule refl :args (@t140)) % 0.23/0.63 (step @p133 :rule refl :args (@t142)) % 0.23/0.63 (step @p134 :rule eq-symm :args (@t17 @t72)) % 0.23/0.63 (step @p135 :rule cong :premises (@p134) :args (@t142)) % 0.23/0.63 (step @p136 :rule nary_cong :premises (@p135 @p31 @p133 @p132) :args (@t144)) % 0.23/0.63 (step @p137 :rule aci_norm :args ((= @t145 @t144))) % 0.23/0.63 (step @p138 :rule trans :premises (@p137 @p136)) % 0.23/0.63 (step @p139 :rule cong :premises (@p138) :args (@t146)) % 0.23/0.63 (step @p140 :rule trans :premises (@p139 @p131)) % 0.23/0.63 (step @p141 :rule cong :premises (@p140) :args (@t147)) % 0.23/0.63 (step @p142 :rule quant-merge-prenex :args ((= @t147 @t148))) % 0.23/0.63 (step @p143 :rule symm :premises (@p142)) % 0.23/0.63 (step @p144 :rule quant_var_reordering :args ((= @t149 @t148))) % 0.23/0.63 (step @p145 :rule trans :premises (@p144 @p143 @p141)) % 0.23/0.63 (step @p146 :rule trans :premises (@p145 @p130)) % 0.23/0.63 (step @p147 :rule quant-merge-prenex :args ((= (forall @t81 @t151) @t149))) % 0.23/0.63 (step @p148 :rule alpha_equiv :args (@t152 (@list @t132) (@list @t1))) % 0.23/0.63 (step @p149 :rule quant-unused-vars :args ((= @t153 @t76))) % 0.23/0.63 (step @p150 :rule nary_cong :premises (@p149 @p148) :args (@t154)) % 0.23/0.63 (step @p151 :rule quant-miniscope-and :args ((= @t155 @t154))) % 0.23/0.63 (step @p152 :rule trans :premises (@p151 @p150)) % 0.23/0.63 (step @p153 :rule nary_cong :premises (@p31 @p133 @p152) :args (@t156)) % 0.23/0.63 (step @p154 :rule quant-miniscope-or :args ((= @t151 @t156))) % 0.23/0.63 (step @p155 :rule trans :premises (@p154 @p153)) % 0.23/0.63 (step @p156 :rule symm :premises (@p155)) % 0.23/0.63 (step @p157 :rule cong :premises (@p156) :args ((forall @t81 @t160))) % 0.23/0.63 (step @p158 :rule trans :premises (@p157 @p147)) % 0.23/0.63 (step @p159 :rule trans :premises (@p158 @p146)) % 0.23/0.63 (step @p160 :rule aci_norm :args ((= (or (or @t94 @t142) @t159) @t160))) % 0.23/0.63 (step @p161 :rule refl :args (@t159)) % 0.23/0.63 (step @p162 :rule bool-and-de-morgan :args (@t8 @t141 true)) % 0.23/0.63 (step @p163 :rule nary_cong :premises (@p162 @p161) :args ((or (not @t161) @t159))) % 0.23/0.63 (step @p164 :rule trans :premises (@p163 @p160)) % 0.23/0.63 (step @p165 :rule bool-impl-elim :args (@t161 @t159)) % 0.23/0.63 (step @p166 :rule trans :premises (@p165 @p164)) % 0.23/0.63 (step @p167 :rule cong :premises (@p166) :args ((forall @t81 (=> @t161 @t159)))) % 0.23/0.63 (step @p168 :rule trans :premises (@p167 @p159)) % 0.23/0.63 (step @p169 :rule aci_norm :args ((= (or (or @t120 @t157) @t45) @t158))) % 0.23/0.63 (step @p170 :rule refl :args (@t45)) % 0.23/0.63 (step @p171 :rule bool-and-de-morgan :args (@t13 @t73 true)) % 0.23/0.63 (step @p172 :rule nary_cong :premises (@p171 @p170) :args ((or (not @t74) @t45))) % 0.23/0.63 (step @p173 :rule trans :premises (@p172 @p169)) % 0.23/0.63 (step @p174 :rule bool-impl-elim :args (@t74 @t45)) % 0.23/0.63 (step @p175 :rule trans :premises (@p174 @p173)) % 0.23/0.63 (step @p176 :rule cong :premises (@p175) :args (@t75)) % 0.23/0.63 (step @p177 :rule refl :args (@t76)) % 0.23/0.63 (step @p178 :rule nary_cong :premises (@p177 @p176) :args (@t77)) % 0.23/0.63 (step @p179 :rule eq-symm :args (@t72 @t17)) % 0.23/0.63 (step @p180 :rule refl :args (@t8)) % 0.23/0.63 (step @p181 :rule nary_cong :premises (@p180 @p179) :args (@t79)) % 0.23/0.63 (step @p182 :rule cong :premises (@p181 @p178) :args (@t80)) % 0.23/0.63 (step @p183 :rule cong :premises (@p182) :args (@t82)) % 0.23/0.63 (step @p184 :rule trans :premises (@p183 @p168)) % 0.23/0.63 (step @p185 :rule eq_resolve :premises (@p18 @p184)) % 0.23/0.63 (step @p186 :rule instantiate :premises (@p185) :args (@t123)) % 0.23/0.63 (step @p187 :rule cnf_or_pos :args (@t166)) % 0.23/0.63 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@p388 @p225) :args (@t236 (@list false true false) (@list @t231 @t227 @t238))) % 0.23/0.63 (step @p404 :rule instantiate :premises (@p8) :args (@t176)) % 0.23/0.63 (step @p405 :rule aci_norm :args ((= (or @t241 @t4) (or @t94 @t240 @t239 @t4)))) % 0.23/0.63 (step @p406 :rule refl :args (@t4)) % 0.23/0.63 (step @p407 :rule aci_norm :args ((= (or @t94 (or @t240 @t239)) @t241))) % 0.23/0.63 (step @p408 :rule bool-and-de-morgan :args (@t7 @t5 true)) % 0.23/0.63 (step @p409 :rule nary_cong :premises (@p31 @p408) :args ((or @t94 (not (and @t7 @t5))))) % 0.23/0.63 (step @p410 :rule bool-and-de-morgan :args (@t8 @t7 (and @t5))) % 0.23/0.63 (step @p411 :rule trans :premises (@p410 @p409)) % 0.23/0.63 (step @p412 :rule trans :premises (@p411 @p407)) % 0.23/0.63 (step @p413 :rule nary_cong :premises (@p412 @p406) :args ((or (not @t9) @t4))) % 0.23/0.63 (step @p414 :rule trans :premises (@p413 @p405)) % 0.23/0.63 (step @p415 :rule bool-impl-elim :args (@t9 @t4)) % 0.23/0.63 (step @p416 :rule trans :premises (@p415 @p414)) % 0.23/0.63 (step @p417 :rule cong :premises (@p416) :args (@t10)) % 0.23/0.63 (step @p418 :rule eq_resolve :premises (@p1 @p417)) % 0.23/0.63 (step @p419 :rule instantiate :premises (@p418) :args ((@list @t99 tptp.efficient_producers tptp.first_movers @t101))) % 0.23/0.63 (step @p420 :rule aci_norm :args ((= (or @t177 @t62) (or @t94 @t120 @t62)))) % 0.23/0.63 (step @p421 :rule refl :args (@t62)) % 0.23/0.63 (step @p422 :rule nary_cong :premises (@p228 @p421) :args ((or @t178 @t62))) % 0.23/0.63 (step @p423 :rule trans :premises (@p422 @p420)) % 0.23/0.63 (step @p424 :rule bool-impl-elim :args (@t14 @t62)) % 0.23/0.63 (step @p425 :rule trans :premises (@p424 @p423)) % 0.23/0.63 (step @p426 :rule cong :premises (@p425) :args (@t63)) % 0.23/0.63 (step @p427 :rule eq_resolve :premises (@p14 @p426)) % 0.23/0.63 (step @p428 :rule instantiate :premises (@p427) :args (@t179)) % 0.23/0.63 (step @p429 :rule cnf_or_pos :args (@t243)) % 0.23/0.63 (step @p430 :rule reordering :premises (@p429) :args ((or @t111 @t229 @t242 (not @t243)))) % 0.23/0.63 (step @p431 :rule chain_m_resolution :premises (@p430 @p50 @p385 @p428) :args (@t242 @t172 (@list @t100 @t223 @t243))) % 0.23/0.63 (step @p432 :rule cnf_or_neg :args (@t112 4)) % 0.23/0.63 (step @p433 :rule chain_m_resolution :premises (@p432 @p43) :args ((not @t102) @t113 @t114)) % 0.23/0.63 (step @p434 :rule cnf_or_pos :args (@t247)) % 0.23/0.63 (step @p435 :rule reordering :premises (@p434) :args ((or @t111 @t102 @t245 @t246 (not @t247)))) % 0.23/0.63 (step @p436 :rule chain_m_resolution :premises (@p435 @p50 @p433 @p431 @p419) :args (@t245 (@list false true false false) (@list @t100 @t102 @t242 @t247))) % 0.23/0.63 (step @p437 :rule cnf_equiv_pos1 :args (@t249)) % 0.23/0.63 (step @p438 :rule reordering :premises (@p437) :args ((or @t250 @t244 (not @t249)))) % 0.23/0.63 (step @p439 :rule chain_m_resolution :premises (@p438 @p436 @p404) :args (@t250 @t169 (@list @t244 @t249))) % 0.23/0.63 (step @p440 :rule cnf_or_pos :args (@t253)) % 0.23/0.63 (step @p441 :rule reordering :premises (@p440) :args ((or @t111 @t110 @t108 @t105 @t252 @t251 @t248 (not @t253)))) % 0.23/0.63 (step @p442 false :rule chain_m_resolution :premises (@p441 @p439 @p403 @p211 @p91 @p68 @p62 @p56 @p50) :args (false (@list true false false false false false false false) (@list @t248 @t236 @t173 @t253 @t104 @t107 @t109 @t100))) % 0.23/0.63 ) % 0.23/0.63 % SZS output end Proof % 0.23/0.63 % cvc5 exiting %------------------------------------------------------------------------------