%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU013+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 : n019.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:50:27 AM UTC 2026 % Result : Theorem 0.48s 0.68s % Output : Proof 0.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU013+1 : TPTP v9.2.1. Released v3.2.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n019.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 16:23:04 EDT 2026 % 0.18/0.36 % CPUTime : % 0.34/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.48/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.48/0.68 % SZS status Theorem % 0.48/0.68 % SZS output start Proof % 0.48/0.68 ( % 0.48/0.68 (declare-sort $$unsorted 0) % 0.48/0.68 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.48/0.68 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.48/0.68 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.48/0.68 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.48/0.68 (declare-const tptp.relation_composition (-> $$unsorted $$unsorted $$unsorted)) % 0.48/0.68 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.48/0.68 (declare-const tptp.empty_set $$unsorted) % 0.48/0.68 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 0.48/0.68 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.48/0.68 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 0.48/0.68 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.48/0.68 (declare-const tptp.function (-> $$unsorted Bool)) % 0.48/0.68 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.48/0.68 (define @t1 () (@var "A" $$unsorted)) % 0.48/0.68 (define @t2 () (@var "B" $$unsorted)) % 0.48/0.68 (define @t3 () (tptp.in @t1 @t2)) % 0.48/0.68 (define @t4 () (@list @t1 @t2)) % 0.48/0.68 (define @t5 () (tptp.function @t1)) % 0.48/0.68 (define @t6 () (tptp.empty @t1)) % 0.48/0.68 (define @t7 () (@list @t1)) % 0.48/0.68 (define @t8 () (tptp.relation @t1)) % 0.48/0.68 (define @t9 () (@var "C" $$unsorted)) % 0.48/0.68 (define @t10 () (= @t2 @t9)) % 0.48/0.68 (define @t11 () (= (tptp.apply @t1 @t2) (tptp.apply @t1 @t9))) % 0.48/0.68 (define @t12 () (tptp.relation_dom @t1)) % 0.48/0.68 (define @t13 () (tptp.in @t9 @t12)) % 0.48/0.68 (define @t14 () (tptp.in @t2 @t12)) % 0.48/0.68 (define @t15 () (and @t14 @t13 @t11)) % 0.48/0.68 (define @t16 () (@list @t2 @t9)) % 0.48/0.68 (define @t17 () (forall @t16 (=> @t15 @t10))) % 0.48/0.68 (define @t18 () (tptp.one_to_one @t1)) % 0.48/0.68 (define @t19 () (= @t18 @t17)) % 0.48/0.68 (define @t20 () (and @t8 @t5)) % 0.48/0.68 (define @t21 () (=> @t20 @t19)) % 0.48/0.68 (define @t22 () (forall @t7 @t21)) % 0.48/0.68 (define @t23 () (tptp.relation_composition @t1 @t2)) % 0.48/0.68 (define @t24 () (tptp.relation @t23)) % 0.48/0.68 (define @t25 () (tptp.relation @t2)) % 0.48/0.68 (define @t26 () (and @t8 @t25)) % 0.48/0.68 (define @t27 () (forall @t4 (=> @t26 @t24))) % 0.48/0.68 (define @t28 () (@list @t2)) % 0.48/0.68 (define @t29 () (tptp.relation_composition @t2 @t1)) % 0.48/0.68 (define @t30 () (and @t6 @t25)) % 0.48/0.68 (define @t31 () (tptp.relation tptp.empty_set)) % 0.48/0.68 (define @t32 () (tptp.empty tptp.empty_set)) % 0.48/0.68 (define @t33 () (and @t24 (tptp.function @t23))) % 0.48/0.68 (define @t34 () (tptp.function @t2)) % 0.48/0.68 (define @t35 () (and @t8 @t5 @t25 @t34)) % 0.48/0.68 (define @t36 () (forall @t4 (=> @t35 @t33))) % 0.48/0.68 (define @t37 () (tptp.powerset @t1)) % 0.48/0.68 (define @t38 () (tptp.empty @t12)) % 0.48/0.68 (define @t39 () (not @t6)) % 0.48/0.68 (define @t40 () (and @t39 @t8)) % 0.48/0.68 (define @t41 () (tptp.empty @t2)) % 0.48/0.68 (define @t42 () (tptp.element @t2 @t37)) % 0.48/0.68 (define @t43 () (tptp.element @t1 @t2)) % 0.48/0.68 (define @t44 () (tptp.relation_dom @t2)) % 0.48/0.68 (define @t45 () (tptp.apply @t9 @t1)) % 0.48/0.68 (define @t46 () (tptp.relation_composition @t9 @t2)) % 0.48/0.68 (define @t47 () (tptp.in @t1 (tptp.relation_dom @t46))) % 0.48/0.68 (define @t48 () (= @t47 (and (tptp.in @t1 (tptp.relation_dom @t9)) (tptp.in @t45 @t44)))) % 0.48/0.68 (define @t49 () (tptp.function @t9)) % 0.48/0.68 (define @t50 () (tptp.relation @t9)) % 0.48/0.68 (define @t51 () (and @t50 @t49)) % 0.48/0.68 (define @t52 () (@list @t9)) % 0.48/0.68 (define @t53 () (forall @t52 (=> @t51 @t48))) % 0.48/0.68 (define @t54 () (and @t25 @t34)) % 0.48/0.68 (define @t55 () (=> @t54 @t53)) % 0.48/0.68 (define @t56 () (forall @t4 @t55)) % 0.48/0.68 (define @t57 () (= (tptp.apply @t46 @t1) (tptp.apply @t2 @t45))) % 0.48/0.68 (define @t58 () (=> @t47 @t57)) % 0.48/0.68 (define @t59 () (forall @t52 (=> @t51 @t58))) % 0.48/0.68 (define @t60 () (=> @t54 @t59)) % 0.48/0.68 (define @t61 () (forall @t4 @t60)) % 0.48/0.68 (define @t62 () (tptp.one_to_one @t23)) % 0.48/0.68 (define @t63 () (tptp.one_to_one @t2)) % 0.48/0.68 (define @t64 () (and @t18 @t63)) % 0.48/0.68 (define @t65 () (=> @t64 @t62)) % 0.48/0.68 (define @t66 () (forall @t28 (=> @t54 @t65))) % 0.48/0.68 (define @t67 () (=> @t20 @t66)) % 0.48/0.68 (define @t68 () (forall @t7 @t67)) % 0.48/0.68 (define @t69 () (not @t68)) % 0.48/0.68 (define @t70 () (tptp.element @t2 (tptp.powerset @t9))) % 0.48/0.68 (define @t71 () (@list @t1 @t2 @t9)) % 0.48/0.68 (define @t72 () (not @t11)) % 0.48/0.68 (define @t73 () (not @t13)) % 0.48/0.68 (define @t74 () (not @t14)) % 0.48/0.68 (define @t75 () (or @t74 @t73 @t72 @t10)) % 0.48/0.68 (define @t76 () (= @t18 (forall @t16 @t75))) % 0.48/0.68 (define @t77 () (not @t5)) % 0.48/0.68 (define @t78 () (not @t8)) % 0.48/0.68 (define @t79 () (or @t78 @t77)) % 0.48/0.68 (define @t80 () (not @t20)) % 0.48/0.68 (define @t81 () (or @t74 @t73 @t72)) % 0.48/0.68 (define @t82 () (@var "BOUND_VARIABLE_7793" $$unsorted)) % 0.48/0.68 (define @t83 () (tptp.one_to_one (tptp.relation_composition @t1 @t82))) % 0.48/0.68 (define @t84 () (not (tptp.one_to_one @t82))) % 0.48/0.68 (define @t85 () (not (tptp.function @t82))) % 0.48/0.68 (define @t86 () (not (tptp.relation @t82))) % 0.48/0.68 (define @t87 () (not @t18)) % 0.48/0.68 (define @t88 () (or @t78 @t77 @t87 @t86 @t85 @t84 @t83)) % 0.48/0.68 (define @t89 () (@list @t1 @t82)) % 0.48/0.68 (define @t90 () (forall @t89 @t88)) % 0.48/0.68 (define @t91 () (@quantifiers_skolemize @t90 1)) % 0.48/0.68 (define @t92 () (or @t86 @t85 @t84 @t83)) % 0.48/0.68 (define @t93 () (or @t78 @t77 @t87 @t92)) % 0.48/0.68 (define @t94 () (forall @t89 @t93)) % 0.48/0.68 (define @t95 () (@list @t82)) % 0.48/0.68 (define @t96 () (forall @t95 @t93)) % 0.48/0.68 (define @t97 () (forall @t95 @t92)) % 0.48/0.68 (define @t98 () (or @t78 @t77 @t87 @t97)) % 0.48/0.68 (define @t99 () (not @t63)) % 0.48/0.68 (define @t100 () (not @t34)) % 0.48/0.68 (define @t101 () (not @t25)) % 0.48/0.68 (define @t102 () (or @t101 @t100 @t99 @t62)) % 0.48/0.68 (define @t103 () (forall @t28 @t102)) % 0.48/0.68 (define @t104 () (or @t78 @t77 @t87 @t103)) % 0.48/0.68 (define @t105 () (or @t87 @t103)) % 0.48/0.68 (define @t106 () (or @t87 @t102)) % 0.48/0.68 (define @t107 () (or @t101 @t100 @t87 @t99 @t62)) % 0.48/0.68 (define @t108 () (or @t87 @t99 @t62)) % 0.48/0.68 (define @t109 () (or @t101 @t100)) % 0.48/0.68 (define @t110 () (not @t54)) % 0.48/0.68 (define @t111 () (tptp.function @t91)) % 0.48/0.68 (define @t112 () (@quantifiers_skolemize @t90 0)) % 0.48/0.68 (define @t113 () (tptp.relation_composition @t112 @t91)) % 0.48/0.68 (define @t114 () (tptp.one_to_one @t113)) % 0.48/0.68 (define @t115 () (tptp.one_to_one @t91)) % 0.48/0.68 (define @t116 () (not @t115)) % 0.48/0.68 (define @t117 () (not @t111)) % 0.48/0.68 (define @t118 () (tptp.relation @t91)) % 0.48/0.68 (define @t119 () (not @t118)) % 0.48/0.68 (define @t120 () (tptp.one_to_one @t112)) % 0.48/0.68 (define @t121 () (not @t120)) % 0.48/0.68 (define @t122 () (tptp.function @t112)) % 0.48/0.68 (define @t123 () (not @t122)) % 0.48/0.68 (define @t124 () (tptp.relation @t112)) % 0.48/0.68 (define @t125 () (not @t124)) % 0.48/0.68 (define @t126 () (or @t125 @t123 @t121 @t119 @t117 @t116 @t114)) % 0.48/0.68 (define @t127 () (@list true)) % 0.48/0.68 (define @t128 () (@list @t126)) % 0.48/0.68 (define @t129 () (tptp.relation_dom @t91)) % 0.48/0.68 (define @t130 () (forall @t16 (or (not (tptp.in @t2 @t129)) (not (tptp.in @t9 @t129)) (not (= (tptp.apply @t91 @t2) (tptp.apply @t91 @t9))) @t10))) % 0.48/0.68 (define @t131 () (= @t115 @t130)) % 0.48/0.68 (define @t132 () (or @t119 @t117 @t131)) % 0.48/0.68 (define @t133 () (@list false false false)) % 0.48/0.68 (define @t134 () (@list false false)) % 0.48/0.68 (define @t135 () (tptp.relation_dom @t113)) % 0.48/0.68 (define @t136 () (forall @t16 (or (not (tptp.in @t2 @t135)) (not (tptp.in @t9 @t135)) (not (= (tptp.apply @t113 @t2) (tptp.apply @t113 @t9))) @t10))) % 0.48/0.68 (define @t137 () (@quantifiers_skolemize @t136 1)) % 0.48/0.68 (define @t138 () (tptp.apply @t112 @t137)) % 0.48/0.68 (define @t139 () (@quantifiers_skolemize @t136 0)) % 0.48/0.68 (define @t140 () (tptp.apply @t112 @t139)) % 0.48/0.68 (define @t141 () (tptp.apply @t91 @t138)) % 0.48/0.68 (define @t142 () (tptp.apply @t91 @t140)) % 0.48/0.68 (define @t143 () (not (= @t141 @t142))) % 0.48/0.68 (define @t144 () (tptp.in @t140 @t129)) % 0.48/0.68 (define @t145 () (not @t144)) % 0.48/0.68 (define @t146 () (tptp.in @t138 @t129)) % 0.48/0.68 (define @t147 () (not @t146)) % 0.48/0.68 (define @t148 () (= @t138 @t140)) % 0.48/0.68 (define @t149 () (or @t147 @t145 @t143 @t148)) % 0.48/0.68 (define @t150 () (= @t140 @t138)) % 0.48/0.68 (define @t151 () (not (= @t142 @t141))) % 0.48/0.68 (define @t152 () (or @t147 @t145 @t151 @t150)) % 0.48/0.68 (define @t153 () (@list false)) % 0.48/0.68 (define @t154 () (tptp.relation_dom @t112)) % 0.48/0.68 (define @t155 () (forall @t16 (or (not (tptp.in @t2 @t154)) (not (tptp.in @t9 @t154)) (not (= (tptp.apply @t112 @t2) (tptp.apply @t112 @t9))) @t10))) % 0.48/0.68 (define @t156 () (= @t120 @t155)) % 0.48/0.68 (define @t157 () (or @t125 @t123 @t156)) % 0.48/0.68 (define @t158 () (not @t148)) % 0.48/0.68 (define @t159 () (tptp.in @t139 @t154)) % 0.48/0.68 (define @t160 () (not @t159)) % 0.48/0.68 (define @t161 () (tptp.in @t137 @t154)) % 0.48/0.68 (define @t162 () (not @t161)) % 0.48/0.68 (define @t163 () (or @t162 @t160 @t158 (= @t137 @t139))) % 0.48/0.68 (define @t164 () (= @t139 @t137)) % 0.48/0.68 (define @t165 () (not @t150)) % 0.48/0.68 (define @t166 () (or @t162 @t160 @t165 @t164)) % 0.48/0.68 (define @t167 () (@var "BOUND_VARIABLE_7724" $$unsorted)) % 0.48/0.68 (define @t168 () (= (tptp.in @t1 (tptp.relation_dom (tptp.relation_composition @t167 @t2))) (and (tptp.in @t1 (tptp.relation_dom @t167)) (tptp.in (tptp.apply @t167 @t1) @t44)))) % 0.48/0.68 (define @t169 () (not (tptp.function @t167))) % 0.48/0.68 (define @t170 () (not (tptp.relation @t167))) % 0.48/0.68 (define @t171 () (or @t170 @t169 @t168)) % 0.48/0.68 (define @t172 () (or @t101 @t100 @t171)) % 0.48/0.68 (define @t173 () (forall (@list @t1 @t2 @t167) @t172)) % 0.48/0.68 (define @t174 () (@list @t167)) % 0.48/0.68 (define @t175 () (forall @t174 @t172)) % 0.48/0.68 (define @t176 () (forall @t174 @t171)) % 0.48/0.68 (define @t177 () (@list @t9)) % 0.48/0.68 (define @t178 () (or @t101 @t100 @t176)) % 0.48/0.68 (define @t179 () (not @t49)) % 0.48/0.68 (define @t180 () (not @t50)) % 0.48/0.68 (define @t181 () (or @t180 @t179 @t48)) % 0.48/0.68 (define @t182 () (forall @t52 @t181)) % 0.48/0.68 (define @t183 () (or @t101 @t100 @t182)) % 0.48/0.68 (define @t184 () (or @t180 @t179)) % 0.48/0.68 (define @t185 () (not @t51)) % 0.48/0.68 (define @t186 () (@list @t137 @t91 @t112)) % 0.48/0.68 (define @t187 () (and @t161 @t146)) % 0.48/0.68 (define @t188 () (tptp.in @t137 @t135)) % 0.48/0.68 (define @t189 () (= @t188 @t187)) % 0.48/0.68 (define @t190 () (or @t119 @t117 @t125 @t123 @t189)) % 0.48/0.68 (define @t191 () (@list false false false false false)) % 0.48/0.68 (define @t192 () (or @t78 @t77 @t101 @t100)) % 0.48/0.68 (define @t193 () (@list @t112 @t91)) % 0.48/0.68 (define @t194 () (tptp.function @t113)) % 0.48/0.68 (define @t195 () (tptp.relation @t113)) % 0.48/0.68 (define @t196 () (and @t195 @t194)) % 0.48/0.68 (define @t197 () (or @t125 @t123 @t119 @t117 @t196)) % 0.48/0.68 (define @t198 () (or @t125 @t119 @t195)) % 0.48/0.68 (define @t199 () (= @t114 @t136)) % 0.48/0.68 (define @t200 () (not @t194)) % 0.48/0.68 (define @t201 () (not @t195)) % 0.48/0.68 (define @t202 () (or @t201 @t200 @t199)) % 0.48/0.68 (define @t203 () (not @t136)) % 0.48/0.68 (define @t204 () (tptp.apply @t113 @t137)) % 0.48/0.68 (define @t205 () (tptp.apply @t113 @t139)) % 0.48/0.68 (define @t206 () (= @t205 @t204)) % 0.48/0.68 (define @t207 () (not @t206)) % 0.48/0.68 (define @t208 () (not @t188)) % 0.48/0.68 (define @t209 () (tptp.in @t139 @t135)) % 0.48/0.68 (define @t210 () (not @t209)) % 0.48/0.68 (define @t211 () (or @t210 @t208 @t207 @t164)) % 0.48/0.68 (define @t212 () (@list @t211)) % 0.48/0.68 (define @t213 () (not @t187)) % 0.48/0.68 (define @t214 () (@list @t187)) % 0.48/0.68 (define @t215 () (@list @t139 @t91 @t112)) % 0.48/0.68 (define @t216 () (and @t159 @t144)) % 0.48/0.68 (define @t217 () (= @t209 @t216)) % 0.48/0.68 (define @t218 () (or @t119 @t117 @t125 @t123 @t217)) % 0.48/0.68 (define @t219 () (not @t216)) % 0.48/0.68 (define @t220 () (@list @t216)) % 0.48/0.68 (define @t221 () (@var "BOUND_VARIABLE_7754" $$unsorted)) % 0.48/0.68 (define @t222 () (tptp.relation_composition @t221 @t2)) % 0.48/0.68 (define @t223 () (= (tptp.apply @t222 @t1) (tptp.apply @t2 (tptp.apply @t221 @t1)))) % 0.48/0.68 (define @t224 () (not (tptp.in @t1 (tptp.relation_dom @t222)))) % 0.48/0.68 (define @t225 () (not (tptp.function @t221))) % 0.48/0.68 (define @t226 () (not (tptp.relation @t221))) % 0.48/0.68 (define @t227 () (or @t226 @t225 @t224 @t223)) % 0.48/0.68 (define @t228 () (or @t101 @t100 @t227)) % 0.48/0.68 (define @t229 () (forall (@list @t1 @t2 @t221) @t228)) % 0.48/0.68 (define @t230 () (@list @t221)) % 0.48/0.68 (define @t231 () (forall @t230 @t228)) % 0.48/0.68 (define @t232 () (forall @t230 @t227)) % 0.48/0.68 (define @t233 () (or @t101 @t100 @t232)) % 0.48/0.68 (define @t234 () (not @t47)) % 0.48/0.68 (define @t235 () (or @t180 @t179 @t234 @t57)) % 0.48/0.68 (define @t236 () (forall @t52 @t235)) % 0.48/0.68 (define @t237 () (or @t101 @t100 @t236)) % 0.48/0.68 (define @t238 () (= @t204 @t141)) % 0.48/0.68 (define @t239 () (or @t119 @t117 @t125 @t123 @t208 @t238)) % 0.48/0.68 (define @t240 () (@list false false false false false false)) % 0.48/0.68 (define @t241 () (= @t205 @t142)) % 0.48/0.68 (define @t242 () (or @t119 @t117 @t125 @t123 @t210 @t241)) % 0.48/0.68 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 0.48/0.68 (assume @p2 (forall @t7 (=> @t6 @t5))) % 0.48/0.68 (assume @p3 (forall @t7 (=> @t6 @t8))) % 0.48/0.68 (assume @p4 @t22) % 0.48/0.68 (assume @p5 @t27) % 0.48/0.68 (assume @p6 (forall @t7 (exists @t28 (tptp.element @t2 @t1)))) % 0.48/0.68 (assume @p7 (forall @t4 (=> @t30 (and (tptp.empty @t29) (tptp.relation @t29))))) % 0.48/0.68 (assume @p8 (and @t32 @t31 (tptp.relation_empty_yielding tptp.empty_set))) % 0.48/0.68 (assume @p9 @t36) % 0.48/0.68 (assume @p10 (forall @t7 (not (tptp.empty @t37)))) % 0.48/0.68 (assume @p11 @t32) % 0.48/0.68 (assume @p12 (and @t32 @t31)) % 0.48/0.68 (assume @p13 (forall @t7 (=> @t40 (not @t38)))) % 0.48/0.68 (assume @p14 (forall @t7 (=> @t6 (and @t38 (tptp.relation @t12))))) % 0.48/0.68 (assume @p15 (forall @t4 (=> @t30 (and (tptp.empty @t23) @t24)))) % 0.48/0.68 (assume @p16 (exists @t7 @t20)) % 0.48/0.68 (assume @p17 (exists @t7 (and @t6 @t8))) % 0.48/0.68 (assume @p18 (forall @t7 (=> @t39 (exists @t28 (and @t42 (not @t41)))))) % 0.48/0.68 (assume @p19 (exists @t7 @t6)) % 0.48/0.68 (assume @p20 (exists @t7 @t40)) % 0.48/0.68 (assume @p21 (forall @t7 (exists @t28 (and @t42 @t41)))) % 0.48/0.68 (assume @p22 (exists @t7 @t39)) 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(@p366 @p361 @p355)) % 0.48/0.68 (step @p368 :rule true_intro :premises (@p367)) % 0.48/0.68 (step @p369 :rule symm :premises (@p368)) % 0.48/0.68 (step @p370 :rule trans :premises (@p369 @p321)) % 0.48/0.68 (step @p371 false :rule eq_resolve :premises (@p370 @p37)) % 0.48/0.68 ) % 0.48/0.68 % SZS output end Proof % 0.48/0.68 % cvc5 exiting %------------------------------------------------------------------------------